Consider the following equation for US per capita consumption of beef: B-330.3 +49.1 In Y, -0.34PB...

 

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Consider the following equation for US per capita consumption of beef: B-330.3 +49.1 In Y, -0.34PB +0.33PRP, -15.4D, (0.13) (0.12) (4.1) (7.4) t = 6.6 N = 28 -2.6 2.7 -3.7 DW = 0.94 R² = 0.70 where B₁ = the annual per capita pounds of beef consumed in the United States in year t. In Y₁ = the log of real per capita disposable real income in the US in year t. PB₁ = average annualized real wholesale price of beef in year t (in cents per pound). PRP, = average annualized real wholesale price of pork in year t (in cents per pound). D₁ = a dummy variable equal to 1 for years in which there was a "health scare" about the dangers of red meat, 0 otherwise. (a) Provide a one-sentence interpretation of the coefficient on In Y₁. (b) Test the hypothesis of positive serial correlation using the Durbin-Watson statistic at the 5 percent level. Write out null and alternative hypotheses, the upper and lower bounds for the inconclusive region, your decision, and why you made that decision. (c) What econometric problems does this regression appear to have? What remedy would you suggest? You decide to use GLS with your regression, obtaining the following results: B = -330.3 +49.1 In Y -0.34PB +0.33PRP -15.4D, (4.1) (0.13) -2.6 (0.12) 2.7 -3.7 p = 0.82 R² = 0.70 (7.4) t = 6.6 N = 28 (d) What function of B, did you use to estimate this regression? What function of Dr did you use? (e) Suppose you want to use an LM test with the original regression. Explain how you would run that test. Specifically, what is the auxiliary equation and LM statistic? What distribution does the LM statistic follow (including the degrees of freedom)? What are the null and alternative hypotheses? What is the critical value at the 5 percent level? When would you reject the null? Consider the following equation for US per capita consumption of beef: B-330.3 +49.1 In Y, -0.34PB +0.33PRP, -15.4D, (0.13) (0.12) (4.1) (7.4) t = 6.6 N = 28 -2.6 2.7 -3.7 DW = 0.94 R² = 0.70 where B₁ = the annual per capita pounds of beef consumed in the United States in year t. In Y₁ = the log of real per capita disposable real income in the US in year t. PB₁ = average annualized real wholesale price of beef in year t (in cents per pound). PRP, = average annualized real wholesale price of pork in year t (in cents per pound). D₁ = a dummy variable equal to 1 for years in which there was a "health scare" about the dangers of red meat, 0 otherwise. (a) Provide a one-sentence interpretation of the coefficient on In Y₁. (b) Test the hypothesis of positive serial correlation using the Durbin-Watson statistic at the 5 percent level. Write out null and alternative hypotheses, the upper and lower bounds for the inconclusive region, your decision, and why you made that decision. (c) What econometric problems does this regression appear to have? What remedy would you suggest? You decide to use GLS with your regression, obtaining the following results: B = -330.3 +49.1 In Y -0.34PB +0.33PRP -15.4D, (4.1) (0.13) -2.6 (0.12) 2.7 -3.7 p = 0.82 R² = 0.70 (7.4) t = 6.6 N = 28 (d) What function of B, did you use to estimate this regression? What function of Dr did you use? (e) Suppose you want to use an LM test with the original regression. Explain how you would run that test. Specifically, what is the auxiliary equation and LM statistic? What distribution does the LM statistic follow (including the degrees of freedom)? What are the null and alternative hypotheses? What is the critical value at the 5 percent level? When would you reject the null?