Econ 1150 Problem Set 3

October 2024

1. We have the population regression:

wagei = β0 + β1educationi + β2AF QTi + ui

where individual i has hourly wage wagei , years of education educationi and AFQT score AF QTi . The Armed Forces Qualifying Test (AFQT) is a general aptitude test and is widely used as a measure of ability or fluid intelligence.

You are trying to estimate the effect of education on hourly wage. However, in your sample regression, suppose you left out AF QTi and estimated:

Assume that E(ui |educationi) = 0 and that β1 > 0, β2 > 0 and cov(educationi , AF QTi) > 0.

(a) Using the Law of Iterated Expectations, show that cov(educationi , ui) = 0.

(b) Using the covariance formula for your sample regression estimate βˆ1, show that βˆ1 con-verges to the sum of the true population parameter β1 and a bias term coming from leaving out AF QTi .

(c) What is the direction of the bias? Will you overestimate or underestimate the relation-ship between wages and years of education?

(d) Explain the economic intuition behind why this bias would occur.

2. Using data from the 2001-2002 United States House of Representatives, you estimate the following regression:

where aauwi is a voting score that measures how supportive member of the House i is on women’s issues (e.g., reproductive rights and gender-based violence), propgirlsi is the propor-tion of member i’s children who are female, nchildi is member i’s total number of children, agei is i’s age, femalei ∈ {0, 1} is an equal to 1 if i is female, and whitei ∈ {0, 1} is equal to 1 if i is white.

(a) If you’re trying to estimate the effect of having daughters on members’ voting behavior. on women’s issues, what is your outcome variable, which are your explanatory variables of interest and which are your control variables?

(b) For a member with two children, what is the marginal effect of having a daughter?

(c) Interpret the constant term and the rest of the coefficients. Are any of them not different from zero at the 5% significance level?

(d) If your variable of interest is propgirlsi , which particular control variable, if not included, will bias your estimate of your effect of interest the most? Why?

(e) How would you argue for that these results identify the causal impact of having daughters on voting behavior. on women’s issues? What is a possible omitted variable?