The data file grunfeld 2 contains annual data on the gross investment, capital stock, and the value of the firm, measured by the value of common and preferred stock for General Electric and Westinghouse, during the period 1935-1954. These data have been used to train econometricians for almost 60 years, and still provide valuable lessons.

a. Create an indicator variable \(G E=1\) for General Electric and \(G E=0\) for Westinghouse. Using the combined data on both firms, use OLS to estimate the model of investment, \(I N V\), as a function of the value of the firms, \(V\), and capital stock, \(K\), also the indicator variable \(G E\) and the interactions of \(G E\) with \(V\) and \(K\). That is \(I N V=f(\) const, \(V, K, G E, G E \times V, G E \times K)\). Test the joint significance of the variables \(G E, G E \times V, G E \times K\) at the \(5 \%\) level. What does this test reveal about the two firms' investment characteristics?

b. Obtain the OLS residuals from (a) and regress their squares on the indicator variable \(G E\). Use the result of this regression to test for heteroskedasticity across the firms at the \(1 \%\) level.

c. Reestimate the model in (a) using OLS with heteroskedasticity robust standard errors. Test the joint significance of the variables \(G E, G E \times V, G E \times K\) at the \(5 \%\) level. Does your conclusion change?

d. Estimate the investment model separately for General Electric and Westinghouse. Let the estimated error variances be \(\hat{\sigma}_{G E}^{2}\) and \(\hat{\sigma}_{W E}^{2}\). For which firm is the estimated error variance smaller?

e. Create a variable \(W\) that takes the value \(\hat{\sigma}_{G E}^{2}\) when \(G E=1\) and takes the value \(\hat{\sigma}_{W E}^{2}\) when \(G E=0\). Estimate the model in (a) by FGLS with weighting variable \(W\). Test the joint significance of the variables \(G E, G E \times V, G E \times K\) at the \(5 \%\) level. Does your conclusion change?