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

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- 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?

2- 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

A linear consumption function is generally expressed as

C = f (Y) = a + bY (a > 0, 0 < b < 1)

This equation indicates that consumption is a linear function of income. ‘a’ and ‘b’ are the two parameters of this equation. An economy spends some minimum expenditure ‘a’ on consumption (C), may be out of their past savings, even when the level of income (Y) is zero. o this, proportion ‘b’ of additional income is added up, as and when income of the economy rises. As consumption cannot increase by an amount more than the increase in income, ‘b’ always lies between 0 and 1. Thus, the consumption rises by a lesser absolute amount than the increase in income.
   
The relationship between the level of consumption and the level of income can be explained with the help of the following, example. Suppose, consumption of a country at zero level of income is Rs. 30 crores. Further, let us assume that the country consumes 80% of the every additional income. The consumption function of the country would be C = 30 + 0.80 Y. Now, we can easily find amounts of consumption expenditure corresponding to different levels of national income. When the national income rises to Rs. 200 crores, its consumption expenditure would be (30 + 0.80 * 200) or Rs. 190 crores and so on.

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