Exercise Session 5

Problem 1

Suppose that you have a sample of n individuals who apart from their mother tongue (Czech) can
speak English, German, or are trilingual (i.e., all individuals in your sample speak in addition to
their mother tongue at least one foreign language). You estimate the following model:

wage = β[0] + β[1]educ + β[2]IQ + β[3]exper + β[4]DM + β[5]Germ + β[6]Engl + ε ,

where


educ

                                               . . .

years of education

IQ

                                               . . .

IQ level

exper

                                               . . .

years of on-the-job experience

DM

                                               . . .

dummy, equal to one for males and zero for females

Germ

                                               . . .

dummy, equal to one for German speakers and zero otherwise

Engl

                                               . . .

dummy, equal to one for English speakers and zero otherwise


(a)   Explain why a dummy equal to one for trilingual people and zero otherwise is not included in
the model.

(b)   Explain how you would test for discrimination against females (in the sense that ceteris
paribus females earn less than males). Be specific: state the hypothesis, give the test statistic
and its distribution.

(c)   Explain how you would measure the payoff (in terms of wage) to someone of becoming trilingual
given that he can already speak (i) English, (ii) German.

(d)   Explain how you would test if the influence of on-the-job experience is greater for males
than for females. Be specific: specify the model, state the hypothesis, give the test statistic and
its distribution.


Problem 2

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 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

Given the following regression model:

𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛[𝑖] = 𝛽[0] + 𝛽[1]𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡𝑅𝑎𝑡𝑒[𝑖] + 𝑢[𝑖]

Where both variables are measured in percentage points, a sample of 100 countries is used in order
to estimate the above model and the following information is given:

𝑉𝑎𝑟(𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛[𝑖][ ]) = 100; 𝑉𝑎𝑟(𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡𝑅𝑎𝑡𝑒[𝑖] ) = 50; 𝐶𝑜𝑣(𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖 ,𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡𝑅𝑎𝑡𝑒[𝑖] ) = −25;
𝑆𝑆𝑅 = 49

i)                    Find the OLS estimation of the effect of interest rates on inflation and the
estimated standard error.

ii)                  Interpret your estimation results.

iii)                Calculate a one-tailed t-test in order to validate the significance of the
estimated slope coefficient at 1% significance level.

iv)                What could you say about the explanatory power of the above model?