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The data in WAGEPAN.RAW are from Vella and Verbeek (1998) for 545 men who worked every year from 1980 to 1987. Consider the wage equation

The variables are described in the data set. Notice that education does not change over time. a. Estimate this equation by pooled OLS, and report the results in standard form. Are the usual OLS standard errors reliable, even if ci is uncorrelated with all explanatory variables? Explain. Compute appropriate standard errors.

b. Estimate the wage equation by random effects. Compare your estimates with the pooled OLS estimates.

c. Now estimate the equation by fixed effects. Why is experit redundant in the model even though it changes over time? What happens to the marriage and union premiums as compared with the random e¤ects estimates?

d. Now add interactions of the form educ and estimate the equation by fixed e¤ects. Has the return to education increased over time?

e. Return to the original model estimated by fixed effects in part c. Add a lead of the union variable, unioni;tþ1 to the equation, and estimate the model by fixed effects (note that you lose the data for 1987). Is unioni;tþ1 significant? What does this result say about strict exogeneity of union membership?