ECONOMETRICA jfiUftHAi nr t ii r t.r n ko\i r.rn i r *gi:iety Efficiency Wages and the Inter-Industry Wage Structure Author(s): Alan B. Krueger and Lawrence H. Summers Source: Econometrics, Vol. 56, No. 2 (Mar., 1988), pp. 259-293 Published by: The Econometric Society Stable URL: http://www.,jstor.org/stable/1911072 Accessed: 18-03-2015 10:40 UTC Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. The Econometric Society is collaborating with JSTOR to digitize, preserve and extend access to Econometrics. STOR http://www.jstor.org This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:40:10 UTC All use subject to JSTOR Terms and Conditions Econometrica, Vol. 56, No. 2 (March, 1988), 259-293 EFFICIENCY WAGES AND THE INTER-INDUSTRY WAGE STRUCTURE By Alan B. Krueger and Lawrence H. Summers1 This paper empirically tests and rejects classical competitive theories of wage determination by examining differences in wages for equally skilled workers across industries. Human capital earnings functions are estimated using cross-sectional and longitudinal data from the CPS and QES. The major finding is that the dispersion in wages across industries as measured by the standard deviation in industry wage differentials is substantial. Furthermore, F tests of the joint significance of industry dummy variables are decisively rejected. These differences are very difficult to link to unobserved differences in ability or to compensating differentials for working conditions. Fixed effects models are estimated using two longitudinal data sets to control for constant, unmeasured worker characteristics that might bias cross-sectional estimates. Because measurement error is a serious problem in looking at workers who report changing industries, we use estimates of industry classification error rates to adjust the longitudinal results. In the fixed effects analysis, the industry wage differentials are sizable and are very similar to the cross-sectional estimates. In addition, the fixed effects estimates are robust under a variety of assumptions about classification errors and are similar using both data sets. These findings cast doubt on explanations of industry wage differentials based on unmeasured ability. Additional analysis finds that the industry wage structure is highly correlated for workers in small and large firms, in different regions of the U.S., and with varying job tenures. Finally, evidence is presented demonstrating that turnover has a negative relationship with industry wage differentials. These findings suggest that workers in high wage industries receive noncompetitive rents. Keywords: Industry wage structure, efficiency wages, rent sharing, fixed effects, measurement error, labor turnover. The essential feature of a perfectly competitive labor market is that workers who accept jobs can expect to receive compensation equal to their opportunity cost. Firms pay a wage that is just sufficient to attract workers of the quality they desire and no higher. Competitive theory makes a strong prediction about the structure of wages. Job attributes which do not directly affect the utility of workers should have no effect on the level of wages. Alternative theories such as the efficiency wage formulations surveyed by Stiglitz (1986) suggest that job attributes having nothing to do with the utility workers receive on the job should have systematic effects on wages because they influence the optimal wage for firms to choose. As Stiglitz (1986), Bulow and Summers (1986), and many other authors have argued, efficiency wage theories have positive and normative implications very different from those of more standard competitive models. 1 We would like to thank Steven Allen, David Bloom, John Bound, William Dickens, Richard Freeman, Robert Hutchens, Lawrence Katz, Edward Lazear, Jonathan Leonard, James Medoff, and Robert Topel for helpful comments. We are also grateful to Chris Cavanagh, Aaron Han, and Bruce Meyer for valuable assistance in deriving the correction for measurement error in dummy variables in longitudinal data. Dickens and Katz (1986a) have independently carried out an analysis which is similar to this one in many respects. Our study differs from theirs primarily in our focus on longitudinal data. We note other differences in the text. Summers' research was supported by the NSF and the Sloan Foundation. Data and computer programs underlying this research are available on request This content downloaded from 147.251.1SJ9127 on Wed, 18 Mar 2015 10:40:10 UTC All use subject to JSTOR Terms and Conditions 260 ALAN B. KRUEGER AND LAWRENCE H. SUMMERS This paper examines the magnitude of wage differentials for equally skilled workers. We focus on the role of industry affiliation in explaining relative wages. Our findings suggest that a worker's industry exerts a substantial impact on his wage even after controlling for human capital variables and a variety of job characteristics. We are led to conclude that there are important variations in wages which cannot be explained by standard competitive theories. These findings complement demonstrations of important relationships between firm size and wages (e.g. Brown and Medoff (1985)) and of large intra-industry wage differences (e.g. Dunlop (1957) and Groshen (1986)) in suggesting the importance of developing and testing alternative models of wage determination even in nonunion settings. We focus on efficiency wage theories as an explanation for the setting of wages. Any economic theory that explains why wages deviate from their standard competitive level must in a tautologous sense explain why firms find it profitable to pay noncompetitive wages. In this sense, any explanation of noncompetitive wages must have an efficiency wage element. That is, it must postulate that over some range profits are an increasing function of the wage rate offered. In some cases, the efficiency wage theory is a triviality. For example, firms may find it unprofitable to violate minimum wage laws because of the fines that will be imposed. Or it may be necessary to pay supra-competitive wages to unionized workers in order to avoid strikes. Our principal interest is however in "pure" efficiency wage models in which firms can find it profitable to raise wages even when they will not be punished by some outside party for failing to do so. The limited evidence that is available suggests that high paying industries may benefit by reducing turnover as suggested by efficiency wage theories. The paper is organized as follows. Section 1 briefly discusses the possible role of efficiency wage theories in explaining wage differentials. Section 2 presents our basic econometric results using data from the Current Population Survey (CPS) and documents the existence of substantial inter-industry variations in wages. Section 3 considers labor quality differences as an explanation of the industry wage structure. By providing fixed effects estimates we cast serious doubt on "unmeasured labor quality" explanations for inter-industry wage differences. Section 4 considers and rejects a number of other possible reconciliations of the results with competitive theory. We present evidence suggesting that wage differentials cannot be attributed to union effects, the short run immobility of labor, or compensating differentials. Section 5 provides some evidence that high wages are efficacious in reducing turnover and thus provides some additional evidence that workers in high wage industries receive rents. Section 6 concludes the paper by reviewing some broader evidence on the importance of industry wage differentials, and by reviewing evidence on the importance of these differentials for economic theory and policy. 1. EFFICIENCY WAGE THEORIES Economists have a clear understanding of how perfectly competitive labor markets without any information or contracting problems would function. Equally productive workers would receive compensation packages that provide equal This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:40:10 UTC All use subject to JSTOR Terms and Conditions EFFICIENCY WAGES 261 levels of utility. Wages would depend only on workers' abilities and not on characteristics of their employers that do not influence other nonpecuniary benefits of employment. Falsification of this prediction would force consideration of alternative theories that predict linkages between job characteristics and wages. Any such theory has the property that at least some employers must be paying more than the going wage for workers of the type they attract. This behavior can be rationalized only by assuming that some firms do not profit maximize, or that some firms find that increasing wages above the going rate is profitable. The latter possibility is the defining characteristic of efficiency wage theories. At least four conceptually distinct efficiency wage theories may be adduced as possible rationales for the payment of noncompetitive wages. Our goal in this paper is to demonstrate the potential importance of efficiency wages, not to distinguish among alternative motives for paying them. We therefore describe these motives only briefly. For formal presentations of the relevant models, and references to the relevant literature, see Stiglitz (1984) and Katz (1986). The profitability of raising wages at least in .some circumstances has been asserted by many authors including Adam Smith, Karl Marx, Alfred Marshall, Henry Ford, and Max Weber. A first model of efficiency wages postulates that they are paid in order to minimize turnover costs. If firms must bear part of the costs of turnover, and if turnover is a decreasing function of the wages firms pay, there may be an incentive to raise wages in order to minimize turnover costs. A second possibility is that increasing wages raises workers' effort level. Workers who are paid only their opportunity costs have little incentive to perform well since losing their jobs would not be costly. By raising wages, firms may make the cost of job loss larger and thereby encourage good performance. Alternatively, a third model postulates that workers' feelings of loyalty to their firm increase with the extent to which the firm shares its profits with them. These feelings of loyalty may have a direct effect on productivity. As expounded by Akerlof (1984) such a model relies on notions about gift relationships that are not well captured by traditional utility functions. A final model is based on selection rather than incentive efforts. Firms which pay higher wages will find that they attract a higher quality pool of applicants. If quality is not directly observable, this will be desirable. If all firms were identical, one would not expect to see different firms paying different wages even if efficiency wage considerations were important. But when there are differences in their ability to bear the costs of turnover, to supervise and monitor their workers, or to measure labor quality, either because of differences in management capacity, or because of differences in the technology of production, then the optimal wage to pay will vary. Thus efficiency wage models unlike standard competitive formulations can explain why characteristics of firms that do not directly affect workers' utility can affect wage rates. It should be clear that demonstrations that similar workers can over long periods of time be paid different wages in different industries makes plausible the idea that some workers are involuntarily unemployed, for involuntary unemploy- This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:40:10 UTC All use subject to JSTOR Terms and Conditions 262 ALAN B. KRUEGER AND LAWRENCE H. SUMMERS ment can simply be thought of as confinement to a low wage home production industry. Previous Studies Previous studies have examined the effect an employee's industry has on wages to test segmented labor market theories that are closely related to the efficiency wage models considered here. Sumner Slichter (1950) was among the first economists to study the industry wage structure. After examining the average hourly wage rate of skilled and unskilled male workers in manufacturing industries between 1923 and 1946, Slichter was struck by the magnitude of industry wage differences for comparable workers. Slichter found several "regularities" in the wage structure. First, he found the average unskilled wage rate in an industry to vary positively with the average hourly earnings of semi-skilled and skilled workers in the industry. Second, he found that industry wages are positively correlated with value added per worker in the industry, positively correlated with profit margins, and negatively correlated with the payroll to income ratio. And lastly, he found that "the wage structure changes over time, but the changes are fairly slow and the wage structure between industries within a period of twenty or thirty years exhibits only moderate changes." Slichter theorized that these facts were evidence that " managerial policy" is important in wage setting. Thurow (1976) phrases the question as follows: "Earnings data and earnings equations are often corrected for both industry and geographic location, but should they be? Wage payments in a marginal-productivity world are supposed to be made on the basis of the skills supplied and not dependent upon the industry or region of use." The answer he finds is that "industry and geographic variables are significant in individual earnings functions____This significance, itself, constitutes a deviation from the norms of a competitive market." Using regression analysis, Wachtel and Betsey (1972) analyze the impact of one digit industries and three occupation groups on the residual of wages after controlling for education, experience and demographic factors. Like Thurow they conclude that " there is a substantial portion of the variance in wage earnings that can be explained by industry structure after the effects of personal characteristics have been eliminated." They further find that an employee's industry and occupation pair is more "important" in explaining wages than other "structural characteristics," such as union status and geographic location. After carefully reviewing the empirical studies on dual labor market theory, Cain (1976) concludes that the importance of industry affiliation in determining wages is the most convincing evidence in support of dual labor markets.2 2 Recently, Dickens and Lang (1985) examine the returns to education and experience across sectors. Their estimating technique allows for the simultaneous determination of the worker's sector and the characteristics of the sectors. As a result they can test whether primary sector jobs are rationed. They conclude that returns to experience and education differ across sectors, and that some workers are involuntarily confined to secondary sector jobs. This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:40:10 UTC All use subject to JSTOR Terms and Conditions EFFICIENCY WAGES 263 However, Cain aptly cautions that the industry effects on wages "may represent transitory demand factors, compensating nonpecuniary effects, or unmeasured human capital variables." These possibilities have not been adequately addressed in the existing empirical studies purporting to establish the importance of labor market segmentation. The empirical work reported below takes up Cain's challenge and examines possible competitive explanations for inter-industry wage differences. 2. DATA, METHODOLOGY, AND BASIC RESULTS In textbook neoclassical labor economics an employee is compensated according to his or her opportunity cost, which is determined by accumulated human capital and the employer's work environment. If an employee's industry is a significant factor in determining wages after controlling for labor quality and working conditions we must look beyond the standard competitive theory and ask why firms choose to pay workers more than their alternative wage. Our initial empirical analysis of industry wage differentials is based on cross-sectional data on individuals collected by the Bureau of the Census for the May 1974, 1979, and 1984 Current Population Surveys. The May CPS contains labor force data for members of the sampled households who are 14 years old or older. In May 1979 the Bureau of the Census asked additional questions on tenure, firm size, plant size, and fringe benefits of a randomly selected sample of households for its Pension Supplement. All of our results for 1979 are based on the Pension Supplement.3 The samples we analyze contain full and part-time private non-agricultural employees 16 years old or older. The earnings variable is usual weekly earnings divided by usual weekly hours. We considered employees who reported earning less that $1.00 an hour or greater than $250.00 an hour to be outliers and eliminated them from the sample. We estimate several standard cross-section wage equations in order to examine the importance of industry affiliation in explaining relative wages. Our strategy is to control for human capital, demographic background, and working conditions as well as possible, and then analyze the effect of industry dummy variables on relative wages. We normalize the estimated industry wage differentials as deviations from the (weighted) mean differential.4 Table I presents results of separate cross-section regressions of log wage on one digit census industries (CIC) with human capital and demographic controls for 1974, 1979, and 1984. The human capital and demographic controls are 9 occupation dummy variables, education, age, sex, race, union status, a central 3 Results are qualitatively the same when the full 1979 sample is used. 4 Since the wage regressions include a constant, we treated the omitted industry variable as having a zero effect on wages, calculate the employment-weighted average of wage differentials for all industries, and report the difference between the industry differentials and the weighted average. The resulting statistics are the proportionate difference in wages between an employee in a given industry and the average employee. The standard errors we report, however, are the unadjusted OLS standard errors. This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:40:10 UTC All use subject to JSTOR Terms and Conditions 264 ALAN B. KRUEGER AND LAWRENCE H. SUMMERS TABLE I Estimated Wage Differentials for One-Digit Industries—May CPS' (Standard Errors in Parentheses) (i) (2) (3) (4) 1984 Total Industry 1974 1979 1984 Compensation Construction .195 .126 .108 .091 (.021) (.031) (.034) (.035) Manufacturing .055 .044 .091 .131 (.020) (.029) (.032) (.032) Transportation & Public Utilities .111 .081 .145 .203 (.021) (-031) (.034) (-034) Wholesale & Retail Trade -.128 -.082 -.111 -.136 (.020) (.030) (.033) (.033) Finance, Insurance and .047 -.010 .055 .069 Real Estate (.022) (.035) (.034) (.034) Services -.070 -.055 -.078 -.111 (.021) (.030) (.032) (.032) Mining .179 .229 .222 .231 (.035) (.058) (.075) (.075) Weighted Adjusted Standard Deviation of Differentials11 .097** .069** .094** .126** Sample Size 29,945 8,978 11,512 11,512 a Other explanatory variables are education and its square, 6 age dummies, 8 occupation dummies, 3 region dummies, sex dummy, race dummy, central city dummy, union member dummy, ever married dummy, veteran status, marriage X sex interaction, education X sex interaction, education squared X sex interaction, 6 age X sex interactions, and a constant. Each column was estimated from a separate cross-sectional regression. b Weights are employment shares for each year. ** F test that industry wage differentials jointly equal 0 rejects at the .000001 level. city dummy, marital status, veteran status, and several interaction terms.5 Table II presents comparable results for two-digit CIC industries and Appendix Table Al contains comparable results for 1984 for three digit CIC industries. The industry dummy variables are jointly statistically significant and they are generally statistically significant individually as well. The results are qualitatively the same when the samples are restricted to nonunion workers. Furthermore, the industry variables have a sizable impact on relative wages. The coefficient for mining in Table II for 1984, for instance, implies that the average employee in the mining industry earns wages that are 24 per cent higher than the average employee in all industries, after controlling for human capital and demographic background. In 1984 the industry differentials ranged from a high of 37 per cent above the mean in the petroleum industry to a low of 37 per cent below the mean in private household services. These large wage differentials suggest that other factors besides opportunity costs are important in explaining wages. The industry variables are very important in explaining variations in log earnings. As an indication of their importance, the standard error of the regression falls by 4.3 percentage points once industry controls are added to a 5 We return to the effects of unions in Section 4. This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:40:10 UTC All use subject to JSTOR Terms and Conditions EFFICIENCY WAGES 265 TABLE II Estimated Wage Differentials for Two-Digit Industries—May CPS (Standard Errors in Parentheses) (1) (2) (3) (4) 1984 Total Industry 1974 1979 1984 Compensation Mining .203 .263 .241 .253 (.022) (.031) (.033) (.033) Construction .228 .137 .126 .112 (.011) (.016) (.020) (.020) Ordnance .202 .091 NA NA (.040) (.067) NA NA Lumber .003 -.035 .001 .038 (.021) (.037) (.037) (.037) Furniture -.059 -.120 -.006 .014 (.025) (.036) (.048) (.048) Stone, Clay & Glass .032 .052 .085 .137 (.022) (.034) (.044) (.044) Primary Metals .082 .114 .162 .262 (.016) (.026) (.037) (.037) Fabricated Metals .057 .039 .071 .132 (.015) (.026) (.033) (.033) Machinery, Excl. Elec. .083 .092 .185 .221 (.013) (.022) (.024) (.024) Electrical Machinery .055 .045 .107 .135 (013) (.021) (.025) (.025) Transport Equipment .120 .156 .191 .267 (.014) (.021) (.025) (.025) Instruments .086 .137 .139 .167 (.025) (.040) (.041) (.041) Misc. Manufacturing -.116 -.110 .014 .034 (.024) (.042) (.053) (.053) Food .010 .019 .057 .109 (.015) (.026) (.027) (.027) Tobacco -.007 -.040 .340 .527 (.063) (.156) (.129) (.129) Textiles -.010 -.034 .011 .023 (.019) (.034) (.039) (.039) Apparel -.087 -.132 -.127 -.123 (.016) (.030) (.032) (.032) Paper .057 .088 .141 .178 (.020) (.033) (.039) (.039) Printing .052 .039 .092 .095 (.017) (.028) (.028) (.028) Chemical .157 .148 .221 .266 (.018) (.029) (.033) (.033) Petroleum .238 .278 .371 .619 (.036) (.062) (.073) (.073) Rubber .007 .023 .054 .098 (.021) (.036) (.041) (.041) Leather -.097 -.233 -.082 -.062 (.034) (.051) (.060) (.060) Railroad .200 .120 NA NA (.023) (.037) NA NA Other Transport .090 .120 .132 .160 (.014) (.022) (.022) (.022) Communications .159 .064 .171 .293 (.016) (.027) (.029) (.029) Public Utilities .138 .068 .259 .336 (.021) (.028) (.032) (.032) This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:40:10 UTC All use subject to JSTOR Terms and Conditions 266 ALAN B. KRUEGER AND LAWRENCE H. SUMMERS TABLE II (Continued) (i) (2) (3) (4) 1984 Total Industry 1974 1979 1984 Compensation Wholesale Trade .035 -.015 .047 .025 (.012) (.020) (.020) (.020) Eating & Drinking -.267 -.125 -.189 -.219 (.012) (.020) (.021) (.021) Other Retail -.141 -.093 -.155 -.186 (.030) (.050) (.067) (.067) Banking .081 -.063 .064 .092 (.014) (.031) (.022) (.022) Insurance .048 .022 .071 .075 (.013) (.027) (.021) (.021) Private Household -.151 -.259 -.366 -.517 (.019) (.034) (.033) (.033) Business Services -.053 -.067 .000 -.031 (.016) (.028) (.023) (.023) Repair Services -.126 -.026 -.056 -.087 (.021) (.032) (.034) (.034) Personal Services -.216 -.107 -.154 -.194 (.015) (.025) (.025) (.025) Entertainment -.145 -.078 -.141 -.163 (.023) (.036) (.034) (.034) Medical Services -.052 -.039 -.082 -.078 (.015) (.022) (.023) (.023) Hospitals .039 .063 .059 .062 (.013) (.018) (.023) (.023) Welfare Services -.333 -.190 -.246 -.330 (.022) (.032) (.027) (.027) Education Services -.127 -.185 -.194 -.216 (.016) (.019) (.028) (.028) Professional Services .085 .060 .062 .023 (.016) (.029) (.026) (.026) Weighted Adjusted Standard Deviation of Premiums .132** .108** .140** .177** See Table I notes. Sample sizes are the same as in Table I. regression that already controls for occupation, human capital, and demographic factors (the complete variable list is given in note a of Table I). In comparison, the union variable only decreases the standard error of the regression by 1.6 percentage points, the human capital controls reduce the standard error by 5.1 percentage points, and race and sex controls reduce the standard error by .2 percentage points when they are added to the same regression. This suggests that if industry wage differences are noncompetitive they have far greater impacts on the allocation of resources than do the wage differences associated with unions or discrimination. Some general observations can be made about the industry wage structure. Durable manufacturing products and chemical industries tend to be high wage industries while wholesale, retail, and service industries tend to be low wage industries. In 1984, for instance, workers in the capital intensive, technologically sophisticated chemical industry were paid 22 per cent more than the average This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:40:10 UTC All use subject to JSTOR Terms and Conditions EFFICIENCY WAGES 267 employee, while workers in the customer oriented retail trade industries were paid 16 per cent to 19 per cent less than the average employee, all else constant. To summarize the overall variability in industry wages we focus on the standard deviation of the industry wage differentials. Although for each industry / = (1,..., K) the estimated wage differential /?, is an unbiased estimate of the true wage differential /?,., the standard deviation of /? is an upwardly biased estimate of the standard deviation of /?. This bias occurs because /?, equals /?,■ + e;, where e, is a least squares sampling error. We adjust the standard deviation of /? by using the formula: (10) SD(/3) « y var(/?) - £ 6}/K where a, is the standard error of /?,. Because this adjustment neglects the covariances among the e,-, it slightly underestimates the standard deviation of /?.6 Industry variations in relative wages are substantial. In 1984 the employment-weighted standard deviation of two digit CIC industry wage differentials was 14 per cent, in 1979 the standard deviation was 11 per cent, and in 1974 the standard deviation was 13 per cent. Thus cross-sectional estimates imply that changing between typical industries has about the same impact on wages as does changing union status. Nonwage Compensation Fringe benefits are an important component of compensation, accounting for as much as 40 to 50 per cent of total compensation in some companies. To adjust for variation in fringes across industries, we multiplied the CPS hourly wage data for each worker by the ratio of total labor costs to wages in the corresponding industry. The industry labor cost and wage data are reported in the National Income and Product Accounts (NIPA). The results of wage regressions with the dependent variable adjusted to reflect nonwage compensation are reported in column (4) of Tables I and II. Since the NIPA and CPS classification schemes do not match perfectly, caution should be taken in comparing these results to the CPS results. Nonetheless, Tables I and II show that consideration of nonwage compensation reinforces rather than reduces industries wage differences. For instance, the wage differential in primary metals 6 The expected value of the variance of /? is given by £[var(/?)]=var(/3)+X; |-£ £ °f2 1 = 1 l = \ J = l where o2 = £(e,2) and o,.y = £(£,£,). Since £(o,2/*0 -EE(o,/AT2) > 0, it follows that £[var(/2)] > var(/?). Standard deviations reported in the text do not adjust for covariance terms in the above equation and thus in expected value underestimate the true standard deviation. However, experimentation with the 1984 CPS shows that accounting for covariance terms increases the estimated standard deviation by only .0007. This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:40:10 UTC All use subject to JSTOR Terms and Conditions 268 ALAN b. KRUEGER AND LAWRENCE h. SUMMERS increases from 16 per cent above the mean to 26 per cent above the mean when we take account of nonwage compensation. Accounting for nonwage benefits tends to increase industry wage dispersion. Wage Differences Through Time Over time both the one and two digit CIC industries show a stable pattern of inter-industry wage variability. The standard deviation of estimated wage differentials shows no trend during the years we studied and the differentials are highly correlated from year to year. Between 1984 and 1979 the correlation in estimated industry wage differentials is .915 and between 1984 and 1974 the correlation is .911. As further evidence of the stability of the inter-industry wage structure over time, Krueger and Summers (1986) find a correlation of .56 between the industry wage differentials for 1984 and the average wage of unskilled male manufacturing workers in 1923.7 Like Slichter, we conclude that the industry wage structure remains fairly constant over time. The stability of the industry wage structure casts doubt on explanations of wage differentials based on the short run immobility of labor or transitory labor demand shocks. It is unlikely that labor is sufficiently immobile over several decades or even one decade to allow such large differentials to persist. In apparent contrast to the predictions of a naive competitive model, we find that the industry an employee is in has a statistically significant and sizable impact on wages even after controlling for supply-side factors. Furthermore, these relative wage differentials persist at about the same level over time, which is inconsistent with explanations based on the short run immobility of labor and the effects of transitory demand shocks. Next we examine other possible competitive rationalizations for our results. 3. LABOR QUALITY EXPLANATIONS OF INDUSTRY WAGE DIFFERENTIALS Perhaps the most plausible competitive explanation for our findings is that there are differences in unmeasured aspects of labor quality across industries. The limited human capital variables available in the Current Population Survey may not adequately control for labor quality. It could be argued that unmeasured labor quality differences, such as motivation and innate ability, vary systematically across industries and are being " picked-up" by the industry controls rather than the human capital controls. As a first approach to this problem, Table III explores the impact of alternative degrees of control for human capital on inter-industry wage variation. If industry wage differentials were due to measured and unmeasured labor quality differences across industries we would expect a substantial fall in the dispersion of industry wages once we control for measured human capital. However, the 7 It should be noted that these raw correlations are underestimates due to sampling errors. This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:40:10 UTC All use subject to JSTOR Terms and Conditions EFFICIENCY WAGES 269 TABLE III Alternative Degrees of Control for Labor Quality—May 1979 CPS, Pension Supplement Weighted Adjusted sd of Industry Wage Correlation Controls Differentials With Table II (1) 8 occupation dummies, sex, nonwhite, region dummies (3), central city dummy, union dummy, ever married, ever married* sex, and veteran status .114** .994 (2) Row (1) controls plus 12 age structure variables .108** .998 (3) Row (2) controls plus 4 education variables .108** 1.000 (4) Row (3) controls plus 4 tenure variables .104** .995 ** F test that industry wage differentials jointly equal 0 rejects at the .00001 level. addition of human capital controls—education, tenure, and age—results in only a one percentage point drop in the standard deviation of the wage differentials in the 1979 CPS Pension Supplement. Despite the increased controls for labor quality the standard deviation of industry wages remains above 10 per cent. Unless one believes that variation in unmeasured labor quality is vastly more important than variation in age, tenure, and schooling, this evidence makes it difficult to attribute inter-industry wage differences to differences in labor quality.8 We further address the problem of unmeasured, unchanging labor quality by analyzing longitudinal data. With these data we can compare the wages of the same person as he or she switches industries. The longitudinal analysis addresses the problem of unmeasured labor quality in the cross-sectional results, but is not without potential biases. These biases include the selectivity of job switchers and increased measurement error. These issues are addressed in the results reported below. Two longitudinal data sets are analyzed. The primary data set was created by pooling three matched May CPS data sets. Since CPS cannot match individuals who changed their address during the year, the sample is not completely representative. Nonetheless, the Census Bureau reports that about 70 per cent of respondents were matched from one year to the next. The data set contains 18,541 employees, and 2,137 of these workers report changes in their one digit industry during the year. However, evidence from Mellow and Sider (1983) who used direct evidence obtained from the employers of a subset of a CPS sample to 8 Evidence suggests that unmeasured ability and upbringing have surprisingly little power in explaining wages. For instance, results presented in Taubman (1977) suggest that the expected difference in earnings between identical twins is about two-thirds as great as between randomly chosen members of the population. Jencks (1972) reports similar results for a host of other variables. This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:40:10 UTC All use subject to JSTOR Terms and Conditions 270 ALAN B. KRUEGER AND LAWRENCE H. SUMMERS TABLE IV The Effects of Unmeasured Labor Quality" (1) (2) (3) (4) Fixed Effects Fixed Effects Fixed Effects Unadjusted for Adjusted for Adjusted for Measurement Measurement Measurement Industry Error Error Ib Error IIC Levels Construction .063 .098 .174 .174 (.033) (.060) (.060) (.024) Manufacturing .028 .055 .107 .064 (.031) (.058) (.058) (.022) Transportation and .019 .060 .049 .114 Public Utilities (.035) (.059) (.059) (.024) Wholesale and -.042 -.068 -.125 -.133 Retail Trade (.031) (.056) (.056) (.023) Finance, Insurance .027 .017 .018 .035 and Real Estate (.036) (.061) (.061) (.025) Services -.040 -.088 -.128 -.079 (.032) (.056) (.057) (.023) Mining .067 .122 .142 .156 (.004) (.057) (.058) (.040) "Data set is three matched May CPS's pooled together: 1974-1975, 1977-1978, and 1979-1980. Sample size is 18,122. Levels are 1974, 1977, and 1979 data pooled. Results of the 1975, 1978, and 1980 sample are qualitatively the same. Controls for fixed effects regressions are change in education and its square, change in occupation, 3 region dummies, change in union membership, experience squared, change in marital status, year dummies, and a constant. Controls for level regressions are the same as Table I plus year dummies. b Adjustment I assumes 3.4 per cent error rate and that misclassifications are proportional to industry size. See Appendix for description. cAdjustment II assumes average error rate is 3.4 per cent and misclassifications are allocated according to employer-employee mismatches. See Appendix for description. estimate the extent of measurement error in answers to CPS questions about industry suggests that a large fraction of reported industry switches do not reflect genuine movements between industries but are instead the result of classification errors. As a result, it is necessary to correct our estimates for measurement error. We make use of the prior information provided by Mellow and Sider on the extent of reporting errors to correct our estimates of industry wage differentials for the effects of measurement error. The correction differs from the standard one because the independent variables we examine are dichotomous. It is detailed in the Appendix. The procedure is implemented under two different assumptions about the nature of the process generating industry classification errors. In Case I we assume the error rate is the same in all industries and that the chance of being misclassified into an industry is proportional to the industry's employment share. In Case II we estimate the chance of spurious classification between industry i and industry j directly from the data used by Mellow and Sider. Table IV presents the results of longitudinal analysis with the matched CPS data. We report the first difference results adjusted for measurement error under our two alternative assumptions. In addition, we report the fixed effects results without adjusting for measurement error, and report the results of a wage regression using levels. The results show that the first difference and level regressions are similar, and in both cases the industry variables are jointly This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:40:10 UTC All use subject to JSTOR Terms and Conditions EFFICIENCY WAGES 271 statistically significant.9 For all industries, the measurement error adjusted first difference and level results have the same sign and about the same magnitude. For instance, the longitudinal results with measurement error correction II show that workers who join (leave) the manufacturing sector gain (lose) a 10.7 per cent pay increase (decrease), while a regression on the levels shows a 6.4 per cent pay premium for manufacturing workers. In some cases, the measurement error corrected results actually suggest that the unmeasured labor quality is lower in the high pay industries. Using data from 1979, Gottschalk and Maloney (1985) find that nearly 70 per cent of job changes are voluntary. There are potentially important selection problems involved in studying workers who voluntarily change industries. For instance, if there is uncertainty as to workers' ability, workers who move from the apparent high wage industries to the low wage industries may be low quality workers, while workers who move from low wage to high wage industries may benefit from better matches. As a partial test for the importance of these problems, we examined the impact on wages of changing industries separately for leavers and joiners. The selection effects operating on workers moving from industry i to j are likely to be different from those operating on workers going from industry j to industry i. We were unable, however, to reject the hypothesis that wage changes were the same for joiners and leavers. This suggests that selectivity forces are not very important in the longitudinal analysis and provides some support for the first difference specification. Longitudinal Evidence from Displaced Workers Perhaps more convincing evidence on the same issue comes from our analysis of a sample of displaced workers. The second longitudinal data set we use is the January 1984 CPS survey of displaced workers. The Census Bureau asked a sequence of retrospective questions to workers who lost their job because their plant closed, they were permanently laid off, or their job was abolished. This data set helps solve the problem of selective job changers because only workers who were involuntarily displaced from their jobs are in the sample. One disadvantage of the data set, however, is that the workers' hourly wage rate and weekly hours are not available. Instead, we use the weekly wage as the dependent variable and restrict the sample to full-time (more than 35 hours per week) workers. On the other hand, the data set has the advantage of following workers who moved to a new location and contains job tenure on the initial job. Table V reports the results of our longitudinal analysis of displaced workers. The first difference estimates are corrected for measurement error in the same fashion as the estimates in Table IV. Because a high proportion (more than half) of the workers in this sample switched industries, measurement error has a 9 A preferable alternative to first-differencing would be to examine changes in wages for workers who move in all directions. Unfortunately, measurement error and the small sample of industry changers makes such an approach infeasible. This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:40:10 UTC All use subject to JSTOR Terms and Conditions 272 ALAN B. KRUEGER AND LAWRENCE H. SUMMERS TABLE V The Effects of Unmeasured Labor Quality for a Sample of Displaced Workers (i) (2) (3) (4) Fixed Effects Fixed Effects Fixed Effects Unadjusted for Adjusted for Adjusted for 1984 Measurement Measurement Measurement Cross- Industry Error Error Ib Error IIC Section Construction .000 .001 .005 .174 (.051) (.051) (.052) (.060) Manufacturing .053 .058 .059 .055 (.049) (.048) (.050) (.060) Transportation and .010 .011 .013 .117 Public Utilities (.054) (.054) (.055) (.064) Wholesale and -.058 -.062 -.068 -.097 Retail Trade (.050) (.049) (.050) (.061) Finance,Insurance .015 .015 .016 -.024 and Real Estate (.056) (.055) (.056) (.067) Services -.062 -.067 -.065 -.097 (.050) (.050) (.051) (.062) Mining .289 .306 .330 .366 (.036) (.036) (.037) (.137) a Control variables for fixed effects models are tenure on previous job, age, 8 occupation change dummy variables, a dummy variable indicating whether the worker moved to a new location, 4 dummy variables for year of displacement, and a constant. Control variables for 1984 cross-section are years since displacement and its square, education, race, sex, 3 region dummy variables, marital status, 8 occupation dummy variables, age and its square, and a constant. Sample size for fixed effects regressions is 2,318 and for 1984 cross-section is 2,592. We are grateful to Doug Kruse for preparing this table. bAdjustment I assumes 3.4 per cent error rate and that misclassifications are proportional to industry size. See Appendix for description. cAdjustment II assumes average error rate is 3.4 per cent and misclassifications are allocated according to employer-employee mismatches. See Appendix for description. substantially smaller effect on the first difference estimates than it does in the first CPS data set, where the rate of true industry mobility is much lower. The industry variables are jointly highly significant in both levels and first-differences. Although the construction and transportation industries appear to be anomalies, these results suggest that workers who are involuntarily displaced from their jobs and switch industries experience substantial wage changes that closely parallel the industry wage structure found in cross-sectional analyses. We interpret this as additional evidence that observed cross-sectional industry wage differences do not only reflect differences in average labor quality.10 There is a final point that militates against the unmeasured labor quality explanation for industry wage differentials. Evidence surveyed in Krueger and Summers (1986) and Dickens and Katz (1986b) indicates that there are strong 10 We note, however, the contrasting findings by Murphy and Topel (1986) who conclude that two-thirds of observed industry annual earnings differences are due to unobserved individual components. There are two major differences in their analysis that might account for these findings. First, Murphy and Topel use an instrumental variable procedure to adjust for measurement error. Second, and probably more importantly, Murphy and Topel focus on changes in occupation-industry cells without controlling for changes in workers' occupations. It is plausible that unobserved worker-specific differences bias cross-sectional estimates of the occupational wage structure but not the industry wage structure. This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:40:10 UTC All use subject to JSTOR Terms and Conditions EFFICIENCY WAGES 273 regularities in the pattern of industrial wages. More profitable industries, those with more monopoly power, and those where labor's share is smaller pay higher wages. The regularities appear to be statistically significant, to hold in different times and places, and to account for a fairly large fraction of inter-industry wage variations. Since it is hard to see why there would be a correlation between unmeasured labor quality and product market characteristics, these results cast further doubt on the unmeasured quality explanation for wage differentials. 4. ALTERNATIVE EXPLANATIONS OF INDUSTRY WAGE DIFFERENTIALS In this section we examine whether the substantial industry wage differentials discussed in Sections 2 and 3 can be given competitive or institutional explanations. We examine the importance of compensating differentials, unions, and other factors. The major conclusion is that industry wage differentials appear robust to additional competitive and institutional explanations. Compensating Differentials Logically, the finding of stable inter-industry wage differentials could be explained by pointing to compensating differentials. The compensating differentials argument is that agreeable and disagreeable job attributes vary systematically with one's industry of employment, and therefore necessitate wage differentials to compensate employees for nonwage aspects of the industry. Since the results considered so far do not control for working conditions, it could be argued that the observed industry wage differentials merely represent compensating differentials. Although Brown (1980), Smith (1979), and several other studies have not been able to document compensating differentials for a range of job attributes, we examine this possibility. We base our analysis of working conditions on the University of Michigan's Quality of Employment Survey (QES). The 1977 QES cross-section contains data on a wide range of working conditions. Several other studies of compensating differentials have relied on QES, such as Preston (1985) and Brown and Medoff (1985). We focus on ten potentially important job attributes—weekly hours, a variable indicating whether health hazards are present on the job, and another indicating whether the hazard is serious, second and third shift dummies, commuting time, two variables indicating the extent of choice of overtime, and two catch-all variables indicating whether the physical work conditions are pleasant.11 These are the same variables Brown and Medoff (1985) hold constant. If the industry differentials do not change substantially once the working condition measures are added to the regression, we would conclude that compensating differentials are not playing an important role in determining the industry wage differentials. u Although the weekly hours variable is possibly endogenous, results are qualitatively the same when it is omitted from the regression. This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:40:10 UTC All use subject to JSTOR Terms and Conditions 274 ALAN B. KRUEGER AND LAWRENCE H. SUMMERS TABLE VI Analysis of Industry Wage Differentials With and Without Controls for Working Conditions—QES 1977a Coefficient (SE) Industry 10 .096** Firm Size (5) 1-99 Employees .073** .78 (6) 1,000 or More Employees .111** Types of Employment C) Self Employed .097** .84 (8) Privately Employed .133** Occupation (9) Blue Collar .108** .79 (10) White Collar .136** a Other explanatory variables are the same as in Table I. Year dummies are also included in rows (7) and (8). Sample sizes for rows (1) through (10), respectively, are 5,534, 1,998, 3,311, 1,619, 3,752, 3,497, 3,378, 46,232, 5,607, and 5,905. Rows (1) and (2), (9) and (10) are 1984 CPS. Rows (3) through (6) are 1979 CPS. Rows (7) and (8) are May 1975, 1976, 1977, and 1978 CPS. Each row was estimated from a separate cross-sectional regression. b Rows (7) and (8) are unweighted; all other rows are weighted by 1984 employment. c Complement is the other reported subsample. ** F test that industry wage differentials jointly equal 0 rejects at the .00001 level. would lead to inequality in wages across industries. In this case our wage equation might not be accurately measuring inter-industry differences in the expected lifetime income of new workers entering different industries. In order to examine these possibilities, we examine industry effects on the wages of young and old workers, and on workers with short and long job tenure. Rows (1) and (2) of Table VIII show that wage premia across industries for the young and old are highly correlated. Furthermore, the standard deviation of the estimated industry wage differential is about 14 per cent for both groups of workers. Similarly, we find that workers with one year or less of job tenure or more than ten years of job tenure have almost equally variable and highly correlated industry wage structures. Again, F tests of the overall significance of the industry wage differentials find that industry of employment has a statisically significant effect on wages for all groups of workers. Varying patterns of human capital accumulation do not appear to provide an explanation for the inter-industry wage structure.12 An important institution that affects wages is company and plant size. Several studies have documented large employer size-wage differentials. For our purposes, the size-wage differential is an important dimension of the wage structure 12 Note also that these findings belie human capital explanations holding that differences in the level of wages across industries are caused by differences in the slope of age or tenure wage profiles. This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:40:10 UTC All use subject to JSTOR Terms and Conditions 278 ALAN B. KRUEGER AND LAWRENCE H. SUMMERS because several explanations of the size-wage differential are based on efficiency wages that result from more costly monitoring in larger establishments. (See Calvo and Wellisz (1978), Oi (1983), and Bulow and Summers (1986) for examples of efficiency wage models applied to different size firms.) Rows (5) and (6) of Table VIII show that industry wage dispersion increases sharply with firm size. This suggests that monitoring difficulties may in fact increase with firm size in some industries. Corroborating evidence comes from an analysis of self-employed workers. Despite the fact that skills are likely to be diverse among the self employed, and the substantial errors in reporting self employment, inter-industry wage variations are about one-quarter smaller among the self employed than among other workers. Rows (9) and (10) of Table VIII show that the industry wage structure is fairly uniform for both blue collar and white collar employees. We also reached the same conclusion when we examined more detailed occupations. Industries which pay workers in one occupation group above their alternative wage tend to pay workers in other occupations above their alternative wage as well. This finding supports the conclusions of Dickens' and Katz' (1986) more extensive examination of industry wage patterns across different occupations for nonunion workers. Since it is unlikely that workers in different occupations within an industry have similar quantities of unmeasured ability, this finding is further evidence against an unmeasured labor quality explanation of industry wage premia. The similarity of the industry wage structure for workers in different occupations suggests that the factor that is responsible for industry wage differences cuts across occupational fines. This may cast some doubt on efficiency wage theories based on differences in monitoring technologies, since monitoring costs are likely to vary somewhat across occupations. It militates in favor of sociological explanations such as that of Akerlof (1984). 5. INDUSTRY WAGE EFFECTS AND TURNOVER The previous sections were aimed at documenting substantial variations in wages across industries that are not explained by the standard competitive model. If workers in high wage industries truly receive economic rents we would expect to find a negative relationship between turnover and industry wage differentials. On the other hand, if the observed wage differentials merely reflect compensating differentials for unobserved and undesirable working conditions we would expect to find no relationship between turnover and industry wage differentials. The relationship between wage premiums and turnover thus provides an alternative test of the textbook competitive model of industry wage determination. It is also of interest because turnover reductions are one possible reason why firms might pay supra-competitive wages. The relationship between wages and turnover is well established in the literature (see Pencavel (1970), Freeman (1980), and Viscusi (1980) for examples). In this section we specifically examine the relationship between industry wage premia and quits and length of employment. In principle, this way we do not capture any effect of human capital on quit behavior. Our approach to analyzing This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:40:10 UTC All use subject to JSTOR Terms and Conditions EFFICIENCY WAGES 279 TABLE IX The Effect of Industry Wage Differentials on Job Tenure and Quits Dependent Variable3 Independent (1) Variables Tenure Quitb Industry wage premium 2.198 -.073 (.676) (.135) Union (1 = yes) 3.179 -.164 Other variables Sample Size R2 (.157) Age dummies (6), Age * Sex (6), Education, Education Squared * Sex, Region Dummies (3), Race Dummy, Sex Dummy, Central City Dummy, Firm Size Dummies (4), Plant Size Dummies (4), Marriage Dummy, Marriage * Sex, Veteran Status Dummy 8,978 .40 (.037) Education, Education Squared, Region Dummies (3), Race Dummy, Sex Dummy, SMSA Dummy, (Age-Education—5) and its square 633 .20 a Mean (SD) of Tenure is 5.70 (7.61); Mean (SD) of Quit is .26 (.44). b Quit equation was estimated with a linear probability model. turnover is to estimate a linear probability model where the dependent variable equals 1 if the employee voluntarily quit his job between 1973 and 1977 and 0 if he remains on the same job. The key independent variable is the industry wage premium, which equals the wage differential (reported in Table II) associated with the employee's industry in 1973. In addition, we control for other factors that influence employee turnover, such as experience, occupation, and education (a complete list of regressors is given in Table IX). The quit analysis is performed on individual-level data from the QES 1973-1977 panel. In addition, we estimate regressions of tenure on industry wage differentials and several other variables. Since a lower turnover rate is reflected in longer job tenure, a finding of a positive relationship between the length of job tenure and industry wage differentials would be consistent with the view that industry wage differentials represent economic rents. Tenure regressions have the advantage of being estimable using the larger sample available in the May 1979 CPS Supplement. Table IX reports the results of the tenure and quit regressions. The effect of industry wage premiums on job tenure is positive and statistically significant, while their effect on quits is negative but statistically insignificant. The statistically insignificant finding for quit rates in part reflects the relatively small sample used for the quit analysis. The quit and especially tenure regressions provide additional evidence that wage premiums do not reflect compensating differentials, since such differentials would not induce reduced turnover. This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:40:10 UTC All use subject to JSTOR Terms and Conditions 280 ALAN B. KRUEGER AND LAWRENCE H. SUMMERS The reduced turnover that appears to accompany higher wages may at least partially offset some of the cost of higher wages. Turnover is costly to firms. Employee separations cost the firm in terms of search, lost production during vacancies, and a loss of specific training. (See Salop (1979) for a formal efficiency wage model based on turnover.) Brown and Medoff (1978) estimate that the elasticity of output with respect to the quit rate is about -.1. The quit analysis implies that at the mean the elasticity of quits with respect to the wage premium is — .07/.26 = —.27. Dickens and Katz (1986b) find qualitatively similar results for nonunion workers. Taken together, these results imply that a 10 per cent increase in the wage differential brings about a .3 per cent increase in output through reduced quits alone. This suggests that although turnover does adversely affect output, reductions in turnover alone are not sufficient to justify wage premiums of the magnitude actually observed unless fixed costs of hiring are very high or labor's share in output is very low. Raff and Summers (1987) show that at Ford Motor Company high turnover was a visible manifestation of problems with very large consequences for output. In this case actions which reduced turnover also produced very large output gains. 6. CONCLUSIONS We believe the results here call into serious question the view that industry wage differentials can plausibly be rationalized with textbook competitive models. These differentials appear to be a pervasive empirical regularity. As we have noted and document more fully in Krueger and Summers (1986), the industry wage structure is remarkably stable across space and time. As Dickens and Katz (1986a) stress, the pattern of industry wage differentials is very similar for workers in different occupations. At a minimum, these findings shift the burden of proof to those wishing to interpret wage differentials in terms of simple competitive models. We have already argued that in a tautologous sense almost any explanation for wage differentials that is consistent with profit maximization must rely in some way on efficiency wages. The failure of wages to adjust to excess supply in the labor market is often discussed in terms of rent sharing. This is the essence of the insider-outsider theories developed in order to explain involuntary unemployment by Lindbeck and Snower (1984 and 1986). The rent sharing explanation for industry wage differentials is discussed in Krueger and Summers (1986), and modelled formally in Rotemberg and Saloner (1986). Rent sharing explanations are intimately related to efficiency wage theories in two senses. First, a reason firms share rents is presumably that failure to do so will result in their work force not cooperating with it by quitting, shirking, or otherwise interfering with production. By paying a higher wage, firms may elicit effort and avoid these consequences. Second, rent sharing is less expensive for firms in an efficiency wage environment where changes in wages have no first order effect on costs than it would be in a standard competitive situation. We prefer to regard rent sharing as a species of efficiency wage theory rather than as an alternative explanation for wage differentials. This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:40:10 UTC All use subject to JSTOR Terms and Conditions EFFICIENCY WAGES 281 The demonstration of important inter-industry wage differentials, if accepted, creates a prima facie case for the existence of involuntary unemployment. Unemployment may be thought of as employment in home production. It is no more surprising that workers should be confined to this "industry" than to other low wage industries. There is a more subtle linkage between inter-industry wage differentials and involuntary unemployment as well. The existence of wage differentials can provide the motivation for "wait" unemployment of the type considered by Hall (1975) and Bulow and Summers (1986). In the presence of involuntary unemployment, there is a case for policies directed at increasing employment. The natural rate of unemployment is likely to be inefficiently high. As Akerlof and Yellen (1985) emphasize, efficiency wage models can illuminate cyclical fluctuations in unemployment as well. The finding here of large interindustry wage differentials suggests that profits may be relatively insensitive to wages over a wide range. This attenuates firms' incentives to adjust wages in the face of unemployment. The results in this paper suggest an important direction for future research. The sources of wage differentials need to be isolated. As Stiglitz (1984) notes, different efficiency wage models have somewhat different implications for a number of positive and normative issues. Alternative noncompetitive, non-efficiency wage theories, while difficult to specify, undoubtedly also have differing implications. Moreover, linking wage premia to variables suggested by efficiency wage theories, if possible, would strengthen the argument by elimination presented here. For example, Krueger (1987) examines differences in wages and turnover between company-owned and franchisee-owned fast food restaurants because the presence of franchisees is likely to facilitate monitoring. Alternatively, to overcome difficulties of identification it may be useful to rely on case studies to test efficiency wage theories. To this end, Raff (1986) and Raff and Summers (1987) present a case study of Henry Ford's introduction of the five dollar day. Finally, production function estimates of the type presented by Brown and Medoff (1978) might permit estimates of at least some efficiency wage effects. Woodrow Wilson School, Princeton University, Princeton, NJ 08544, U.S.A. and Department of Economics, Harvard University, Cambridge, MA 02138, U.S.A. Manuscript received May, 1986; final revision received April, 1987. TABLE Al Estimated Wage Differentials for Three-Digit CIC Industries—May 1984 CPS' (Standard Errors in Parentheses) cic Industry (SIC) Wage Differential 040 041 MINING Metal mining (10) Coal mining (11,12) .296 .253 (.070) (.087) This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:40:10 UTC All use subject to JSTOR Terms and Conditions 282 ALAN B. KRUEGER AND LAWRENCE H. SUMMERS TABLE AI (Continued) Wage CIC Industry (SIC) Differential 042 Crude petroleum and natural gas extraction (13) .256 (.043) 050 Nonmetallic mining and quarrying, except fuel (14) .070 (.095) 060 CONSTRUCTION (15,16,17) .129 (.025) MANUFACTURING Nondurable Goods Foods and kindred products 100 Meat products (201) -.028 (.056) 101 Dairy products (202) .176 (.067) 102 Canned and preserved fruits and vegetables (203) .042 (.060) 110 Grain mill products (204) .099 (.097) 111 Bakery products (205) .011 (.065) 112 Sugar and confectionary products (206) .116 (.104) 120 Beverage industries (208) .126 (.066) 121 Miscellaneous food preparations and kindred products (207, 209) .004 (.070) 122 Not specified food industries NA NA 130 Tobacco manufacturers (21) .339 (.128) Textile mill products 132 Knitting mills (225) -.079 (.072) 140 Dyeing and finishing textiles, except wool and knit goods (226) .200 (.171) 141 Floor coverings, except hard surface (227) .011 (.122) 142 Yarn, thread and fabric mills (228, 221-224) .036 (.056) 150 Miscellaneous textile mill products (229) .032 (.097) Apparel and other finished textile products 151 Apparel and accessories, except knit (231-238) -.137 (.037) 152 Miscellaneous fabricated textile products (239) -.102 (.079) Paper and allied products 160 Pulp, paper, and paperboard mills (261-263, 268) .177 (.057) 161 Miscellaneous paper and pulp products (264) .112 (.072) 162 Paperboard containers and boxes (265) .136 (.072) Printing, publishing, and allied industries 171 Newspaper publishing and printing (271) -.020 (.049) 172 Printing, publishing, and allied industries, except newspapers (272-279) .144 (.036) Chemicals and allied products 180 Plastics, synthetics, and resins (282) .070 (.100) 181 Drugs (283) .225 (.085) 182 Soaps and cosmetics (284) .296 (.092) 190 Paints, varnishes, and related products (285) .252 (.116) 191 Agricultural chemicals -.129 (.111) 192 Industrial and miscellaneous chemicals (281, 286, 289) .292 (.046) Petroleum and coal products 200 Petroleum refining (291) .374 (.074) 201 Miscellaneous petroleum and coal products (295, 299) .598 (.381) Rubber and miscellaneous plastic products 210 Tires and inner tubes (301) .306 (.116) 211 Other rubber products, and plastics footwear and belting (302-304, 306) 016 (.090) 212 Miscellaneous plastics products (307) .027 (.050) This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:40:10 UTC All use subject to JSTOR Terms and Conditions EFFICIENCY WAGES TABLE Al (Continued) 283 Wage CIC Industry (SIC) Differential Leather and leather products 220 Leather tanning and finishing (311) -.027 (.381) 221 Footwear, except rubber and plastic (313, 314) -.088 (.067) 222 Leather products, except footwear (315-317, 319) -.074 (.145) Durable Goods Lumber and wood products, except furniture 230 Logging (241) .089 (.085) 231 Sawmills, planing mills, and millwork (242, 243) .001 (.049) 232 Wood buildings and mobile homes (245) -.039 (.116) 241 Miscellaneous wood products (244, 249) -.099 (.088) 242 Furniture and fixtures (25) -.008 (.050) Stone, clay, glass, and concrete products 250 Glass and glass products (321-323) .012 (.076) 251 Cement, concrete, gypsum, and plaster products (324, 327) .072 (.075) 252 Structural clay products (325) .385 (.220) 261 Pottery and related products (326) .067 (.171) 262 Miscellaneous nonmetallic mineral and stone products (328, 329) .174 (.089) Metal industries 270 Blast furnaces, steelworks, rolling and finishing mills (331) .208 (.054) 271 Iron and steel foundries (332) .105 (.083) 272 Primary aluminum industries (3334, pt 334, 3353-3355, 3361) .259 (.107) 280 Other primary metal industries (3331-3333, 33339, pt 334, 3351, 3356, 3357, 3362, 3369, 339) .112 (.069) 281 Cutlery, hand tools, and other hardware (342) .037 (.103) 282 Fabricated structural metal products (344) .106 (.051) 290 Screw machine products (345) .137 (.171) 291 Metal forgings and stampings (346) .036 (.088) 292 Ordnance (348) .134 (.116) 300 Miscellaneous fabricated metal products (341, 343, 347, 349) .048 (.058) 301 Not specified metal industries -.097 (.381) Machinery, except electrical 310 Engines and turbines (351) .293 (.104) 311 Farm machinery and equipment (352) .278 (.075) 312 Construction and material handling machines (353) .174 (.068) 320 Metalworking machinery (354) .020 (.067) 321 Office and accounting machines (357, except 3573) .371 (.103) 322 Electronic computing equipment (3573) .252 (.043) 331. Machinery, except electrical, n.e.c. (355, 356, 358, 359) .152 (.037) 332 Not specified machinery NA NA Electrical machinery, equipment, and supplies 340 Household appliances (363) .035 (.090) 341 Radio, TV, and communication equipment (365, 366) .220 (.044) 342 Electrical machinery, equipment, and supplies, n.e.c. (361, 362, 364, 367, 369) .066 (.034) 350 Not specified electrical machinery, equipment, and supplies .423 (.380) This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:40:10 UTC All use subject to JSTOR Terms and Conditions 284 ALAN B. KRUEGER AND LAWRENCE H. SUMMERS TABLE Al (Continued) CIC Industry (SIC) Wage Differential Transportation equipment 351 Motor vehicles and motor vehicle equipment (371) .244 (.037) 352 Aircraft and parts (372) .210 (.050) 360 Ship and boat building and repairing (373) .058 (.068) 361 Railroad locomotives and equipment (374) .273 (.269) 362 Guided missiles, space vehicles, and parts (376) .004 (.061) 370 Cycles and miscellaneous transportation equipment (375, 379) -.025 (.107) Professional and photographic equipment, and watches 371 Scientific and controlling instruments (381, 382) .108 (.065) 372 Optical and health services supplies (383, 384, 385) .109 (.062) 380 Photographic equipment and supplies (386) .290 (.100) 381 Watches, clocks, and clockwork operated devices (387) .342 (.270) 382 Not specified professional equipment NA NA 390 Toys, amusement, and sporting goods (394) .121 (.087) 391 Miscellaneous manufacturing industries (39, except 394) -.040 (.067) 392 Not specified manufacturing industries -.070 (.269) TRANSPORTATION, COMMUNICATIONS, AND OTHER PUBLIC UTILITIES Transportation 400 Railroads (940) .268 (.052) 401 Bus service and urban transit (41, except 412) .073 (.065) 402 Taxicab service (412) -.203 (.146) 410 Trucking service (421, 423) .074 (.035) 411 Warehousing and storage (422) .095 (.095) 420 Water transportation (44) .114 (.082) 421 Air transportation (45) .320 (.047) 422 Pipe lines, except natural gas (46) -.253 (.171) 432 Services incidental to transportation (47) -.026 (.072) Communications 440 Radio and television broadcasting (483) -.132 (.061) 441 Telephone (wire and radio) (481) .301 (.037) 442 Telegraph and miscellaneous communication services (482,489) .049 (.075) Utilities and sanitary services 460 Electric light and power (491) .277 (.043) 461 Gas and steam supply systems (492, 496) .301 (.068) 462 Electric and gas, and other combinations (493) .300 (.073) 470 Water supply and irrigation (494, 497) .081 (.122) 471 Sanitary services (495) .062 (.191) 472 Not specified utilities .498 (.270) WHOLESALE TRADE Durable Goods 500 Motor vehicles and equipment (501) -.006 (.072) 501 Furniture and home furnishings (502) .051 (.116) 502 Lumber and construction materials (503) .115 (.089) 510 Sporting goods, toys, and hobby goods (504) .139 (.220) 511 Metals and minerals, except petroleum (505) .071 (.136) 512 Electrical goods (506) .123 (•059) This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:40:10 UTC All use subject to JSTOR Terms and Conditions EFFICIENCY WAGES 285 TABLE AI (Continued) CIC Industry (SIC) Wage Differential 521 Hardware, plumbing and heating supplies (507) .013 (.070) 522 Not specified electrical and hardware products NA NA 530 Machinery, equipment, and supplies .068 (.040) 531 Scrap and waste materials (5093) -.033 (.100) 532 Miscellaneous wholesale, durable goods (5094) .164 (.156) Nondurable Goods 540 Paper and paper products (511) .003 (.111) 541 Drugs, chemicals, and allied products (512, 516) .033 (.076) 542 Apparel, fabrics, and notions (513) -.007 (.112) 550 Groceries and related products (514) .019 (.047) 551 Farm products—raw materials (515) -.109 (.074) 552 Petroleum products (517) .159 (.073) 560 Alcoholic beverages (518) .138 (.083) 581 Farm supplies (5191) .063 (.100) 582 Miscellaneous wholesale, nondurable goods (5194, 5198, 5199) -.081 (.082) 571 Not specified wholesale trade .366 (.269) RETAIL TRADE 580 Lumber and building material retailing (521, 523) -.109 (.055) 581 Hardware stores (525) -.304 (.063) 582 Retail nurseries and garden stores (526) -.184 (.094) 590 Mobile home dealers (527) -.276 (.191) 591 Department stores (531) -.190 (.029) 592 Variety stores (533) -.103 (.082) 600 Miscellaneous general merchandise stores (539) -.268 (.100) 601 Grocery stores (541) -.121 (.028) 602 Dairy products stores (245) -.135 (.145) 610 Retail bakeries (546) -.131 (.089) 611 Food stores, n.e.c. (52, 543, 544, 549) -.254 (.076) 612 Motor vehicle dealers (551, 552) -.023 (.038) 620 Auto and home supply stores (553) -.040 (.057) 621 Gasoline service stations (554) -.269 (.047) 622 Miscellaneous vehicle dealers (555, 556, 557, 559) -.268 (.122) 630 Apparel and accessory stores, except shoe (56, except 566) -.229 (.041) 631 Shoe stores (566) -.232 (.086) 632 Furniture and home furnishings stores (571) -.102 (.058) 640 Household appliances, TV, and radio stores (572, 573) -.169 (.060) 641 Eating and drinking places (58) -.201 (.068) 642 Drug stores (591) -.246 (.045) 650 Liquor stores (592) -.450 (.086) 651 Sporting goods, bicycles, and hobby stores (5941, 5945, 5946) -.323 (.095) 652 Book and stationery stores (5942, 5943) -.223 (.097) 660 Jewelry stores (5944) -.089 (.082) 661 Sewing, needlework, and piece goods stores (5949) -.371 (.116) 662 Mail order houses (5961) -.269 (.103) 670 Vending machine operators (5962) -.147 (.145) 671 Direct selling establishments (5963) .129 (.094) 672 Fuel and ice dealers (598) -.144 (.108) 681 Retail florists (5992) -.150 (.083) 682 Miscellaneous retail stores (593, 5947, 5948, 5993, 5994, 5999) -.143 (.058) 691 Not specified retail trade -.010 (.381) This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:40:10 UTC All use subject to JSTOR Terms and Conditions 286 ALAN b. KRUEGER AND LAWRENCE H. SUMMERS TABLE AI (Continued) CIC Industry (SIC) Wage Differential FINANCE, INSURANCE, AND REAL ESTATE 700 Banking (60) .048 (.030) 701 Savings and loan associations (612) .078 (.058) 702 Credit agencies, n.e.c. (61, except 612) .049 (.056) 710 Security, commodity brokerage, and investment companies (62,67) .185 (.055) 711 Insurance (63, 64) .116 (.030) 712 Real estate, including real estate-insurance-law offices (65,66) .004 (.033) BUSINESS AND REPAIR SERVICES 721 Advertising (731) .092 (.074) 722 Services to be dwellings and other buildings (734) -.140 (.053) 730 Commercial research, development, and testing labs (7391, 7397) .199 (.079) 731 Personnel supply services (736) -.157 (.049) 732 Business management and consulting services (737) .024 (.064) 740 Computer and data processing services (737) .214 (.054) 741 Detective and protective services (7393) -.021 (.059) 742 Business services, n.e.c. (732, 733, 735, 7394, 7395, 7396, 7399) -.007 (.042) 750 Automotive services, except repair (751, 752, 754) -.151 (.080) 751 Automotive repair shops (762, 7694) -.058 (.050) 752 Electrical repair shops (762) .224 (.122) 760 Miscellaneous repair services (763, 764, 7692, 7699) -.062 (.058) PERSONAL SERVICES 761 Private households (88) -.382 (.032) 762 Hotels and motels (701) -.148 (.034) 770 Lodging places, except hotels and motels (702, 703, 704) -.484 (.107) 771 Laundry, cleaning, and garment services (721) -.214 (.055) 772 Beauty shops (723) -.037 (.050) 780 Barber shops (724) -.035 (.191) 781 Funeral service and crematories (726) -.261 (.103) 782 Shoe repair shops (725) NA NA 790 Dressmaking shops (pt 729) -.584 (.269) 791 Miscellaneous personal services (722, pt 729) -.219 (.083) ENTERTAINMENT AND RECREATION SERVICES 800 Theaters and motion pictures (78, 792) -.056 (.069) 801 Bowling alleys, billiard and pool parlors (793) -.391 (.116) 802 Miscellaneous entertainment and recreation services (791, 794, 799) -.147 (.040) PROFESSIONAL AND RELATED SERVICES 812 Offices of physicians (801, 803) -.076 (.040) 820 Offices of dentists (802) .053 (.057) 821 Offices of chiropractors (8041) -.340 (.171) 822 Offices of optometrists (8042) -.363 (.269) 830 Offices of health practitioners, n.e.c. (8049) -.400 (.270) 831 Hospitals (806) .063 (.025) 832 Nursing and personal care facilities (805) -.135 (.032) 840 Health services, n.e.c. (807, 808, 809) -.023 (.046) 841 Legal services (81) .079 (.044) 842 Elementary and secondary schools (821) -.216 (.039) 850 Colleges and universities (822) -.132 (.039) This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:40:10 UTC All use subject to JSTOR Terms and Conditions EFFICIENCY WAGES TABLE Al (Continued) 287 Wage CIC Industry (SIC) Differential 851 Business, trade, and vocational schools (824) -.128 (.128) 852 Libraries (823) -.095 (.156) 860 Educational services, n.e.c. (829) -1.489 (.220) 861 Job training and vocational rehabilitation services (833) -.194 (136) 862 Child care services (835) -.275 (.056) 870 Residential care facilities, without nursing (836) -.288 (.079) 871 Social services, n.e.c. (832, 839) -.166 (.048) 872 Museums, art galleries, and zoos (84) -.194 (.145) 880 Religious organizations (866) -.276 (.039) 881 Membership organizations (861-865, 869) -.070 (.055) 882 Engineering, architectural, and surveying services (891) .206 (.050) 890 Accounting, auditing, and bookkeeping services (892) .051 (.055) 891 Noncommercial educational and scientific research (892) -.055 (.122) 892 Miscellaneous professional and related services (899) .241 (.156) Weighted Adjusted Standard Deviationb .160** a Other explanatory variables are education and its square, 6 age dummies, 8 occupation dummies, 3 region dummies, sex dummy, race dummy, central city dummy, union member dummy, ever married dummy, veteran status, marriage X sex interaction, education X sex interaction, education squared X sex interaction, and 6 age X sex interactions. b Weights are employment shares for each industry. ** F test that industry wage differentials jointly equal 0 is rejected at the .000001 level. APPENDIX Correcting for Measurement Error in Dummy Variables in Longitudinal Data Economic variables are frequently measured with error. In this Appendix, we derive a first difference estimator that is consistent if a set of dummy variables is measured with error.13 The Statistical Model Consider the following linear first difference model:14 (1) AWl = AD*'a + AE, (t = l,...,N), where A w, is the change in log wage, A D* is a K vector of change in industry dummy variables, a is a K vector of parameters, and At, is a mean 0 iid disturbance. The symbol A denotes a change in a variable. There are K +1 industries and N observations. Because of collinearity, only K industries are in equation (1). 13 We are grateful to Bruce Meyer, Aaron Han, and Chris Cavanagh who provided indispensible assistance in the derivation of the techniques described here. See Freeman (1984) for the one dummy variable case. 14 Since the change in industry status is probably orthogonal to the change in other independent variables, such as marital status and education, equation (1) may be a reasonable approximation. This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:40:10 UTC All use subject to JSTOR Terms and Conditions 288 ALAN b. KRUEGER AND LAWRENCE H. SUMMERS To facilitate the subsequent analysis, we shall write (1) in matrix notation as (1') Aw = AD*a + Ae where Aw and Ae are NX 1 vectors and AD* is an NX K matrix. Because industry status is reported with error, AD* is not observable. Instead, for each industry ; we observe A D„, which is the true change in industry status plus a classification error Ae„: (2) AD„ = AD* + Aeit (i-1,...,K+1; t = 1,...,N). The values ADit, ADf, and Aeit can take on are limited: 4D„ = 1, 0, -1; AD* = ( 2> 1, I 1, 0, -«i,-< 0, -1; Assumption 1: Industry classification errors eit are independently and identically distributed over time. We introduce the following notation: r[j = prob [worker t is classified in industry j given that he truly is in industry i at a point in time]; k + i F/j = prob [worker l initially in industry ; moves to industry j ]. We further assume that all individuals have the same error and transition probabilities so rjj = rtj and F,'j = F,, for all t. The distribution of Ae, conditional on is given in Table A2. The expected value of Aeit conditional upon AD/* =( — 1,0,1) is K+l E(Ae„\AD*) = { (ryl+ !■„-), if AD* = 1, if AD* = Q, (ryl + i>,), if 40*=-l. Since is not independent of this problem differs from a textbook measurement error problem. We make two further assumptions about the misclassification process. Assumption 2: E(Ae„) = 0 for i = \,...,K+l. This is equivalent to assuming that the observed net industry flows are an unbiased estimate of the true net industry flows. Assumption 3: Prob(AD? = l)=prob(AD* = -1) for i = 1,..., K+ 1. The distribution of industry employment is in a dynamic steady state. A Ithough this assumption is clearly violated over a long time period, it is probably a reasonable assumption over the short time periods considered in the empirical work. With these two assumptions, the conditional expectation of Ae„ can be compactly expressed as E(Ae,l\ADir)-(r1,, + rlj)AD*, where 1 y J-' #-..+ y j*\ **J*l rj.i j*l L'J + l ri.J This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:40:10 UTC All use subject to JSTOR Terms and Conditions EFFICIENCY WAGES 289 + I + i tc + to to to + tc + tc + tC This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:40:10 UTC All use subject to JSTOR Terms and Conditions 290 ALAN B. KRUEGER AND LAWRENCE H. SUMMERS Thus A Dlt can be written (3) 40„-(l-ij,,-r(il-)4D,r + »'„ where p„ is a mean 0 disturbance that is uncorrelated with A Dft and vls for s ¥= t. Equation (3) can be expressed in matrix notation for the K industries and N observations as (4) AD = AD*[I-R] + p, where AD* = N X K matrix with AD* atypical element; I = KxK identity matrix; R = KX K diagonal matrix with (iy_, + rt ■) on the diagonal; v = N X K matrix of disturbances. Solving (4) for AD* and substituting the result in (1') yields (5) Aw = AD[I-R]~1ct-p[I-R]~1a + Ae. From (5) it is apparent that an OLS regression of A w on A D yields a biased and inconsistent estimate of « because AD and p are correlated. But a consistent estimate can be obtained if prior information is available on the rtJ. Estimator: A consistent estimator of a is given by ac: (6) &c = (AD^AD*)-1 [T- R]~l (AD'AD) aOLS. Proof: Substitution of &OLS = (AD'AD)'1 AD'Aw yields &c = (AD*'AD*)~l[I-R]~x AD'Aw. Substitution of (1') for Aw gives ac= (AD*'AD*)~1[T-R]'1 AD'{AD*a + Ae}. Finally, substitution for A D' gives (7) ac = (AD*'AD*)~l[I-R]'1 {p' R]AD*'} {AD*a + Ae} = a + (AD*'AD*)~l {[I - R]'1 p'AD*a+ [I- R]'1 p'Ae + AD*'Ae) , and the probability limit of (7) is phm(ac) = a + phm^AD*'AD*^ |[/ - «]"1 plim|p'AD*j a + [/-R]"1plim|-^: p'Ae^j + plim | 4D*4ej j = a. Limiting Variance/ Covariance Matrix To simplify the problem of deriving the variance/covariance matrix of &c, we assume AD*'AD* [I - R] is known with certainty. We also assume phm((l/N) AeAe') = aAeTNXN. The asymptotic variance/covariance matrix V of &c is then given in (8) (8) V = Aa'QaAA' + A aA2eA + o£eS2 where A = plim (l/N) (AD*'AD*)~l [I - R}~\ A = plim ((1/N)p'p), and Q = plim((l/A0 AD*'AD*)P Intuitively, the last term of (8) equals the variance/covariance matrix of