Econometrics. A. Consider a linear consumption function expressing real consumpt

Question

Econometrics.

A. Consider a linear consumption function expressing real consumption expenditures, Y, as a function of real disposable income, X1. Both variables are measured in billions of 1982 dollars. The model is estimated using OLS and employs a time-series sample of size n=123. The following results are obtained.

          Y=450 + 0.90X1                ESS=2.8                RSS=I .5                      Y = 900

1- Interpret the estimated consumption function.

2- What percentage of total variation tn consumption is explained by the regression model as a whole?

3-  Is there a need to interpret the adjusted R2 rather than the unadjusted R2? Explain.

4- What are the features of the estimates of the parameters of this model and the corresponding sample regression line? Explain each briefly. [Hint, see on the features of OLS.]

5- Based on the available information, is there a reason to worry about autocorrelation in this model? Why or why not? Heteroscedasticity? Why or why not?

6- Suppose both theory and previous empirical work using models similar to the one above suggest that ßo=400. Besides the differences in the samples and possibly omitted variables, what else could have caused the estimated intercept of the above model to be larger than 400?

Explanation / Answer

1. The relation between consumption and income is positive. With one billion increase in the income, the consumption increases by 0.90 billion.

2. To calculate the percentage of total variation tn consumption is explained by the regression model we need to calculate the R^2.

R2 = ESS/TSS

ESS + RSS = TSS

given that: ESS = 2.8

RSS = 1.5

TSS = 2.8+1.5 = 4.3

thus R2 = 2.8/4.3 = 0.6511 = 65.11%

thus 65.11% of total variation tn consumption is explained by the regression model as a whole.

3. No the need to interpret adjusted R2 is not required as we have only one independent variable in the model and adjusted R2 values are required when we have more than one independent variable in the model. Adju. R2 tells the effect on the model fitness when we introduce a new independent variable in the model.

4. Features of the model and the regression lines

a. From the regression results we can see that MPC is 0.9, meaning that from every $1 income earned the individual is spending 90 cents.

b. The equation has a positive intercept too which is $450, thereby meaning that thought the income of the person is nil, he spends $450 somehow as his expenditure. This means that it is his autonomous expenditure.

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