Chapter 1
LABOR SUPPLY OF MEN: A SURVEY
JOHN PENCAVEL*
Stanford Unioersity and National Bureau of Economic Research
I. Introduction
This survey of male labor supply covers the determinants of whether men work
for pay in the labor market and, if so, the determinants of their hours of work.
Issues pertaining to the size and structure of the population are not addressed.
Also, I shall be concentrating on the work behavior of men prior to their
retirement from the labor force.1 Moreover, even though there are noteworthy
investigations into the labor supply of men in many different countries, this
survey is restricted almost entirely to the Anglo-American literature. Even with
the subject so restricted, there is much material to survey. The economics
literature on the determinants of work behavior of men and women is an old one,
and during the past 20 years this literature has multiplied many times over as
labor supply has become the most active area of all labor economics research.
This early and continuing interest in the determinants of market work derives in
part from questions of public policy: a century ago these questions concerned
regulations on the use of child labor, compulsory school attendance, and restrictions
on the length of the working day; more recently, the questions have
involved income and commodity taxation, the reform of welfare programs, and
movements in productivity.
*A number of friends have helped me prepare this survey. Above all, I am indebted to Angus
Deaton for constructive and thorough comments on an incomplete version of this paper and to Tom
MaCurdy for his careful criticism of several large portions of this manuscript. I also received
comments on particular sections of the paper from Orley Ashenfelter, David Card, John Ham, Mark
Killingsworth, Tom Kniesner, and Ian Walker. Jeremy Rudin was an excellent research assistant and
the manuscript was typed professionally and cheerfully by David Criswell. To all these people, I am
most grateful for their help. Support from the Sloan Foundation to the Department of Economics at
Stanford University is gratefully acknowledged.
1Edward Lazear's paper in this Handbook (Chapter 5) contains information on retirement.
Handbook of Labor Economics, Volume I, Edited by O. Ashenfelter and R. Layard
©Elsevier Science Publishers BV, 1986
4 J. Pencavel
Conjectures about whether an increase in remuneration brought forth more
work effort can be traced back at least to the mercantile economists,a but the
careful statement of the issues is much more recent. Robbins (1930) is usually
credited with the proposition that constrained utility maximization yields an
ambiguous implication about the wage-slope of the labor supply curve although
Jevons (1888) was quite explicit on the matter.3 After pointing out that in the
absence of knowledge about the form of the utility function it was impossible to
sign the slope of the labor supply curve, Jevons proceeded to cite instances in
which the sudden increase in the prices of goods induced greater hours of work
and so he surmised that, in fact, the labor supply function was negatively sloped
with respect to wages. The first major empirical effort to examine the wage-slope
of the labor supply curve4 was Paul Douglas's Theory of Wages (1934). In one
chapter drawing upon data collected from the 1920 Census of Manufactures, he
regressed for each age-sex group in 38 U.S. cities the employment-to-population
ratio on real annual earnings in manufacturing industry holding constant the
fraction of the city's population who were either foreign-born or black. For men
in all age groups he found a negative correlation though only for the very young
and the old was this association significantly different from zero. In another
chapter he examined both time-series and cross-section (across industries and
across states) data on hours of work and hourly earnings and from these he
concluded that the elasticity of hours with respect to wages "is in all probability
somewhere between -0.1 and -0.2..." (p. 312). In his careful treatment of the
data and in his awareness of the problems impeding inferences, Douglas's work is
really quite outstanding.5 After The Theory of Wages, the landmarks in the
research on labor force participation are as follows: Schoenberg and Douglas
(1937); Woytinsky (1940); Durand (1948); Bancroft (1958); and Long (1958).
2See the references cited in Douglas (1934, p. 270). Long (1958, p. 40) refers to Sir Edward West's
summary in 1826 of evidence presented to Committees of the Houses of Parliament "that the
labourer in a scarce year, when his wage will furnish him with a much less than the usual quantity of
food, will, in order to attain his usual supply of necessaries, be willing to do much more work than
usual, even at a reduced rate of wages".
3jevons wrote (1888, pp. 179-180): "Supposing that circumstances alter the relation of produce to
labour, what effect will this have upon the amount of labour which will be exerted? There are two
effects to be considered. When labour produces more commodity, there is more reward, and therefore
more inducement to labour. If a workman can earn ninepence an hour instead of sixpence, may he
not be induced to extend his hours of labour by this increased result? This would doubtless be the
case were it not that the very fact of getting half as much more than he did before, lowers the utility
to him of ar~y71~urtheraddition. By the produce of the same number of hours he can satisfy his desires
more completd3/; and if tlieArksomeness oflabour has reached at all a high point, he may gain more
pleasure by relaxifig that labour than by consuming more products. The question thus depends upon
the direction in which the balance between the utility of further commodity and the painfulness of
prolonged labour turns. In our ignorance of the exact form of the functions either of utility or of
labour, it will be impossible to decide this question in an a priori manner .... "
4Earlier though more casual empirical work appears in Frain (1929) and Teper (1932).
5Rees (1979) provides a modern perspective on Douglas' labor supply research.
Ch. 1: Labor Supply of Men 5
With respect to hours of work, there is the work of Lewis (1957), Bry (1959),
Jones (1961), and Finegan (1962).
Modern research on labor supply is characterized by a more careful attempt to
separate the measurement of income from substitution effects. It dates from
Mincer's (1962) paper on the labor force participation rate of married women
and Kosters' (1966) dissertation on the hours worked by men. Since the mid-1960s,
progress in computing technology-especially the development of more efficient
methods of storing on magnetic tapes and processing information on individuals
and the enormous reduction in the costs of applying multivariate statistical
techniques to these data-has resulted in a vast outpouring of empirical research
in labor supply. This literature has already been the subject of a number of very
good surveys: Heckman and MaCurdy (1981); Heckman, Killingsworth and
MaCurdy (1981); Keeley (1981); and Killingsworth (1981, 1983). Each of these
tends to be a survey of the economics literature. This survey strives to be a little
different, namely a survey of the topic and our knowledge of it as well as what
economists have written about it. This is why I have devoted an important part,
Section 2, to a summary statement of the major empirical regularities in male
labor force participation and male hours of work. It is these and other regularities
that economists' theories should be trying to explain and, if economics is indeed
a science rather than a branch of applied mathematics, then it is the task of
economists to confront the theories with the evidence. As will become clear, there
has been a great deal of empirical work on male labor supply and much of it has
been imbedded explicitly in the standard neoclassical allocation theory. In fact,
one of the most pleasing aspects of labor supply research during the last 20 years
has been its careful attention to the theoretical underpinnings. At the same time,
the overwhelming proportion of this empirical work has not questioned the
validity of the conventional model; this model has been treated as a maintained
hypothesis. Empirical research has concentrated on quantifying the magnitude of
the presumed relationships. Such quantification is naturally an important ingredient
of any science, but in many laboratory sciences refined attempts at calibration
represent a stage of research that usually follows, not precedes, the testing of
hypotheses. In male labor supply research, very little formal testing of the
standard model has been undertaken. Labor supply research cannot be indicated
for "measurement without theory", but it can be described as "measurement
without testing". The theory is by no means empty of refutable implications and,
at least when asked, most economists would grant that ultimately the implications
or assumptions of any economic theory must correspond with actual
behavior. So why has the great volume of empirical work involved so little testing
of the standard model?
I suspect that one reason can be attributed to the fact that not merely are we
reluctant to reject a theory until we have a viable substitute close at hand- this is
a familiar proposition in the sociology of science-but also we hesitate even to
6 J. Pencavel
test a theory until an alternative, behavioral, hypothesis is available.6 The answer
"I don't know" is something that an economist will say after being pushed by
careful questioning, but he will not readily volunteer this response.
A more substantive reason for the lack of hypothesis testing in labor supply
research is that many economists view such tests as tantamount to questioning
whether a consumer's income-compensated demand curve for a commodity
slopes downwards with respect to its price. After all, so the argument would go,
the neoclassical theory of labor supply is a straightforward extension of the
consumer's allocation problem and surely we believe that demand curves slope
downwards? Putting aside the issue of whether that basic proposition of consumer
theory has itself been corroborated, it is usually agreed that, in the absence
of adverse evidence, the confirmation of a hypothesis increases with the number
of favorable test outcomes: if the theory of consumer behavior had been found to
be an apt description of the demand for apples, oranges, cherries, bananas, and
many other fruit, an economist will wager it also applies to the demand for pears.
But it is by no means clear that the exchanges taking place in the labor market
are well described by analogies to the individual's behavior with respect to the
purchases of fruit, that the evidence about the demand curves for fruit is relevant
to the supply of work effort. As Coase (1937), Phelps Brown (1960, pp. 289-293),
Simon (1951), and others have emphasized, labor market transactions possess
many dimensions-the wages to be paid, the level of work effort to be applied,
the range of activities to which the employee may be directed, the duration of the
contract, and so on- and the particular combination of wages and hours worked
represents only a subset of the bundle of items involved in the exchange. It is not
at all obvious that this subset may be siphoned off from the rest and appropriately
characterized by the sort of allocation process that the conventional
model applies. I am not suggesting that the preferences of workers have nothing
to do with their market work decisions, only that what I call below the canonical
model may not be the most useful characterization of the way in which preferences
and opportunities come together to determine outcomes in the labor
market.
Nevertheless, the research attempts to measure the relevant parameters precisely
have resulted in some notable advances in our understanding of the issues.
For instance, the economics and econometrics of hours of work as distinct from
labor force participation decisions are much better understood than they were 20
years ago. Though the literature on nonlinear budget constraints is by no means
recent, it h~ been only in the past ten years that their implications for empirical
work have been fully ~explored. The development and application of tractable
dynamic models of labor supply have also represented a major advance in our
6Cf. Lakatos (1970,p. 179, n. 2): "The reluctanceof economistsand other social scientists to
accept Popper's methodologymayhavebeen partlydue to the destructiveeffectof naivefalsificationism
on budding researchprogrammes."
Ch. 1: Labor Supply of Men 7
understanding of the issues. We have much more and much better information
today on the major empirical regularities in work behavior and especially on the
importance of unobserved variables in accounting for variations across indi,,iduals
in their hours of work. In all these respects, the standards of enquiry and
critical debate in labor supply research have risen tremendously compared with
the state of affairs 20 years or so ago. It is in this sense that undeniable progress
has been made.
An outline of this survey is as follows. In the next section, Section 2, I identify
the major time-series and cross-section empirical regularities in male labor supply
behavior. It is these that any economic theory should be designed to address.
Section 3 presents first the canonical static model of labor supply and then it
immediately proceeds to deal with the problems in applying this model at the
aggregative level. The static model is then amended to handle the situation of
nonlinear budget constraints. Section 3 concludes with an outline of the most
popular life-cycle model of labor supply. Section 4 addresses the issues in and
results from the estimation of the static model. In this section, problems in
specifying the model are first considered and then the results are presented from
the U.S. nonexperimental literature, the British literature, and the U.S. experimental
literature. Section 5 discusses the estimates from the applications of the
life-cycle model. Some conclusions and suggestions for further research are given
in Section 6.
2. Empirical regularities
2.1. Trends in work behavior
For a century or so, at least in North America and West Europe, a declining
fraction of a man's lifetime has been spent at market work. This decline has been
manifested in a number of ways: more years have been spent at school and the
age of entry into full-time market employment has advanced; workers have been
wholly or partially retiring from the labor force at younger ages; fewer hours
have been worked per day and per week; and there have been more holidays and
longer vacations. In addition, I suspect that work effort per hour has decreased,
although this is difficult to verify. Consider now these different dimensions of
work behavior.
Changes during the last 80 years or so in the labor force participation rates of
men of different ages are documented for the United States, Britain, Canada, and
Germany in Tables 1.1, 1.2, 1.3, and 1.4. The age group that maintained the
closest association with the labor market has been men aged 25 to 44 years; for
all four countries in all these years, more than 90 percent of these men were
classified as members of the labor force. However, from the turn of the century
Table 1.1
United States: Male labor force participation rates
(expressed as a percentage) by age over time.
J. Pencavel
Age
(in years) 1890 1900 1910 1920 1930 1940 1950 1960 1970(a) 1970(b)1982
10-13 17.8 17.7 9.2 6.0 3.3
14/16-19 57.1 61.1 56.2 52.6 41.1 34.4 39.9 38.1 47.8 58.4 58.1
20-24 92.0 91.7 91.1 90.9 89.9 88.0 82.8 86.2 80.9 86.6 86.0
25-44 97.6 96.3 96.6 97.1 97.5 95.0 92.8 95.2 94.4 96.8 95.1
45-64 95.2 93.3 93.6 93.8 94.1 88.7 87.9 89.0 87.3 89.4 81.0
>65 73.9 68.3 58.1 60.1 58.3 41.5 41.6 30.6 25.0 26.8 17.8
All 87.4 87.3 86.3 86.5 84.1 79.0 79.0 77.4 76.8 80.6 77.2
Notes: The Censuses after 1930 did not count children aged less than 14 years in the labor
force. The age category "14/16-19" relates to 14-19 years for the years from 1890 to 1960
and to 16-19 years thereafter. The age category "All" describes all males aged 14 years and
over from 1890 to 1960 and all males aged 16 years and over thereafter. The data for the
years 1890, 1900, 1910, 1920, 1930, 1940, and 1950 are from Long (1958, Table A-2, p. 287).
The data for 1960 are from U.S. Department of Commerce, Bureau of the Census, U.S.
Census of Population 1960." Employment Status and Work Experience, Subject Reports
PC(2)-6A, Table 1. The data for 1970(a) are from U.S. Department of Commerce, Bureau of
the Census, 1970 Census of Population: Employment Status and Work Experience, Subject
Reports PC(2)-6A, Table 1. The data for 1970(b) and for 1982 are from the monthly
Current Population Survey of households and are not strictly comparable with the decennial
census data in the other columns. The data for 1970(b) are from Employment and Earnings,
January 1971, Table A-l, page 115 and those for 1982 from Employment and Earnings,
January 1983, Table 3, page 142.
Table 1.2
Great Britain: Male labor force participation rates
(expressed as a percentage) by age over time.
Age
(in years) 1891 1911 1931 1951 1966 1981
< 20 84.7 83.8 70.6 64.6
20-24 98.1 97.3 97.2 94.9 92.6 89.2
25-44 97.9 98.5 98.3 98.3 98.2 97.5
45-64 93.7 94.1 94.3 95.2 95.1 90.2
65 + 65.4 56.8 47.9 31.1 23.5 10.8
All 90.5 87.6 84.0 77.8
Notes: The category " < 20" relates to males aged 14-19 years in 1931, to
~males aged 15-19 years in 1951 and 1966, and to males aged 16-19 years in
lg8L The category "All" relates to males aged 14 years and over in 1931, to
males-aged 15 ~ears and over in 1951 and 1966, and to males aged 16 years
and over in 1981. The data for the years 1891, 1911, 1931, 1951, and 1966
come from Department of Employment and Productivity, British Labour
Statistics Historical Abstract 1886-1968, London, HMSO, 1971, Table 109,
pp. 206-207. Those for 1981 are from Central Statistical Office, Annual
Abstract of Statistics 1983 Edition, 1983, Table 6.16, p. 130.
Ch. 1: Labor Supply of Men
Table 1.3
Canada: Male labor force participation rates
(expressed as a percentage) by age over time.
Age
(in years) 1911 1931 1951 1971 1980
14/15-19 64.6 51.4 48.1 46.6 51.9
20-24 92.2 92.3 91.8 86.5 79.7
25-44 97.1 97.6 96.3 92.7 92.2
45-64 94.4 94.8 90.6 85.9 83.3
65+ 52.1 55.8 38.5 23.6 14.0
Notes: The youngest age category is 14-19 years in 1911, 1931,
and 1951 and is 15-19 years in 1971 and 1980. For the years 1911,
1931, and 1951, the data are from Long (1958, Table A-11, p. 305).
For the years 1971 and 1980, the sources are the International
Labour Organization's Yearbook of Labour Statistics for 1975-76
and 1983, respectively.
for each and every age-group, the labor force participation rates of men in all
these countries has fallen. The decline has been most marked for older men: for
men aged 65 years and over, as recently as the early 1930s labor force participation
rates of 58 percent, 48 percent, and 56 percent were recorded in the United
States, Britain, and Canada, respectively. Twenty years later these rates had
fallen by about the same 17 percentage points in each of these countries. A
similar change was registered in Germany from 47 percent in 1925 to 27 percent
in 1950. The post World War II period~has witnessed further declines in each
country in the labor force participation rates of older men. These declines have
often been attributed to the expansion of government-organized social security
Table 1.4
Germany: Male labor force participation rates
(expressed as a percentage) by age over time.
Age
(in years) 1895 1907 1925 1939 1950 1970 1981
14/15-19 83.6 86.1 85.0 86.0 74.2 66.6 46.4
20-24 95.1 95.7 95.0 96.2 93.4 86.4 81.4
25-44 97.2 97.4 97.4 98.0 96.3 96.7 95.8
45-64 91.8 89.4 91.4 87.0 89.6 85.7 83.7
65+ 58.8 50.2 47.4 29.7 26.7 16.0 7.0
Notes: Betwcen 1895 and 1950, the youngest age group is 14-19 years; for 1970 and
1981, the youngest age group is 15-19 years. For the years 1895, 1907, 1925, and 1939,
"Germany" consists of that area defined by her post World War I frontiers without the
Saar. For the other years, "Germany" means the Federal Republic of Germany, excluding
Berlin. The source for the data for 1895, 1907, 1925, 1939, and 1950 is Long (1958, Table
A-16, p. 313). For the years 1970 and 1981, the sources are the International Labour
Organization's Yearbook of Labour Statistics for 1973 and 1983, respectively.
10
Table 1.5
United States and Britain: labor force participation rates
(expressed as percentages)
of males and females combined over time.
United States Britain
Year Participation Year Participation
1890 54.0 1891 61.3
1900 54.8 1901 59.9
1910 55.7 1911 60.4
1920 55.6 1921 58.6
1930 54.6 1931 57.7
1940 52.2 1951 57.7
1950 53.4 1961 59.3
1960 55.4 1971 61.4
1970 55.7 1981 61.0
Notes: The U.S. data in all years describe males and females
aged 14 years and older and the British data in all years
describe males and females aged 20 years and older. The U.S.
data come from the Decennial Censuses and the precise sources
are the same as those given beneath Table 1.1. The sources for
the British data are the same as those given beneath Table 1.2.
J. Pencavel
systems and, indeed, it is unlikely that the taxes and benefits associated with the
operation of these systems have not affected the labor force participation rate of
older people, v On the other hand, it should be noted that the participation rates
of older men were already declining before the period of the great expansion of
government social security.
At the same time as the labor force participation rates of men were falling,
those of women were rising. Indeed, as Table 1.5 shows for the United States and
Britain, these changes largely offset one another. The absence of a trend in the
overall (male and female) labor force participation rate prompted Klein and
Kosobud (1961) to classify it as one of the "great ratios of economics". Both in
1910 and in 1970, the participation rate of all people aged 14 years and over in
the United States was 55.7 percent; in 1981 in Britain, the participation rate of all
people aged 20 years and over differed by only three-tenths of one percent from
the rate in 1891.
Year-to-year movements in the labor force participation rate reflect the state of
the business cycle as wall as underlying trends. A convenient and simple way of
7parsons (1980) claims the Social Security disabilityprogram is responsible for the declines during
the post World War II period in the labor force participation rate of men aged 45-54 years. This
interpretation is challenged by Haveman and Wolfe (1984) and then defended by Parsons (1984).
Ch. 1: Labor Supply of Men 11
describing these cycles and trends is to fit the following equation to annual U.S.
data from 1955 to 1982 for the civilian labor force participation rates of different
groups of males in the population:
azj, = + (1)
In this equation, ALit = Lit - Lit_ 1 and Lit is the civilian labor force participation
rate (expressed as a percentage) of group j in year t and AUtr = Ut r - utr__l
and Utr is the unemployment rate (expressed as a percentage) of white males aged
35-44 years in year t. The unemployment rate of this group is a better indicator
of the stage of the business cycle as it operates in the labor market than is the
overall unemployment rate and the superscript "r" on U designates this as the
"reference" group. The responsiveness of the participation rate to the business
cycle is measured by fl while a reflects a linear time trend. The equation error is
represented by et and the index j runs over nine age groups and two racial
groups.
The consequences of estimating eq. (1) by ordinary least squares are shown in
Table 1.6. According to these estimates, over the past 27 years there has been a
downward trend of almost three-tenths of one percent per year in the participation
rate of white men and of almost one-half of one percent per year in the
participation of black men. These trends are especially marked for young black
men and for older men, both black and white. Although most of the estimates of
fl are negative (suggesting the participation rate falls in a recession), 8 these
effects are small and not statistically significant except for younger men. 9 In
general, very little variation in annual movements of male participation rates is
removed by this cyclical indicator and Mincer's (1966) summary diagnosis-" some
net cycle elasticity plus much residual variation due to other factors"-remains
apt. 1°
For Britain, a time series on the male labor force participation rate for
different age-groups is not published for the entire post-war period, n So I
constructed an annual series for the entire adult male labor force participation
8The phenomenon of the labor force contracting in a recession is sometimes described as "the
discouraged worker effect", that is, the costs of searching for acceptable employment rises in a
recession to a degree such that it no longer pays someindividuals to continue searching.
9Afinding of long standing is that school enrollment rates of young people rise in a recession. See,
for example, Duncan (1956).
l°Equation (1) was also estimated with a different cyclical indicator, namely, the inventory-sales
ratio in manufacturing and wholesale and retail trade. Very similar results were obtained with this
variable as those reported in Table 1.6.Note that this is also the case for white men aged35-44 years
for whom there is a real danger of a spurious correlation between L and Ur in eel. (1).
nA series exists on an important subset of the male labor force (namely, all except employers, the
self-employed, some part-time employees, and the military), but for men this was discontinued in
January 1971. Analyses of these series are in Corry and Roberts (1970, 1974).
12
Table 1.6
United States: Estimates of trend (a) and cycle (fl) in male civilian
labor force participation rates by race and age, 1955-1982.
J. Pencavel
Age
(in years) a fl R2 D-W
White
Total,
> 16 - 0.284"(0.051) - 0.094(0.059) 0.09 1.59
16-17 0.181(0.246) - 1.103"(0.285) 0.37 1.61
18-19 0.078(0.229) -0.800*(0.266) 0.26 1.29
20-24 0.015(0.158) -0.201(0.184) 0.04 1.81
25-34 -0.057(0.038) -0.121"(0.044) 0.22 1.78
35-44 -0.075*(0.027) -0.042(0.031) 0.07 2.24
45-54 -0.169"(0.039) 0.056(0.046) 0.05 1.00
55-64 -0.651"(0.123) 0.008(0.143) 0.01 1.82
_>65 - 0.796" (0.142) 0.085(0.165) 0.01 1.49
Black and other
Total,
>_16 -0.492"(0.116) 0.162(0.134) 0.05 1.48
16-17 -0.626*(0.388) -1.105"(0.449) 0.19 2.44
18-19 -0.780*(0.329) -0.634(0.382) 0.10 2.24
20-24 - 0.438(0.222) - 0.711(0.257) 0.23 1.59
25-34 -0.256"(0.115) -0.125(0.133) 0.03 2.41
35-44 0.220*(0.097) -0.090(0.112) 0.02 2.18
45-54 -0.319(0.212) -0.215(0.245) 0.03 2.66
55-64 - 0.686" (0.324) 0.008(0.375) 0.01 2.02
> 65 - 0.861"(0.273) 0.147(0.316) 0.01 2.17
Notes: Estimated standard errors are in parentheses next to their associated
regression coefficients. "D-W" is the Durbin-Watson statistic. For ease of reading,
an asterisk has been placed next to those point estimates more than twice their
estimated standard errors. The data are taken from the Employment and Training
Report of the President 1981 and from recent issues of Employment and Earnings.
rate over the 31 years from 1951 to 198112 and estimated the cyclical and trend
movements in this labor force participation rate by fitting eq. (1) to the data. As a
cyclical indicator, however, I used the deviations of the index of industrial
production from a linear time trend, positive deviations corresponding to a low
level of aggregate business activity and negative deviations to a high level of
business activity. The labor force participation rate (expressed as a percentage)
and this cyclical indicator were first-differenced and then, as in eq. (1), an
12To be precise, I constructed the ratio of the male labor force (called in Britain the working
population) to the male home population aged 15 years and over. Both numerator and denominator
are measured at the same moment, the middle of each year, and both relate to Britain (not the United
Kingdom). The sources for the data were issues of the Annual Abstract of Statistics published by the
Central Statistical Office. The mean value of this male labor force participation rate over the 1951-81
period is 0.836 with a standard deviation of 0.047.
Ch. 1: Labor Supply of Men 13
ordinary least-squares equation was fitted to the data over the years 1952-1981.13
The resulting estimates (with estimated standard errors in parentheses) are as
follows:
= - 0.446", /~= - 0.015 , R 2=0.02, D-W=l.36.
(0.094) (0.022)
According to these estimates, the male labor force participation rate in Britain
over the last 30 years displays a small procyclical movement that would not be
deemed significantly different from zero by conventional criteria and a negative
trend of almost one-half of a percentage point per year. A comparison of these
estimates with those in Table 1.6 for the entire U.S. male labor force indicates
that movements in the British male labor force participation rate look very
similar to those in the United States.
Hours worked by men declined markedly during the first four decades of the
twentieth century. For the United States, this is evident from the data in Table
1.7 which are taken from the decennial Censuses of Population and which relate
to men working in manufacturing industry only. They show that, whereas in
1909, 92 percent of all males were working more than 48 hours per week, the
percentage had fallen to 54 percent in 1929 and then to 7 percent in 1940. This
dramatic decline between 1929 and 1940 was in part the consequence of the Fair
Labor Standards Act of 1938 which required that all hours over a standard
workweek be compensated at the rate of 1.5 times the regular wage. Initially the
standard workweek was set at 44 hours; since 1940 it has been 40 hours. 14
The U.S. trends from 1940 onwards are indicated by the data in Table 1.8
which are not restricted to manufacturing industry. This table suggests that there
has not been a pronounced change in hours worked per week since 1940 except
for a reduction in the fraction working 41-48 hours and a greater bunching in the
13If 1t is the index of industrial production in year t (published in issues of the MonthlyDigestof
Statistics) and if Tt is a linear time trend, then I fitted to the annual data for the years 1948-81 the
following ordinary least-squares equation:
I t ~ 64.28 + 2.277 Tt,
(2.28) (0.114)
where the figures in parentheses are estimated standard errors. (The mean value of It over these years
is 104.1) I then formed as a cyclical indicator, Ct, the difference between the predicted value of the
index, I t, and the actual value of the index, I t : Ct = ~ - 1t. Thus, when Ct is positive, a recession is
implied while when Ct is negative a high level of aggregate business activity is implied. (Defining it in
this way, Ct moves in the same direction as the unemployment rate, the cyclical indicator used in
describing variations in U.S. labor force participation rates.) Then, in accordance with the specification
in eq. (1), annual changes in the male labor force participation rate were regressed on ACt, where
ACt = Ct - Ct- 1. The results are not altered if the cyclical indicator is formed from regressing I t on a
quadratic time trend nor if a linear time trend is added to eq. (1).
14Some evidence assessing the effectsof the FLSA on hours worked (especially in the 1940s) is
contained in Lewis (1958). More information gauging the importance of the overtime provisions for
hours worked is found in Ehrenberg and Schumann (1981).
14 J. Pencavel
Table 1.7
United States: Percentage distributionof weekly hours in manufacturing industry
by employed males from the decennial censuses of population.
Hours worked 1909 1919 1929 1940 1950 1960 1970
< 34 ~ ) 0.5 13.3
35-39 12.2 J 4.9
40 7.9 t 2.8 51.3
41-43 1.0 14.2
44-47 3.8 14.8 1.9
48 32.6 26.9 7.4
49-53 7.3 16.4 25.1
54 15.4 9.1 6.3 / 3.9
55-59 30.2 13.7 15.1
60 30.5 9.1 } }
> 60 8.7 3.0 7.5 3.0
6.9
3.5
64.3
17.1
5.6
2.6
7.8 10.1
4.7 4.9
56.4 53.1
}19.3 }18.6
)7.8)8.8
) 4.0 )
Notes: The data relate to all employed males in 1960 and 1970 and to all employed wage
and salary workers in the years earlier. The 1970data describe males aged 16 years and over.
In the years 1929-60, the data describe males aged 14 years and over. The Census collected
data on "prevailing hours of labor" in 1909 and 1919 and on "customary hours of labor" in
1929. In the Census of 1940 and in subsequent years, the hours of work relate precisely to the
census week. A small number of workers whose hours were not reported in 1929, 1940, and
1950 are not included in constructing the frequency distributions above. The 1970 data are
from the Industrial Characteristics volume (Table 39) of the 1970 Census of Population. The
1960 data are from the Industrial Characteristics volume (Table 9) of the 1960 Census of
Population. The 1950 data are from the Industrial Characteristics volume (Table 11) of the
1950 Census of Population. The 1940 data are from Sixteenth Census of the United States
1940: Population Vol. Ill The Labor Force Part I: U.S. Summary, Table 86, p. 259. The 1929
data are from Fifteenth Decennial Census of the United States 1930: Manufactures 1929, Vol. I,
General Report, Table 5. The 1919 data are from the Fourteenth Census of the United States
Taken in the Year 1920, Vol. VIII, Manufactures 1919, General Report and Analytic Tables,
Table 17. The 1909 data are from the Thirteenth Census of the United States Taken in the Year
1910, Vol. VIII, Manufactures 1909, General Report and Analysis, Chapter XII, Table 8, p.
316.
distribution of hours worked at 40 hours. This spike at 40 hours per week is
typically attributed to the overtime provisions of the Fair Labor Standards Act
and the rising fraction of employees working these hours corresponds to the
expansion of the Act's provisions: at the time of its implementation, less than
one-fifth of all employees were covered by the overtime provisions; by the late
1970s, this figure had grown to approximately 58 percent.
The absence of a strong trend in hours worked during the post World War II
period is ~sistent with the series on hours worked compiled from household
interviews as part of the Current Population Survey (Table 1.9). These data are
available on a consistent basis from 1955 and, as distinct from the data derived
from the establishment surveys, they do not describe hours paid for, but hours
worked by those at work. (Individuals on vacation, ill, or on strike are not
covered by these hours of work data in Table 1.9.) The annual observations on
hours worked per week by male wage and salary workers clearly reveal procycli-
Ch. 1: Labor Supply of Men
Table 1.8
United States: Percentage distribution of hours worked
of employed males during the Census week
in 1940, 1950, 1960, and 1970.
Hours worked 1940 1950 1960 1970
1-14 1.59 2.02 4.42 4.54
15-29 5.79 4.75 4.60 5.71
30-34 4.47 3.37 3.09 5.03
35-39 4.56 2.86 4.48 4.91
40 33.53 41.45 41.59 43.06
41-48 29.37 19.29 19.59 17.41
49-59 8.87 10.69 10.36 9.99
>_60 11.83 15.57 11.87 9.35
Notes: These data describe all U.S. males aged 14 years
and over who were employed during the Census week and
who reported their hours of work. The 1940 data relate to
wage and salary workers only. Also, in 1940, the categories
labelled above as "1-14" and "15-29" are, in fact, less than
14 hours and 14-29 hours, respectively. The 1940 data are
from Sixteenth Census of the United States: 1940, Vol. IH,
The Labor Force, Part 1: U.S. Summary, Table 86, p. 259.
The 1950 data are from U.S. Census of Population 1950, Vol.
IV, Special Reports, Part I, Chapter A, Employment and
Personal Characteristics, Table 13. The 1960 data are from
U.S. Census of Population 1960 Subject Reports, Employment
Status and Work Experience, Table 12. The 1970 data are
from U.S. Census of Population 1970 Subject Reports, Employment
Status and Work Experience, Table 17.
15
cal movements, 15 but after accounting for these cyclical effects there is little
evidence of a trend over the past 27 years. These inferences come from fitting the
following equation to the annual observations on weekly hours worked:
Ahj,= aj + /3jAU, r + ej,, (2)
where Ahi, = hi, - hi,_ 1 and hit is the average weekly hours worked by group j
in year t, kUtr= U,r- Otrl and U,r is the unemployment rate (expressed as a
percentage) of white men aged 35-44 years in year t (the superscript "r"
denoting my choice of these men as a reference group), and ej, is a stochastic
error term. Any linear trend in hours worked is measured by a while /3 is
supposed to reflect business cycle influences on hours. The index j runs over the
six groups identified for the U.S. data in Table 1.9 and the ordinary least-squares
estimates of the parameters aj and /3j are given in Table 1.10. There are
significant cyclical movements in hours worked for all workers except those in the
older age groups. Most of the estimated trend terms (the a's) are negative, but
none would be judged significant by conventional criteria except for that for
lSFor an analysis of weekly hours worked over the business cycle, see Bry (1959).
16
Table 1.9
United States, 1955-82, and United Kingdom, 1938-82:
Average weekly hours worked by male employees.
J. Pencavel
United Kingdom:
All adults
United States
14/16All
17 years 18-24 years 25-44 years 45-64 years > 65 years
1938 47.7
1946-49 46.9
1950-54 47.9
1955-59 48.4
1960-64 47.5
1965-69 46.4
1970-74 45.2
1975-79 44.0
1980-82 43.0
42.6 20.9 40.2 44.2 43.6 38.0
42.5 18.4 39.9 44.5 43.7 35.7
42.7 21.0 39.2 45.1 44.0 35.0
41.8 22.5 38.1 44.1 43.3 32.5
41.6 22.3 38.0 43.8 43.1 30.8
40.8 20.6 37.1 43.0 42.2 30.6
Notes: The U.K. data relate to full-time manual workers and are taken from each October's
earnings and hours enquiry of the major industries. The data are published in various issues of the
Ministry of Labour Gazette and of the Department of Employment Gazette. The United States' data
derive from household interviews in the Current Population Survey and they measure the average
hours actually worked (not those paid for) of male employees in nonagricultural industries at work.
(Consequently, those absent from work because of illness, vacation, or strike are not represented in
these figures.) For the years 1955-58, the data are published in the Current Population Reports,
Labor Force Series P-50, issues number 63 (Table 3), 72 (Table 18), 85 (Table 18), and 89 (Table 24).
For the years 1959-64, the data are from Special Labor Force Reports, Table D-7 of each issue,
Report numbers 4, 14, 23, 31, 43, and 52. For the years 1965-82, the data are taken from each
January's issue of Employment and Earnings which give the figures for the preceding year. Before
1967, the youngest age group relates to those aged 14-17 years and from 1967 it relates to 16-17
years.
workers aged 65 years and over who reveal a declining trend of about 0.3 hours
per year over the 1956-1982 period.
Although the downward trend in weekly hours worked in the United States
seems to describe the data up to 1940 and not after that date, the length of the
work year may have fallen because of increases in paid vacations and holidays.
The only consistent time-series data relating to this dimension of work of which I
am aware are the occasional surveys of employee compensation, a summary of
which is presented in Table 1.11. Although the data in this table suggest that
hours actually worked have fallen compared with hours paid for, the recorded
changes are small.16
British long-term experience with weekly hours worked has been similar to that
for the United States. The standard working week for manual workers set down
in various collective bargaining agreements ranged from 48 to 60 hours or more
16There exist several studies investigating whether the absence of a trend during the post World
War II period in weekly hours worked is spurious. Jones' (1974) study may be most thorough, but
anyway the conclusions of Kniesner (1976b) and Owen (1979) are similar: hours worked have fallen
little or not at all during this period and this influence survives adjustments for paid vacations and
holidays.
Ch. 1: Labor Supply of Men
Table 1.10
United States and Britain: Estimates of trend (a) and cycle (fl)
in weekly hours worked by male employees.
17
a /~ R2 D-W
Britain, 1949-1981
All adult
manual workers -0.073(0.083) -0.082*(0.020) 0.34 1.81
United States, 1956-1982
All -0.075(0.055) -0.163"(0.062) 0.22 2.29
14/16-17 years -0.088(0.197) -0.731"(0.223) 0.30 1.29
18-24 years -0.145(0.081) -0.328"(0.091) 0.34 1.51
25-44 years -0.044(0.066) -0.194"(0.074) 0.21 2.19
45-64 years 0.003(0.321) - 0.525(0.363) 0.08 2.95
>_>_65 years -0.329*(0.088) 0.103(0.100) 0.04 2.05
Notes: Estimated standard errors are given in parentheses next to their associated regression
coefficients. "D-W" is the Durbin-Watson statistic. For ease of reading, an asterisk has been
placed next to those point estimates more than twice their estimated standard errors. The data
sources are given in the notes beneath Table 1.9.
before World War I. This fell further to 44 and 45 hours after World War II. A
comprehensive survey of hours actually worked by British manual workers was
conducted in October 1938 by the Ministry of Labour. In the principal industries,
it found that the average hours worked by adult male manual workers were 47.7
while the frequency distribution of hours worked was as follows: 15.5 percent of
these employees worked less than 44 hours, 16.4 percent worked from 44 hours to
less than 47 hours, 27.6 percent worked between 47 and 48 hours (inclusive), and
39.2 percent worked more than 48 hours.
The movement since 1938 in weekly hours worked by male manual workers is
given in the first column of Table 1.9. Again, to determine whether or not a trend
exists in these post World War II data, eq. (2) was fitted to the annual
observations on hours worked from 1949 to 1981. As was the case when eq. (1)
was fitted to the British male labor force participation rate, eq. (2) was estimated
using as a cyclical indicator the deviation of the index of industrial production
from its fitted linear trend. The ordinary least-squares estimates of eq. (2) fitted
to the British data are given in the first line of Table 1.10 and they are similar to
the U.S. results: there is a strong procyclical variation in hours worked in Britain
and no significant time trend. The strong cyclical influence on hours worked
probably accounts for much of the difference in the frequency distribution of
hours between September 1968 and April 1981 as shown in Table 1.12. That is to
say, the fraction of male employees working between 35 and 39 hours increased
from 18.5 percent in September 1968 to 22.0 percent in April 1977 and to 28.3
percent in April 1981 while the percentage working in each of the categories
above 42 hours decreased uniformly from 1968 to 1977 to 1981. However, these
18
Table1.11
United States:Paidleavehoursas a percentageof totalhours
paid for,1958,1966,1977.
1958 1966 1977
Manufacturing:
Nonofficeworkers
Officeworkers
Allworkers
Nonmanufacturing:
Nonofficeworkers
Officeworkers
Allworkers
All nonfarmindustries:
Nonofficeworkers
Officeworkers
Allworkers
6 8.4
8 10.5
7 9.0
4 5.5
7 8.9
5 6.9
5 6.6
7 9.2
6 7.6
Notes: The 1958data are from U.S. Department of Labor,
Composition of Payroll Hours in Manufacturing, 1958, Bureau
of Labor Statistics Bulletin number 1283, October 1960. The
1966 data are from U.S. Department of Labor, Employee
Compensationin the PrivateNonfarmEconomy, 1966,Bureauof
Labor Statistics Bulletin number 1627, June 1969. The 1977
data are fromU.S.Departmentof Labor, EmployeeCompensation
in the Private Nonfarm Economy, 1977, Bureau of Labor
Statistics, Summary80-5,April1980.
J. Pencavel
years exhibited a growing slack in the level of aggregate business activity as
indicated, for instance, by the male unemployment rate (seasonally unadjusted
and including school leavers) which stood at 3.2 percent in September 1968, at
7.0 percent in April 1977, and at 12.6 percent in April 1981.
What is not reflected in these data on hours worked in a given week is the
increasing length of paid vacations in Britain over the post-war period. I know of
no data that document the number of days paid for, but not worked in Britain.
However, the information in Table 1.13 suggests that there has been a substantial
increase in paid vacations. These data are taken from national collective bargaining
agreements and they concern the length of paid vacations to which covered
workers are entitled. Whereas, in fact, annual paid vacations were unusual for
manual workers in Britain before World War II, the data in Table 1.13 indicate
that there have been substantial increases in the length of paid vacations during
the last 30,,years. The increases in paid vacations were especially pronounced
during periods of gov'ernment-mandated wage controls and incomes policies that
diverted attention to less visible ways (than cash) of increasing employee compensation.
17
The discussion above has documented the trends this century in male labor
lVSeeDepartmentof Employment,EmploymentGazette, Vol. 89, No. 4, April 1981,p. 184.
Ch. 1: Labor Supply of Men
Table 1.12
Britain: Percentage distribution of weekly hours worked
by male cmployees in 1968, 1977, and 1981.
September 1968 April 1977 April 1981
0 < h < 24 2.0 1.8 1.6
24 < h _<30 2.1 2.0 2.1
30 < h < 35 4.2 5.5 6.8
35 < h < 37 7.3 11.2 12.4
37 < h _<39 11.2 10.8 15.9
39 < h < 40 20.1 26.2 27.6
40 < h _<42 7.1 5.3 5.4
42 < h < 44 8.0 7.3 6.1
44 < h _<46 6.6 6.0 5.0
46 < h < 48 7.0 5.9 4.3
48 < h < 50 5.2 4.3 3.1
50 < h < 54 7.0 5.3 3.7
54 < h _<60 7.0 4.9 3.4
60 < h _<70 4.0 2.5 1.8
70 < h 2.0 1.0 0.8
Notes: These data cover all men (both manual and nonmanual
workers) whose pay for the survey period was not affected by
absence. The 1968 data are from Department of Employment and
Productivity, New EarningsSurvey1968,H.M.S.O., 1970, Table 83,
p. 120. The 1977 data are from Department of Employment, New
Earnings Survey 1977, PartA: Report and Key Results, H.M.S.O.,
1977, Table 27, p. A35. The 1981 data are from Department of
Employment, New Earnings Survey 1981, PartA: Report and Key
Results, H.M.S.O., 1981, Table 27, p. A90.
19
force participation rates and hours worked. Just as men have spent a declining
fraction of their lives at work for pay, so have they spent an increasing fraction at
school. Some evidence of this is provided by the cohort analyses in Tables 1.14
and 1.15. These data are taken from surveys in 1970 and in 1971 of men of
different ages and they document the striking association between the age of the
cohort and the years spent at school, is
2.2. Cross-sectional variations in work behavior
Some important variations in labor force participation across individual men are
documented by the linear probability estimates in Table 1.16. These are reproduced
from Bowen and Finegan's (1969) monumental work on the 1960 Census
of Population. As is evident from Table 1.16, there is a strong positive relationlSThey
are a biased indicator of the degree to which schooling levels completed have risen over
time insofar as mortality rates are associated with years of schooling. On this association, see
Grossman (1975).
20
Table 1.13
United Kingdom: Manual workers' basic paid vacation entitlements as
set down in national collective bargaining agreements, 1951-1982.
J. Pencavel
Percentage of workers with basic vacations of
Between 2 Between 3
Year < 2 weeks 2 weeks and 3 weeks 3 weeks and 4 weeks > 4 weeks
1951 31 66 2 1
1955 1 96 2 1
1960 97 1 2
1965 75 22 3
1970 41 7 49
1975 1 1 17
1980 2
1982 2
3
51 30
24 74
5 93
Notes: Until 1965, the column given as "3 weeks" is, in fact, "3 weeks and over". In
addition to these annual vacations, workers are usually entitled to payment of wages for
public or statutory holidays or days in lieu of these payments. The data for 1951-65 are
from the Department of Employment and Productivity, British Labour Statistics Historical
Abstract 1886-1968, London, H.M.S.O., 1971, Table 34, p. 91. Data for 1970 onwards are
from various issues of the Department of Employment's Gazette.
Table 1.14
United States: Schooling completed by the male population in 1970 by age.
Percentage of cohort whose highest
schooling levels completed were
Years of Year of Median years >_4 years > 2 years _>4 years of >_8 years of >_5 years of
age in 1970 birth school completed of college of college high school elementary school elementary school
_>75 _<1895 8.3 5.3 8.8 20.9 57.1 79A
70 74 1896-1900 8.6 6.2 10.1 24.5 64.1 85.3
65-69 1901-1905 8.8 7.4 11.8 27.6 68A 88.0
60-64 1906-1910 9.6 8.7 13.9 34.7 75.1 91.5
55-59 1911-1915 10.7 9.3 14.9 41.4 79.8 93.4
50-54 1916-1920 12.0 10.8 17.2 49.7 84.7 95.0
45-49 1921-1925 12.2 14.1 21.2 55.6 87.1 95.7
40-44 1926-1930 12.2 16.4 23~7 57.3 88.4 96.4
35-39 1931-1935 12.4 18.6 26.2 64.3 90.2 96.8
30-34 1936-1940 12.5 18.5 26.6 68.9 92.7 97.6
25-29 1941-1945 12.6 19.5 29.6 74.2 94.7 98.2
Notes: These data are constructed from those given in Table 199 of U.S. Department of Commerce, Bureau of the
Census, 1970 Censusof Population, Volume I, Characteristics of the Population, Part 1, U.S. Summary, Section 2, June
1973.
ship between participation and schooling: for prime-age males (that is, those
aged 25-54 years), a person with 17 or more years of schooling has almost a 9
percent higher probability of being in the labor force than someone with 0-4
years of schooling who is otherwise identical in his observable characteristics.
This participation-schooling relationship among older men is especially strong.
For prime-age males, ceteris paribus, a white man is almost 2 percent more likely
Ch. 1: Labor Supply of Men
Table 1.15
Britain: Highesteducational qualificationattained
by male population in 1971by age.
21
Years of Year of
age in 1971 birth
Percentageof cohort whosehighest educational
qualificationswereat the levelof
"Higher education.... Middle education.... Lowereducation"
> 65 < 1906 5.1 14.9 80.0
60-64 1907-1911 7.6 23.6 68.8
50-59 1912-1921 6.1 25.8 68.1
40-49 1922-1931 10.7 27.2 62.1
30-39 1932-1941 14.2 33.2 52.6
25-29 1942-1946 13.6 41.9 44.5
Notes: The level "Higher education" includes university degrees, equivalent professional
qualifications, and other qualificationsbeyond the GCE "A" levelstandard. "Middle education"
includes any subjects passed at the GCE "A" leveland "0" level plus clerical and commercial
qualifications and apprenticeships."Lower education" means no qualificationsattained. The data
are from Office of Population Censuses and Surveys, Social Survey Division, The General
Household Survey 1971, Introductory Report, H.M.S.O.,Table 7.15.
to be in the labor force than a black man. A married man with his spouse present
is much more likely to be in the labor force (8 percent more likely for prime-age
males, other things equal) than a man with a different marital status. Greater
nonwage income is associated with lower participation and participation probabilities
form an inverted U-shape with respect to age: they rise until 25 years of
age, then remain constant until the middle-to-late fifties at which point they
decline rapidly.
Some empirical regularities with respect to the hours worked by men are
evident from the ordinary least-squares regression results presented in Table 1.17.
These estimates describe the work behavior of 23059 men aged from 25 to 55
years of age at the time of the 1980 Census of Population.19 The column "weekly
hours" relates to the number of hours usually worked during those weeks the
person worked in 1979; the column "weeks per year" relates to the number of
weeks during 1979 in which a person did any work for pay or profit (including
paid vacation and paid sick leave); and the column "annual hours" relates to the
product for any person of "weekly hours" in 1979 and "weeks per year" in 1979.
t9The sample of 23059 men was determined as follows.Thereare 94025 dwellingunits included in
the Public Use Sample Tape "C" sample nationwide file.Of these, 8,021units were rejected because
they were vacant, another 25725 units were rejected because no male was listed as household head
(or, if a woman was listed as the household head, no husband or live-in partner was listed), another
22198 units were rejected becausethe male was not agedbetween25 and 55 years (inclusive),another
1097 were rejected because the male received some farm income, and another 12933 were rejected
because either the male's labor incomewas truncated (being less than $- 9,995or more than $75000)
or the male's data on labor supply weremissing.This yields a sampleof 24051 men of whom992 had
zero hours of work in 1979.
22
Table 1.16
Ordinary least-squares estimates of labor force participation
equations fitted to data on individual men from the 1/1000
sample of the 1960 U.S. Census of Population.
J. Pencavel
(1) (2) (3) (4)
Age-group 18-24 years 25-54 years 55-64 years 65-74 years
hobs 3095.0 22 415.0 4967.0 3392.0
modv 94.0 96.7 85.2 38.7
Estimates of:
Intercept 79.3 83.7 73.5 48.4
Years of schooling
0-4 Reference Reference Reference Reference
5-7 5.3(3.3) 4.1(0.7) 5.4(1.8) 5.9(2.3)
8 9.4(3.2) 5.2(0.7) 10.5(1.7) 14.5(2.3)
9-11 9.2(2.9) 6.3(0.6) 13.4(1.8) 17.9(2.7)
12 10.3(2.9) 6.9(0.6) 13.5(2.0) 20.4(2.9)
13-15 6.5(3.1) 8.1(0.7) 17.2(2.2) 25.1(3.5)
16 11.2(3.5) 8.5(0.7) 18.0(2.7) 31.9(4.5)
> 17 5.6(5.3) 8.8(0.7) 26.6(3.1) 39.7(5.5)
Ethnicity
Black Reference Reference } }
Other nonwhite 1.2(4.9) 2.7(1.3) Reference Reference
White 1.5(1.3) 1.8(0.4) 1.9(1.7) 0.5(2.8)
Marital status
Never married } } Reference Reference
Separated or divorced - 6.7(0.9) Reference 4.0(2.4) 1.7(4.0)
Widowed 0.7(2.7) 1.2(3.5)
Married spouse present Reference 7.8(0.3) 12.6(1.7) 12.7(2.9)
Nonwage income
< $500 Reference Reference Reference
$500-999 - 4.1(0.5) - 19.0(1.6) -- 31.1(2.3)
$1000-1999 - 10.1(0.7) - 35.1(1.8) - 39.9(1.9)
$2000-2999 - 13.9(1.2) - 34.0(2.6) - 44.8(2.5)
$3000-4999 7.0(1.2) - 36.7(3.0) 55,2(3.3)
>_$5000 13.2(1.4) - 30.3(3.1) 40.9(4.3)
Years of age
18/55/65 Reference Reference Reference
19/56/66 7.0(1.9) - 1.6(1.9) 0.5(2.9)
20/57/67 7.5(1.8) 1.5(2.0) - 1.6(2.9)
21/58/68 10.5(1.8) - 2.0(2.0) 2.4(3.0)
22/59/69 8.2(1.8) - 1.3(1.9) 4.7(3.1)
23/60/70 11.3(1.8) 5.5(2.0) ....6.4(3.1)
24/61/71 8.6(1.8) - 6.0(2.1) 12.2(3.1)
62/72 5.6(2.1) - 9.2(3.3)
63/73 10.8(2.1) -- 8.5(3.5)
64/74 9.1(2.1) - 13.8(3.5)
25-34 Reference
35-44 - 0.4(0.3)
45-54 - 1.2(0.3)
/~ ratio 10.5 92.2 45.4 40.0
Notes: These estimafes are from Bowen and Finegan (1969, Tables A-38, A-l, A-14, and A-15).
Standard errors are given in parentheses next to estimated coefficients. The number of observations
is given by "hobs" and the mean of the dependent variable is given by "modv". All the variables
above are in the form of dummy variables with "Reference" indicating the category omitted from
the list of variables. Under the group of variables "Years of age" the first column (18,19,20,etc.)
relates to the 18-24 year olds in column (1), the second column (55,56,57,etc.) relates to the 55-64
year olds in column (3), and the third column (65,66,67,etc.) relates to the 65-74 year olds in
column (4). The group described as "Separated or divorced" under "Marital status" includes
married men with their spouses absent. "Nonwage income" represents the sum of rental income,
interest, dividends, alimony, pensions, and welfare payments.
Ch. 1: Labor Supply of Men
Table 1.17
Ordinary least-squares estimates of male hours and weeks worked
equations fitted to data from 1/1000 sample of the
1980 U.S. Census of Population.
23
Independent variable Dependent variable
Mean and
standard Weekly Weeks per
deviation Definition hours year
Annual
hours
Constant 36.2 34.91
9.53 Average hourly earnings -0.226 -0.107
(10.00) in dollars (0.006) (0.005)
0.477 Interest, dividend, and 0.089 0.010
(2.318) rental income in thousands (0.026) (0.022)
of dollars
0.307 Other income of the indi- - 0.214 - 1.141
(1.502) vidual in thousands of (0.039) (0.034)
dollars
5.978 Family income minus male --0.027 0.001
(7.547) bead's in thousands of (0.008) (0.007)
dollars
37.98 Age in years 0.385 0.471
(8.89) (0.072) (0.062)
1521.3 Age squared in years -0.005 -0.005
(704.0) (0.001) (0.001)
0.46 1 = Completed high school 1.098 2.200
(0.50) (0.229) (0.198)
0.46 1 = Completed any college 2.152 3.020
(0.50) education (0.237) (0.205)
0.43 1 = Any children aged 0.199 0.237
(0.74) 0-6 years (0.090) (0.078)
0.82 1 = Any children aged 0.133 0.044
(1.06) 7-16 years (0.062) (0.054)
0.84 1 = Married and spouse 1.068 1.803
(0.36) present (0.197) (0.170)
0,02 1 = Married and spouse 1.044 0.112
(0.15) absent (0.424) (0.366)
0.05 1 = Hispanic - 1.981 - 1.711
(0.21) (0.284) (0.245)
0.07 1 = Black - 2.736 - 1.549
(0.26) (0.229) (0.198)
0.02 1 = Not White nor Black - 1.508 - 1.489
(0.15) nor Hispanic (0.390) (0.337)
0.06 1 = Self-employed 4.473 - 0.260
(0.24) (0.246) (0.213)
0.19 1 = Employed by local, state, - 1.133 0.274
(0.39) or Federal government (0.152) (0.131)
0.05 1 = Health disability - 1.342 5.312
(0.22) (0.262) (0.226)
0.83 1 = Lived in a metropolitan -0.518 0.679
(0.38) area (0.160) (0.138)
0.06 1 = Lived in New England 0.400 0.095
(0.23) (0.289) (0.250)
1194.88
-13.78
(0.36)
4,62
(1.57)
-55.38
(2.40)
-1.17
(0.52)
38.33
(4.40)
- 0.43
(0.06)
132.61
(14.06)
219.20
(14.57)
20.70
(5.55)
7.55
(3.83)
121.47
(12.09)
59.41
(26.04)
160.51
(17.44)
- 190.34
(14.05)
-130.32
(23.94)
219.20
(15.12)
- 43.94
(9.30)
- 262.86
(16.05)
2.68
(9.79)
26.98
(17.76)
24
Table 1.17continued
J. Pencavel
Independent variable
Mean and
standard
deviation
Dependent variable
Weekly Weeks per Annual
Definition hours year hours
0.16 1= Lived in Mid-Atlantic -0.434 0.608 4.81
(0.37) states (0.213) (0.183) (13.04)
0.19 1= Lived in East North 0.731 0.639 64.99
(0.39) Central states (0.205) (0.177) (12.60)
0.07 1= Lived in West North 0.546 0.599 53.11
(0.26) Central states (0.267) (0.231) (16.40)
0.16 1= Lived in South Atlantic 0.475 0.897 62.03
(0.37) states (0.214) (0.185) (13.14)
0.06 1= Lived in East South 0.065 0.253 20.39
(0.23) Central states (0.290) (0.251) (17.85)
0.10 1= Lived in West South 1.492 0.879 112.58
(0.30) Central states (0.241) (0.208) (14.82)
0.05 1= Lived in Mountain states 0.143 0.251 21.34
(0.23) (0.294) (0.254) (18.05)
R2 0.096 0.117 0.130
Notes: The mean (and standard deviation in parentheses) of weekly hours is 43.41 (9.26),
that of weeks worked is 48.89 (8.08), and that of annual hours is 2131.07 (579.26). There are
23059 observations in each regression equation. Another 992 observations had zero annual
hours of work so the labor force participation rate of this group was 95.9 percent. The East
North Central states are Ohio, Indiana, Illinois, Michigan, and Wisconsin. The West North
Central states are Iowa, Minnesota, Missouri, Kansas, Nebraska, South Dakota, and North
Dakota. The East South Central states are Kentucky, Tennessee, Alabama, and Mississippi.
The West South Central states are Arkansas, Louisiana, Oklahoma, and Texas. The omitted
region consists of California, Oregon, Washington, Alaska, and Hawaii.
The notes to Table 1.17 provide mean values and standard deviations of these
variables. According to these estimates, a dollar higher average hourly earnings is
associated with 14 fewer hours worked per year, the responsiveness of weekly
hours being greater than the responsiveness of weeks per year. The behavioral
implications of this negative hours-earnings association are not clear, however:
the interviewees are asked their earnings (wage income plus self-employment
income) in 1979 and the variable "average hourly earnings" consists of annual
earnings divided by annual hours of work; consequently, any errors in measuring
hours of work are communicated to the measure of average hourly earnings.
Increases in interest, dividend, and rental income are positively (though weakly)
associated v~ith hours, of work while other income of the individual (mainly
public assistance and social security and, as such, it is typically work-related
income) is negatively associated with work behavior. The hours-age relationship
forms an inverted U-shape with the maximum occurring around 44 years of age.
Men with higher schooling levels completed work longer hours as do fathers with
Ch. 1: Labor Supply of Men
Table 1.18
Percentage distribution of hours workedin 1974accordingto hours worked in 1967.
25
Hoursin 1967
0-1499 1500-1849 1850-2149 2150-2499 2500-2999 3000-3499 >_3500
Percentofobservations
in 1967 5.5 7.0 29.0 23.7 19.3 9.4 6.0 100
[ 0-1499 35.7 16.7 10.1 8.7 5.0 8.1 7.4
11500-1849 12.4 26.1 10.5 10.7 8.5 2.5 7.6
Hours 11850-2149 14.7 31.7 49.5 28.2 20.7 17.3 11.9
in {2150-2499 14.1 15.1 18.1 28.6 27.4 15.3 9.7
1974 12500-2999 13.5 4.8 7.8 16.1 23.3 30.2 17.1
13000-3499 5.9 3.0 2.4 5.8 9.6 18.0 23.1
~>_3500 3.7 2.6 1.6 1.8 5.6 8.6 23.2
Total 100 100 100 100 100 100 100
Notes: The underlyingdataconsistof 2209menallof whomweremarriedin the firstyearof interview(1968)
and all of whomworkednolessthan250hoursin both1967and 1974.
younger children, married men, non-Hispanic white men, self-employed men,
men who claimed a health disability, and men who were not government
workers. 2° Some marked regional variations in hours worked are evident. It is
important to observe that only between 9.7 percent and 13.0 percent of the
sample variation in these measures of work behavior is accounted for by the
least-squares combination of variables in Table 1.17. Indeed, the inability of
empirical studies of working hours to remove anything more than a relatively
small fraction of the observed variation in a large sample's hours is striking.
Notwithstanding the popular notion that, each and every year, virtually all
men work 2000 hours per year (40 hours per week and 50 weeks per year), in fact
there exists a substantial amount of variation across individuals in their hours of
work and also important variations for many individuals from year to year. Some
indication of the temporal variations in annual hours of work is provided by the
data in Table 1.18 which are taken from a paper by Hill and Hoffman (1977) that
also analyzes men from the Michigan Panel. The data in Table 1.18 describe 2209
men all of whom were married in the first year of interview (1968) and all of
whom were at work for at least 250 hours in both the years 1967 and 1974. The
first column of Table 1.18 shows that 5.5 percent of these men worked 0-1499
hours in 1967; of these men who worked 0-1499 hours in 1967, 35.7 percent also
2°In the dummy variable categories,the omitted groups are men who did not complete high school,
men without any children, unmarried men, non-Hispanic white men, men neither self-employednor
working for the government,men with no health disability,men not livingin a metropolitan area, and
men living in California, Oregon, Washington,Alaska, and Hawaii.
26 £ Pencavel
worked 0-1499 hours in 1974. The main diagonal in Table 1.18 tends to have
larger entries than the off-diagonal terms, but this is by no means always the
case: thus, of those who worked 2500-2999 hours in 1967, 23.3 percent worked
the same hours in 1974, whereas 27.4 percent worked 2150-2499 hours, an
indication of some regression towards the mean. The authors describe these
changes as "pervasive" and, indeed, 51.1 percent of the variance of the logarithmic
change in these men's annual earnings between 1967 and 1974 was attributable
alone to the variance of the logarithmic change in hours worked.
3. Conceptual framework
3.1. The canonical model
The model that guides most economists' analyses of the determinants of the
supply of working hours derives most directly from Hicks' (1946) paragraph 11 of
his Mathematical Appendix. According to this characterization, the labor supply
function is derived from a general model of consumer demand in which a fixed
endowment of a commodity is divided into one part for sale on the market and
another part reserved for direct consumption. In this instance, the endowment
consists of a fixed block of time, T, that in the simplest of cases is to be divided
between hours worked in the market, h, and hours spent in other activities,
l: T= h + l. The reservation demand for hours of "leisure", l, simply consists of
what is left over from market sales of h. In this canonical model, there is no
savings decision to be made and the individual is fully informed of all the values
of the relevant variables and parameters. An individual with personal characteristics
A (such as his age or race) possesses a well-behaved (real-valued, continuous,
quasi-concave) utility function defined over his consumption of commodities, x,
and his hours of work, h:
U= U(x, h; A, e), (3)
where e stands for the individual's "tastes". Whether e is called a taste component
or an individual's "ability in home production" or whatever, the essential
point is thag unlikethe variables in A, e is unobserved to the researcher. In
accordance with the empirical findings reported above whereby a substantial
fraction of the variation in hours of work across individuals is not removed by
variables observed by the economist, the presence of e in the utility function
allows for individuals to differ from one another in ways not observed by the
researcher.
Ch. 1: Labor Supply of Men 27
The partial derivative of U in eq. (3) with respect to x is assumed to be
positive and that with respect to h is assumed to be negative, at least in the
neighborhood of the observed hours of work. 21 If throughout the analysis the
relative prices of the different commodities do not change, then x represents a
Hicksian composite commodity. The individual sells his services to the consumer
in the product market either directly when he is "self-employed" or indirectly
when he is employed by a firm to contribute towards producing a commodity. In
either case, the individual's total compensation, c, for his market work depends
positively upon how much of his time is alloted to this activity: c = c(h). In the
simplest of cases, each hour of work is rewarded at the same fixed rate, w, and
c(h) = wh. The average and marginal payment for his work time are now the
same and, if p denotes the fixed per unit price of the bundle of commodities x
and if y represents income independent of the working decision, then the
individual's budget constraint is linear and homogeneous of degree zero in p, w,
and y:
px = wh + y. (4)
The individual is assumed to do the best he can given the constraints he faces.
Or, more formally, the individual chooses values of x > 0 and h >_0 that
maximize eq. (3) subject to the budget constraint (4)fl2 Observe that this problem
has been characterized in terms of a single individual's objective function and
budget constraint. This is by no means necessary. Suppose this individual's utility
depends upon his spouse's market work time (h2) in addition to his own work
time (hi):
U = U(xl, hi, h2; A,e). (5)
If his spouse's utility function contains the same arguments and if the two of
them pool their incomes and expenditures,
plXl Jr p2X2 = wlh I + w2h 2 q- y, (6)
in the simple case of a linear budget constraint where w~ and w2 denote the
2XAnothercharacterization of the problem involvesdefining the utility function over activities that
are produced by a household production function whose inputs are purchased goods and time. In
Becker's (1965) formulation, time at market workdoesnot directly enter the utility function at all and
so the question does not arise of whether U is decreasing in h. See Atkinson and Stern (1979) and
Chapter 4 by Gronan in this Handbook.
22The problem is sometimeswritten in terms of leisure, 1,and the endowment of time, T, by having
the individual select x > 0 and / > 0 < T to maximize U(x, 1; A, e) subject to px + wl = wT + y = I,
where I is called full income. This formulation in an empirical context poses the problem of what
value to assign to T, the results not being invariant to this assignment. I prefer the formulation of the
problem in the text that involves variables whose counterparts in the data are more easily defined.
28 J. Pencavel
hourly wage rates paid to individuals 1 and 2, respectively, and x 1 and x2
represent the consumption of commodities by individuals 1 and 2, respectively,
then the problem becomes one of selecting xl, x2, hi, and h 2 to maximize
the utility functions of the two individuals subject to their joint budget constraint
(6). As stated, this is a bargaining problem and typically the solution may
be satisfied with many different combinations of x 1, x2, hi, and h 2. To
determine which of the many possibilities will obtain requires the introduction of
particular behavioral postulates that yield specific solutions.23 The usual method
of handling these problems is to assume that the social choice conditions for the
existence of a well-behaved aggregate (household) utility function have been met
or that the household's utility function is identical with that of the "head" of the
household who integrates the welfare of all the household's members [see
Samuelson (1956) and Becker (1974)]. Under these circumstances, xl, x2, hi, and
h 2 are chosen to maximize eq. (5) subject to the budget constraint (6). Clearly, in
these household models, each individual's allocation of his work time depends
upon not only his own wage rate, but also the wage rate of his spouse.
Return to the formulation whereby a single individual selects x > 0 and h > 0
to maximize U(x, h; A, e) subject to a linear budget constraint px = wh + y. It is
important to distinguish the characteristics of the interior solution for hours of
work, h > 0, from the corner solution, h = 0. In the case of the individual
selecting a positive number of hours to supply to the market, the first-order
condition for a constrained maximum24 requires that commodities and hours of
work be chosen such that the negative of the marginal rate of substitution (m) of
working hours for commodities equals the real wage (w/p):
w au/ah
- m(x,h; A,e) = - (7)
p OU/Ox "
The reduced form equations, the commodity demand and working hours supply
functions, are derived by solving eq. (7) jointly with the budget constraint (4):
x=x(p,w,y; A,e)}
h h(p,w,y; A,e) ' if h>0. (8)
The properties of this hours of work equation are discussed below. This interior
solution for hours of work may be expressed differently by making use of the
concept of the individual's reservation wage, w*. The real reservation wage,
w*/p, is the slope of an indifference curve between commodity consumption and
23Forinstance,Manserand Brown(1979)assumea Nashsolutionto thisbargainingproblem.
24The assumption that the utility function is quasi-concave ensures the satisfaction of the
second-orderconditionsfor a constrainedmaximum.
Ch. 1: Labor Supply of Men 29
hours at work evaluated at h -- 0 and, for any given individual, typically the value
of this reservation wage will vary from one indifference curve to another, i.e. the
reservation wage will depend upon x and so indirectly upon y for any given A
and e:w*(y,A,e). Equivalently, the real reservation wage is equal to the
negative of the marginal rate of substitution of working hours for commodities
evaluated at h = 0: w*/p = - m(x,0; A, e). The reservation wage is the individual's
implicit value of his time when at the margin between participating in the
labor market and not participating. 25 If, at that margin, the market's valuation of
his time, w, exceeds the individual's implicit value of his time, w*, then he will
participate in the labor market and supply a positive number of hours of market
work. Then eqs. (7) and (8) will hold enabling us to write:
ifw>w*, thenh=h(p,w,y;A,e)>O. (9)
On the other hand, if at the margin between participating and not participating
in the labor market the individual places a greater value on an extra unit of his
time than does the market (that is, if w* > w), then naturally the individual will
reserve his entire allocation of time for himself and the solution to the constrained
maximization problem will be a comer h = 0. Consequently, we may
write:
ifw<w*, thenh=0. (10)
Consider now the properties of the labor supply function h = h(p, w, y; A, e)
derived in eq. (8). The zero homogeneity property that was introduced through
the budget constraint carries over to the commodity demand and labor supply
functions: a given proportionate change in p, w, and y leaves the optimizing
values of x and h in eqs. (8) unchanged. A second property of the labor supply
function so derived is manifested when examining the effect of a small increase in
w on the supply of h: 9h/Ow. The Slutsky equation decomposes this effect into a
substitution effect, s, and an income effect, h. Oh/Oy:
Oh 3h
--=s+h-- (11)
Ow Oy "
The substitution effect, s, measures the utility-constant (or income-compensated)
effect of an increase in the wage rate on the individual's hours of work and the
theory of constrained utility maximization outlined above restricts s to be
positive: an increase in the wage rate raises the price of an hour not worked in
the market and, at the same level of utility, this induces less consumption of
non-market time and more time allocated to market work. At the same time, an
250r the real reservation wage, w*/p is the value of the real wage such that hours of work are zero
exactly, i.e. from eq. (8), h(1, w*/p, y; A, e) = O.
30 Z Pencavd
increase in the wage rate augments the individual's wealth allowing him to
consume more of those things that increase his utility and to consume less of
those things that generate disutility (such as hours of market work). This is the
income effect of a wage increase on hours of market work and it is given in eq.
(11) by h.Oh/Oy. This term is negative provided nonmarket time is a normal
commodity. Consequently, the sign of the uncompensated effect of an increase in
the individual's wage rate on his hours of work [the left-hand side of eq. (11)] is
indeterminate in sign and depends on the relative magnitudes of the substitution
and income effects.
As in other constrained maximizing problems where the constraint is linear,
the optimizing eqs. (8) possess a symmetry property according to which
(Ox/Ow)~ =-(Oh/Op)~, where the ~ subscript denotes that these derivatives
involve "pure" price changes, i.e. they are evaluated with utility held constant. In
addition, under these circumstances of an interior solution to the maximization
problem where the constraint is linear and the utility function is quasi-concave,
the derived hours of work equation will be a continuous function of the budget
constraint variables.
Frequently, eq. (11) is expressed in terms of elasticities:
E = E* + (rope), (12)
where E = (Oh/Ow)(w/h) ~ 0 is the uncompensated wage elasticity of hours of
work, E* = (sw)/h > 0 is the income-compensated wage elasticity, and mpe =
w. 3h/Oy is the marginal propensity to earn out of nonwage income. The second
term on the right-hand side, mpe, is often described in the empirical literature as
the "total income elasticity".26 If both commodities and nonworking time are
"normal" (i.e. if both Ox/Oy > 0 and - Oh/Oy > 0), then the mpe is less than
zero but greater than minus unity. 27 If nonworking time is "inferior", then a
dollar increase in nonwage income increases the consumption of commodities by
more than one dollar.
Substitute the optimizing commodity demand and labor supply functions (8)
into the utility function (3) to express the individual's maximized utility as an
indirect function of commodity prices, the wage rate, and nonlabor income:
V=V(p,w,y; A,e). (13)
This indirect utility function also possesses the zero homogeneity property in p,
w, and y: because ~in equiproportionate change in p, w, and y leaves the
optimizing x and h unchanged according to (8), so must the maximized value of
26It may be written as the product of (wh)/y and (Oh/Oy)(y/h).
27Differentiating the budget constraint with respect to y (and in so doing recognizing the
dependence of x and h on y) yieldsthe Engelaggregationcondition p(Ox/Oy)-w(Oh/Oy)= 1.
Ch. 1: Labor Supply of Men 31
utility be unaltered. It isstraightforward to show that 0 V/Op = - )~x, 0 V/Ow =
hh, and OV/Oy = X, where 7~ is the marginal utility of nonlabor income when
evaluating the utility function at its optimum so that, combining these results,
0 V/Op
x(p,w,y; A,~),
OV/Oy
OV/Ow
h(p,w,y; A,~).
oV/Oy
(14)
These equations, Roy's Identity, imply that the functional form of the commodity
demand and labor supply equations may be derived relatively easily once a
particular form of the indirect utility function, eq. (13), has been specified. 28
3.2. Aggregation
The theory outlined above applies to a single individual. It has often been applied
to data that have been aggregated across individuals. Thus, some claim to have
estimated the income and substitution effects (or the net wage effect OhlOw) of
eq. (8) by using data across industries or occupations and by specifying the
dependent variable as the average hours worked of individuals in a given industry
or occupation. [For instance, Metcalf, Nickell, and Richardson (1976) and S.
Rosen (1969).] Others use time-series observations on average hours worked by
all employees (both male and female) in the economy to fit eq. (8). [For instance,
Abbott and Ashenfelter (1976, 1979), Barnett (1979, 1981), Darrough (1977), and
Phlips (1978).]
There are two issues to address. The first one assumes all individuals occupy an
interior solution to their constrained maximization problem and enquires into the
conditions under which each individual's labor supply function can be aggregated
into a macro labor supply function that possesses the properties of eq. (8). The
second and more relevant issue looks into the aggregation problem when some
individuals are at a comer solution and others are at an interior solution to their
maximization problem.
2SThe dual to the budget-constrainedutility maximizationproblem characterizesthe individual as
selecting x and h to minimizethe net cost, px - wh, of attaining a prescribed levelof utility. The
reduced form equations correspondingto this problem are the utility-constant commoditydemand
and labor supply functions and if these functions are substituted back into the objectivefunction,
px - wh, the net expenditure function is derived.
32 J. Pencavel
The first issue is not identical to the standard problem in the consumer
demand literature because in that literature all consumers are assumed to face the
same commodity prices whereas in the labor supply context one price, the wage
rate, varies across individuals. The papers listed above using aggregate data to
estimate labor supply functions have specified as arguments some average of the
wage rates of the workers and an average nonwage income. Therefore, consider
the case in which the arithmetic mean of these variables is used in a macro labor
earnings equation and in which the macro earnings equation is to be derived by
aggregating each worker's labor earnings function. In these circumstances, each
worker's rope (marginal propensity to earn = w. Ohlay) must be the same and it
must be independent of the wage rate and nonwage income. In addition, the
commodity demand functions must be linear in both wages and nonwage income.
[See Deaton and Muellbauer (1980, pp. 159-161) and Muellbauer (1981).] These
are nontrivial restrictions on the form of the labor supply and commodity
demand equations although they do not rule out some interesting cases. 29
The second aggregation problem has more serious implications and to appreciate
these difficulties let us invoke a set of extreme assumptions, namely, that a
population of individuals is identical in all characteristics observed by the
economist (i.e. they have the same y and A and face the same p and w), but they
have different values of the unobserved variable e. Let f(e) be the density of e in
the population. These differences in e generate a distribution of reservation wages
across these individuals. Suppose this distribution of reservation wages is described
by the density function ~(w*) and suppose ~/i(w*) is the cumulative
distribution corresponding to the density function. The cumulative distribution
function qb(~*) is interpreted as giving for any value ~* the probability of the
event "w* < ~* ". The proportion of these individuals who offer positive hours of
work to the labor market consists of those whose values of w* satisfy eq. (9), that
is, those for whom w* < w. Equivalently, the labor force participation rate (~r) of
this group is simply the cumulative distribution of w* evaluated at w* = w:
~(p,w,y,A)=q~(w;p,y,A),
where the dependence of the labor force participation rate on the variables
assumed to be the same in this hypothetical population (namely, p, w, y, and A)
has been made explicit. Because the cumulative distribution function is necessarily
a monotone nondecreasing function [i.e. ~(w*) < ~(~*) for w* < ~*], an
increase in the wage rate offered to these individuals cannot reduce the labor
force parti~cipation rate:
a~ a~(w)
aw aw =,t,(w) > O.
29The labor supply equation derived from a Stone-Geary utility function is a special case of the
class of permissible functions that aggregate. The more general class accommodates a wider range of
substitution possibilities than does the Stone-Geary.
Ch. 1: LaborSupplyof Men 33
Exactly how much the labor force participation rate increases (if at all) will
depend upon the shape of the density function ~(w*) in the neighborhood of
w* ~ w.30
The variable most often used in studies of labor supply with aggregated data
measures the average hours worked per employee. This may be written
fh(p, w, y; A, e)f(e) de
e(h[w>w*)= ~r(p,w,y,A) '
where the integration is over all those at work and where the hours of work
function is that corresponding to the interior solution of the constrained utility
maximization problem, eq. (8). Unless the conditioning event w > w* is satisfied
for the entire population, i.e. unless ~r= 1, the partial derivatives of ¢(h Iw > w *)
are not the same as the partial derivatives of eq. (8), h(p, w, y; A, e), and it is the
latter to which the income and substitution effects outlined in Section 3.1 relate.
Studies that regress average hours work,~d per worker on average wage rates and
nonwage income and that interpret the resulting estimates in terms of income
and substitution effects are compounding the effects of changes in these variables
on (1) the hours worked by those who are at work both before and after these
changes with the effects on (2) the composition of the population between
workers and non-workers.
These problems of aggregating over individuals some of whom are occupying
interior solutions to their constrained utility maximization problem and others
corner solutions are likely to be more innocuous for studies restricted to prime-age
males (for whom ~r does not fall far short of unity) than for those relating to
young men, older men, and women. The aggregate time-series studies mentioned
above, however, are fitted to data describing all workers, male and female, young
and old, urban and rural and for the entire adult population, of course, the labor
force participation rate has been substantially less than unity (see table 1.5). At
this grand level of aggregation, there are the additional problems raised by the
fact that the microeconometric evidence suggests differences in the utility functions
of men and women even after allowing for differences in the unobserved
components e. So even though during this century the labor force participation
rate of all adults in the United States has changed relatively little, the composition
of the labor force has changed considerably: according to the U.S. decennial
Censuses, whereas in 1900 some 18 percent of the labor force were women, in
3°Thus, while an increase in w may increase or may decrease hours worked per employee,an
increase in w cannot decreasethe fraction of the population at work.On this, see Lewis(1967), Ben
Porath (1973), and Heckman (1978). The distinction between the labor force and the number
employed is not crucial to this argument.Whetherhours spent searchingfor a job is includedin the
definition of the offerto sellhours or it is excluded(so that ~rmeasuresthe fraction of the population
who are employed), this doesnot affectthe substanceof the argument.
34 J. Pencavel
1970 the figure had more than doubled to 37 percent. These problems of deriving
meaningful behavioral parameters from aggregate time-series data are further
aggravated by the difficulties that arise when individuals face different nonlinear
budget constraints (discussed in Section 3.3) and when the conditions are almost
certainly not satisfied for the identification from these data of a labor supply
function-after all, while some are regressing hours per worker on the average
wage rate and interpreting the results in the terms of the income and substitution
effects of a labor supply equation, others are taking virtually the same aggregate
data, running very similar regression equations, and interpreting the results in
terms of the parameters of a structural labor demand function! Both groups of
researchers tend to find a negative partial correlation between hours and wage
rates: one group interprets this as a negatively-inclined labor supply function
while the other group confirms the existence of an inelastic labor demand
function! 31 The inescapable conclusion is that the equations fitted to aggregate
time-series data are not to be regarded as supplying meaningful evidence on the
parameters of behavioral hours of work equations and so, in evaluating the
empirical work in Section 4 below, I omit a discussion of the estimates from
aggregated data.
A somewhat different set of aggregation issues arises in those few studies that
use as the measure of labor supply not average hours worked, but the labor force
participation rate of different cities. This procedure was employed by Mincer
(1962) in his influential work on the labor supply of married women. He cast the
wife's decision-making in a family context and he proposed and implemented a
specification that distinguished more clearly than had previous researchers between
the income and substitution effects operating on the wife's behavior. In his
application, he used as his measure of labor supply the labor force participation
rates of married women across different metropolitan areas of the United States.
This use of aggregate participation rates as the measure of labor supply was
followed in a number of subsequent studies, some of them dealing with the labor
supply of men. 32 In these papers, the authors have often interpreted the coefficients
on the wage rate and nonwage income variables in terms of the derivatives
31Some of the labor demand studies use hours per worker [e.g. Nadiri and Rosen (1974)] as the
variable to be explained while others use total manhours [e.g. Sargent (1978)]. In either case an
identification problem arises. As an example, compare the work of Abbott and Ashenfelter (1976,
1979) with that of Coen and HAckman(1970). Both use highly aggregated annual observations on
variables covering a similar period-from 1929 to 1967 in the case of Abbott and Ashenfelter and
from 1924 to 1E965 (excluding 1941 to 1948) in the case of Coen and HAckman. Abbott and
Ashenfelter maintain they are estimating a labor supply equation in a system of consumer demand
equations while Coen and HAckmanmaintain they are estimating a labor demand equation in a
system of input demand functions. In fact, both sets of authors seek to explain first-differences in
hours worked, in labor earnings, or in manhours worked. Abbott and Ashenfelter (1979) estimate an
uncompensated wage elasticity of the supply of hours worked of -0.07 for the linear expenditure
system and of - 0.14 for their form of the Rotterdam model. Coen and Hickman's preferred estimate
of the elasticity of the demand for manhours with respect to wages is -0.19.
32See Ashenfelter and Heckman (1974), Bowen and Finegan (1964, 1969), Greenhalgh (1979), and
Kosters (1966, 1969).
Ch. 1: Labor Supply of Men 35
for the average individual of the hours of work eq. (8) expressed as a fraction of
total time available. What justification can be provided for this? 33
Assume that the period relevant to the constrained utility maximization
problem is the individual's lifetime so that the budget constraint variables are
defined in terms of their "permanent" values. The individual then determines the
proportion of his life to be spent at market work, the particular timing of that
participation being determined (it is assumed) by factors orthogonal to the labor
supply problem. In this case, among a group of individuals with the same p, w,
and y, the probability that one of them is at market work is the same as the
proportion of available lifetime hours allocated to market work. What is crucial
in this chain of reasoning is that the proportion of his lifetime supplied to market
work (equal by assumption to the participation rate) should correspond to an
interior solution to the constrained maximization problem for all individuals in
the relevant population. Otherwise, instead of eq. (8) being applicable to all
individuals, it holds for only a subset of the population with the remainder
described by a corner solution, namely eq. (10). In fact, virtually all men in the
United States are in the labor force at least part of their lives: according to the
1970 U.S. Census of Population, of all men aged 55 years and over who were not
in the labor force during the Census week of 1970 and who responded to the
question concerning their last year worked, a little over 1 percent had never
worked at all. Although all but a tiny fraction of men work in the market at some
stage in their life, there remain a number of heroic assumptions in this chain of
reasoning-the particular timing of a person's participation is unlikely to be
uncorrelated with the permanent budget constraint variables nor in many applications
of this procedure do the authors exercise great care in distinguishing
permanent budget constraint variables from their currently observed counterparts-such
that it is difficult to accept the interpretation of the coefficients on
the wage rate and nonwage income variables in cross-city labor force participation
rate equations as the parameters on an hours of work function such as
eq. (8).
3.3. Nonlinear budget constraint
Now return to the analysis of the individual's allocation of time and consumption.
Section 3.1 assumed the simplest form for the budget constraint according
to which each and every hour supplied by the individual to the market is
rewarded at the fixed rate w. This assumption does not require that each
employer does nothing more than specify for each job a fixed wage per hour,
leaving the individual employee to choose how many hours he wishes to work.
Even if each employer specified not merely the wage rate but also the number of
hours each employee is expected to work, provided the wage offer does not vary
33The argument that followsis taken fromHeckman(1978).
36 J. Pencavel
systematically with the stipulated hours and provided the entire range of hours of
work is covered by the employers' offers, then a continuous linear budget
constraint arises from the aggregation over many employers' wage-hours packages.
Nevertheless, there seem to be important instances in which a continuous,
linear budget constraint does not accurately describe an individual's work-income
opportunities and as a result the wage rate can no longer be assumed exogenous
to the individual. For instance, the presence of quasi-fixed hiring and training
costs that are more closely related to the number of employees rather than to
their total hours worked encourages firms to offer higher wage rates for longer
hours worked per employee [Lewis (1969)]. If this is the case, the wage-hours
contract offered by each employer is such that relatively long work hours are tied
to relatively high hourly wage rates and consequently the market hours-wage
locus facing an individual worker is no longer linear. Even if the employeremployee
contract should grant the employee considerable discretion over his
hours of work, some payments systems will result in a nonlinear budget constraint.
Such is the case when the employee is rewarded (at least in part) by what
he produces on the job (such as with piece-rate systems or sales commissions)
and this in turn is not a simple linear function of his hours worked. Furthermore,
if it is his after tax compensation that is relevant to the individual's allocation
decisions 34 and if the tax rates on his income are not independent of the amount
of that income, then again the individual is no longer presented with a linear
budget constraint. Even if statutory tax rates did not change with income,
effective tax rates might vary because of systematic income tax evasion or
because of the latitude exercised by administrators in the tax revenue and welfare
disbursement agencies. Finally, there are fixed costs and benefits to working, that
is, expenditures and compensation that do not vary over all values of an
individual's hours of work. As an example of a fixed compensation, some health
insurance schemes are available to each individual workers more cheaply when
provided to all employees as a group and these benefits take the form of a
lump-sum payment that does not depend upon an individual's precise hours
worked (although they are sometimes available only if a certain minimum
number of hours are regularly worked). Fixed money costs of work arise from
travel expenses or necessary expenditures for the performance of the job; these
costs must be incurred if any hours are worked in the market, but once the
individual is at work they do not change with the number of hours worked. 35
The modifications required by a nonlinear budget constraint for the theory of
the allocat~i~ of time in Section 3.1 depend upon the particular form taken by
the budget constraint. There are three cases to be considered: the first is when the
budget constraint may be assumed to be fully differentiable and it forms a convex
34This has been tested in H. Rosen (1976), Hausman and Wise(1976), and Johnson and Pencavel
(1984), all of whom couldnot reject the hypothesisthat the relevantvariable was after-tax wagesnot
before-tax wages.
35Fixed time costs consist of the expenditure of time in travelling to and from work. For an
analysis of these, see Mosesand Williamson(1963), Oi (1976),and Cogan(1981).
Ch. 1: Labor Supply of Men 37
set (so, if taxes are the cause of budget constraint nonlinearities, they are
progressive at all levels of income) in which case the techniques of differential
calculus may be applied and local comparisons of -m with the slope of the
budget constraint identify the individual's optimum allocation of consumption
and work; the second is when the budget constraint forms a convex set, but it is
piecewise linear with kinks at various levels of income; and the third is when the
budget constraint set is nonconvex because of regressive tax rates or "lumpy"
fixed costs. Consider each of these three cases in turn.
Where the budget constraint forms a convex set and where it is continuous
throughout and fully differentiable, then once again Kuhn-Tucker methods can
be applied to determine whether an individual works in the market and, if he
works, the number of hours he chooses. In particular, let c be the individual's
total compensation for his market work and let c be a positive function of hours
worked, h : c = c(h; B) with c'(h; B) > O, c"(h; B) < 0, and where B stands for
variables that affect the position of the compensation function and that are
exogenous to the individual worker. The individual may now be characterized as
choosing x > 0 and h > 0 to maximize U(x, h; A, e) subject to the budget
constraint px = c(h; B)+ y. For an interior solution, the negative of the marginal
rate of substitution of working hours for commodities, - m, equals the real
marginal rate of compensation:
c'(h; 8) aU/ah
. . . . m(x,h;A,e).
p OU/Ox
An analogous modification is made to the condition that determines whether an
individual will work: if c'(0; B)< w*, then h =0. For this type of budget
constraint, a typical procedure is to replace the true nonlinear constraint with
that artificial linear constraint which would induce the same hours of work by the
individual. That is, if h denotes the hours of work and Y the commodity
consumption bundle that solve the constrained utility-maximization problem and
if ~ = c'(h; B), then the linearized budget constraint is the equation pY = ~/~ + )7,
where )~ is known as "linearized nonwage income" or, sometimes, as "virtual"
income [Burtless and Hausman (1978)] (see Figure 1.1). The hours of work eq. (8)
may then be written as h = h(p, ~, .9; A, e). 36
The problem is only slightly less straightforward in the second case when the
income tax system is progressive throughout, but the tax rate rises with income in
discrete steps so the budget constraint has linear segments connected by kinks.
Each segment of the budget constraint is defined by its real after-tax wage rate
36Observe that, because hours of work are affected in part by the unobserved variables e and the
artificial budget constraint is linearized around the observed hours of work, k and )7 are also going to
be affected by e. Consequently, in estimation, k and )7 cannot be treated correctly as exogenous
variables. Hall (1973), Hausman and Wise (1976), and Rosen (1976) calculate the marginal wage rate
and linearized nonwage income not in the manner described, but at the same number of working
hours for everyone in tkeir sample. This leads to an analogous sort of inconsistency that comes from
not instrumenting the marginal wage and linearized nonwage income variables.
38 J. Pencavel
Total
Income
"•%•Slope0 Hours
of ~Ip
Figure 1.1
and by its real level of linearized nonwage income (i.e. by the height of the
nonwage income axis if the slope of the budget constraint is extended to the
vertical axis). The familiar tangency condition between the real net wage rate and
- re(x, h; A, e) holds for any point chosen along one of the linear segments. An
individual will locate at any kink if, at this point, his -m(x, h,; A,e) lies
between the slopes of the budget constraint on either side of this kink. Once
again, because the budget constraint is convex, local comparisons of -m with
the slope of the budget constraint are sufficient to identify the hours of work
corresponding to maximum utility.
Local comparisons of the slope of the indifference curves with the slope of the
budget constraint are not sufficient to identify the global utility optimum when
the budget set is nonconvex, the third case. Examples of this are provided in
Figures 1.2 and 1.3. In Figure 1.2, the income tax system is regressive as is the
case when the implicit tax rate on welfare income (received at relatively low levels
of total income) exceeds the explicit personal income tax rate. In Figure 1.3, there
are fixed money costs of working of the amount ab' so that the budget constraint
is Oab if thi~,individual works and Oab' if the individual does not work in the
market. For those who Work, these fixed money costs are tantamount to a lower
level of nonwage income. These fixed costs can be avoided altogether, however,
by not working in the market and their lumpiness induces a discontinuity into the
hours of work function: if only a relatively small number of hours are worked
(relative, that is, to the market wage rate), then insufficient labor income will be
earned to offset the fixed money expenditures of working, let alone to compensate
for the disutility of market work; once the net wage rate rises sufficiently to
Ch. 1: Labor Supply of Men
Total
Income
~ ,Y2)
.~ Uo(Y!/p,O)
hl 0 Hours
Figure 1.2
39
induce the individual to work, he works sufficient hours to generate enough labor
income to pay the fixed costs of work and to offset the disutility of hours at work.
These minimum hours of work are called reservation hours (h r in Figure 1.3).
When the budget constraint is nonconvex, the hours of work function may not be
a continuous function of the slope of the budget constraint.
With a nonconvex budget constraint such as that in Figure 1.2, the individual
must evaluate his utility at all locations along the frontier of his budget constraint.
He is fully capable of doing this because he knows the form of his own
utility function, he knows A and ~, and he knows the values of his budget
constraint variables. He proceeds by dividing up his utility-maximizing problem
into distinct stages, each stage corresponding to a particular corner or segment of
his budget constraint. At the first stage he evaluates the utility of not working; in
this case his consumption would be Yl/P and his utility would be
Uo(Yl/p,O; A, e). At this next stage, he moves to the segment of his budget
constraint between 0 and h a hours where wx is the slope of his budget constraint.
Given p, w~, and y~ and conditional upon working between 0 and h~ hours, he
could determine whether a tangency condition (a local maximum) obtains
between his indifference curve and his budget constraint. It may not, but if it
does a maximum level of utility is given by Vl(p, Wl,Yl, A, e). He then proceeds
to the segment of his budget constraint to the left of hi where the net wage is w2
and linearized nonwage income is Y2. Again, given p, wz, and Y2 and conditional
upon working more than hI hours, the individual ascertains whether a tangency
condition obtains. If it does, his maximum level of utility is given by
40 J. Pencavel
Total
Income
b t
hr 0 Hours
Figure1.3
112(p, w 2, Y2; A,/?).37 Having determined the existence of any local maxima in the
interior of his budget constraint, if there is more than one, he selects that with the
greater utility. He checks to ensure that the utility associated with any interior
local maximum exceeds U0. If no local maximum exists in the interior of his
budget constraint, his maximum in Figure 1.2 must be at zero hours of work. If
the local maximum in the interior of his budget constraint dominates U0, then his
hours of work are determined by the application of Roy's Identity:
( c9~/cgwi)/(t9 ~/ayi) = h(p, w~, y~; A, e).
Even if the economist knows the form of the individual's utility function, he
cannot replicate the individual's procedure exactly unless e does not exist. This is,
in fact, how Wales and Woodland (1979) proceed by presuming full knowledge of
each individual's utility function (i.e. they suppress e) and of his budget constraint,
but assuming that there are errors in measuring hours of work, errors that
are distributed independently of p, w, y, and A.
3.4. Restrictions on hours of work by employers
The models=described to this point are characterized by the fact that an
individual faces a budget constraint covering all possible hours of work. As
mentioned at the beginning of the previous section, this does not necessarily
37Ifat a higher levelof income,another segmentof the budget constraint existedwith a lowernet
wage than w2 (a kink thatbent out wouldexist),the direct utility function at this kink wouldhaveto
be evaluated.
Ch. 1: Labor Supply of Men 41
mean that each employer offers this continuum of possibilities, only that the
market as a whole presents this set of opportunities. However, there exists a long
tradition in economics of regarding this notion as fanciful and of characterizing
the effective choices for the individual as those of working a "normal" or
"standard" work schedule (hours per day, days per week, and weeks per year) or
of not working at all. The employer may require overtime to be worked during a
period of an unusually high level of business activity and may occasionally put
his employees on short time when business is unusually slack, but at all times the
employee's hours choices (if he works at all) are supplanted by his employer's
discretionary actions.
Under these circumstances, the individual's constrained maximization problem
consists simply of choosing x and h to maximize U(x, h; A, e) subject to the
constraints px = wh + y, x > 0, and h equals either h or 0, where h denotes the
employer's "take-it-or-leave-it" hours. The individual's choice degenerates into a
simple_comparison between his maximum utility if he works, U=U((wh+
y)/p, h; A, e) and his utility when not at work Uo = U(y/p,O: A, e). If it is the
case that U-> U0, h could exceed the hours he would choose (given the same
values of the o+her exo_genousvariables) if the employer allowed any hours to be
worked. Or, again, if U > U0' h might fall short of the hours the individual would
choose (given the same values of the other exogenous variables) if the employer
permitted him to work any number of hours the individual wishes. If this is the
case, the individual's hours of work do not correspond to a situation in which the
slope of the budget constraint is tangent to the individual's indifference curve.
This attribute distinguishes this class of models from those in Sections 3.1
and 3.3.
Of course, in any labor market in which these hours of work restrictions are a
permanent and regular feature, it is incorrect to specify the other variables
constraining an individual's behavior to be the same in the presence of the hours
constraints as in their absence. For, in evaluating the pecuniary and nonpecuniary
net benefits of alternative jobs, individuals will gravitate towards those
employers who fix working hours close to workers' preferences while employers
who stipulate unpopular working hours will tend to experience difficulties in
recruiting or retaining workers. In this manner, the wage rate will respond to
these variations in the supply of workers to different employers and compensating
wage differentials will arise. It would be an error, therefore, to estimate
market equilibrium models in which workers are characterized as being con--
strained to work the number of hours mandated by their employers without at
the same time treating the wage rate paid to these workers as jointly determined.38
Suppose these employer-mandated hours of work restrictions obtain and that
an individual determines he is better off by working h hours than by not working
at all. Let h0 = h(p, w, y; A, ~) be the hours this individual would work if the
3SThisis exactlyhowhoursconstraintsare modelledin Abowdand Ashenfelter(1981).
42 J. Pencavel
employer allowed him to work any number of hours. Then the information
required to help determine this individual's preferences for work and consumption
(given p, w, y, and A) is h0, but h0 is not observed and only h is available.
Under these circumstances, some economists have argued that time spent searching
for the desired number of hours should be included in h0 and they have used
the sum of h and hours of unemployment, UN, as an estimate of h0:/7l+ UN = ho.
[For instance, Cohen, Rea and Lerman (1970), Garfinkel (1973), Greenberg and
Kosters (1973), and Hill (1973).] Or when only some unknown fraction, a, of
reported hours of unemployment represent the offer to sell labor, observed hours
of work (h) may be expressed as a function of reported hours of unemployment
(UN) plus a vector of variables believed to affect the hours an individual would
choose to work in the absence of the employer's mandates: 39
= h0(p,w,y; A,e)- a(UN). (15)
Stochastic versions of this equation have been estimated by Dickinson (1974),
Morgan (1979), Kalachek, Mellow and Raines (1978), Ashenfelter and Ham
(1979), and Ashenfelter (1980). Whereas the earlier papers took account of
unemployment in this way on the argument that they would measure more
accurately or confidently conventional income and substitution effects, the more
recent literature has interpreted the stochastic version of eq. (15) as "... a method
for testing whether measured unemployment may be thought of as involuntary"
[Ashenfelter (1978)]. According to this argument, ':if, on the one hand, measured
unemployment is simply another name for voluntary non-market time", then a
should be zero; "if, on the other hand, measured unemployment is closely related
to the extent to which workers face constraints on their labor market choices,"
then a should be positive. In fact, with cross-section data, a has been estimated
as greater than unity [Dickinson (1974)], as almost exactly unity [Morgan (1979)],
as 0.92 [Kalachek, Mellow and Raines (1978)], and as about 0.78 [Ashenfelter
and Ham (1979)]; with aggregate time-series data [Ashenfelter (1980)],4° the
estimates of a ranged from 0.36 to 0.48 (with an estimated standard error of
about 0.18) when the unemployment variable was treated as exogenous and to be
equal to 0.04 (with a standard error of 0.23) when the unemployment variable
was instrumented.
In view of the reams written on the subject of "voluntary" and "involuntary"
unemployment, the proposal of resolving the empirical relevance of the issue
simply by ~determining whether the coefficient a in eq. (15) is estimated to be zero
39It is unfortunate that the utility function and budget constraint underlying eq. (15) are not
written down explicitly because it is not obvious how UN enters either the objective function or the
constrainc Without knowing that, the behavioral interpretation of eq. (15) is difficult to discern.
4°As Ashenfelter (1978) himself recognizes, the results from the aggregate time-series analysis were
never in doubt: as the estimates of eq. (2) in Section 2.1 made clear, hours of work move closely with
the unemployment rate over the business cycle whereas wage rates, nonlabor income, and commodity
prices [the other right-hand side variables in eq. (15)] display considerably less business cycle
variability. It is claimed that eq. (15) provides a structural explanation for this association.
Ch. 1: Labor Supply of Men 43
must have considerable appeal to the profession. 41 Unfortunately, it is not so
straightforward a matter for, according to the view that "measured unemployment
is simply another name for voluntary non-market time", the duration of
unemployment represents one part of the individual's optimal allocation of time
and income and, as such, is jointly determined with hours of work and commodity
consumption. According to this view, given the variations in individuals'
hours of work left unaccounted for by the typical variables available to the
economist, it is by no means surprising that, even after removing the influence of
the variables p, w, y, and A, one object of choice in this allocation problem
(hours of unemployment) is correlated with another dimension (hours of work).
Would the existence of a partial correlation across households between expenditures
on food and expenditures on clothing necessarily imply that clothing is
rationed? The more relevant test is not whether a is zero, but rather a test of
whether UN is endogenous. 42 However, this test comes up against the serious
problem of an appropriate instrumental variable: what is the variable that can be
validly excluded from an hours of work equation and that, at the same time,
accounts for variations in the duration of unemployment? I do not know of
one. 43 If this is so, then we are not capable of discriminating between the two
different characterizations of unemployment. 44
41When asked by some surveys, many individuals claim they would like to work a different number
of hours from those they are currently working and some economists infer from this that the model in
this section is the relevant one. This is surely an incorrect inference. It is not clear how the respondent
interprets the question, but it is likely he answers the question assuming all other variables remain
constant. In this case this may only mean that employers are not indifferent to the number of hours
that their employees work. If the market offers tied wage-hours packages and the worker selects the
best combination of wages and hours on his opportunity locus, then the relevant model is that in
Section 3.3 above.
42Deaton (1982) also makes the argument that the relevant test in this context is an exogeneity test.
In his case, he notes that, when commodities and hours of work are weakly separable in the utility
function, the commodity demand equations may be written as a function of the prices of each
commodity and of total income, wh + y, instead of as a function of w and y separately. When h is
freely chosen, wh + y is endogenous. Provided commodities and hours are weakly separable, the form
of the commodity demand functions is the same whether hours are constrained or not. Using data on
1,617 households from the British Family Expenditure Survey, Deaton estimates such a system of
hours-constrained commodity demand equations where an instrument for total income, wh + y, is
provided by wb + y, b being a parameter of the preference structure as estimated from the
unconstrained version of the model. The results are ambiguous though Deaton infers they slightly
favor the model characterizing hours of work as unconstrained. As he fully recognizes, there are a
number of stringent assumptions in Deaton's application of this procedure and, indeed, the weak
separability hypothesis is itself decisively rejected, but future work may be able to relax some of these
assumptions and a modification of this methodology may yield some insights.
43In Ashenfelter's (1980) aggregate time-series study, the instrumental variables consisted of higher
order terms of the wage rate, nonlabor income, and the prices of commodities. As he himself
observes, the validity of these variables as instruments leans heavily on having identified correctly the
functional form of the hours of work equation and, because we are not at all confident of the
appropriate functional form, these variables are not very satisfactory instruments. In his study of
individuals, Ham (1983) proposed using industry, occupation, and local unemployment rates as
instruments for each individual's unemployment experience. Whether these are valid instruments
depends upon the interpretation of the stochastic error term in the hours of work equation. In Ham's
analysis (as in the model of labor supply in this survey paper), the error term represents variations in
preferences that are unobserved to the researcher. It is unlikely that the distribution of these "tastes
44 J. Pencavel
A more fundamental issue that this rationing literature on hours of work does
not address is the relevant wage rate at which individuals are being rationed.
When dealing with rationed commodities where all consumers face the same
prices, the price of a rationed commodity may be well defined. But in the case of
individuals facing different wage rates, it is crucial that we identify the wage rate
when rationed. In other words, in accounting for observed, rationed, hours of
work h in eq. (15), what is the relevant wage rate, w, on the right-hand side? In
aggregate studies such as Ashenfelter's, the wage rate used is the average wage
received by all those at work and not unemployed so the implicit assumption is
that rationed individuals and unrationed individuals face the same exogenous
wage. In studies of this kind when data on individuals are used, for individuals
experiencing some unemployment the wage rate that rations these men when
unemployed is assumed to be the same as the wage rate they receive when
employed. What is the appropriate rationed wage rate when an individual
experiences no spell of employment and is always recorded as unemployed? Such
individuals are deliberately excluded from these studies. 45 Because no exchange
of labor services takes place while an individual is unemployed, no wage rate is
recorded and observationally this is equivalent to the situation that arises when
the reservation wage, w*, exceeds the offered wage, w. In other words, the
situation is observationally equivalent to what some economists call "voluntary
unemployment".
3.5. Life-cycle models
All the models outlined above have been static, one-period descriptions of
behavior. An important development in research on labor supply over the past
for work" parameters is independent of the unemployment experiences of these men; that is, those
men with greater tastes for leisure will tend to take longer or more frequent spells of unemployment.
Then, if industry, occupation, and local unemployment rates are correlated with the unemployment
experiences of individual men (as Ham maintains), then these unemployment rates must also be
correlated with the utility function parameters imbedded in the error term of the hours of work
equation. In other words, these unemployment rates do not serve as appropriate instruments.
*CAdifferent procedure for testing for the presence of employer-mandated restrictions on hours of
work is contained in Ham (1982). For a sample of prime-aged male workers experiencing no
unemployment and claiming no underemployment, he estimates a labor supply function that allows
for the possil~y of sample selection bias resulting from excluding these unemployed and underemployed
workers. He then tests whether the estimates that make no adjustment for the exclusion of
the unemployed and underemployed differ significantly from those that do make that adjustment. He
finds a significant difference and argues that the differences move in the direction suggested by the
proposition that these unemployed and underemployed workers are constrained by employers'
restrictions on hours of work.
45For example, Lundberg (1983) writes: "The sample was restricted to two-head households in
which both husband and wife worked at some time .... The exclusion of these households was.., to
ensure a wage observation for each individual."
Ch. 1: Labor Supply of Men 45
ten years has been the specification and estimation of fife-cycle, multi-period,
models according to which consumption and labor supply decisions in each
period are made with regard to prices and wage rates in all periods. Utility is
defined over lifetime consumption and lifetime hours of work and similarly the
budget constraint incorporates incomes and expenditures in different periods plus
the opportunity to reallocate incomes and expenditures across periods by borrowing
and lending. Whereas in the static models discussed above interest and
dividend income from previous savings decisions was treated as exogenous, in a
fife-cycle context it becomes endogenous and only inherited assets and unanticipated
net returns on capital are genuinely exogenous. The fife-cycle counterparts
to eqs. (8) in Section 3.1 relate consumption and hours worked at age t to prices
and to wage rates at each and every age where future budget constraint variables
are appropriately discounted to the present.
The notion that an individual's or a household's consumption and working
decisions are made with the future very much in view squares with some basic
patterns of life-cycle behavior. The prototype is described by a young married
couple starting out with few assets and working long hours, a portion of these
hours representing on-the-job training; then moving to a higher asset position,
continuing to work long hours (at least for the man) and starting to raise a family
with the impfied financial responsibilities for the future; and later in life working
fewer hours and concomitantly running down their assets. Also, recall from
Section 2.2 above that in U.S. cross-section data both male labor force participation
probabilities and male hours of work display an inverted-U shape with
respect to age. Hourly wage rates also map out an inverted-U shape with age
although the peak in hours worked precedes the peak in wage rates.46 The
correspondence of the hours and wage profiles with respect to age conforms to
the most basic implication of the life-cycle labor supply model, namely that an
individual will supply more hours to the market during those periods when his
wage rate is highest; this is the effect of evolutionary wage differences on hours
worked. The hours-age and wage-age profiles of black men are flatter than those
of white men with the peaks of both profiles occurring at younger ages for black
men than for white men. Weekly hours and weekly wages also follow an
inverted-U shape with respect to age in British data presented by Browning,
Deaton and Irish (1983). They present these graphs separately for manual and
nonmanual workers: for manual workers, wages peak a little later than hours; for
nonmanual workers, the peaks in the two series are roughly coincident. At all
ages, manual workers have higher hours and lower wages than nonmanual
46Accordingto the life-cycleinterpretation,the fact that the peak in hours worked precedesthe
peak in wage rates impfiesthat the rate of interest exceedsthe individual'srate of time preference.
Weiss (1972) expressesthis well: "The rate of interest induces an earlywork effortsince labour
earnings can be invested at a higher rate of return. The subjective discount rate induces the
postponement of work sincefuture effortseemslesspainfulwhenviewedfromthe present."
46 J. Pencavel
workers. The life-cycle model of labor supply outlined below is an attempt to
provide an explicit and formal characterization of these empirical regularities.47
The empirical implementation of the life-cycle model would appear to require
a great volume of data: to understand an individual's labor supply today, the
economist needs information on prices and wages throughout the individual's
life! In fact, the empirical work on life-cycle labor supply has proceeded by
placing sufficient restrictions on the form of the lifetime utility function that the
parameters governing the dynamic allocation of consumption and hours can be
estimated with relatively little data. To date, there exist two general approaches
to this dynamic allocation problem. One derives from the literature on habit
persistence and stock adjustment and specifies the individual's utility function in
period t as conditional on the individual's consumption and hours of work in the
previous period. The notion that the standards by which individuals gauge their
welfare are molded by their prior experiences is, of course, an old one. Preferences
displaying this state dependence in the labor supply literature have been
estimated at the aggregative level by Philips (1978) and employed in aggregate
business cycle simulations by Kydland and Prescott (1982) and they have been
estimated with individual panel data by Hotz, Kydland and Sedlacek (1982) and
Johnson and Pencavel (1984).48 Whereas in this specification the lifetime utility
function is intertemporally not (strongly) separable, 49 the opposite hypothesis is
maintained in the second approach to the individual's life-cycle labor supply
problem. Substantially more research has been conducted along the lines of the
second approach and so I proceed to outline its central features in a little more
detail.
Assume the lifetime utility function is additive over time and write the
individual's utility in period t as a strictly concave function of commodities
consumed in period t, x t, and of hours worked in period t, h t : Ut(x t, ht; A t, et) ,
where, as before, A t denotes exogenous variables observed by the researcher
while eI is a component unobserved by the researcher. Let the rate of time
preference be given by p and suppose a fixed "lifetime" of N + 1 periods. Then
the individual's utility function is
N
E (1 + p)- tUt(x t, h,; A t, el). (16)
t=o
a7The life-~yclemodel would attribute the greater hours with lower wages of British manual
workerscompai'~edwith nonmanualworkersin termsof the greaterlife-cyclewealthof the latter.
4SThe interpretation of these models in the interesting special case of the Stone-Geary utility
function,is provided in the papersby Phlipsand Spinnewyn(1982)and Pollak(1970).
49However,when a consumerfullyrecognizesthe evolutionof his tastes as he ages, Spinnewyn
(1981) shows that the intertemporalmodel of consumer behavior with habit persistencecan be
transformed into a model without such persistence by a suitable redefinition of the cost of
consumption and wealth.
Ch. 1: Labor Supply of Men
The lifetime budget constraint is
47
N
Ko+ Y'~ (l+r)-t(wtht-ptxt)=0, (17)
t=0
where K o denotes initial wealth and r is the rate of interest which for convenience
is assumed to be fixed. Bequests have been neglected although it is
straightforward to permit a role for them. The individual selects x t > 0 and
ht > 0 for each period to maximize (16) subject to the constraint (17), the
first-order conditions for which are eq. (17) and
au,
= Ot~opt, t = 0 ..... N, (18)
Ox t
0u,
--->Ot~owt, t=O,...,N, (19)
Oht
where 0 = (1 + p)/(1 + r) and where X0 is the Lagrange multiplier attached to
the budget constraint and is interpreted as the marginal utility of initial wealth
when evaluating the utility function at its optimum. If eq. (19) is a strict
inequality, the individual does not work in period t; if it is an equality, then some
hours of work are supplied to the market. In what follows, given the high labor
force participation rates of price-age men, I assume (19) is satisfied by an
equality.
Now solve eqs. (18) and (19) for consumption and working hours in any
period:
xt=x(XoOtpt,XoOtwt;At, et), t=0 ..... N, (20)
ht=h(XoOtpt, hoOtwt;At, et), t=0 ..... N. (21)
In these equations, 2,0 is endogenous, a function of the lifetime budget constraint
variables and of At and er Indeed, it can be shown that 3ko/OKo<O,
3~o/3W t <_O, and 3)~o/OPt > 0 [see Heckman (1974a, 1976a)]. Eqs. (20) and (21)
have been called "?~o-COnstant" functions or, more felicitously, Frisch demand
and supply functions [Browning (1982)] in recognition of Ragnar Frisch's extensive
use of additive utility functions. Given the assumed concavity of the utility
function, these Frisch demand and supply functions possess many of the properties
of conventional demand and supply functions: 3ht/O(~,oOtwt)> 0 and
axt/3(hoOtpt) < 0; there is a symmetry property -Oht/O(hoOtpt) =
48 J. Pencavel
OXt/O(~oOtWt) X0; and these functions are homogeneous of degree zero in ~o 1,
Pt, and wt 5° [see Heckman (1974a)].
Because the period-specific utility function represents one branch of the entire
lifetime utility function, the Frisch labor supply eq. (21) is not independent of
monotonic transformations of Ut. The important feature of these equations for
empirical analysis is that they relate consumption and labor supply decisions in
any period to variables outside that period only through ~0 and that otherwise
within-period prices and wage rates determine x t and h t. The variable A0 is a
sufficient statistic in that it contains all the information concerning the lifetime
budget constraint variables which is relevant to the current choice of consumption
and hours of work. Moreover, although A0 varies across individuals in
accordance with differences in their lifetime budget constraint variables and in
other exogenous variables, for a given individual ~'0 is constant over his lifetime
when future wages and prices are known with certainty. The derivative of h t with
respect to w t in eq. (21) shows how an individual's hours respond to evolutionary
wage changes, i.e. changes in wages along on individual's wage-age profile. As
MaCurdy (1982) has emphasized, corresponding to the two classes of variables
(the current period variables and the life cycle component, ~'0) in eqs. (20) and
(21), the formulation of an empirically tractable model of life-cycle behavior
naturally decomposes into two stages: the first is the specification of the Frisch
equations and the second is the formulation of an equation to determine A0At
the first stage, the immediate problem is, of course, that A0 is not directly
observed. Moreover, A0 is not a random variable uncorrelated with wages and
prices. Because it is not random, it cannot be consigned to some error term.
However, as we shall see below, for certain forms of the Frisch equations, 2,0 (or
a simple transformation of X0) may be expressed as an additive fixed effect that,
in estimation with panel data, is easily accounted for by first-differencing the data
over time. 51 The second stage of the estimation procedure relates ~0 to its
5°Instead of obtaining the Frisch equations by solving the first-order conditions from explicit
constrained utility maximization, Browning (1982) shows they may be derived more simply by
defining a consumer's within-periodprofit function as follows:
H,(ho 1,iit, fit; A,, et) = max {holUt (x,, hi; A,, e,) - if,x, + ~tht },
xt,ht
where it = Otpt, ft = Otwt, and naturally hoa maybe called"the price of utility". Then, by applying
the envelopetlaegremto thisprofit function,the negativeof eq. (20)is derivedfrom 01]t//tgit and eq.
(21) is derived f~OmOHt/O~ ~. As is the case for a price-takingfirm'sprofit function,this consumer's
profit function is intzreasingthe price of output (hol), is decreasingin the prices of inputs (it and
- ft), and is convex and linearlyhomogeneousin hot, it, and ft.
51If the Frisch hours eq. (21) is written with hours or earnings on the left-hand side (as distinct
from some transformation of them suchas their logarithms),thenfor h0to be specifiedas an additive
fixedeffectthe within-periodutility functionmust be quasi-homotheticin commoditiesconsumedand
hours worked. See Browning,Deaton and Irish (1983).
Ch. 1: LaborSupplyof Men 49
determinants, namely the lifetime budget constraint variables, the rate of time
preference, A t, and er Observations on the entire budget constraint variables are,
of course, not available so lifetime profiles must be simulated by using the
observed income and wage data of people of different ages. Moreover, an explicit,
closed-form solution for X0 is often not possible so instead the expression for ~0
is approximated. Clearly, this second stage is less cleanly specified and estimated
than the first stage, but knowledge of X0 is essential to describe an individual's
labor supply response to parametric wage changes, i.e. wage changes that shift
the entire wage-age profile.
A model involving decision-making over time would appear to require allowance
for uncertainty about the future values of variables and an important
aspect of this life-cycle model is that it accommodates such uncertainty in a
tractable form. To see this, first rewrite the certainty model by defining by
recursion Xo(1 + O)t/(1 + r) t = A t and so the first-order conditions eqs. (18) and
(19) become:
- - = )~tPt' (22)
ax t
0v,
- - - = X,w,, (23)
Oht
2~'= ~1-i~p( 1 +r ) X,+l, (24)
where ?tt is the marginal utility of wealth in period t. The Frisch demand and
supply functions eqs. (20) and (21) are the same with ~', replacing hoot:
xt=x(XtPt,~twt;ht, et), t=O,...,N, (25)
ht=h(Xtp,,?~tw,;At, e,) , t=0 ..... N. (26)
Eq. (24) defines the optimal savings strategy and the lifetime problem decomposes
into two levels. At the first level, an individual allocates his wealth over his
life such that his marginal utility of wealth evolves as he ages according to eq.
(24). At the second level, conditional upon wealth allocated to a given period, the
within-period allocation problem is addressed. Strong separability of the lifetime
utility function is more than sufficient to decentralize the life-cycle problem in
this way.52
Now allow for uncertainty in the form of the individual being unsure of real
wages or real rates of interest or even his preferences in the future. In these
52Infact,weakseparabilityis sufficientand necessary.SeeBlackorby,Primontand Russell(1975).
50 ~ Pencavd
circumstances, suppose the consumer revises his plans each period as new
information on these variables is revealed and, in particular, suppose he maximizes
his current and discounted expected utility subject to his period-by-period
budget constraint. The first-order conditions describing the solution to this
problem are identical to eqs. (22) and (23), but eq. (24) is now modified to read
X,= (1 + p)-le[(1 + r)X,+a],
where r in this formula is the rate of return to be paid on each dollar of assets
held at the beginning of period t +1. Because both r and ~t+l are random,
g[(1 + r)~'t +1] will typically involve the covariance between these two terms, but
if a riskless rate of return exists, say, i, then the previous equation may be
written
l+p
~ktl-~- ~ -- g(~kt+l) (27)
or the expected (at period t) marginal utility of wealth in period t + 1 is
proportional to the marginal utility of wealth in period t, similar to a Martingale
stochastic process [MaCurdy (1976)]. 53 The consumer's savings policy implies
that the means of all future values of ~ are revised to account for all forecasting
errors at the time they are realized. And because At is a sub-Martingale, through
eqs. (22) and (23), (0 U/Oxt)/p t and (0 U/Oh t)/wt also follow a sub-Martingale.
So, according to this model, at the start of the life-cycle the consumer sets ~ 0 so
that it takes account of all the information on the future values of variables
available at that time. As new information is acquired over time so ?~t is revised
according to eq. (27). At each age, in order to satisfy eqs. (22), (23), and (27), the
consumer requires knowledge of the variables observed in that period to determine
his optimal consumption and hours of work and to update his marginal
utility of wealth. Consequently, whereas eqs. (20) and (21) form the basis of
empirical work of life-cycle labor supply under the assumption of perfect
foresight, eqs. (25) and (26) constitute the analogous equations under conditions
of uncertainty.
In the presence of uncertainty, when estimating an equation based on eq. (26),
the error term will include forecast errors and, because wt, At, and e t contain
components unforeseen before their realization, wt (even if measured without
error), A~and e t will not be distributed independently of the equation's
disturbance~'~Finding,~ariables that are correlated with w t and A t and yet are
uncorrelated With unanticipated components of these variables (i.e. finding
genuine instruments) is difficult.
53This result and the conditionsunderlyingit were derivedby MaCurdy(1976). That all prices
followa Martingaleor sub-Martingaleprocesswas conjecturedby Alchian(1974).
Ch. 1: Labor Supply of Men 51
Certain features of the fife-cycle model have considerable appeal. For instance,
anyone who has estimated static labor supply functions can testify to the
awkward problems in deriving an accurate measure of nonwage income, that is,
the income an individual would receive at h = 0. The life-cycle model avoids
these difficulties. Whereas the static model has to be augmented with explanations
in terms of family responsibilities in order to account for the age-pattern of
hours of work, the fife-cycle model addresses this empirical regularity explicitly. 54
Few would deny that there are circumstances in which the future values of
certain variables affect current working decisions. The more pertinent issues are,
first, whether these effects are sufficiently important to account for the key
variations in male labor supply and, second, whether the particular model
sketched above incorporates the essential features of intertemporal decision-making.
We shah return to these two issues when the empirical work on life-cycle
labor supply is discussed in Section 5 below.
4. Estimation of the static model
4.1. Specification
What guidance has the theory of labor supply outlined in the previous section
provided for empirical work? As far as the conventional static model is concerned,
I know of no attempts with individual data to specify all of the refutable
implications of the theory- the positivity of the substitution effect, the symmetry
condition, the zero homogeneity condition-as a series of research hypotheses
that are either corroborated or refuted by the data. 55 This is surely surprising in
view of the extensive literature that has been concerned with testing the predictions
from the consumer's allocation problem (without the hours of work
dimension) and that has done so by applying the theory to data aggregated over
individuals. The availability of data sets containing observations on the actual
decision-making units, the individual or the household, and on the same individu-
54The distinctive age-hours of work pattern is apparent in Current Population Survey data
organized by Smith (1983). She presents data on annualhours of work by age,by sex, and by race
from the four Surveysfrom 1977to 1981.For instance, for all men in 1981(unadjusted for all other
characteristics) those aged16-17 yearswereestimated to workan averageof 715 hours, 18-19 years
worked 1209hours, 20-24 years worked 1634hours, 25-34 years worked2016 hours, 35-44 years
worked 2126 hours, 45-54 years worked 2108 hours, 55-59 years worked 2037 hours, 60-64
years worked1839hours, and those65 yearsand overworked1241hours.
55Occasionally one or other of these implications has been tested. For instance, Wales and
Woodland(1976)determinedin theirhusband and wifejoint allocationmodelwhetherthe matrixof
compensated wage and price elasticities was correctly signed. For approximately half of their
observations it was and for the otherhalf it was not.
52 J. Pencavel
als over time means that the observable implications of the theory do not need to
be augmented by a series of heroic aggregation assumptions in order to subject
the theory to empirical scrutiny. Of course, many other problems remain in
implementing the theory, but these turn out not to be specific to labor supply
issues and they are rarely resolved except under exceptional circumstances by
applying the theory to data aggregated over individuals.
While the implications of the conventional theory of labor supply have rarely
been modelled as a series of testable hypotheses, researchers do not seem to be
reluctant to treat the qualitative implications of the theory as maintained
hypotheses. For instance, Burtless and Hausman (1978) estimate a labor supply
model that allows for a distribution across individuals of values for the effect of
nonwage income on hours, but in doing so they constrain this effect to be
nonpositive. In fact, the estimates of this effect pile up close to zero and one
wonders how many individuals would have positive values if the estimation
scheme did not prohibit it.56 In many studies, it seems as if estimates that do not
generate positive substitution effects for hours of work or that suggest nonmarket
time is an inferior good are not interpreted as refutations of the theory, but as
indicating some error in implementing the theory. This is, of course, supposed to
be an attribute of a discipline in its "normal science" phase although some would
question quite legitimately whether the conventional model of labor supply had
earned the right to this status.
Perhaps the primary contribution to date of the theory to empirical research on
labor supply has been that of distinguishing the effects on hours of work of
changes in wage rates from changes in nonwage income. Although this may
appear a trivial contribution, it distinguishes the economist's approach to the
topic of market work behavior from that of most other social scientists.57
Moreover, as Mincer (1963) showed, the distinction may be usefully applied to
understanding other patterns of behavior besides hours of work.
Although there have been a number of instances to the contrary, the general
procedure has not been to specify a particular expression for the direct or
indirect utility function (or expenditure function) and then to estimate the implied
hours of work function. More often, an hours of work function convenient
for estimation has been specified ab initio and the popular choice has been one
that is linear in the parameters. That is, eq. (8) has been specified as follows:
56Theyreport that aboutone-fifthof the samplehas an estimatedelasticityof hourswithrespectto
nonwage income of between -0.01 and zero.Theirrestrictionon the effectof nonwageincomeon
hours of work arises fromthe global requirementon theirestimatingtechniquethat the substitution
effectbe non-negativefor all individualsand for all valuesof the exogenousvariables.
57Forinstance,see the interestingsociologicalstudyof labor supplyin Smith-Lovinand Tickamyer
(1978).
Ch. 1: Labor Supply of Men 53
where i denotes individual i. In this form, ei is a stochastic disturbance term
representing individual i's unobserved "tastes for work" and the zero homogeneity
condition is a maintained hypothesis. Normalizing p to unity, the uncompensated
wage effect is a I ><0 while, provided leisure is not an inferior good,
a= < 0. Consequently, the substitution effect, s, is given by al - hot2 which should
be positive according to the allocation model outlined in Section 3.1 above.
Provided otI > ha 2, eq. (28) implies a larger substitution effect for those who work
longer hours.
Because any labor supply equation possessing all the properties of utility-maximizing
hours of work functions implies a particular expression for the direct
utility function, one may derive the form of the utility function when a linear
hours of work equation such as (28) is specified:
(o20+o2x+3A+'ol}a~ exp a2~ --- at '
where a x> ot2h. 58 Although x and h do not appear symmetrically in this
unfamiliar utility function and although the error term occupies an unintuitive
role, these will be small considerations if it is important to have a convenient
hours of work estimating equation.
Questions concerning the form of the utility function, however, have received
little attention compared with the research investigating the consequences of the
error term, ei. The reason for this concern is that eq. (28) describes only those
men whose optimizing problem is solved by working a positive number of hours;
for others, the individual's problem is solved by setting h to zero. In other words,
letting aX i stand for the deterministic part of the right-hand side of eq. (28), the
correct specification is as follows:
h i = aX i + ei, if wi > w'~(pi , Yi, Ai, e~),
hi=0, if wi < w*(pi, yi, Ai, ei),
(29)
(30)
where the dependence of the reservation wage, w*, on Pi, Yi, Ai, and ei has been
made explicit. Clearly, if observations on only those men for whom h i > 0 are
used to estimate (28) by ordinary least squares, then h i > 0 implies aX i + ei > 0
or ei >- aX i. Thus, when restricting the estimation of (28) to the sample of
working men, ei is not distributed independently of Xi even though ei may be
distributed randomly in the population; because ~(eil Si) #=0, one of the conditions
under which ordinary least-squares provides a consistent estimator is
violated. Expressed differently, when eq. (28) is fitted to the sample of working
5SThisis derived in Deaton and Muellbauer(1981,p. 96) and in Hausman (1981).Deaton and
Muellbauer(1981)considerthe casewhen the compositecommoditytheoremdoesnot holdand the
differentcomponentsof x are identified.
54 J. Pencaoel
men, observations are not selected from the population randomly, but systematically
according to the requirement ei > - aX~ and a sample selection bias results. 59
The magnitude of the bias is likely to be less serious for those samples from
populations for which most observations satisfy the criterion w i > w*. In other
words, the least-squares selection bias is likely to be more important in describing
the hours of work behavior of older and younger men than of prime-age males. 6°
An alternative and insightful characterization of this sample selection problem
[attributable to Heckman (1976b)] recasts the issue as a conventional case of
omitting a term from a least-squares regression equation. Define Awi = w i - w*
and observe that Awi > 0 if the individual works in the market [so that eq. (29)
holds] while Awi < O, if h i = 0. Denote the determinants of Aw i by Z i which will
include Pi, Yi, A~, and ei as well as the variables influencing the offered wage
rate:
Awi = 3Z i + u i,
where u i is a random variable assumed to have expectation zero and finite
variance. Then, the regression of h i given Xi over the sample of workers (i.e. over
the sample for whom Awi > 0) is
e( hilXi, aw , > O) = + e( ilu, > - Zi)
= olgi -l- Zi, (31)
where ~i denotes the parameters governing the joint density of ei and u i. Because
Z i incorporates the effects of ei, the expected value of ei given u i > - 8Z i will not
be zero. Applying ordinary least squares to (31) is equivalent to omitting the term
q~, the conditional mean of ei, from the regression and thus the bias that results
may be understood in terms of conventional omitted-variable bias arguments.
For instance, consider a variable such as nonwage income, y, that appears in
both X i and Z i. A least-squares regression of h i on Xi for a sample of workers
that omits the conditional mean of ei, q~, results in estimates of the coefficient on
nonwage income, say ~2 from eq. (24), that may be written approximately as
, &2 = 012 q'- Oq~/Oy.
59The sample selection bias is not solved by Hall's (1973) procedure of fitting eq. (28) to workers
and nonwork-er~ together (setting h to zero for nonworkers). This procedure requires that eq. (29)
hold not for w 5:~-w*, but frr~w ><w*, a requirement that contradicts the theoretical structure.
6°In the labor supply case, the sample selection problem is further complicated by the absence of
observations on one of the independent variables, the wage rate facing (and not being accepted by)
nonworkers. In his study of married women, Heckman (1974b) proposed and implemented a model
that combines an equation determining wage rate offers with an equation determining the marginal
rate of substitution of hours for commodities. Both equations were characterized by errors that were
correlated with the exogenous variables because of sample selectivity problems.
Ch. 1: Labor Supply of Men 55
The coefficient a 2 measures the effect of nonwage income on hours worked on
the part of those already working and this is the derivative that figures in the
analysis of interior solutions to the individual's constrained utility-maximization
problem. This analysis suggests that, provided leisure is not an inferior good,
a 2 < 0. The term Oep/Oy measures the effect of nonwage income in changing the
sample of observations, i.e. the sample who work from the population. Suppose
that those with greater nonwage income have tastes for work that are less inclined
against work than those with little nonwage income (after controlling for the
other determinants of work behavior). Then, as y is increased, so the composition
of the sample is altered towards those with less aversion to work. Consequently,
Oep/Oy > 0, ~2 > 0/2, and the estimated effect of nonwage income on
hours of work will be biased in such a way as to indicate a less negative income
effect than is really the case.
The sample selection bias can be addressed in a number of different ways.
Perhaps the most common procedure is Heckman's (1976b) two-step estimator
which replaces ~(.), the conditional mean of ei, in eq. (31) with its value
predicted from a previously-estimated equation. Although our understanding of
the issues has been greatly enhanced by the large literature that has arisen on the
subject of sample selection bias, I know of no evidence from empirical studies of
male labor supply (whether old, young, or prime-age men) that documents
grievous biases from a strategy of restricting estimation to the sample of workers
and of not making any correction for this deliberate nonrandom selection of the
observations.6a
The following section presents the empirical results from fitting static labor
supply functions. It is impossible for me to graph each fitted hours of work
equation as a function of the observed values taken by the variables of interest.
Yet this is exactly what is needed for a full understanding of the implications of
any given set of estimates. Unfortunately, only rarely are such graphs presented.
The normal substitute is to present the implied values of the behavior responses
calculated at sample mean values or, less frequently, the average of the behavioral
responses calculated for each observation.62 Some papers do not even do this nor
do they provide sufficient information for such calculations to be made by an
interested reader. It is high time the editors and referees of all journals required
that every empirical paper considered for publication present descriptive statistics
on their samples analyzed.
61The paper by Wales and Woodland (1980) provides a convenient list of alternative methods. Also
they report some sampling experiments with different estimators.
62These two methods of summarizing the behavior responses-either calculating the behavioral
responses at the mean values of the variables or calculating the implied responses for each
observation and then forming the average- may yield quite different values depending upon the form
of the function and the distribution of the values of the variables. Although the latter may well be a
preferable procedure, it is well nigh impossible to simulate all the studies to perform the calculations
reqttired.
56 J. Pencavel
The summary estimates I shall concentrate on are those measuring, first, the
effect of a proportional increase in wage rates on the proportional change in
hours worked and, second, the effect of a small increase in nonwage income on
hours worked and, given wages, on earnings. The former is, of course, the
uncompensated elasticity of hours of work with respect to wages (E) and the
latter I call the marginal propensity to earn (mpe) out of nonwage income.
Following eq. (12), the income-compensated elasticity of hours of work with
respect to wages (E*) is simply the difference between E and the rope:
Oh w Oh
E=----;Ow h mpe=W--Oy and E*=E-mpe.
Being independent of the units in which the budget constraint variables are
measured, estimates of elasticities are more conveniently compared across different
studies than are changes in hours worked over a given period of time (a year
maybe or a week) per dollar or pound change in the wage rate. From the value of
the mpe may be inferred how much of an increase in nonwage income is spent on
the consumption of commodities. The consumption literature provides information
on the marginal propensity to consume out of nonlabor income,63 but this
research focuses upon the division of an additional dollar of nonlabor income
between consumption and saving holding labor income fixed, an issue involving
intertemporal considerations. By contrast, the static model of time and consumption
outlined in Section 3.1 takes such savings decisions as being determined at a
prior stage of the individual's allocation problem and the question that arises
from this model is the within-period division of an additional dollar of nonlabor
income between the consumption of commodities and of leisure. Most of the
estimates of this rope come from the labor supply research to be surveyed shortly,
but some educated guesses about the probable magnitude of this can be formed
from measured effects of nonwage income on commodity consumption. Such
estimates have been presented by Deaton (1982) using data on 1617 households
from the British Family Expenditure Survey of 1973. In straightforward leastsquares
linear regressions that impose little prior structure on the data, he relates
household expenditures on nine different categories of consumer goods to the
husband's wage rate, nonwage income, 64 the number of children, the number of
workers in the family, and a home ownership dummy variable. Nonwage income
exerts a po~i~ye effecton the consumption of each category of goods and the sum
of these marginal propensities to consume (~Pi Oxi/OY) is about unity implying
63See,for instance, Holbrookand Stafford(1971).
64The husband's wagerateis definedas the ratioof "normal" weeklyearningsto "normal" hours
worked per weekand thenadjustedfor incometaxes.Nonwageincomeis, in fact, the net incomeof
the household minus the husband'searnings.
Ch. 1: Labor Supply of Men 57
a zero value for the rope.65 I know of no comparable study with U.S. data, but
insofar as one may generalize from these results then a value of the mpe not far
from zero is to be expected.
When comparing estimates of these behavioral responses from different research,
it should be remembered that the points of evaluation differ across studies
and, moreover, that for any given study these behavioral responses themselves
vary from observation to observation. The manner in which these behavioral
responses differ across observations is determined once the functional form for
the estimating equation has been chosen. For example, when a linear hours of
work equation is estimated both E and the mpe will necessarily be greater for
individuals with relatively high wages. There is no strong prior reason to believe
either that this should be true or that it should not be. Therefore, in specifying
hours of work estimating equations, some economists feel more comfortable
working with utility functions familiar from the research on consumer behavior.
In research on labor supply, most of the (direct) utility functions posited have
been additive in commodity consumption and in each individual's hours of work.
The additivity assumption will necessarily bring with it restrictions on the
relationship between E and the mpe and, in particular, analogous to Deaton's
(1974) reasoning, additivity of the direct utility function can be shown to imply
E = (mpe) + o~-11*-' [1 + (mpe)], (32)
where/~ = (wh)/y and ~0= (O?~/3y)(y/?~) < 0 is the elasticity of the marginal
utility of nonwage income with respect to nonwage income.66 In other words for
someone for whom nonwage income is a very small fraction of total income (i.e.
for someone whose value of/~-1 is very small), additivity of the direct utility
function will restrict the estimated value of his mpe to be similar to his estimated
value of the uncompensated elasticity of hours of work with respect to wages (E)
and for this individual the compensated elasticity, E* = ~0 1/~ 1(rope)[1 + (mpe)],
will tend to be a small number. Of course in some data nonwage income appears
for a number of people not to be such a small part of total income so for such
individuals E will not approximate the mpe, but nevertheless eq. (32) shows that
65In fact, the estimates of the mpe after imposing more structure on the data are similar to these
least squares regressions. See Atkinson and Stern (1980) and Deaton (1982).
66More generally, direct additivity of the household utility function U = q~[f0 (x ) - fl (h1) - f2 (h 2)]
implies the following relationships for the elasticity of hours of work of individual 1:
Elj = Ix{ 1(mpe)l [ I~j+ oa l(rnpe)j] + 8ljo~ llz{t(mpe)l , j = 0,1,2,
where ~u=l if j=l and 81j=0 otherwise, where (mpe)o=pOx/3y, and where El0 must be
interpreted as the negative of the uncompensated elasticity of hours of work with respect to
commodity prices. Note that, because a part of income is endogenous, ~o here is different from the
usual concept of Frisch's money flexibility.
58 J. Pencavel
additivity builds in restrictions among the behavioral responses that the data are
unlikely to conform to.
It is useful as a reference for our discussion below to illustrate eq. (32) with a
utility function (or a variant of it) that has been used relatively often in labor
supply analysis. Abstracting from variations in personal characteristics A and in
individual tastes e, consider the following additive (strongly separable) utility
function described by the parameters b, c, B, and to:
U(x,h) = [(1- B)(x-c) ° + B(b-h)°] 1/', (33)
where 0 < B < 1, x > c, b > h, and to < 1. This utility function goes by different
names-sometimes the nonhomothetic constant-elasticity-of-substitution function,
sometimes the one-branch utility tree-but I shall refer to it as the
generalized Stone-Geary utility function [Pollak (1971)]. This function conveniently
nests some special cases that have frequently been used in fitting labor
supply functions. 67 The optimizing hours of work function from eq. (33) is
B~w-¢( y + bw - cp )
h=b- [(1_ B)~pl_g+ B~wI_~] , (34)
where ~ = (1- p)-i > 0 and the rope and the uncompensated elasticity of hours
of work with respect to wages (E) are as follows:
B¢wt-~
rope = --
(l- B)~p~-~+ B:w~
= - 1 + [1 + (mpe)] [~bh-1 + (1 - ~')]. (35)
The behavioral responses corresponding to the Stone-Geary utility function are
obtained by letting ~ equal unity, whereas the conventional constant-elasticityof-substitution
function is obtained in eq. (33) by setting the "reference" parame 7
ters,,~ and b, to zero and replacing the term B(b - h) o with - B*h p. Chipman's
(1965) "weakly homothetic" utility function results when p ~ -~. With utility
function (33), to = - ~-ly(y + bw - cp) -1, so that with the definitions of the rope
and E above,:'eq. (32) is. easily derived.
67Within the class of empiricalwork making use of nonexperimentaldata on individual workers,
eq. (33) covers the functional formsused by Betancourt (1971), Blundell and Walker (1981, 1983),
Brown, Levin, Rosa, Ruffelland Ulph (1982-83), Hurd and Pencavel(1981), Rosen (1978), Wales
(1973), and Wales and Woodland (1979). In addition, the hours of work equation derived from eq.
(29) is similar to that estimatedby Atkinson and Stern(1980, 1981).
Ch. 1: Labor Supply of Men 59
In short, whether derived explicitly from a particular utility function or simply
written down ab initio, the hours of work estimating equation involves selecting a
specific functional form and the choice of this function inevitably embodies some
assumptions about the differences in the behavioral responses (i.e. the differences
in E and the mpe) across individuals. Unfortunately, at present an assessment of
these assumptions is difficult because so little is known about these variations.
In most cases, the static model has been estimated by fitting a regression
equation such as eq. (28) to cross-section data collected from a sample survey of
households or of individuals. The precise questions asked vary from survey to
survey, but normally an individual (or his spouse) is asked about his hours
worked (and his weeks worked) in a given week (year) or in a typical week (year),
his labor earnings during a specified period of time or his usual hourly earnings,
and his income from other sources. The response to these questions form the
basis of the observations on the purported labor supply function.
In an econometric exercise associating quantities (hours of work) and prices
(wage rates), prior to estimation it is appropriate to enquire whether what is
being estimated is a supply function, a demand function, or some hybrid.
Suppose that a worker with a specific set of characteristics valued by firms faced
a horizontal demand curve for his services, i.e. the worker may choose any hours
to work at a given wage rate. Workers with different characteristics of varying
values to firms would face horizontal demand curves at different levels of real
wages. Provided some of these characteristics were not at the same time associated
with these workers' preferences for income or leisure,68 then in a cross-section
of individuals the revealed wage-hours combinations would reflect the
intersection of different horizontal demand curves with a fixed (for a given set of
variables determining preferences) labor supply function. This provides one
rationalization of the common presumption that a regression of hours worked on
wage rates and other variables maps out a labor supply function.
As noted in Section 3.3 above, most firms appear not to be indifferent to the
hours worked by each of their employees: the presence of quasi-fixed hiring and
training costs that are more closely tied to the numberof employees than to their
hours worked encourages firms to offer higher wage rates for longer hours worked
[Lewis (1969)]. If this is the case, the worker faces a wage-hours locus such that
shorter hours of work are renumerated at a lower hourly wage rate. Once again,
across workers with the same preferences, their labor supply function is traced
out by a series of different (nonhorizontal) labor demand schedules, each demand
curve indexed by a particular quality of labor. Provided identifying variables
exist, the labor supply function can be estimated by a regression of hours worked
68What are the (identifying) variables that appear in the demand function for hours by employers
and that do not enter the supply function for hours of work? Perhaps the most obvious candidates for
such variables are indicators of the level of local labor market activity.
60 J. Pencavel
on wage rates, but now of course account must be taken of the fact that the wage
offered by employers is no longer independent of each worker's own decisions.
4.2. Empirical results from U.S. nonexperimental data
A brief chronology of the major phases of modern empirical research on male
labor supply may be listed as follows. Kosters' (1966, 1969) analysis of the hours
worked of married men aged between 50 and 64 years old ranks as the first
modern empirical study of this topic both by virtue of its close attention to its
theoretical underphmings and by virtue of his use of a sample of observations on
individuals; 69 there soon followed many studies [a number of them being
brought together in Cain and Watts (1973)] whose methods were similar to
Kosters', but which analyzed other groups in the labor force; in response to the
diversity of results from these studies and in an attempt to account for them, the
next phase of research [as best illustrated by DaVanzo, DeTray and Greenberg
(1973, 1976)] was the application of a variety of different procedures to a single
body of data; the 1970s also saw increasing attention to the econometric
implications of nonrandom sample selection [Heckman (1974b, 1976b)] and
nonlinear budget constraints [Burtless and Hausman (1978), Wales and Woodland
(1979)]; meanwhile, from the mid-1970s, new sources of information were
becoming available, namely the results from the various negative income tax
experiments and the estimates from British research; finally, the 1970s witnessed
increasing attention to the fife-cycle models of labor supply and, at the time of
writing, this seems to be the most active area of male labor supply research.
In order to trace this chronology a little more closely, return to Kosters'
original analysis of the hours worked by employed married men aged 50-64
years. His observations were drawn from the 1 in 1000 sample of the 1960 Census
of Population and he estimated to these data ordinary least-squares equations
linear in the logarithms of the variables. One such equation is the following which
was estimated with 8467 observations:
lnhi=- 0.094 lnwi- 0.0073 lnyi+... +~i, R2=0.10,
(0.0044) (0.0015)
where estimated standard errors are in parentheses beneath coefficients and
where the dots,indicate that 16 other variables were included in the regression
equation. The income-c0mpensated wage elasticity of hours of work (E*)
69Anumber of studiesprecededKosters' that examinedthe issuesat an aggregatelevel-Douglas
(1934) had measured the associationbetween hours worked and earnings at the industry level,
Finegan(1962)at the occupationallevel,Winston(1966)at the nationallevel-but Kostersappearsto
have been the first to applythe theoryto the unit whosebehaviorit is meant to describe.
Ch. 1: Labor Supply of Men 61
implied by the estimates is +0.041 when evaluated at the (geometric) mean
values of the observations. The estimate of -0.094 for the uncompensated wage
elasticity was robust with respect to changes in equation specification and,
moreover, accorded well with previous estimates-with Douglas's (1934) preferred
estimate "in all probability somewhere between -0.1 and -0.2" and with
Winston's (1966) estimates of -0.07 to -0.10, though less so with Finegan's
(1962) estimates of -0.25 to -0.35. On the other hand, the estimate of -0.0073
for the nonwage income elasticity of the supply of working hours appeared to be
sensitive to changes in functional form and in the precise definition of nonwage
income.
Kosters' procedures with relatively minor modifications were soon being applied
by other researchers to different samples. A stimulus to this research was
provided by the prominent public policy debate over the costs of welfare reform
which were intimately tied to the labor supply effects of taxes and transfers. In
part as a consequence of this emphasis on welfare reform, a number of studies
that reported in early 1970s restricted their empirical work to samples of the
relatively poor. In constructing such samples, observations were discarded on
the basis of values taken by a variable (income) that is clearly related to the
endogenous variable of interest (hours of work). This induces an analogous sort
of sample selection bias as that discussed in Section 4.1 above.7°
This feature of male labor supply studies of the early 1970s- that observations
on relatively high income individuals or households were eliminated from their
samples-represented only one dimension in which the various research papers
differed from one another. They also differed in the precise definitions of the
variables, the particular functional relationship posited, the assumptions made
about commodity prices, and the set of nonbudget constraint variables included
in the hours of work regression equations. These differences in the implementation
of the labor supply model yielded sufficiently disparate estimates as to
provide little practical assistance to questions of public policy. In view of these
differences, it was important to address the question: "With respect to which set
of assumptions and procedures are the hours of work estimates sensitive and with
respect to which are they robust?" This was taken up by DaVanzo, DeTray and
Greenberg (1973) who applied many different procedures to a single body of
data, namely, 5294 white, married, male heads of households aged 25-54 years
drawn from the 1967 Survey of Economic Opportunity (SEO). Their Rand report
is full of valuable information for anyone embarking on his own labor supply
7°For an elaboration of this point in the labor supplycontext,see Cain and Watts' (1973)lucid
statement. For a more generaltreatment of the issue,see Goldberger(1981). Studies that imposed
some sort of income criterion in definingtheir analysis sample included those of Boskin (1973),
Fleischer, Parsons, and Porter (1973), Greenberg and Kosters (1973), Hall (1973), Hill (1973),
Kalachek and Raines (1970),Kurzet al. (1974),and Rosenand Welch(1971).
62 .1. Pencavel
study. 71 The same question was addressed by Masters and Garfinkel (1977) in
their extensive analysis of data from the 1967 SEO and from the 1972 Michigan
Panel Study of Income Dynamics (PSID). The differences in procedures among
the studies and the consequences of these different procedures may be summarized
as follows.
1. Problems in measuring the hours and wage rate variables. In studies based
on data from the 1960 Census of Population or the 1967 Survey of Economic
Opportunity, the hours of work variable combined one dimension of work
behavior (namely, hours per week) in one year (in 1960 for the Census and in
1967 for the SEO) with another dimension of work (namely, weeks worked per
year) in a different year (in 1959 for the Census and in 1966 for the SEO). 72 Then
this dependent variable often appeared in the construction of the wage rate
variable (i.e. for the Census data, annual labor income in 1959 was divided by
this estimate of hours worked) so that any errors in measuring true hours worked
in 1959 or in 1966 will appear in the wage rate variable inducing a spurious
negative correlation between hours worked and wage rates. What contribution, if
any, was this making to the frequent finding of a negatively-sloped labor supply
curve? The answer, it seemed, was that the slope of the male ordinary least-squares
estimated hours of work function was more negative when such a wage variable
was used than when an alternative wage rate variable (such as an instrumented
wage rate) was constructed. Evidence on this is contained in Bloch (1973),
DaVanzo, DeTray and Greenberg (1973), Masters and Garfinkel (1977), and
Borjas (1980). Nevertheless, even after trying to rid the wage variable of this
spurious correlation, most studies found a negative (uncompensated) own-wage
elasticity of hours of work at sample mean values: for instance, DaVanzo,
DeTray and Greenberg (1973) report estimates between -0.15 and --0.09, 73
Masters and Garfinkel (1977) "best estimate" is -0.110, and Ashenfelter and
Heckman's (1973) is -0.156.
71Much of their analysis was conducted with a sample of 2012 men who reported being unaffected
by unemployment and by poor health and who received no work-related transfer payments. They
then considered the consequences of adding to the original sample 3282 men who reported these
characteristics.
72Many other definitions of the hours worked variable have been used. A common one is the
product of the number of weeks worked in a given year and the average number of hours worked per
week during those weeks in which the individualworked. Some studies add an estimate of hours spent
unemployed to the number of hours worked.
73DaVanzo,"DeTray and Greenberg's estimates reported here are derived from Tables 11 and 12 of
their Rand stud~where the'dependent variable is measured as annual hours of work and where the
wage rate and nonwage income variables are instrumented. The sample in this case consists of those
2012 men who reported no unemployment or health disabilitynor receipt of any work-related transfer
payments. Other variables included in these equations are age, age squared, schooling, household size,
number of children less than six years of age, various variables denoting location of residence, the
spouse's annual earnings, and the annual earnings of other family members.
Ch. 1: Labor Supply of Men 63
2. The measurement of nonwage income. This variable was particularly difficult
to measure accurately. Koster's procedure was to form this variable by
deducting the husband's earnings from total household income, but this meant y
included transfer income that was not independent of the husband's hours of
work. Also, y excluded income in the form of the service flow from durable
goods and housing. Moreover, this definition of nonwage income incorporated
the earnings of the wife and of other members of the household and, therefore, it
is not exogenous with respect to the husband's labor supply behavior if the work
decisions of each member of the household are made jointly.74 In other studies
[e.g. Ashenfelter and Heckman (1973)], y is explicitly measured by aggregating
the responses to the survey's questions about the net income received in the form
of rents, dividends, interest, private transfers, and alimony payments. Another
procedure [e.g. Fleisher, Parsons and Porter (1973)] is to assume that y is
proportional to the household's net worth (where the factor of proportionality is
given by the relevant rate of return). These different procedures generate markedly
different estimates of the effect of nonwage income on hours of work. For
instance, the rope (i.e. w .3h/Oy) at sample mean values is estimated at -0.27
in Ashenfelter and Heckman (1973), -0.06 in Bloch (1973), -0.08 in Fleisher,
Parsons, and Porter (1973), approximately -0.32 in Kalachek and Raines (1970),
and -0.047 in Masters and Garfinkel (1977). However, these estimates are
sensitive to the particular specification of the estimating equation and, indeed, it
is by no means uncommon for a positive (partial) association to exist between
nonwage income and hours of work. For instance, of the 57 different estimated
coefficients on net worth reported in Tables 6, 9, 11, and 12 of DaVanzo, DeTray
and Greenberg's Rand study, only 16 would be judged as significantly different
from zero on conventional two-tailed t-tests and, of these 16, exactly one-half is
positive and one-half is negative. Positive (partial) correlations between male
hours worked and nonwage income are reported in Cohen, Rea and Lerman
(1970), Dickinson (1974), Garfinkel (1973), Hill (1973), Kniesner (1976), and
Masters and Garfinkel (1977) and they would probably have been calculated in
Burtless and Hausman (1978), Hausman (1981), and Hurd and Pencavel (1981) if
the estimation procedure had not prohibited it. In view of these widely varying
estimates on nonwage income, when an equation such as eq. (24) is fitted and the
substitution effect is calculated residually as a 1-ha 2, given the negative (un-
74This raises another class of differencesamong the various empirical studies, namely, the
treatmentof the wife'slaborearnings.Sometimesher earningsare incorporatedinto nonwageincome
in which case the tacit assumptionis that theseearningsproducean incomeeffecton the husband's
hours of work, but no substitutioneffect.On other occasions,the wife'swagerate is includedas a
separate independentvariable,but oftenits estimatedcoefficientis insignificantlydifferentfromzero
by conventionalcriteria. Thiswas DaVanzo,DeTrayand Greenberg'sfindingand, moreover,their
estimates for the coefficienton the husband'swageratewereaffectedonlytriviallyby differentways
of specifyingthe wife'searnings.
64 J. Pencavel
compensated) effect of wages on hours of work that is typically estimated (i.e.
given a 1< 0), it is by no means unusual for the implied substitution effects for
male workers to be negative at the sample mean values of h. Such negative effects
appear in the empirical work of, for instance, Cohen, Rea and Lerman (1970),
DaVanzo, DeTray and Greenberg (1973), Fleisher, Parsons and Porter (1973),
Hall (1973), Kniesner (1976), Kosters (1966), and Masters and Garfinkel (1977).
This hardly constitutes a resounding corroboration of the conventional static
model of labor supply.
3. The treatment of taxes. Sometimes, as in Kosters' study and in Ashenfelter
and Heckman's (1973) study, no allowance was made for personal income taxes
either in forming the wage rate or the nonwage income variable. On other
occasions, as in Boskin (1973) and in Hall (1973), the budget constraint was
assumed to be continuous and to form a convex set and budget constraint
variables net of taxes were constructed, but then the joint determination of all
these budget constraint variables with hours of work was ignored. There have
been few instances [one is Kurz et al. (1974)]75 in which the budget constraint
variables were adjusted for taxes and, in addition, they were treated as endogenous.
In order to assess the effects of adjusting the budget constraint variables
for taxes, we should like to see from the same body of data estimates of hours of
work equations based on pre-tax budget constraint variables and instrumental
variable estimates based on post-tax budget constraint variables. I know of no
study that presents this information for men though Mroz (1984) has undertaken
such a comparison for married women and found relatively small differences
between the two sets of estimates.
Is the assumption that the after-tax budget constraints for most men are
continuous and form a convex set an important departure from the truth? Some
think so. Therefore, they have proposed and applied more elaborate algorithms
that are designed to search over each segment of a piecewise-linear budget
constraint in order to determine the parameters describing the utility-maximizing
hours of work. For instance, Wales and Woodland (1979) assume they know
without error each individual's net wage rate and nonwage income and they use
these budget constraint variables together with the unknown parameters of the
individual's constant-elasticity-of-substitution utility function (posited to be the
same and nonstochastic for all individuals) to impute each individual's hours of
work along each segment of his piecewise-linear budget constraint. For each
individual, therefore, there is a relationship between the different possible values
of the "" '~ . " 'utility~functlons parameters and his imputed hours of work, given the
values of his budget constraint. Among many possible values of the parameters
75However, the procedures of Kurz et al., do not yield a consistent estimator because nonlinear
transformations of the imputed wage rate and nonwage income variables were used in the hours of
work equations.
Ch. 1: Labor Supply of Men 65
of the utility function, those are selected that minimize the sum over all
individuals of the squared difference between the imputed hours and the actual
hours. The only sources of error in their model are errors in maximization or the
effects of random variables (examples of which, write Wales and Woodland, are
unanticipated expenditures or illness) that cause the individual to work different
hours from those given by his budget constraint variables and utility function.
They applied their algorithm to a sample (from the Michigan PSID) of 226
married men whose wives did not work in the labor market and their estimates of
the utility function parameters implied values of the (uncompensated) wage
elasticity of hours of work of 0.14 and of the marginal propensity to earn of
-0.70. This wage elasticity lies above the central tendency of estimates while the
marginal propensity to earn is an even more noticeable outlier and one might be
inclined to wonder whether the more conventional estimation methods have
seriously misestimated these behavioral parameters. However, Wales and
Woodland derived similar estimates when they applied the more conventional
approach of linearizing the budget constraint around the observed hours of work
for each man so that the more elaborate algorithm did not appear to be
responsible for the estimates of the relatively high wage elasticity and aberrant
marginal propensity to earn.
Other studies using these sorts of algorithms have also yielded odd estimates.
For instance, Hausman's (1981) work is a generalization of Wales and Woodland's
to allow for stochastic variation in preferences across individuals, but otherwise
he proceeds on similar lines.76 With a sample of 1085 married men from the 1975
Michigan PSID, Hausman has the benefit of almost five times as many observations
as Wales and Woodland. 77 Fitting a linear hours of work function,
Hausman estimated an (uncompensated) wage elasticity of male working hours
of zero and a marginal propensity to earn of approximately -0.77. TM Although
this latter estimate is not without precedent, it differs sharply from the implications
of estimates of nonwage income on consumption. Hausman's estimate
implies that an additional dollar of nonwage income induces such a reduction in
working hours that (at sample means) labor earnings fall by 77 cents and the
consumption of commodities increases by only 23 cents. Income effects in
consumption could be this small, but the prevailing evidence suggests the
contrary.
76An excellent exposition of Hausman's work [and that of Burtless and Hausman (1978)] is
contained in Heckman and MaCurdy (1981)and Heckman,Killingsworthand MaCurdy (1981).
77Thisincrease in the size of the sample is not achievedcostlessly,however.Whereas Wales and
Woodland examined onlythose men whosewivesdid not workin the labor market, Hausman made
no distinction between men whosewiveswereworkingand those who were not.
78Thisvalue is derived as follows.Hausmanreports a meangrosswagerate of $6.18and predicted
mean hours of 2181.Thisimplieslabor incomeof $13 479. Supposesomeonewith thisincomefacesa
marginal tax rate of 25 percent.Then the meannet wagerate is approximately$4.64 ( = $6.18× 0.75).
Given his estimate of ah/ay of -0.166, the rope for such an individualis -0.77.
66 J. Pencavel
In short, these studies, using more elaborate computational algorithms, yield
estimates of the key behavioral parameters that diverge from the central tendency
of estimates and that are somewhat implausible. Because these studies pay
greater attention to some issues (especially the piecewise-linear nature of the
budget constraint and perhaps also its nonconvexity) at the cost of the neglect of
others (e.g. they treat wage rates and nonwage income as exogenous and not
measured with error), it is by no means evident that their estimates of the male
labor supply function are to be regarded as preferable to those derived from more
prosaic and perhaps more robust estimating methods.79
4. Assumptions about commodity prices. In most cross-section studies it was
assumed that all individuals face the same prices for commodities so that
variations in the money wage rate and money nonlabor income correspond to
variations in the real values of the variables. There were a few studies [e.g. Bloch
(1973), Boskin (1973)] that made use of some Bureau of Labor Statistics information
on the cost of living in different regions and cities. If such geographic
cost-of-living adjustments are not made, then this rationalizes the presence of
region and city size dummy variables that often appear in estimated labor supply
equations. When this BLS information on cost-of-living differences by city size
and by region was used to deflate the wage rate variable, both DaVanzo, DeTray
and Greenberg (1973) and Masters and Garfinkel (1977) report small changes in
the estimated coefficient in the wage rate.
5. Issues of functional form. Kosters' linear-in-the-logarithms specification
reported above is unusual in this literature. More frequently, as discussed in
Section 4.1 linear equations along the fines of eq. (28) have been estimated.
Occasionally the following semi-logarithmic specification in wage rates has been
posited:
hi=oto+alln +a 2 "l-ot3Ai+ei,
i i
which restricts the uncompensated wage effect to be smaller (in absolute value)
for high wage individuals. There is, of course, no a priori reason to believe that
the data will naturally conform to the restrictions on the behavioral parameters
impfied by these functions. In view of the prominent role occupied in introductory
texts by the so-called backward-bending labor supply curve, it was natural
for researchers to determine the empirical relevance of such a phenomenon.
Normally this 'has been effected by adding quadratic terms in the wage rate to
79This conjecture about the robustness-that methods such as Hausman's and Wales and Woodland's
are less robust with respect to small departures from the assumptions that underlie them as
compared with the more conventional estimation methods- is also contained in Heckman (1983).
Ch. 1: Labor Supply of Men 67
equations such as eq. (28) [e.g. Bloch (1973), DaVanzo, DeTray and Greenberg
(1973), Hill (1973), Rosen and Welch (1971)] or by estimating a free form
whereby the efficient a I is allowed to vary across different wage intervals [e.g.
Cohen, Rea and Lerman (1970), DaVanzo, DeTray and Greenberg (1973),
Garfinkel (1973), Greenberg and Kosters (1973), Hall (1973)]. There have been
instances in which evidence for such a backward-bending hours of work function
for males has been reported [e.g. Cohen, Rea and Lerman (1970)], but forwardbending
curves have also been estimated [e.g. Hurd (1976), Kurz et al. (1974)],
and from an overview of the empirical results, there does not appear to be
powerful evidence for nonlinearities in the wage-hours relationship for men.
However, most of this research on functional form has been incidental to other
issues and a systematic empirical investigation of the variation of income and
substitution effects across individuals has yet to be undertaken in labor supply
research. 80
6. Nonbudget constraint variables included in the hours of work equation. The
various studies on male labor supply differ from each other in the set of control
variables entered in the hours of work regression equation. For instance, some
studies include a measure of the individual's educational attainment [e.g. Cohen,
Rea and Lerman (1970), Garfinkel (1973), Hill (1973), Kniesner (1976), Kosters
(1966), Rosen and Welch (1971)] while other studies exclude it [e.g. Ashenfelter
and Heckman (1973), Bloch (1973), Boskin (1973), Hausman (1981), Hurd
(1976), Masters and Garfinkel (1977)]. When such a variable is included, its
estimated coefficient is almost always positive and significant by conventional
criteria suggesting that, other things equal, more formally educated men work
longer hours. Moreover, DaVanzo, DeTray, and Greenberg's investigation found
that the size and sign of the wage coefficient was extremely sensitive to the
presence of years of schooling in the estimated hours of work equation. 81 As
another example, a measure of the number of dependents in the household is
sometimes included in an equation accounting for variations in the working
hours of men [e.g. Bloch (1973), Boskin (1973), Cohen, Rea and Lerman (1970),
Hausman (1981), Masters and Garfinkel (1977)] and it is sometimes excluded
[e.g. Ashenfelter and Heckman (1973), Fleisher, Parsons and Porter (1973),
Garfinkel (1973) Rosen and Welch (1971)]. When a variable of this kind is
included, it tends to reveal a signifcantly positive (partial) association with hours
of work. In general, researchers have been somewhat cavalier in their choice of
nonbudget constraint variables to be included in an hours of work equation, but
unfortunately DaVanzo, DeTray, and Greenberg's experiment with their school-
8°Astart is containedin Dickinson(1979,1980).
81Someresearchersmaywellbe seducedintoomittingschoolingfromthe hoursof workregression
equationbecausethentheymayclaimit as an instrumentfor wagerates.
68 J. Pencavel
ing variable indicates that the presence or absence of certain nonbudget constraint
variables may profoundly affect the inferences about the wage elasticity of
hours of work. It is not unusual for no explicit reason to be given for the presence
in the hours of work regression equation of these nonbudget constraint variables.
Most researchers seem to have in mind that variables such as education or family
size are systematically associated with differences in tastes for work (or, equivalently,
differences in nonmarket productivity) so that they correspond to what I
have denoted as the variables A in the description of the contrained maximization
problem above. Nevertheless, as I have emphasized in Section 2, in addition
to these taste variations that are believed to be associated with variables (such as
education and family size) observed to the researcher, there is also a very
important unobservable taste component (as represented by e in Section 2).
Usually this unobserved taste component is simply tacked on as the stochastic
term to the hours of work equation, but there exist other ways of addressing the
issue of variation in observed tastes. For instances, Greenberg and Kosters (1973)
constructed a variable designed to represent differences in preferences for asset
accumulation by measuring the difference between an individual's actual net
assets and those net assets predicted on the basis of his age and wage rate from a
prior regression equation and then expressing this difference as a fraction of total
imputed wealth. This inclusion of this so-called preference variable changed their
estimated coefficient on nonwage income in an hours of work regression equation
from positive to negative. The problem with this variable, as Cain and Watts
(1973) note, is that its construction makes use of information about the wage rate
and nonwage income and thus it is natural to wonder whether it incorporates
some part of the conventional wage and income effects of the budget constraint.
A number of the estimates from U.S. nonexperimental data of the static
model's behavioral responses are brought together in Table 1.19 Although the
major studies are included, this table is not exhaustive. In several cases [such as
Wales and Woodland (1976, 1977)] insufficient information is provided in the
publications with which to calculate the compensated wage-elasticities or the
mpe. In other cases [e.g. Hall (1973)] many different estimates are presented and I
gave up the attempt to summarize them adequately with a few numbers. I have
also excluded studies such as those of Hausman (1981) and Hurd and Pencavel
(1978) that in estimation restricted the effect of nonwage income on hours to be
nonpositive. In drawing inferences from Table 1.19, the caveats given in Section
4.1 above should be kept in mind. These estimates are drawn from different
estimating'-rquations ,and from different functional forms and evaluating the
estimated parameters at sample mean values of the variable provides only a very
rough and inexact method of comparing behavioral responses. Table 1.19 reveals
that, of the estimates presented, Wales and Woodland's (1979) are considerably
different from the rest, a result I attribute both to the restriction between E and
Ch. 1: Labor Supply of Men
Table ,'.19
Estimates from U.S. nonexperimental data of behavioral responses for men.
69
E rope E*
Ashenfelter and Heckman (1973) - 0.16 - 0.27 0.12
Bloch (1973) 0.06 - 0.06 0.12
Boskin (1973) - 0.29 - 0.41 0.12
DaVanzo, DeTray and Greenberg (1973) -0.15 -0.004 -0.14
Dickinson (1974) - 0.11 0.08 - 0.19
Fleisher, Parsons and Porter (1973) -0.19 -0.23 0.04
Garfinkel (1973) 0 0 0
Greenberg and Kosters (1973) - 0.09 - 0.29 0.20
Ham (1982) -0.16 -0.11 -0.05
Hausman and Ruud (1984) -0.08 -0.63 0.55
Kniesner (1976a) - 0.17 - 0.01 - 0.16
Kosters (1966) - 0.09 - 0.14 0.04
Masters and Garfinkel (1977) - 0.11 - 0.05 - 0.06
Wales and Woodland (1979) 0.14 - 0.70 0.84
Notes: The estimates reported for DaVanzo, DeTray and Greenberg (1973)
correspond to those given on the last line of Table 11 of their Rand report where
both the wage rate and nonwage income variables were instrumented. Those for
Ham (1982) correspond to those given in column (1) of Table IV of his paper.
Those for Kniesner (1976a) apply to those men whose wives were not at work
for pay. For Masters and Garfinkel (1977), I took what they described as their
"best estimates" of E and the rope even though the coefficients reported did not
derive from the same regression equation. Boskin's (1973) results are those for
white men only. Dickinson's (1974) rnpe is calculated from his estimate coefficient
on "other (nontransfer) family income". Hausman and Ruud's estimates
are calculated for a household with an assumed marginal tax rate of 25 percent
so the husband's net wage rate is $4.31 and the wife's net wage rate is $2.63.
the mpe implicit in their use of the CES function 82 and to their estimating
method which may well not be robust with respect to small departures from the
assumptions underlying its use. Of the remaining studies, the largest estimate of
E is 0.06 [Bloch (1973)] and the smallest is -0.29 [Boskin (1973)]. The central
tendency of estimates of E lies between -0.17 and -0.08 and a simple average
of all the estimates of E in Table 1.19 (excluding Wales and Woodland's) is
-0.12. Table 1.19's estimates of the mpe (again excluding Wales and Woodland's)
range from a low of -0.63 [Hausman and Ruud (1984)] to a high of 0.08
[Dickinson (1974)]. The estimates of the mpe are more disparate than those for E
and I hesitate to infer its value from such a varied set of estimates. Certainly, the
large negative numbers seem very unlikely. In five cases in Table 1.19, the
compensated wage elasticity of hours of work, E *, is negative. Of the six positive
S2As equation (35) makes clear, in the CES case when b = 0, E = - ~ +(1 - ~)(mpe).
70 J. Pencavel
values of E* (excluding Wales and Woodland's and Hausman and Ruud's), the
mean is 0.11. If E is -0.12 and E* is 0.11, the mpe is -0.23.
4.3. Empirical results from British data
Modern British research on male hours of work got under way in the 1970s and
from the beginning the work has consistently been concerned with the implications
of the taxation of income on the supply of labor and so the studies
invariably adjust each individual's budget constraint variables for such taxes. 83
The first papers were those of Brown, Levin and Ulph (1976) and Layard (1978).
The data analyzed in the former study came from a survey conducted at the end
of 1971 by a private market research firm. With a relatively small and perhaps
unrepresentative sample84of 284 married men whose wives were not at work in
the labor market, Brown, Levin and Ulph (1976) estimated (with a conventional
ordinary least-squares regression linear in parameters but nonlinear in the budget
constraint variables) an (uncompensated) own-wage elasticity of hours of work of
between -0.085 and -0.131 at sample mean values.85 This was derived from a
curious specification in which both lineafized nonwage income and a measure of
"other income" were included.86 Subsequent work by Brown (1981) and his
associates using similar procedures yielded comparable wage elasticities and
marginal propensities to earn of between -0.31 and -0.35. Other methods were
also applied to these data including a study by Ashworth and Ulph (1981) that,
independently of the work of Wales and Woodland (1979) and Burtless and
Hausman (1978), proposed and implemented the procedure of searching over
each individual's entire piecewise linear budget constraint to determine the
utility-maximizing hours of work. With a generalized constant-elasticity-of-substitution
indirect utility function applied to 335 married men, Ashworth and
Ulph (1981) derived estimates that implied an uncompensated wage elasticity of
hours of work of between -0.07 and -0.13 and a marginal propensity to earn of
between - 0.36 and -0.57.
Layard's (1978) study involved a much larger sample of 2700 married men
from the General Household Survey of 1974 and, with a linear specification along
83The British studies of male workers always use weekly hours of work as the dependent variable.
84The authors themselves were aware of both the small size and possible nonrandom nature of their
sample. A very informative discussion of these data is contained in Brown (1981).
SSAlthough ~his wage elasticity is estimated to be negative at sample mean values, it becomes less
negative as the ~ge rate rises and, indeed, it eventually takes on positive values. In other words, they
estimate an hours of work function that is a mirror-image of the textbook backward-bending
function.
86In a later study [Brown (1980, p. 60)], this is justified on the argument that "other income" is, in
fact, dependent upon the male's labor supply. Of course, if this is the case, then it should be included
in calculating the wage slope of the budget constraint.
Ch. 1: Labor Supply of Men 71
the lines of eq. (24), he estimated an uncompensated wage elasticity of -0.13 and
a small (in absolute value) marginal propensity to earn of -0.04. Indeed, with
such an income effect, his implied compensated wage effect on hours of work was
negative.
In Britain the availability of cross-section information from the Family Expenditure
Survey (FES) on both hours of work and expenditures on different
groups of commodities has permitted the joint estimation of labor supply and
commodity demand equations as implied by eq. (8). Provided the allocation
model underlying eq. (8) is correct, estimating such a system of equations has the
advantage of generating much more efficient estimates. The greatest potential for
these data is to test that allocation model, but curiously they have not been used
for this purpose to date. Nevertheless, some indications of how these tests would
fare are provided in the papers making use of these data. Consider, for instance,
the work of Atkinson and Stern (1980, 1981) who specified a generalized
Stone-Geary utility function where that generalization is the novel one involving
explicit use of Becker's (1965) particular formulation of the household production
approach to the allocation of time. In fact, when all the commodities may be
aggregated into one composite, their hours of work function closely resembles eq.
(30). They select a sample from the 1973 FES consisting of 1617 households with
a male head employed full-time (not self-employed) and whose earnings placed
him within the (fairly wide) range in which the slope of the after-tax budget
constraint was approximately constant. They identify nine different categories of
household consumption expenditures plus the hours of work of the men.87 Their
results suggested uncompensated wage elasticities (evaluated at their sample
pre-tax mean values) ranging from -0.15 to -0.23 although, as in Brown, Levin
and Ulph (1976), the estimated hours of work function is a forward-falling curve
and at relatively high wages they estimate a positive wage elasticity. They tend to
find that leisure is an inferior commodity and ultimately they impose the
constraint that pure leisure is not valued for its own sake (i.e. it has value only
insofar as it contributes to the production of utility-generating activities). As is
often the case with the Stone-Geary specification, the extent of nonconvexity
implied by the estimates is crnsiderable and, in particular, many men work more
hours than permitted by the estimates of the maximum amount remaining after
allocating time to other activities.
Another study estimating a system of commodity demand and labor supply
equations is Blundell and Walker's (1982). From the 1974 FES, they select a
sample of only 103 households in which both the husband and the wife work, a
term being included to account for this deliberate nonrandom selection of female
SVTheearningsof the wifeand of othersin the householdare includedin nonwageincome.
72 J. Pencavel
workers. They also specified a generalized Stone-Geary utility function88 in
which six groups of commodities and the hours of work of the husband and of
the wife appear as arguments. Their parameter estimates implied (at sample mean
values) an uncompensated wage elasticity of male hours of work of -0.23 and a
marginal propensity to earn of -0.36 with, therefore, an implied (compensated)
wage elasticity for men of 0.13. Because the wife's marginal propensity to earn
was estimated to be -0.22, their results implied that an additional dollar of
nonwage income would raise consumption by only 42 cents (i.e. 1- 0.36- 0.22).
Blundell and Walker do not indicate how many of their 103 husbands and wives
are working more hours than permitted by the estimated parameters describing
the maximum feasible hours of work, but there are surely some although
probably a smaller proportion of their sample than of Atkinson and Stern's. They
test and reject the hypothesis that the husband and wife's time allocation decision
is weakly separable from the household's decisions about the consumption of
commodities, but maintained throughout the analysis is the hypothesis that
expenditures on housing are separable from all other decisions. In a subsequent
study of 308 working married couples drawn from the 1977 FES and specifying
four categories of consumer goods (but excluding alcohol, tobacco, housing, and
other durable goods (expenditures), Blundell and Walker (1983) report an uncompensated
wage elasticity of male hours of work of -0.004 (evaluated at 39.6
weekly hours of work, the mean value for their earlier sample) and an mpe of
- 0.203.
The preliminary results from another British project financed by H. M.
Treasury are becoming available at the time of writing this survey paper [Brown,
Levin, Rosa, Ruffell and Ulph (1983)]. This new project involved both a new
survey (conducted in late 1980) and a new sample of 3307 households who
provided sufficient information for analysis. In an initial investigation of 810 oneand
two-worker households, the researchers applied a similar algorithm to that
used by Ashworth and Ulph (1981) and Wales and Woodland (1979) to search
over each individual's entire piecewise linear budget constraint. Unfortunately,
this algorithm did not identify a well-defined maximum of the likelihood function
although the estimates of the parameters of the nonstochastic generalized
Stone-Geary function [identical to eq. (33)] are described as being "in the fight
area'~. At the sample mean values of the wage rate and nonwage income, the
worker in single-worker families is estimated to have an uncompensated wage
elasticity of hours of work of -0.32, a compensated wage elasticity of 0.18, and a
marginal prriaensity to earn of -0.50. In two-worker families, the husband
88The generalizationtakesthe formof specifyingthe "subsistence"or "reference"quantitiesnot as
parameters, but as functionsof commodityprices and of householdstructure. In fact,becauseall
households are assumedto facethe sameprices for commodities,the only effectivegeneralizationis
one whichallowsthe subsistencequantitiesto varyacrosshouseholdswithdiffcrentnumbersand ages
of children.
Ch. 1: LaborSupplyof Men
Table1.20
Estimatesof the behavioralresponsesfor Britishmales.
73
E rope E*
Ashworth and Ulph (1981) - 0.13 - 0.36 0.23
Atkinson and Stern (1980) 0.16 -0.07 -0.09
Blundell and Walker (1982) - 0.23 - 0.36 0.13
Blundell and Walker (1983) -0.004 -0.20 0.20
Brown, Levin, and Ulph (1976) -- 0.13 - 0.35 0.22
Brown et al. (1982-83) { Single worker -0.33 0.50 0.17
Two workers - 0.14 - 0.44 0.30
Layard (1978) - 0.13 - 0.04 0.09
Notes: The estimates for Brown, Levin and Ulph (1976) are those where the wife
does not work for pay. The estimates for Brown et al. (1982 83) are those for a
family with two children.
possesses an uncompensated wage elasticity of between -0.14 and -0.06 (the
former estimate for husbands with two children and the latter for husbands with
no children), a compensated wage elasticity of between 0.30 and 0.39, and a
marginal propensity to earn to between -0.45 and -0.42. In these two-worker
families, the wife's marginal propensity to earn is estimated at approximately
-0.15 so that together these estimates imply a family's marginal propensity to
earn of about -0.60 or, expressed differently, only 40 percent of a small increase
in exogenous nonwage income is spent on the consumption of commodities°
A summary of these British estimates is contained in Table 1.20. All the
estimates of the uncompensated wage elasticity of hours of work are negative and
a simple average of the eight estimates is --0.16. Five of the eight estimates are
between -0.16 and -0.13. As was the case with the studies with U.S. males, the
variations in the mpe and in E* among the studies is considerably greater than
the variation in E. Of the six positive estimates of E*, the average is 0.21.
4.4. Empirical results from U.S. experimental data
The fundamental implication of the allocation model outlined in Section 3.1 is
that, for a population of individuals at a given time or for a given individual over
time, other things equal, exogenous movements in budget constraints should
induce movements in the supply of labor. This most basic proposition stood an
excellent opportunity of being tested by the various negative income tax (NIT)
experiments that were conducted in the United States in the decade from 1968 to
1978. With the laboratory sciences as a conscious example, these experiments
selected a sample of households in a given locality and then introduced to a
fraction of this sample (the experimental households) a different budget constraint
while continuing to observe the other households (the controls). The
consequences of changes in the budget constraint for the supply of labor could be
74 J. Pencavel
inferred by contrasting the behavior of the experimental households with that of
the control households during the experiment and/or by contrasting the behavior
of the experimental families during the experiment with their behavior before (or
after) the experiment. 89
In fact, inferences from the experiments were much more difficult to draw.
There were several reasons for this. First, the sample of (experimental and
control) households studied was drawn selectively from the low-income population.
This was a natural decision in view of the concern with welfare reform, but
its effect was to introduce problems deriving from the truncation of a variable
(income) directly related to the major variable of interest (labor supply). Second,
this low-income sample of households was then not allocated randomly between
the experimental and the control groups, but rather the allocation design was a
more complicated one that partly tried to mitigate the budgetary costs of the
experiment. Third, during each experiment, changes took place outside the
experiment's control that affected the budget constraints of the participating
households and that may have affected the control and experimental households
differentially. For instance, in the middle of New Jersey's experiment, the state's
welfare program was reformed in such a way that, for a number of experimental
households, it now offered a more generous opportunity than the experiment's
and so these households opted out of the experiment. As another example, the
first NIT payments in Seattle were made (in November 1970) at a time when the
area was experiencing a drastic and unprecedented rise in unemployment arising
from the extensive layoffs in its aircraft industry and it was feared that an
idiosyncratic labor market situation existed from which it was hazardous to
extend inferences about the effects of a negative income tax to more typical labor
market settings. Fourth, even if the sample of experimental households and the
sample of control households had been the same at the outset, greater attrition of
controls subsequently from the experiment rendered the two samples different
from one another. 9° Fifth, as in all welfare and tax programs, incentives existed
for individuals to misreport their incomes so that statutory and actual tax rates
diverged. Indeed, it has been conjectured that the particular incentives created by
the NIT experiments operated to exaggerate the magnitude of true labor supply
89This is the method prescribed in Orcutt and Orcutt's (1968) classic statement of the case for
sociai"experiments.
9°Of course, the problem of attrition existsin all panel data, not merelyin the NIT experimental
data. A frequently-citedpaper on the subject of attrition is that by Hausman and Wise (1977)who
claimed that in theGary experimentattrition bias wasless with a "structural" modelof earningsthan
with an analysis-of-variance(AOV)model. However,this inference was drawn from a comparison
between, on the one hand, a "structural" model thatincluded almost all the determinantsof attrition
in the earnings equation and, on the other hand, an AOV model that excluded many of the
determinants of attrition fromthe earningsequation. The implied constraint in the AOV model was
clearly not warranted and their comparisonwas therebyquite invalid.
Ch. 1: LaborSupply of Men 75
effects.91 Sixth, because most of the experimental households were eligible to
receive NIT payments for three years,91 it has been argued that the labor supply
effects should be interpreted as those induced by temporary changes in net wage
rates and nonwage income.93 Seventh, because only a relatively small fraction of
an area's population had their budget constraints altered by the experiments and
because these changes were temporary, the inducements to make institutional
adjustments in work schedules were considerably less than would be the case for
a national and permanent NIT program. For instance, approximately two-thirds
of the husbands in the Gary experiment worked in the steel mills on work
schedules that permitted them little flexibility in working hours in their existing
jobs. There would have been greater pressures on the employers and the unions
to renegotiate different hours of work schedules if it had not been the case that
only a relatively small fraction of all employees in these steel mills were enrolled
in the experiment and if the experiment had lasted for more than three years. In
this sense, the experimental-control differences would tend to understate the
adjustments that would occur if the budget constraint changes were not confined
to a relatively small population over a relatively short space of time. All these
issues certainly impede drawing straightforward inferences from the experimental
data although, given the size of the differences in NIT payments between
experimental and control households in some of the experiments, it is unlikely
that these problems entirely nullify simple experimental-control comparisons.
The NIT experiments were conducted on 1357 households in New Jersey and
Pennsylvania from 1968 to 1972, 809 households in rural areas of North Carolina
and Iowa from 1969 to 1973, 1800 households in Gary, Indiana, from 1970 to
1974, and 4800 households in Seattle and Denver from 1970 to 1980. Not only
were many more households analyzed in the Seattle-Denver experiment compared
with the others, but also it involved more generous NIT payments. For the
typical male, in each case the experimental treatment meant changing his budget
constraint from Oala 2 to Oblb2a 2 in Figure 1.4.94 In other words the NIT
experiment paid a grant (or support) of G dollars regardless of the household's
income and then applied a relatively higher tax rate ~-on all income in excess of
G. The breakeven level of income, b2 in Figure 1.4, occurred when the household's
receipts in the form of the grant, G, equalled tax payments, ~'(wh + y). For any
individual located to the fight of b2 both before and after the introduction of the
9tSee Ashenfelter(1978),Greenberg,Moflitand Friedman(1981),and Welch(1978).
9aSome households in Seattle and Denver experimentwere elig~bleto receivepayments for five
years.
93The original workinvestigatingthis issueis Metcalf's(1973,1974).
94Figure 1.4 assumes a pre-experimentalbudget constraintcharacterizedby a continuouslyrising
marginal tax rate. For somehouseholds(especiallysingleheadsof households),the non-experimental
welfare programs (such as AFDC) generatebudget constraints similar to the experimentalbudget
constraint Ob1b2a 2.
76 J. Pencavd
Total
Income
a 2
b]
a I
0 Hours-'=
Figure 1.4
NIT experiment, his opportunities were enhanced and his pre-experimental
budget constraint px = wh + y became px = G +(1 - r)(wh + y), where r is the
differentially higher tax rate applied on income by the NIT experiment. There
were also some individuals who were located on their pre-experimental budget
constraints to the left of b2, but who determined upon the introduction of the
experiment they would be better off by so reducing their hours of work as to
locate on bib 2 and become eligible for NIT payments. Other things equal, the
flatter an individual's indifference curve (i.e. the greater an individual's elasticity
of substitution between income and leisure), the greater the probability of his
moving from above the breakeven level of income pre-experimentally to below
the breakeven level of income during the experiment. 95 The values of G and r
differed across and within the four experiments 96 and once again the assignment
of'experimental households among the different NIT programs (each described
95Expressed,differently, consider an experimental individual who is indifferent between a point on
his budget constraint to the left of b2 and a point to the right of b2. For this individual, the
experimentally-inducedchange in the budget constraint involves no income effect, only a substitution
effect. This is essentiallyAshenfelter's (1983) insight that the substitution effect can be measured from
estimating the relationship between the fraction of individuals below the breakeven level of income
and the slope of the arm bib2.
96In the Seattle-Denver experiment, there were some "treatments" in which z itself was not a
constant, but instead fell as income rose.
Ch. l: Labor Supply of Men 77
by a particular combination of G and z) was not random. In particular, there
was a tendency for households with relatively low pre-experimental incomes to be
assigned to the less generous NIT programs (i.e. those with relatively low G and
high ~) thereby reducing the expected budgetary cost of the experiment.97 This
implies that the particular experimental parameters, G and T, applied to each
household depended upon its pre-experimental earnings and these in turn were
not independent of its experimental labor supply insofar as there is correlation
over time in a household's work behavior. In short, contrary to some claims, the
experimental treatments were not genuinely exogenous both because each
household decided whether to received NIT payments by being below the
breakeven level of income b2 and because the particular program parameters it
faced were not assigned to it randomly.98
To determine whether the data collected by the NIT experiments conform to
the basic notion that differences in work behavior are associated with differences
in budget constraints, the following ordinary least-squares regression equation
was estimated:
L s = t~oX i + t81E s + u i, (36)
where L s stands for a dimension of individual i's work behavior 99 (such as his
weekly hours of work or whether or not he was employed in the labor market), Es
takes the value of unity for an individual allocated to the experimental sample
and of zero for an individual in the control sample, Xj measures other characteristics
of the individual (and, in the Seattle-Denver research, X i also includes the
variables determining the assignment of individuals to different treatments), and
us is a stochastic disturbance term. Sometimes eq. (36) was estimated with data
97Anexcellent analysis of the implications of the assignment process is contained in Keeley and
Robins (1980) who advise including the variables determining the assignment of households to
different NIT programs in equations designed to infer the labor supply effects of the experiments.
98This fact vitiates many of the original arguments in support of undertaking such social
experiments. These arguments claimed that conventional income and substitution effects would be
much easier to measure with experimental data because the experiment induced exogenous changes in
the budget constraints of experimental households. As noted earlier, because of the nonrandom
assignment of households between the control sample and the experimental sample and because of
nonrandom assignment within the experimental sample of households to different treatments, the
changes in the budget constraint were not truly exogenous to the households. Moreover, the
nonlinearity of the budget constraints creates a further reason for the budget constraint variables to
be endogenous. What appears to be a more convincing argument in defense of the experiments is that
the within sample variations in the budget constraint variables (and especially in nonwage income)
tend to be larger than in nonexperimental data and this holds out the hope of measuring the
parameters associated with these budget constraint variables more precisely.
99Instead of work behavior, a few studies [such as Ashenfelter's (1978)] focus upon the experimental
effect on net earnings. There is good reason for this in view of the fact that the NIT-induced
change in earnings is proportional to the excess transfer cost of the program over the cost calculated
on the basis of pre-experimental incomes alone.
78 J. Pencavel
drawn from midway during the experiment in which case Xi usually included
some measure of an individual's pre-experimental labor supply. On other occasions,
data were pooled from the experimental and the pre-experimental period
and experimental-control differences during the experiment were distinguished
from such differences before the experiment. The estimates of 131 in eq. (36) were
consistently (though not invariably) negative: for white husbands in the New
Jersey-Pennsylvania experiment, the experimental group averaged 5.6 percent
fewer hours of work per week than the control group [Rees (1974)]; for black
husbands in Gary, the experimental group averaged 6.5 percent fewer hours of
work per month than the control group [Moffitt (1979)]; and in the SeattleDenver
experiment, husbands in the experimental group worked 2.2 percent
fewer hours per week than those in the control group [Keeley et al. (1978a)]. The
differences among the NIT experiments in the point estimates of 131 were less
marked than the differences in their estimated standard errors: the
experimental-control differences measured in the New Jersey-Pennsylvania,
North Carolina-Iowa, and Gary experiments were often insignificantly different
from zero by conventional criteria while those in the Seattle-Denver experiment
were clearly significantly different from zero, a consequence of the substantially
greater size of the Seattle-Denver experiment. Experimental husbands were also
less likely than controls to be employed at any moment midway through the
experiment-a 2.6 percent difference for white husbands in New Jersey-Pennsylvania
[Rees (1974)], a 4.9 percent differential in Gary [Moffitt (1979)], and a
2.3 percent differential in Seattle-Denver [Pencavel (1982)]. These estimated
experimental-control differences tend to understate the magnitude of the experimental
labor supply response because the experimental-control dummy Ei in eq.
(36) measures the effect of the experiment averaged over those experimental
families who receive NIT payments by being below the breakeven level of income
and those whose incomes place them above the breakeven level. In other words,
/~1 in eq. (36) understates the experimental effects conditional upon being below
the breakeven level of income.
The results reported in the previous paragraph were designed to answer the
question of whether changes in budget constraints result in changes in work
behavior. The evidence suggests that, beyond any pre-experimental differences,
the~changes introduced by the NIT experiments did induce differences between
the experimental and control husbands' work behavior. Of course, the allocation
model of Section 3.1 has implications beyond the simple one of maintaining that
changes in bixdget constraints cause changes in work behavior; in any changes in
budget constraints, this model distinguishes the effects of changes in wage rates
from those attributable to changes in nonwage income. It is natural to determine,
therefore, whether the experimentally-induced changes in net wage rates and in
net nonwage income each generated effects on work behavior that are compatible
with the neoclassical static allocation model. Moreover, distinguishing the effects
Ch. 1: Labor Supply of Men 79
on work behavior of the NIT tax rate from the effects of the guarantee level is
essential if the purpose is to draw inferences from these experiments about how
other welfare programs (with different program parameters) would operate.
There have been many different forms of specifying the net wage and nonwage
income effects on work behavior induced by the NIT experiments although, as
others have observed [e.g. Ashenfelter (1978)], many of the models used by
analysts of the experimental data (especially those in New Jersey-Pennsylvania
and in North Carolina-Iowa) were specified in ways that make it difficult to
recover income and substitution effects from them. In those studies where these
behavioral responses (or their transformations) are identified, most of the important
differences among the studies have turned on the way in which each
household's budget constraint has been measured. As Figure 1.4 makes clear, for
both experimental and control households, the nonlinearity of the budget constraint
renders the net wage rate endogenous to the labor supply decision.
Hausman and Wise (1976) addressed this problem by measuring the budget
constraint variables for each individual at the same number of working hours
(namely, 1500 hours per year), but this has the effect of simply assigning the
wrong budget constraint to all individuals except those who happen to be
working 1500 hours. A procedure not so different from this is applied by Keeley
et al. (1978a, 1978b) who take up Ashenfelter and Heckman's (1973) proposal of
measuring the budget constraint variables in the second year of the SeattleDenver
experiment as those that would obtain at each individual's pre-experimental
hours of work. Of course, these measures can only be correct if, in fact,
each individual did not change his work behavior as a consequence of the NIT
experiment or for any other reason. Johnson and Pencavel (1982) also measure
the change in the budget constraint along these lines, but then they treat these
variables so constructed as measured with error and apply an instrumental
variable estimator. Moffitt (1979) measures the tax rate by averaging each
individual's marginal tax rate over the entire length of his budget constraint.
Johnson and Pencavel (1984) and MaCurdy (1983) linearize each individual's
budget constraint around his observed hours of work during the Seattle-Denver
experiment and then treat these budget constraint variables as endogenous by
replacing them with their values predicted from a prior regression. Burtless and
Hausman (1978) use a generalization of Wales and Woodland's (1979) procedure
described in Section 4.3 where the generalization takes the form of permitting
each individual's utility function to contain a component that is unobserved to
the researcher and that varies (according to a specified distribution) across the
population. Wales and Woodland's (1979) method of determining the unknown
parameters of the hours of work function by searching over all segments of the
piecewise linear budget constraint must now be specified such that each individual's
location on a particular segment (given his net wage rate and net nonwage
income) is known only probabilistically. As in Wales and Woodland's study,
80
Table 1.21
Estimates of the behavioral responses for men from the NIT experiments.
J. Pencavel
E mpe E*
Ashenfelter (1978a)
Ashenfelter (1978b)
Burtless and Greenberg (1982)
Hausman and Wise (1977)
Johnson and Pencavel (1982)
Johnson and Pencavel (1984)
Keeley and Robins (1980)
3 Year
5 Year
0.21 0.02 0.19
0.17 -0.01 0.18
0.08 - 0.04 0.12
-0.12 -0.18 0.06
0.10 -0.01 0.11
-0.16 -0.29 0.13
0.02 -0.17 0.19
- 0.09 0.14 0.05
Notes: Ashenfelter's estimates are from the North Carolina-Iowa rural experiment
and Hausman and Wise's are from the New Jersey-Pennsylvania
experiment. All the other estimates make use of data from the Seattle-Denver
income maintenance experiment and all these estimates have been evaluated at
the same number of hours of work (namely, 1880.97) and the same net wagerate
($2.293). These are the mean values of working experimental husbands in the
pre-experimental year whose incomes in that year would have placed them
below the breakeven level and they are taken from the sample analyzed by
Keeley and Robins (1980).The earlierwork by Keeley, Robins, Spiegelman and
West (1978a, 1978b) uses the same estimating procedure as in Keeley and
Robins (1980), but in the later study the sample includes Chicanos, unlike the
earlier work. The difference between Ashenfelter's (a) and (b) estimates is
explained in footnote 100.
Burtless and Hausman assume they measure each individual's budget constraint
without error.
Table 1.21 summarizes the estimates of the rope and the wage elasticities of
hours of work from a number of the analyses of the hours of work of husbands in
the NIT experiments. This table does not list every study that claims to be
measuring these behavioral responses, but only those studies that satisfy two
conditions: first, they provide sufficient structure on the estimated relationships
that the results have some claim to correspond to the behavioral responses; and,
second, they impose sufficiently few prior estimating restrictions as to supply an
opportunity for the data to reveal whether they really conform to the implications
of the static allocation model. This second condition implies that I have omitted,
for example, Homer's (1977) paper with the New Jersey-Pennsylvania experimental
data that measures the parameters of a Cobb-Douglas utility function
and Burtless:,and Hausman's (1978) paper on the Gary experimental data that
constrains no individual"to have a positive mpe. The first condition means that I
have excluded studies such as Watts' (1974) and Moffitt's (1979) that involved
specifications in which the income and wage effects on hours of work were
supposed to be gleaned from the estimated coefficients on the experimental tax
rate and the guarantee level in an hours of work equation and where other
Ch. 1: Labor Supply of Men 81
variables also incorporating measures of wages and nonwage income were
included in the regression.
Of the studies listed in Table 1.21, Hausman and Wise's (1977) makes use of
the New Jersey-Pennsylvania experimental data, Ashenfelter's (1978) makes use
of the North Carolina-Iowa experimental data,i°° and the rest make use of the
Seattle-Denver experimental data. All the summary estimates in Table 1.21
relating to the Seattle-Denver experiment have been calculated at the same
values of working hours and wage rates, as the notes to the table make clear. The
point estimates of the uncompensated wage elasticity, E, range from a low of
-0.159 [Johnson and Pencavel (1982)] to a high of + 0.015 [Ashenfelter (1978)].
The point estimates of the mpe range from a low of -0.290 [Johnson and
Pencavel (1982)] to a high of +0.015 [Ashenfe!ter (1978)]. The estimates of E*,
the compensated wage elasticity, in the different studies range from a low of
0.050 [Keeley and Robins (1980)] to a high of 0.192 [Ashenfelter (1978)]. This
relatively narrow range of estimates of E* comes about through offsetting values
of E and the rope, the range of estimates of E and mpe being considerably
greater. The tendency is for the uncompensated hours of work function to be
positively sloped with respect to wage rates at sample mean values. By estimating
i°°The two sets of estimates for Ashenfelter's analysis of the data from the rural experiment
correspond to two different parameterizations of the experimentally-induced change in earnings. He
posits an hours of work function for family member 1 as h1= hl(wl, w2, y), where w2 is the net
wage rate of family member 2. The experimentally-induced change in this person's earnings is
Ohl Oh1 dw C~hl
Wl dhl = wi - dw 1+ w1 + wi
OWl 0W2 2 ~-y dy
[ ( 0hi 9hl'][Ohl]
where dw i (the change in wage rates induced by the experiment) is given by zwi, dw 2 = - rw2,
and dy (the change in nonwage income induced by the experiment) is G - zy. So what is designated
in Table 1.21 as scheme (a) regresses the change in earnings on the tax rate ~"and on G - Lv- Observe
that the coefficient on r incorporates any cross-wage effects. The estimates under E for Ashenfelter
(a) in Table 1.21 sets these cross wage effects to zero. Ashenfelter's second parametefization makes
use of the Slutsky decomposition to write the previous equation
w d :-WlLWll ) +w2 0w2J j,+Wl I
where the term G - r(wih i + w2h 2 + y) corresponds to the NIT payments and where the asterisk
denotes compensated wage effects. Here the change in earnings is regressed on the tax rate T and on
NIT payments. Again the coefficient on ~"reflects a cross-wage effect and again the estimates under E
for Ashenfelter (b) in Table 1.21 sets these cross-wage effects to zero. This second parameterization is
similar to that used by Keeley et al. (1978a, 1978b). They set cross-wage effects to zero and divide the
last equation in this footnote by wv
82 J. Pencavel
the labor supply parameters separately for households on the three year experimental
program from those on the five year program, Burtless and Greenberg
(1982) derive values for E* and the rope that diverge in the manner that Metcalf
(1973, 1974) conjectured: the compensated wage-elasticity is larger and the rope
is smaller (in absolute value) for the three year experimental husbands compared
with the five year experimental husbands.
It is important to point out that the responses whose point estimates are
presented in Table 1.21 are not normally estimated with much precision. For
example, Hausman and Wise's point estimate of E of 0.095 comes with an
estimated standard error of 0.043 so that a 95 percent confidence interval ranges
from 0.001 to almost 0.180. Or the largest of the point estimates of E in Table
1.21, Ashenfelter's 0.207, has an estimated standard error of 0.122 so that a 95
percent confidence interval spans a range from -0.032 to + 0.446. It is difficult
to draw the inference from estimates such as these that the NIT experiments have
permitted the relevant behavioral responses to have been measured with much
precision.
4.5. Conclusions
If the estimates from Tables 1.19, 1.20, and 1.21 are put together, it appears that
the estimates of E, the uncompensated wage elasticity of hours of work, from the
American nonexperimental data tend to be more negative than those from the
data collected in the NIT experiments. This difference between the estimates
from the experimental and those from the nonexperimental data conforms to
Metcalf's (1973, 1974) conjecture: the temporary nature of the NIT experiments
will tend to cause the estimate of the mpe to be smaller (in absolute value) and
the estimate of the compensated wage elasticity, E*, to be larger when estimated
from experimental data than their "permanent" values. If this is the case, then
indeed we should expect the estimates of E to be larger when fitted to experimental
then to nonexperimental data. British men appear to be similar to
American men in their value for E, although this E decomposes into a more
negative mpe and a larger E* for the British. If a single number has to be
attached to each of the behavioral responses, then for American prime-age menX~
the (uncompensated) wage elasticity of hours of work is -0.10 and their rope is
- 0.20.
The inf~er~ces in the previous paragraph are drawn from a comparison of the
central tendency of the point estimates in Tables 1.19, 1.20 and 1.21. It would be
misleading to present these summaries without at the same time emphasizing
both the diversity of estimates and the imprecision with which these point
estimates are measured. Moreover, if the estimates are interpreted as tests of the
static model of labor supply (and no doubt some would not want to take this
Ch. 1: Labor Supply of Men 83
step), then the frequency of negative values for the income-compensated wage
elasticity of hours of work casts serious doubt on its empirical relevance.
5. Estimation of the life-cycle model
The discussion of the Life-Cycle Models in Section 3.5 concentrated on those
assuming strong separability of the lifetime utility function and the presentation
of empirical work in this section restricts itself to this class of models. Also, as in
the discussion of the empirical work on static models, I omit discussion of the
estimation of life-cycle labor supply behavior at the macroeconomic level as in
the work of Lucas and Rapping (1969) and others. The reason is in part because
of major aggregation problems: such work normally seeks to explain movements
in aggregate manhours worked and confuses individuals occupying a comer
solution to their allocation problem with those at interior solutions. Indeed, the
larger part of the movement in aggregate manhours over the business cycle is
attributable to movements in the numbers of workers employed and not to
movements in the hours worked of those continuous employed. 101 Because the
microeconomic evidence reported below is restricted to individuals at interior
solutions to their constrained optimization problem, it is not straightforward to
go from these estimates to draw implications about corresponding parameters
estimated with macroeconomic data. 1°2 It is not surprising, therefore, that as
Altonji (1982) has shown the estimates of the macro parameters are by no means
robust with respect to small changes in the assumptions underlying their calcula-
tion.
In the microeconomic research described in this section, it should be remembered
that, although the life-cycle model has important refutable implications
(for instance, the Frisch demand and supply functions possess symmetry, homogeneity,
and sign properties), there has been virtually no work testing the
X°lFor evidence on this, see Coleman (1983). By contrast, Hall (1980, p. 95) claims: "Both
recessions of the 1970's saw pronounced reductions in average hours of work." As Coleman shows,
Hall's inferences are in error. His index of aggregate hours is calculated using both the hours per
worker and the number of workers series from the BLS establishment surveys. His series on total
employment is from the household Current Population Survey. The ratio of aggregate hours from the
establishment survey to numbers employed from the CPS yields a variable hours per worker series,
but it does not correspond to anything observed in the U.S. economy. When Coleman uses either the
ratio of hours to employment both from the establishment surveys or the ratio of hours to
employment both from the CPS, the hours per worker series displayslittle annual variability. In other
words, most of the cyclical variabilityin aggregate manhours is attributable to changes in the number
of workers employed and not to changes in hours worked per employee.
102Often these macroeconomic models are described as if economic agents operate under uncertainty.
As MaCurdy (1982) shows, this further aggravates the problems of identifying from aggregated
data the effect on labor supply of parametric wage changes (which is what Lucas and Rapping
maintain they are measuring).
84 J. Pencavel
empirical relevance of these implications. The life-cycle model has been characterized
as the maintained hypothesis and empirical work has taken the form of
gauging the parameters describing the presumed life-cycle allocation. Of course,
the measurement of the parameters of well-specified models is a necessary
ingredient of any science, but such information is not the same as that derived
from offering the model good opportunities of being refuted and discovering it
has survived such tests of its validity.
As we shall see, these life-cycle models are most convincingly estimated when
the research makes use of successive observations over time of the same individuals
(i.e. panel data). Because an important component of this work involves
regressing changes (over time) in the hours worked of individuals on corresponding
changes in their wage rates, it might be noted that the simple correlation
between these two variables is negative at least in the U.S. data. For instance,
Abowd and Card (1983) report that when changes in the logarithm of hours
worked are regressed on changes in the logarithm of wages rates (controlling for
no other variables) the estimated coefficient is -0.36 for 1531 prime-age male
heads of households in ten years of the Michigan panel and it is -0.28 for 1321
men aged less than 65 years in 1975 in six survey years of the National
Longitudinal Survey of Older Men.1°3 However, in view of the problems documented
in Section 4.2 in measuring hours and wages accurately, there is every
reason to wonder how much of this negative correlation between the observed
values of the variables is attributable to measurement errors and how much to an
association between the true values of the variables. After all, often the wage rate
variable is formed by dividing the respondent's annual earnings by hours worked
so any error in measuring hours will produce a spurious negative correlation
between hours and wage rates and this negative correlation will normally persist
when taking first-differences in the variables.
In addition, both the measured hours and the measured wage rate variables do
not precisely correspond to their counterparts in the economic model. That is,
with respect to wage rates, there are all the problems described in Section 3.3
concerning nonlinear budget constraints (taxes, nonlinear compensation schedules,
etc.) while hours of work are often computed as the product of two variables
(average hours worked per week and weeks worked per year) and therefore are
unlit,,ely to correspond exactly to the true value of the variable. Also, according to
one influential model, labor supply should exclude time spent in on-the-job
training yet the hours reported rarely deduct such human capital investment.
These proble'ms concerning measurement error in wage rates and hours worked
may well be exacerbated by first-differencing the variables because permanent
components in these variables are thereby eliminated and "noise" components
account for a relatively larger part of the measured total. Therefore, if only for
1°3Similarinferencescanbe drawnfromdatain Altonji's(1983)paper.
"r~
f~
~z
.~'=
"N
f~
Ch. 1: Labor Supply of Men
g
g
o
o
U.,
o~,
~ .~ .~
o
z
=o
o o
2 o o o
g
~--.~ ~ ~ ~
~'X3
.... ~ ~
~ 0
c~
o
<
o o o o~Do
-~ ~; ~ ~.~
~ ~-~N .~,~
Z~= o
~ o ~
~'1 0 0
~" ~,~
o
I
o~
~ 0-~ 0
-~ ",.m~-,n
~ ~ 0 ~
Eo
~ d
.o .~ .o
g
F,
~ o~
85
~.£
2~
o
o~
c~u.1
Z=
og
~-~o
..~0
0
86 J. Pencavel
purely statistical reasons, it would seem essential in this work to address
explicitly the problems of measurement error in wages and hours. In fact, these
reasons are compounded by economic considerations arising out of behavior
under uncertainty. Consequently, the research surveyed below is restricted to that
work taking explicit account of measurement error in these variables. 1°4 Table
1.22 contains a summary of estimates of the intertemporal substitution elasticity
and other features of the research.
The archetypal study of male life-cycle labor supply was MaCurdy's (1981). He
specified individual i's utility function at age t to be the addilog:
Ui(xit, hit; Ai,, eit) = bit(xit) ~'1-- ~-lcit( hit) z/, (37)
where
"Y=T 1+1, T >0, 0<'YI<I, bit >O, cit=exp['/ l(-[~Ai,-eit)].
The objective function is thus not merely additive over time, it is also additive in
consumption and hours within any given period. The Frisch hours of work
equation for individual i at age t is
In hit = +i -t- ",/In w i, + BAit + 8t +eit, (38)
where ~bi=),ln)k0i and 8=Tln0. The first term on the right-hand side is
invariant for a given individual over time and is different from individual to
individual. The parameters of eq. (38) supply information on how an individual's
hours of work differ over time in response to anticipated, evolutionary, wage
changes, i.e. wage changes along a worker's wage age profile. The proportional
change in hours of work induced by a proportional increase in wage rates as a
worker ages is measured in eq. (38) by -/> 0, the intertemporal substitution
elasticity.1°5
To estimate eq. (38), MaCurdy used ten annual observations on 513 white,
continuously-married, men from the Michigan PSID who were aged 25-46 years
in 1967 and who were observed in each of the ten years from 1967 to 1976. The
variables in Air could be any whose values did not change over this ten-year
period. The estimates of ~/ from first-differencing eq. (38) ranged from 0.14 to
l°4Abowd and"Card (1983"),do allow for measurement error in wages, but on the other hand they
assume e. in eq. (16) to be zero, i.e. that the researcher knows each individual's utility function
exactly. If their model is augmented to allow for unmeasured characteristics of individuals, then once
these e. are permitted to be correlated for each individual over time Abowd and Card's variance
components procedure no longer identifies the intertemporal substitution elasticity.
l°SBecause the utility function has been assumed to be additive over time, the intertemporal
substitution elasticity is equivalent to the specific substitution elasticity.
Ch. 1: Labor Supply of Men 87
0.35 with standard errors on these coefficients of 0.07 and 0.16, respectively, t°6
When yearly dummy variables were included in the first-differenced form of eq.
(38), -/ was estimated much less precisely although its point estimate changed
little: the point estimates now ranged from 0.10 to 0.45 with standard errors of
0.125 and 0.29, respectively, t°7 By including yearly dummy variables in the
first-differenced equation, the coefficient on the wage rate cannot be interpreted
as the response of labor supply to changes in wages induced by business cycle
forces. So these point estimates implied that, as a male worker ages, a doubling of
his wage rates induces a proportional increase in his hours worked of from ten
percent to 45 percent.
These general inferences from the Michigan PSID have been confirmed by
Altonji (1983) and by Ham (1983). The sample analyzed by Altonji is slightly
different from MaCurdy's1°8 and he also considers the consequences of using
different sets of instrumental variables for the change in In wit. The consequences
for the estimated intertemporal substitution elasticity of the change in the sample
are small: when Altonji uses the same variables MaCurdy used as instruments,
his estimates of 7 center around 0.27 with standard errors about two-thirds of
this value. As an instrument for the change in In wit (where w~t is computed by
dividing total earnings by hours worked), Altonji also uses an alternative measure
of the wage variable derived by asking workers paid on an hourly basis about
their hourly wage rate. Because this information is available for only a subset of
workers, the use of this variable reduces his sample size by about 60 percent. The
estimates of 7 are now around 0.04 with estimated standard errors even larger
than this. Similar results are derived when the lagged value of this alternative
wage variable is used as an instrument. Ham (1983) uses eight years of data from
the Michigan PSID from 1971 to 1979 (including men from the poverty subsampie)
to estimate a different functional form for the Frisch equation, namely, that
postulated by Browning, Deaton and Irish (1983) in eq. (42) below. Evaluated
near the mean values of wages and working hours, Ham's estimates of the
intertemporal substitution elasticity are around 0.04.109 In short, Altonji's and
1°6The higher of these estimates of "y come from adding y In hit to both sides of eq. (38) and
regressing changes in hours on changes in earnings.
l°7The coefficient on t is given by 71nO ~ ~'(p- r) so the coefficients on these yearly dummy
variables (after division by y) may be interpreted as the difference between the rate of time
preference and the rate of interest. MaCurdy's estimates imply that on average r exceeds p by two to
four percentage points,
l°SAltonji uses data from the 12 years of the panel from 1967 to 1978 on continuously married (to
the same spouse) men aged 25-48 years in 1967. He includes observations even if they did not work
in all 12 years, he includes nonwhites as well as whites, and he includes households from the more
heavily sampled low income areas. The result is an increase in the total number of observations from
5,130 to over 8,000.
l°9Ham does not provide information on the mean wage and hours of work of the men in his
sample. I have evaluated his point estimates in Table A1 of his paper at 2100 hours of work and at a
wage of $6.00 per hour. These are approximately the average values of these variables for the
Michigan panel in 1975, the midpoint in Ham's longitudinal data.
88 J. Pencavel
Ham's research with the Michigan PSID underscore MaCurdy's findings of an
intertemporal substitution elasticity whose point estimate is less than 0.45 and
that is not estimated with precision,n°
Section 3.5 maintained that the Frisch labor supply equation may also be used
as the basis for empirical work when agents make decisions under uncertainty.
This is an important point and it is convenient to illustrate this by making use of
the particular utility function (37) above. [The argument here draws liberally on
MaCurdy (1982).] In this case, the first-order condition corresponding to eq. (28)
may be written
In hit = "y In )kit -~- ~l In wit q- [~Ait -~- Eit. (39)
It can be shown that In hit follows a stochastic process with drift and may be
represented as
t l
In'i,= ~ 6j+lnhi0+ ~6,j,
j=0 j=l
where ~Tijis the individual's forecast error at age j that arises from the values of
variables at age j diverging from the values expected (at age j- 1) to obtain at
age j. Substituting this expression for In )kit into eq. (39) and first-differencing
yields:
A In hit = a* + 3,A In wit + flAAit d- eit - eit_ 1q- Oit, (40)
where a* = "y6 and v, = Yvit. Compared with the equation derived by firstdifferencing
eq. (38) (i.e. the certainty case), it is evident that under uncertainty
assumptions have to be made about the nature of the forecast error v~,.Now the
marginal utility of income in period t will depend upon wages, wealth, and the
individual's characteristics in period t and also upon the future path of expected
wages. So suppose y In kit in eq. (39) may be expressed as
N
3' Ink, it = [91,A~, + ~_, gtjgit(ln w ij ) + [~2tKi, + t~i,,
j=t
where Kit is the real value of the consumer's wealth at the start of period t and
n°Altonji also tried to measure the intertemporal substitution elasticity from the within-period
marginal rate of substitution between hours and food consumption. Because substitution within a
branch of the lifetime utility function is being estimated (no essential use is made of intertemporal
data), his period-specificpreferencesare estimatedonly up to a positivemonotonictransformation
and thus the degreeof intertemporalsubstitutabilitycannotbe inferred.Thissameproblemexists(as
they fully recognize)with Blundelland Walker's(1984)research:only the sign of the intertemporal
substitution elasticitymay be inferred,not its numericalmagnitude.
Ch. 1: LaborSupplyof Men 89
the coefficients bit, ?tj, and/~2t change as individuals age. The revision in y In )~it
at age t is
N
l)it=t)lt[hit-~it-l(ait)] q- E ctj[~it(lnwij)-~it-x(lnwij)]
j=t
--I-b2t [Kit- ~it-l( git)] "[-~it- ~it-l( ~it),
where o~it_l denotes individual i's expectations at age t- 1 of the associated
variables. It is implausible to assume that the economist knows each individual's
expectations perfectly and consequently this further restricts the set of variables
that may serve as instruments for A In wit in eq. (40). These must be variables, of
course, that are uncorrelated with unanticipated changes in wage rates, wealth,
and preferences and yet that are associated with A lnwit. Appropriate instruments
are lagged values of wages and prices, variables known by the individual
with certainty at the time that forecasts are made.
Now let us compare MaCurdy's estimates of the intertemporal substitution
elasticity with those derived earlier by Becker (1975) and Smith (1977) who
proceeded by constructing synthetic cohorts from individual observations drawn
from the 1960 Census and the 1967 Survey of Economic Opportunity, respectively.
That is, to say, they grouped individuals by age and averaged observations
over individuals at the same age so that eq. (38) reads
In ht= ~ d- vln Wt~- flat ~-~l q- ~t, (41)
where t denotes each age and the bars indicate means. If the value of ~ is the
same at all ages (i.e. there are no cohort effects), then group means act as
instruments and the ordinary least-squares estimator applied to (41) yields
consistent estimates. In Becker's work, )~was estimated for white men to be 0.448
(with an estimated standard error of 0.105) and for nonwhite men to be 0.098
(with a standard error of 0.040).111 When eq. (41) was estimated in its level form
to individuals sorted by years of schooling, there was a tendency for ~, to fall
with years of schooling. This tendency was not apparent when eq. (41) was
estimated by first-differencing the variables between successive ages. Becker did
not invariably estimate positive values for y although, when negative effects were
estimated, they tended to be small (in absolute value) relative to their estimated
standard errors. In Smith's research the logarithm of the wife's wage rate (again
averaged over individuals at the same age) was included on the right-hand side of
eq. (41). This is consistent with preferences being defined over the hours worked
of the wife as well as over the husband's hours and commodity consumption and
with period-specific utility not being additive in the hours worked by the husband
111These results of Becket's correspond to his use of three-year moving averages of the underlying
data. The estimates from the original observations are similar. Smith's results (to be reported shortly)
also derive from forming three-year moving averages of all variables.
90 J. Pencavel
and by the wife. His estimates of 7 for white married men were 0.322 (standard
error of 0.047) and for black married men were 0.231 (standard error of 0.107).
The estimate of the logarithm of the wife's wage rate (so the effect of an
evolutionary increase in the wife's wage rate on the husband's hours of work) was
negative though typically it was estimated very imprecisely. The effect of the
logarithm of the husband's wage on the wife's hours of work was also negative
though larger (in absolute value and also in relation to its estimated standard
error). A formal test of the symmetry condition of the Frisch male and female
labor supply equations was not conducted.
The most stringent assumption required for data on synthetic cohorts to
identify the intertemporal substitution elasticity is that X0 (or ~) be constant for
all age groups or, if it is not, that it be distributed independently of In wt- In fact,
if after controlling for other effects X0 is lower for those age groups with
currently lower average wage rates (e.g. if younger workers have greater lifetime
wealth, but at present are facing lower wage rates than older workers), then the
coefficient on ln w t in eq. (41) will not identify the intertemporal substitution
elasticity, but will incorporate vintage effects. This cohort bias can be addressed
if synthetic cohorts are constructed in several different calendar years and A0 is
allowed to have a different value for each cohort. In this event, the variables in
eq. (41) would bear a subscript t for the cohort and a subscript k for the
calendar year that the cohort mean was observed. This was precisely how
Browning, Deaton and Irish (1983) proceeded by constructing synthetic cohorts
from successive British Family Expenditure Surveys. In other words, instead of
one observation on each cohort that would derive from a single cross-section of
individuals, Browning, Deaton and Irish had seven observations on each cohort
starting with the tax year 1970/71 and ending with 1976/77. Their cohorts were
categorized in 1970/71 into five-year age-groups from 18-23 years old to 54-58
years old (so there were eight cohorts in all) and for each cohort (and for manual
and nonmanual workers separately) they formed averages for married men. The
hours variable measured weekly hours worked and it was the response to the
Survey's question concerning "normal hours". The wage variable was defined as
the ratio of "normal" wage and salary income per week (after the payment of
income taxes) to "normal hours", the left-hand side variable.
The particular form specified by Browning, Deaton and Irish for the Frisch
labo]~ supply equation was11z
. . . . . . 1/2 - (42)htk = ]l;~+ ~/1G'~ ~/2Yk+ ]/3 In w,k+ ~'4(Pk/Wtk) + "'" + eta,
ll2This Frisch labor supplyequationis derivedby differentiatingthe consumer'sprofitfunction,
//, with respect to w where17 is givenby
17i(~ ,p, w) = ao ~-1 - alp + a2w +2y,~(pw) '/~- 6~p ln(pX) + 7~wln(wk),
and where aI and a2 are permittedto depend uponvariablesother than p, w, and k.
Ch. 1: Labor Supply of Men 91
where the bar indicates the average value of the variable for cohort t in calendar
year k. C denotes a vector of cohort dummy variables, Y a vector of calendar
year dummy variables, and the dots indicate other variables included in the
equation (see Table 1.22). All cohorts were assumed to face the same commodity
prices, Pk, in any calendar year k. If ~ is zero, commodities and male labor
supply are additive within periods. The intertemporal substitution elasticity [the
derivative of the logarithm of htk in eq. (42) with respect to the logarithm of wtk ]
is given by h ~-k113,~- (1/2)'t~( pk/wtk)l/2].
Their estimate of ~,] in eq. (42) was 17.2 with an estimated standard error of
5.5 and their estimate of -/,~ was 26.0 with an estimated standard error of 10.5.
Evaluated at approximate mean values, an intertemporal substitution elasticity of
0.05 was implied. 113 Unlike MaCurdy's results, these estimates were sensitive to
the omission of the calendar year dummies. The estimate of ~,,~ implies that,
within each period, leisure time and commodity consumption are complements.
The first-differenced (over calendar time) version of eq. (42) where A In wt~ and
A(pk/Wtk) 1/2 were instrumented yielded similar point estimates to those from
fitting eq. (42) in level form although standard errors were larger and the test
statistics fell slightly short of standard threshold levels. (See Table 1.22 for the
instruments used.) Again the estimates were sensitive to the omission of the
calendar year dummy variables.
Browning, Deaton and Irish's survey data also provided information on
consumption expenditures though, unlike working hours, these represented actual
and not "normal" consumption. They reported the consequences of estimating
the Frisch commodity demand equation corresponding to eq. (42):
-- c,.1---"-¢'-" c. ~ ~.. c, ." -- \t t 1/2
X,k=O;,tn^~+olc.+o;,nok+Os,,, _, ~ _ , __, +''" -]- ~k , (43)
where symmetry would require 8~ to equal -'~J in eq. (42). 114 The estimated
consumption intertemporal substitution elasticity, the effect of a proportional
increase in p over the life cycle, is measured to be -1.38.115 In the estimates of
eq. (43) and of its first-differenced version, the value of 8~ implied that withinperiod
commodity consumption and leisure time are substitutes, a result contradicting
the estimates of y~ in eq. (42). In the first-differenced equation,
however, the estimate of 8~ is less than its estimated standard error.
113Theseestimates are evaluatedat meanweeklyhoursof workof 43.6 and the approximatemean
of (pk/w,k) a/2, namely1.15.
]14Becauseall cohortsare assumedto facethe samecommodityprices, the vectorof yeardummies
(Yk) and the term InPk cannotbothbe includedin this equation. IncludingInp and excludingY is
equivalent to including Y and restrictingthe coefficientson all the elementsof Y to be the same. In
fact, an F-test did not rejectthat constraint.Equation(43)maybe derivedfromthe consumer'sprofit
functionin footnote 112 by takingthe derivativeof the negativeof H with respect to p.
ix5The consumptionintertemporal substitution elasticityis givenby x t[~ _ (1/2) ~ (w/p)1/2 ].
The statement in the text is derivedby evaluatingtheir estimated eqs. 5.10 and 6.5 at x = 53.3 and
(w/p) 1/2 = 0.87.
92 3". Pencavel
As shown in the discussion of Becker's and Smith's research above, a single
cross-section of individuals may be used to compute the intertemporal substitution
elasticity if synthetic cohorts are constructed from these data. However,
under a string of exacting assumptions, the individual observations from a
cross-section may be used more conventionally to estimate this elasticity. The
essential idea here starts by recognizing that the unobserved variable ~0i is a
function of an individual's lifetime wage path and his initial wealth and it
continues by noting that, if lifetime wages and initial wealth can be expressed as
a function of age and age-invariant characteristics, then ?~0iin the Frisch labor
supply equation may be replaced by these variables. In particular, MaCurdy
(1982) replaced ~ki in eq. (38) by variables measuring each individual's father's
education, his mother's education, the socio-economic status of his parents, and
the individual's own education and then fitted the resulting equation using
observations on 561 white, continuously married, prime-age men from the
Michigan PSID. He estimated this equation with each year's observations from
1967 to 1975 so there were nine separate estimates for the coefficient on In wit,
estimates of 3' according to eq. (38). The estimates of 3' ranged from a low of
-0.07 in the 1975 cross-section to a high of 0.28 in the 1974 cross-section with
estimated standard errors of 0.23 and 0.47, respectively. The simple average of
these nine estimates of 3' was 0.15. Only the age squared and education squared
variables are identifying the variation in predicted wages, so it is not surprising
that none of these nine coefficients passed the conventional thresholds of being
significantly different from zero. These imprecise estimates are not very encouraging
with respect to the use of individual observations from a single cross-section
to measure the intertemporal substitution elasticity in this way.116
To summarize, the estimates to date of the male intertemporal substitution
elasticity, 3', range from -0.07 to 0.45 with a central tendency of 0.20 (see Table
1.22). This means that evolutionary changes in wage rates generate relatively
small changes in the hours worked of men aged from about 25 to 65 years: a 10
percent increase in his wages will induce about a 2 percent increase in his hours
worked. The estimated standard errors surrounding these point estimates are also
worthy of note: as often as not, the null hypothesis that hfe-cycle changes in
wages have no effect on hours worked by prime-aged men cannot be rejected at
conventional levels of significance. There is ample support here for someone
whose research ignores the effects of evolutionary changes of wages on male
hours worked.
It is importar~t to note that the research described in the preceding paragraphs
is directed towards only One part of the life-cycle characterization; it supphes
n6MaCttrdy (1983) uses cross-section consumption data from the Denver Income Maintenance
Experiment to estimate the within-period marginal rate of substitution between commodity consumption
and hours of work and then proceeded to the longitudinal dimension of the data to estimate a
particular monotonic transformation of the utihty function. The 121 men studied appear to display
implausibly large wage elasticities though the reasons for the peculiar results are not apparent.
Ch. 1: Labor Supply of Men 93
information on how an individual will allocate his working hours as he ages in
response to evolutionary changes in his wage rates. In addition, there is the
question of the response of labor supply at any age to changes in the entire wage
profile. That is, two individuals both at age t' and facing the same wages at t'
will supply different hours of work at t' (and at all other ages) if their entire
life-cycle wage profiles differ (i.e. if their wages at ages other than t' differ).
Answering this question requires relating each individual's marginal utility of
wealth variable, X0i, or its transform such as ~k~in eq. (38) to each individual's
lifetime budget constraint variables, his rate of time preference, Ait , and e~t. For
male workers this second step seems to have been undertaken only by MaCurdy
(1981) who relates his estimated fixed effects for different workers in eq. (38) to
exogenous, age-invariant variables that determine each individual's lifetimebudget
constraint. These variables consist of family background characteristics, terms in
the individual's own schooling, and estimated parameters describing the life-cycle
growth in wage rates and initial nonwage income. His estimates suggest that, if a
consumer experiences a ten percent increase in wage rates at all ages, he will
increase his hours of work at all ages by between 0.5 and 1.3 percent. Again, the
supply schedule of male hours of work is relatively inelastic w:~threspect to the
life-cycle wage profile.
Empirical research at the microeconomic level on male life-cycle labor supply
is barely a few years old so surely it is premature to offer a confident evaluation
of its performance. Some provisional judgments can be made, however. Does the
extensively-used intertemporally additive model incorporate the essential features
of life-cycle decision-making? The capacity of the model to take account of many
aspects of intertemporal decision-making is really quite impressive. Not merely
can it, in principle, be set in a context of uncertainty, but it can be generalized to
allow for human capital investment, transactions costs associated with the
purchase of consumer durables, and a variety of capital market imperfections
(such as differential borrowing and lending rates of interest or transactions costs
in financial capital markets). See MaCurdy (1981b). These are all prevalent
features of the economy so their tractability within this fife-cycle model adds to
its appeal.
At the same time, the empirical implementation of this model already makes
great demands on available data and augmenting the model to allow for these
additional features probably exceeds the capacities of current data sets. If this is
the case, then one respoiase is to embark on the collection of more mid more
detailed information. Perhaps this should be done, but it should not proceed
without some assessment of whether this extraordinary effort and expense will
yield sufficiently high returns and this, in turn, requires some evaluation of
whether the relationships emphasized in the fife-cycle literature are important
enough to account for the key variations in male labor supply.
At this stage of the research, the focus of the fife-cycle research has been upon
the labor supply responses to evolutionary movements in wages. The evidence to
94 J. Pencavel
date indicates that these labor supply responses for prime-age men are very
inelastic with respect to life-cycle changes in wages. Similarly, across male
workers, the labor supply responses to differences in entire wage profiles appear
to be small. In other words, the greater part of the variations in male labor
supply across workers and over time is left unexplained by this research.n7 A
great deal of effort has been brought to bear on what appears to be relationships
of second-order of importance.
6. Conclusions
A great deal of research, much of it careful and some of it ingenious, has been
undertaken on male labor supply during the past two decades. The vast proportion
of that work-both that based on the static model and that based on the
life-cycle model-indicates that the elasticities of hours of work with respect to
wages are very small. In other words, the focus of most economists' research has
been on behavioral responses that for men appear to be of a relatively small
order of magnitude. In the case of applications of the static model of labor
supply, there are a number of instances in which the income-compensated wage
elasticity of hours of work is estimated to be negative. This, of course, violates an
important (some would judge it to be "the" important) implication of that model
and consequently it casts doubt on the empirical relevance of the model.
Of course, the static model can always be rescued from such a conclusion by
arguing that what is at fault is not the allocation model itself, but rather the
string of auxiliary hypotheses (assumptions about functional forms, measurement
of the variables, etc.) that are required to apply the theory. Logically, this is a
fully defensible position: that the theory's implications are at variance with
observation means that at least one (and perhaps no more than one) of the
hypotheses associated with the theory and its application is refuted. The problem
with this defence is that, if the auxiliary hypotheses are continually being called
upon to "save" the theory, then this comes close to denying the theory can ever
be tested. It is not as if the model has already survived many different attempts to
refute it. If this were the case, a few instances of its apparent failure might be
attributed to the nonsatisfaction of the auxiliary assumptions. But, with this
mode!, few scholars have conducted their research with the aim of testing the
theory; most have been interested in quantifying a relationship whose existence is
presumed to be true. As a by-product of this concern with measurement, they
ll7$ome indication of this is provided by the consequences of fitting the hours of work equation
whose estimates are reported in Table 1.17 above to the sample of 23,059 men stratified by years of
age. In other words, I estimated 31 ordinary least-squares regressions, each one fitted to the hours
worked and other data for men at each of the 31 years of age from 25 years to 55 years. All the
right-hand side variables listed in Table 1.17 (except, of course, the age variables) were used as
regressors. The size of the samples ranged from 514 men for those aged 55 years to 1,154 men for
those aged 32 years. As illustrative of the poor explanatory power of the estimated linear combination
of the right-hand side variables, the central tendency of the R2s in these equations was 20% with a
range extending from a high of 0.307 for men aged 45 years to a low of 0.135 for men aged 48 years.
Ch. 1: Labor Supply of Men 95
have turned up a number of instances in which the behavioral responses take on
values that violate the theory's predictions. Under these circumstances, the
scientific procedure is surely to regard the theory as it has been formulated and
applied to date as having been refuted by the evidence.
This does not mean that budget constraints have nothing to do with male
hours of work. On the contrary, evidence from the Negative Income Tax
experiments strongly suggests that changes in male work behavior are not
independent of changes in their budget constraints. So prices and wages affect
work decisions, but perhaps not in the particular way described by the familiar
constrained utility-maximizing model. Or this model may be an apt description
of some of the population, but a different characterization of behavior may be
more appropriate for others. In this case, no single model of labor supply is
adequate to account for the behavior of all individuals.
There is still much more work to be done with the canonical model. My severe
judgments about its empirical relevance will have to be revised if it is shown that
its apparent shortcomings to date are, in fact, the consequence of the manner in
which it has been applied. If this is the case, then I hope more research with
individual or household data will be conducted into the model's implications for
the consumption of commodities and for savings. Consumption and savings
behavior is supposed to be part of the same allocation process as hours of work
and yet the empirical work on these issues has only recently explicitly recognized
this. Also, I hope more will be done to integrate time spent in unemployment
with decisions concerning hours of work. Current research treats unemployment
in different ways: sometimes unemployment is classified as a state indistinguishable
from being out of the labor force; sometimes time spent in unemployment is
simply added to hours worked in the belief that both activities represent the
supply of time to market activities; and sometimes time spent in unemployment
is characterized as part of the optimal allocation of an individual's scarce
resources, but as behaviorally distinct from hours worked. Little research has
been directed towards determining which of these different treatments is the
correct one. Furthermore, given the substantial resources that have already been
directed towards measuring the effects of wages on work behavior and given the
relatively small responses to wages that have been estimated for men, it would be
useful if economists redirected some of these efforts into accounting more
satisfactorily for variations in labor supply that are associated with other variables.
In particular, because only a relatively small proportion of the variation in
hours of work of prime-age men in the population is removed by the set of
variables on which information is collected in most surveys, we need to know
more about what this "unobserved heterogeneity" represents. Are these differences
attributable to differences in the particular forms of the employment
contracts under which individuals work? Are they associated with differences in
discount rates among individuals? Are they attributable to attitudes and values
that seem to be acquired from parents? There is a great deal that we do not know
and that is waiting to be discovered.
96 J. Pencavel
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