2. Analyze the following regression results from a regression explaining aggrega
ID: 1126496 • Letter: 2
Question
2. Analyze the following regression results from a regression explaining aggregate U. S. consumption from 1929-2003. C-5+935 Yd+.015 (W/P) where C = aggregate real consumption Yd-aggregate real disposable income (WP) = aggregate real wealth Mean Yd-5,000 Mean (W/P) 16,000 Mean C 4,920 Range of Yd: (400 12,000) Range of (W/P): (1,200-40,000) (All numbers in billions of 2003 dollars) (.90) (.01) (standard errors in parentheses) n-75 R-squared: 975 D-W (d): 1.250 In your answer, consider questions regarding likely violation of the assumptions of the classical linear regression model, as well as "significance." In this problem, students should look at the specification of the model to see whether any important variables have been omitted (such as interest rate). Functional form? Omitted variables? They should find the t-scores and determine whether they are statistically significant at the 0S level.Explanation / Answer
1. One of the likely violation is positive serial correlation as DW value is less than 1 which could also mean that there non-constant variance. Another violation may be multicollinearity since R-square is too high. To check multicollinearity we must look at the correlation matrix of wealth and income.
Due to positive serial correlation, the standard error may be underestimated and hence hypothesis testing won’t be reliable.
2. Yes, it appears there is a omitted variable bias. The regression form doesn’t take into account the real interest rate which is expected to have a negative relationship with the consumption variable.
3. The t-test score of coefficient of Yd = 0.935/.90 = 1.04
The t-test score of coefficient of W/P = 0.015/.01 = 1.50
The t_critical at 5% level of significance is 1.993. Nether of the estimated parameters of Yd and W/P are significant at that level since t-test statistic is less than t_critical
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