In this assignment, we estimate the cost function of the US electricity industry. A cross-section data set on 145 firms from 44 states in the year of 2005 is collected. The variables in the data are...

In this assignment, we estimate the cost function of the US electricity industry. A cross-section data set on 145 firms from 44 states in the year of 2005 is collected. The variables in the data are total costs, factor prices (the wage rate, the price of fuel, and the rental price of capital) and output. These variables are contained in the file “electric.wf1”, including total cost (TC), output (Q), wage rate (wage), the rental price of capital (capital), and fuel price (fuel). The cost function takes the Cobb-Douglas form, which can be written as XXXXXXXXXX ? ? ? ? i ? i i i i TC ? Q p p p (1) where TCi is the total cost for firm i, Qi is the firm i’s output, and pi1 to pi3 are factor prices for inputs for firm i (wage, capital, and fuel respectively). Taking the natural log of equation (1), we obtain the following linear relationship: log(TCi) = ?1 + ?2 log(Qi) + ?3 log(pi1) + ?4 log(pi2) + ?5 log(pi3) + ei,(2) where ?1=log(?) and ?i is the error term. 1. Provide economic meanings of the each slope coefficients. Estimate the equation (2) by the ordinary least-squares method. 2. Plot the squared of residuals from equation (2) against log(Qi) (squared residuals on the y-axis). Comment on the main features in the variability of the total cost, in relation to the problem heteroskedasticity, giving economic interpretations. 3. Conduct White’s test, as a general test for heteroskedasticity. It is suggested from the residual plot in Question 2 that the variance of the term is expressed as 2 2 2 / log( ) ? i ? ? Qi ,(3) where var( ) 2 i i ? ? e . 4. Conduct the GLS (or weighted least-squares) assuming the form of the heteroskedasticity given in XXXXXXXXXXReport the GLS and OLS (ordinary least squares) regression results in the equation form and compare them with OLS results (compare estimated coefficients, standard errors, t-test results and R2 ). Briefly describe how the GLS makes difference in estimation results. 6. Based on the GLS regression, test the hypothesis that ?3 + ?4 + ?5 = 1 using the F-test (Wald test). Explain the economic meaning of this hypothesis. 7. Test for the normality of the error term in the GLS regression using the Jarque-Bera test. Determine whether there is any evidence of non-normality of error term. You will notice from the histogram of the residuals that there are extreme values in the error term., which is a likely cause of the error term showing non-normality. This means that some firms are extremely cost inefficient. 8. Conduct the RESET test for the GLS regression. Is there any evidence of specification error? 9. Combining the results obtained in Questions 7 and 8, discuss the main problems associated with the model and suggest (at least one) possible solutions in the context of model specification. Each questions carries equal mark of 5. All the statistical tests from Question 5 should be based on GLS regression. You can access these tests by clicking View button from the GLS regression output (not from the OLS regression output