Consider the data file mroz on working wives. Use the 428 observations on married women who participate in the labor force. In this exercise, we examine the effectiveness of alternative standard errors for the IV estimator. Estimate the model in Example 10.5 using IV/2SLS using both MOTHEREDUC and FATHEREDUC as IV. These will serve as our baseline results.

a. Calculate the IV/2SLS residuals, \(\hat{e}_{I V}\). Plot them versus EXPER. Do the residuals exhibit a pattern consistent with homoskedasticity?

b. Regress \(\hat{e}_{I V}^{2}\) against a constant and EXPER. Apply the \(N R^{2}\) test from Chapter 8 to test for the presence of heteroskedasticity.

c. Obtain the IV/2SLS estimates with the software option for Heteroskedasticity Robust Standard Errors. Are the robust standard errors larger or smaller than those for the baseline model? Compute the \(95 \%\) interval estimate for the coefficient of EDUC using the robust standard error.

d. Obtain the IV/2SLS estimates with the software option for Bootstrap standard errors, using \(B=200\) bootstrap replications. Are the bootstrap standard errors larger or smaller than those for the baseline model? How do they compare to the heteroskedasticity robust standard errors in (c)? Compute the \(95 \%\) interval estimate for the coefficient of EDUC using the bootstrap standard error.