Part 1: GMM for Cross-sectional data
For this part, use the same dataset used in Assignment 3, but without sub-setting it.
dat$ex76 <- with(dat, age76-ed76-6)
We want to estimate the return to education using the following model:
log(wage76) = β0 + β1ed76 + β2ex76 + β3(ex762/100) + β4black + β5smsa76r + β6kww + u
In Table 2 of Card (1993), the author considers parental education and family structure as controls. Do you think we should control for these variables? Explain. You can cite Card’s arguments if you want.
In Table 4, we see that David Card explores the possibility of kww being endogenous. To solve the problem,he tries to use iq as instrument for kww. Can you explain why kww may be endogenous and why iq may be a good instrument for kww? You can cite Card’s arguments if you want.
Estimate the model by OLS and interpret the coefficients of ed76 and kww.
Estimate the model using the following methods:
a. IV using nearc4 as instrument for ed76
b. IV using nearc4 as instrument for ed76 and iq as instrument of kww.
c. 2SLS using nearc2 and nearc4 as instrument for ed76.
d. 2SLS using nearc2 and nearc4 as instrument for ed76 and iq as instrument for kww.
e. GMM using nearc2 and nearc4 as instrument for ed76.
f. GMM using nearc2 and nearc4 as instrument for ed76 and iq as instrument for kww.
For each model, interpret the coefficients of ed76 and kww. Assume that heteroskedasticity may be present when you do significance tests. Can you explain the difference between these estimates and the OLS estimates?
Do you see an efficiency gain in f versus d and e versus c?
Using estimations e and f of question 4, test the validity of the over-identifying restriction. Interpret your result.
Using estimation f of question 4, test individually if ed76 and kww are exogenous.
Discuss the strength of the instruments nearc4, nearc2 and iq.
Using estimation f of question 4, test the hypothesis that black workers from SMSA areas have the same wage as non-black workers not from SMSA areas, holding the other regressors fixed. Test the hypothesis using the Wald and LR statistics.
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