Use the data in WAGEPAN.DTA to answer the following questions.
(i) Using lwage as the dependent variable, estimate a model that only contains an intercept and the year dummies d81 through d87. Use pooled OLS, RE, FE, and FD (where in the latter case you difference the year dummies, along with lwage, and omit an overall constant in the FD regression). What do you conclude about the coefficients on the year dummies?
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(ii) Add the time-constant variables educ, black, and hisp to the model, and estimate it by OLS and RE. How do the coefficients compare? What happens if you estimate the equation by FE?
(iii) What do you conclude about the four estimation methods when the model includes only variables that change just across t or just across i?
(iv) Now estimate the equation
by random effects. Do the coefficients seem reasonable? How do the nonrobust and clusterrobust standard errors compare?
(v) Now estimate the equation
by fixed effects, being sure to include the full set of time dummies to reflect the different interecepts. How do the estimates of b1 and b2 compare with those in part (iv)? Compute the
usual FE standard errors and the cluster-robust standard errors. How do they compare?
(vi) Obtain the time averages unioni and marriedi. Along with educ, black, and hisp, add these to the equation from part (iv). Verify that the CRE estimates of b1 and b1 are identical to the FE estimates.
(vii) Obtain the robust, variable addition Hauman test. What do you conclude about RE versus FE?
(viii) Let educ have an interactive effect with both union and married and estimate the model by fixed effects. Are the interactions individually or jointly significant? Why are the coefficients on union and married now imprecisely estimated?
(ix) Estimate the average partial effects of union and married for the model estimated in part (viii). How do these compare with the FE estimates from part (v)?
(x) Verify that for the model in part (viii) the CRE estimates are the same as the FE estimates when they should be.