Econometrics – Spring 2018

Problem Set 5



This project is due on Tuesday, the 24th of April in class. A hard copy has to be handed in

before your lecture begins.

Question 1

Discuss an application of difference-in-differences estimator and how this technique can be used to

isolate the program/policy effect. Carefully frame the problem (what is it that you are trying to evaluate?)

and define the variables involved. The application can be taken from the textbook or lectures.

Question 2

You want to estimate the equation

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We believe cov(w1i, ui) = 0. But we have variables z1i and z2i that you can use as instrumental

variables.

a) How would you implement two stage least squares to estimate α1?

b) What properties should z1i and z2i satisfy?

c) Can you test whether z1i and z2i satisfy each of the conditions in (b)? Explain carefully.

Question 3

Consider the regression

GHi = α0 + α1ROi + ei

where GHi = 1 if individual i has good health and GHi = 0 otherwise. Further, ROi = 1 if individual

i is randomly offered subsidized health insurance and ROi = 0 otherwise.

(a) Why must you account for heteroskedasticity with this linear probability model?

(b) Do you need to worry that cov(ROi, ei) = 0 and hence you may obtain inconsistent results? Care-

fully explain your answer.

(c) A researcher argues that you have omitted variable bias since you do not account for other charac-

teristics. Evaluate her claim.

Question 4

You have a panel data set that has observations for years 1, 2 and 3 for everyone. Some individuals

take training in year 2 and do not work in this year. No one takes training in years 1 or 3. You want to

estimate the return to training by running the following regression for years 1 and 3

Yit = β1Si + β2Ait + β3A + β4TRit + ai + uit

where Yit denotes income for person i in year t, Si is the level of schooling person i, Ait is the age of

person i in year t, and TRit is a dummy variable coded 1 if person i has received training by year t and

zero otherwise. The problem you face is that TRit is likely to be correlated with ai.

1. How would you use a first difference model to estimate the causal effect of training on income?

What do you need to assume about the correlations between TRi3, ui1 and ui3. Can you estimate

the coefficient on Si with this approach? Carefully explain your answer.

2. Suppose that someone argues that individuals tend to enter training in year 2 if they have a low

value of ui1 . Suppose you are told that the unemployment rate in individual i’s area in year 1,

URi1 is likely be correlated with TRi1 but not with ui1 or ui3 . How would you now estimate the

coefficient on training? Carefully explain your answer.