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Calculation Of Variance And Estimate Standard Errors

Question

Consider the investment behavior of two large corporations, General Electric and Westinghouse. These firms compete against each other and produce many of the same types of products. We might wonder if they have similar investment strategies. Investment data for 20 years for these two corporations are stored in file Inv.wf1. For each variable, the first 20 observations relates to General Electric and the last 20 observations relates to Westinghouse. The variables, for each firm, are

INV = gross investment in plant and equipment

V = value of the firm = value of common and preferred stock

K = stock of capital

A simple investment function is

INV = β1 + β2V + β3K + e      (1)

If we combine, or pool, the data for both firms, we have T = 40 observations with which to estimate the parameters of the investment function. But pooling the two sources of data is valid only if the regression parameters and the variances of the error terms are the same for both corporations. If these parameters are not the same, and we combine the data sets anyway, it is equivalent to restricting the investment function

A         Modelling the Investment function for two firms.

  1. Estimate the investment function (1) for the General Electric corporation. Write the estimated regression equation of the investment function (1) in the usual format. Test for the significance of the individual coefficients as well as the overall utility of the estimated equation.
  2. Estimate the investment function (1) for the firm, Westinghouse. Write the estimated regression equation of the investment function (1) in the usual format. Test for the significance of the individual coefficients as well as the overall utility of the estimated equation.
  3. Using the indicator variable approach (with Indicator Variable D is 1 for the 20

Westinghouse observations, and 0 otherwise) by including the intercept indicator variable and a complete set of slope indicator variable,

INV = β1 + δ1D + β2V + δ2 (D*V) + β3K + δ3 (D*K) + e,

and the Chow test, test whether the investment function for the two firms are identical.

  1. Estimate the investment function (1) assuming that the coefficients are the same for both firms and pooling the data from both firms. Write the estimated regression equation of the investment function (1) in the usual format. Interpret the coefficient estimates. Test for the significance of the individual coefficients as well as the overall utility of the estimated equation.

B         Investigating whether the Error Variances for the two firms are the same.

  1. Re-consider the estimation results of the investment equation for the two firms in parts a and b. Test at the 10% significant level, the null hypothesis of equal error variance against the alternative that the error variances for General Electric is greater than that for Westinghouse.
  2. Assuming that the error variances are different, but the coefficients are the same for both firms, pool the data from both firms and estimate the responses of investment to capital stock and value, using
  3. Generalized least squares; and
  4. Least squares with White’s variance estimator.

Compare the two sets of estimates and their standard errors.

 

Summary

The question belongs to Statistics and it discusses about calculation of variance and estimate standard errors.

Total Word Count 824

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