ECON0060 Advanced Microeconometrics
Problem Set 5: To be discussed and not to be handed in
1. Consider the following model determining college completion. Let y = 1 if an individual com- pletes college and y = 0 otherwise. Let z1 be a vector of variables, let z2 be a continuous variable, and let d1 be a dummy variable. Assume that
y* = z1 δ1 + √1 z2 + √2 z2(2) + ε
y = 1 [y* ≥ 0]
where ε ~ N (0, 1).
(a) What is the formula for the probability that y = 1 conditional on (z1 , z2 )? (b) What variables would you include in the vector z1 ?
(c) What is the partial efect of z2 ? How would you estimate it?
(d) Suppose z2 is household income, would you expect √1 to be positive or negative? What about √2 ?
(e) Now suppose the model is
y* = z1 δ1 + √1 z2 + √2 d1 + √3 z2 d1 + ε y = 1 [y* ≥ 0] .
What is the partial efect of z2 ? How would you measure the efect of d1 on the probability that y = 1? How would you estimate these efects?
(f) Describe how you would obtain estimates of the standard errors of the estimated partial efects.
2. Download the data http://www.stata.com/data/jwooldridge/eacsap/bwght.dta. Use the data and use Stata or R to answer this question. After downloading the data, to load it into R, you can install and use the package “haven” and use the command “read stata” . Alternatively, using Stata, you can obtain the data by starting Stata and typing the command
use http://www.stata.com/data/jwooldridge/eacsap/bwght.dta
Be sure to turn in your Stata or R output in addition to answering the questions in (a)-(d) below.
(a) Use the generate command to define a binary variable smokes that =1 if a woman smokes during pregnancy, and equals zero otherwise. Estimate a probit model for smokes with covariates motheduc, white, and log(faminc). At white=0 and faminc evaluated at the sample average, what is the estimated diference in the probability of smoking for a woman with 16 years of education and one with 12 years of education?
(b) Do you think that faminc is exogenous in the smoking equation. What about motheduc? Why or why not?
(c) Assume that motheduc and white are exogenous in the probit regression from part (a). Also assume that fatheduc is exogenous to this equation. Estimate the reduced form of log(faminc) to see if fatheduc is partially correlated with log(faminc).
(d) Test the hypothesis that log(faminc) is exogenous in the probit regression from part (a).