Use a 50% random subsample of the wage-hours data in Section 21.3

(a) Can \(\beta\) be directly interpreted as a labor supply elasticity? Explain.

(b) For the following estimators: (1) pooled OLS, (2) between, (3) within, (4) first differences, (5) random effects GLS, (6) random effects MLE give (i) \(\widehat{\beta}\) (estimated coefficient of Inwg), (ii) default standard error, and (iii) panel bootstrap standard error with 200 replications.

(c) Are the estimates of \(\beta\) similar?

(d) Is there a systematic difference between default standard errors and panelrobust standard errors?

(e) Will the pooled OLS estimator in part (b) be consistent for \(\beta\) in a fixed effects model? Will the pooled OLS estimator be consistent for \(\beta\) in a random effects model?

(f) Perform a Hausman test of the difference between the fixed and random effects (GLS) estimates of \(\beta\) in this model. Do this manually using the earlier regression output with the default standard errors. What do you conclude and which model is favored?
(g) Given the preceding evidence, do you believe that the labor supply curve is upward sloping Explain.

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21.3. Linear Panel Example: Hours and Wages An important issue in labor economics is the responsiveness of labor supply to wages. The standard textbook model of labor supply suggests that for people already working the effect of a wage increase on labor supply is ambiguous, with an income effect pushing in the direction of less work offsetting a substitution effect in the direction of more work. Cross-section analysis for adult males finds a relatively small positive response to hours worked. However, it is possible that this association is spurious, merely reflect- ing a greater unobserved desire to work being positively associated with higher wages.