Y = 0 + 1 X + u, where Y=Private consumption expenditure (PPP $) and X=Income (G
ID: 3059893 • Letter: Y
Question
Y = 0 + 1X + u, where Y=Private consumption expenditure (PPP $) and X=Income (GDP in PPP $).
a) Determine the estimated consumption function. Also provide R2, t-ratios and the F-statistic and the corresponding p-values, DW statistic.
b) Do the results in part (a) concur with the a priori expectations?
c) Interpret the estimated slope coefficient of X. Is it significantly different than zero ?
d) Is there any evidence of heteroscedasticity (HC) and autocorrelation (AC) in the model. How do you know?
Variable Coefficient Std. Error t-Statistic Prob. 0.605856 35624655 0.015768 4766072. 38.42336 7.474636 0.0000 0.0000 R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat 0.984660 Mean dependent var 0.983993 S.D. dependent var 6200046. Akaike info criterion 8.84E+14 Schwarz criterion -425.4329 F-statistic 1.130687 Proh/F-statistic) 2.12E+08 49005120 34.19463 34.29214 1476.355 0.000000 Breusch-Godfrey Serial Correlation LM Test: obs*R-squared 3.344751 Prob. Chi-Square(1) 0.067420 White Heteroskedasticity Test: Qhs*R-squared 0.985043 Prob. Chi-Square(2) 0.611084Explanation / Answer
(a) The consumption function is: Y = 7.474636 + (38.42336 * X).
R-squared = 0.98466.
Adjusted R-squared = 0.983993.
F-statistic = 1476.355.
p-value (F-statistic) = 0.00000
DW statistic = 1.130687.
Also, we have the t-ratios and the p-values of the following:
(b) Yes, the results in part (a) concur with the a priori expectations.
(c) For every 1 unit increase in Income, the private consumption expenditure will increase by 0.605856 units.
The estimated slope coefficient is significantly from zero since it has a p-value which is less than 0.05.
(d) There is no evidence of heteroscedasticity in the model since the p-value of the White heteroscedasticity test is greater than 0.05, thereby failing to reject the null hypothesis of heteroscedasticity.
There is also no evidence of autocorrelation in the model since the p-value of the Breusch Godfrey Serial Correlation LM test is greater than 0.05, thereby failing to reject the null hypothesis of autocorrelation.
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