ECO671, Spring 2015, Models for Dichotomous Dependent Variables
Prof. Bill Even
Insert all your answers in this Word document, leaving the original questions in place. Be
sure to provide both the stata code and the relevant results in your answers. You are not
allowed to discuss the solutions to your homework with anyone other than your teammate
and me.
1 (40 points) I extracted a sub-sample of data from the Survey of Consumer Finances data
collected between 1983 and 2007. For this problem, you will use a probit model to examine the
determinants of whether a household owns a home. The stata data set is
g:\eco\evenwe\eco671\scf83_07_home.dta. The variables contained in the data set can be seen
by executing “describe” in stata after opening the data set.
a. Compare the homeownership rates of black and white respondents.
statistically significant at the .05 level? Explain.
Is the difference
b. Estimate a probit model of homeownership as a function of real income, a quadratic in age,
education, race, Hispanic status, marital status, sex and year of the observation. Are the results
here consistent with what you found in (a)? Explain.
c. Recall that in Stata you can import coefficient estimates into a row vector (e.g. “beta”) after
estimation of a model by typing:
matrix beta=get(_b)
If you want a particular coefficient out of beta (e.g. the income coefficient) you would follow the
above statement by:
matrix betainc=beta[1,"income"]
This command extracts the first row and “income” column from the beta vector.
With the above tools in hand, use the probit model coefficients to calculate the predicted
probability that a single white non-Hispanic female who is 40 years old with $50,000 of income
and a high school degree would own a home in 2007. The norm(.) function will be useful here
since it evaluates the standard normal cdf.
d. For the same person as defined in (c), use a combination of matrix commands and the norm(.)
function to compute the marginal probability effect of an additional $10,000 of income on the
probability of homeownership.
e. Use the margins command in Stata to verify the estimate you provided in (c) and (d).
f. Test the null hypothesis that the probit coefficients for whites and blacks are identical using a
likelihood ratio test.1 Indicate whether the null is rejected at the .05 significance level by either
or both test statistics. [Hint: this is like a Chow test only it’s in a maximum likelihood model.]
g. Estimate how much higher or lower homeownership for black respondents would be if they
had the same characteristics as whites. Interpret these results in light of the racial difference in
homeownership that you calculated in (a).
[Hint: the predict command can be used to generate predicted probabilities for everyone in a
sample, even if the regression was estimated using only a subsample of the data. For example;
probit y x if white==1
predict phat
will generate predictions for everyone in the sample, not just whites]
g. Repeat step (a-d) using a logit (see logit in Stata) and a linear probability model. Compare
the results of the three models by using Stata to generate the necessary information to fill out the
table below. Be sure to provide the commands that you used to generate the figures in this
table. Use the margins command in Stata to generate the relevant estimates in all 3 models.
Probit
Effect of $1000 of additional
income on probability of
homeownership for person in
(c)
Average of predicted
probabilities for sample
Predicted probability of
homeownership for person
described in (c).
1
See lrtest in Stata to perform a likelihood ratio test.
Logit
Linear
probability
model