Use the data in 401KSUBS.RAW for this exercise. The equation of interest is a linear probability model:
pira = β0 + β1p401k + β2inc + β3inc2 + β4age + β5age2 + u.
The goal is to test whether there is a tradeoff between participating in a 401(k) plan and having an individual retirement account (IRA). Therefore, we want to estimate β1.
(i) Estimate the equation by OLS and discuss the estimated effect of p401k.
(ii) For the purposes of estimating the ceteris paribus tradeoff between participation in two different types of retirement savings plans, what might be a problem with ordinary least squares?
(iii) The variable e401k is a binary variable equal to one if a worker is eligible to participate in a 401(k) plan. Explain what is required for e401k to be a valid IV for p401k. Do these assumptions seem reasonable?
(iv) Estimate the reduced form for p401k and verify that e401k has significant partial correlation with p401k. Since the reduced form is also a linear probability model, use a heteroskedasticity-robust standard error.
(v) Now, estimate the structural equation by IV and compare the estimate of β1 with the OLS estimate. Again, you should obtain heteroskedasticity-robust standard errors.
(vi) Test the null hypothesis that p401k is in fact exogenous, using a heteroskedasticity-robust test.
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