代写ECON3360/7360: Problem set 3

ECON3360/7360: Problem set 3

ECON3360/7360: Problem set 3

The University of Queensland

The questions in this problem set are made to mimic actual nal exam for this course. Work each

of questions thoroughly and fully understand the material. However, students are required to do all the

problems for preparation of nal exam. Your tutor is not allowed to answer your questions directly related

to the problem set during the assignment period.

1 Binary dependent variable - Are there racial discrimination in

the mortgage market? (12 marks)

Background The data are gathered from mortgage application in 1990 in the Boston, Massachusetts,

area, 28% of black applicants were denied mortgages but only 9% of white applicants were denied. But this

comparison does not really answer the question whether the bank treat the black and white the same way,

because the black and white applicants were not necessarily "identical but for their race." We need a method

for comparing rates of approval, holding other applicant characteristics constant. The binary variable to

be explained is approve, which is equal to one if a mortgage loan to an individual was approved. The key

explanatory variable is white, a dummy variable equal to one if the applicant was white. The other applicants

in the data set are black and Hispanic.

To test for discrimination in the mortgage loan market, a linear probability model can be used:

approve = 0 + 1white + controls + u1 (1)

A. If there is discrimination against minorities, and the appropriate factors have been controlled for,

what is the sign of 1?

B. Suppose the estimation of (1). Adding the control variables, hrat; obrat; loanprc; unem; male; married,

dep, sch, cosign, chist, pubrec, mortlat1, mortlat2, and vr and estimating a probit model of approve on

white. How do you get the estimated probability of loan approval for whites.

C. What are the advantages/disadvantages of using LPM compared to using probit model?

D. What is the dierence between using probit model and logit model in C?

E. Provide a fully specied density for approvejcontrols for probit and logit models respectively.

F. Provide the procedure of formal test for discrimination against non-white? Provide test statistics

and null hypothesis.

1

2 Binary dependent variable - The eect of job training program

on unemployment probabilities(10 marks)

Background This problem is based on experimental data on a job training program for a group of men

from Jan 1976 to Dec 1977. Men could enter the program starting in Jan 1976 through about mid-1977.

The program ended in Dec 1977. The idea is to test whether participation in the job training had an eect

on unemployment probabilities in 1978.

A. Consider a linear regression of train on several demographic and pre-training variables: unem74,

unem75, age, educ, black, hisp, and married. What is potential problems of estimating this model by linear

regression?

B. Provide a fully specied conditional distribution and a procedure to estimate a probit model for

part A using MLE.

C. Provide a procedure to examine whether participation in job training can be treated as exogenous

for explaining 1978 unemployment status.

D. Suppose that we run a linear probability model regression of unemp78 on train. Interpret the

coecient estimates on train.

E. Run the Probit estimation of unemp78 on train. What is the implication we obtained from the Pro-

bit coecient estimate on train if it is much larger than the coecient obtained from the linear probability

model in D?

3 Count Data - The elasticity of demand for smoking (16 marks)

Consider following model:

cigs = 0 + 1white + 2educ + 3age + 4age2 + 5ln(cigpric) + 6ln(income) + u (2)

The variable cigs is the number of cigarettes smoked per day.

A. Provide a conditional Poisson model for equation (2).

B. Given your answer in A, does cigs seem a good candidate for having a conditional Poisson distribu-

tion?

C. What is the consequence of mis-specication for the conditional Poisson distribution for cigsjcontrols?

D. Provide careful interpretation of 5. Provide the rationale for why 6 is called income elasticity of

demand for cigarette?

E. Are the Poisson maximum likelihood standard errors valid? Suppose we can estimate 2 that can

be used to relax the Poisson variance assumption. How do you adjust standard errors to allow arbitrary

conditional variance using the estimate of 2 in C?

F. Suppose the estimated ^2 is .5. How does it aect the t-statistic for the coecient on age?

2

G. After the Poisson regression model estimation how do you obtain a Pseudo-R squared? Describe a

procedure to obtain Pseudo-R squared.

H. Suppose obtained Pseudo-R squared is very low for the Poisson regression model. What does this

imply for the estimate 5.

4 Sample Selection - Wage oer equation for married women (14

marks)

Suppose we are studying labor demand for married women.

ln(wage) = 0 + 1educ + 2exper + 3exper2 + u (3)

A. Suppose we estimate the wage equation (3) by OLS using only the data for working women. Why

is the OLS estimator for 1 biased?

inlf = 0 + 1educ + 2exper + 3exper2 + 4nwifeinc + 5kidlt6 + u (4)

where inlf is women's labor force participation dummy variable, nwifeinc is family income except married

women's wage, kidlt6 is dummy variable equal to one if a women has children under age 6 and equal to zero

otherwise.

B. Explain why, for the purpose of testing and, possibly, correcting the wage equation for selection

into the workforce, it is important for nwifeinc and kidlt6 to help explain inlf.

C. What must you assume about nwifeinc and kidlt6 in the wage equation? Provide a procedure for

the test of nwifeinc and kidlt6 as relevant exclusion restrictions.

D. Provide a procedure to obtain the inverse Mills ratio.

E. Provide a procedure to implement the Heckman's 2-step approach for log wage equation in (3).

Also describe MLE procedure that is equivalent to Heckman's 2-step approach for log wage equation.

F. How do you test whether sample selection of working women is important from the result in E.

State the null hypothesis and a test statistic.

G. What object can be obtained after the Heckman's 2-step approach for log wage equation in (3).

Using this object provide a formula to get the marginal eect of additional year of education on wage?

5 Stata Exercises in Chapter 17 (18 marks)

代写ECON3360/7360: Problem set 3