Econometrics Exercise session 5

Problem 1

Are rent rates influenced by the student population in a college town? Let rent be the average
monthly rent paid on rental units in a college town in the United States. Let pop denote the total
city population, avginc the average city income, and pctstu the student population as a percentage
of the total population. One model to test for a relationship is

(i) State the null hypothesis that size of the student body relative to the population

has no ceteris paribus effect on monthly rents. State the alternative that there is an

effect.

 (ii) What signs do you expect for  and ?


(0.844)    (0 .039)                       (.081)                               (.0017)

(iii) The equation estimated using 1990 data from RENTAL.RAW for 64 college towns is





What is wrong with the statement: “A 10% increase in population is associated with

about a 6.6% increase in rent”? Interpret the coefficient on pctstu.

 (iv) Test the hypothesis stated in part (i) at the 1% level.


Problem 2

Suppose you are interested in studying the tradeoff between time spent sleeping and working and to
look at other factors affecting sleep. You specify the following model:

where  and  (total work) are measured in minutes per week and  and  are measured in years.


(112.28)     (.017)                        (5.88)                 (1.45)



Suppose we estimated the following regression:



where we report standard errors along with the estimates.

(i)      Is either educ or age individually significant at the 5% level against a two-sided
alternative? Show your work.


(ii)

(38.91)        (.017)



Dropping educ and age from the equation gives


Are educ and age jointly significant in the original equation at the 5% level? Justify

your answer.


(iii) Does including educ and age in the model greatly affect the estimated tradeoff between
sleeping and working?

 (iv) Suppose that the sleep equation contains heteroskedasticity. What does this mean

about the tests computed in parts (i) and (ii)?


Problem 3

When estimating wage equations, we expect that young, inexperienced workers will have relatively
low wages and that with additional experience their wages will rise, but then begin to decline
after middle age, as the worker nears retirement. This lifecycle pattern of wages can be captured
by introducing experience and experience squared to explain the level of wages. If we also include
years of education, we have the equation:

a)      What is the marginal effect of experience on wages?

b)      What sign do you expect for each of the coefficients? Why?

c)      Estimate the model using data cps_small.gdt. Do the estimated coefficients have expecting
signs?

d)      Test the hypothesis that education has no effect on wages. What do you conclude?

e)      Test the hypothesis that education and experience have no effect on wages. What do you
conclude?

f)       Include the dummy variable black in the regression. Interpret the coefficient and comment
on its significance.

g)      Include the interaction term of black and educ. Interpret the coefficient and comment on
its significance.

h)      Transform dependent variable in logarithmic form and estimate the equation. Interpret the
coefficients.





Problem 4

consider a simple model to compare the returns to education at junior colleges and four-year
colleges; for simplicity, we refer to the latter as “universities.” The population includes working
people with a high school degree, and the model is:

                                                     (1)

where

jc  is number of years attending a two-year college, univ is number of years at a four-year
college. exper  is months in the workforce.

Note that any combination of junior college and four-year college is allowed, including

jc =0 and univ = 0. Use the data twoyear.dta

i)     Test the hypothesis that . The hypothesis of interest is whether one year at a junior
college is worth one year at a university.

 (ii) The variable phsrank is the person’s high school percentile. (A higher number is

better. For example, 90 means you are ranked better than 90 percent of your graduating

class.) Find the smallest, largest, and average phsrank in the sample.

 (iii) Add phsrank to regression (2) and report the OLS estimates in the usual form. Is

phsrank statistically significant? How much is 10 percentage points of high school

rank worth in terms of wage?

 (iv) Does adding phsrank to regression (2) substantively change the conclusions on the returns to
two- and four-year colleges? Explain.