Keynes Postulated That the Marginal Propensity to Consume (MPC = $\frac { \Delta C } { \Delta Y _ { p d } }$

Essay

Keynes postulated that the marginal propensity to consume (MPC = $\frac { \Delta C } { \Delta Y _ { p d } }$ )is between zero and one. He also hypothesized that the average propensity to consume (APC = $\frac { \Delta C } { \Delta Y _ { p d } }$ )would fall as personal disposable income $Y _ { p d }$ increased.
(a)Specify a linear consumption function. Show that the assumption of a falling APC implies the presence of a positive intercept.
(b)Using annual per capita data, estimation of the consumption function for the United States results in the following output for the years 1929-1938: $\hat { C } _ { t }$ = 981.35 + 0.735 $Y _ { p d , t }$ , R² = 0.98, SER= 50.65
(158.65)(0.038)
Can you reject the null hypothesis that the slope is less than one? Greater than zero? Test the hypothesis that the intercept is zero. Should you be concerned about the sample size when conducting these tests? What other threats to internal validity may be present here?
(c)Given the GDP identity for a closed economy, $Y _ { t } \equiv C _ { t } + I _ { t } + G _ { t }$ show why economists saw important policy implications in finding an APC that would decrease over time.
(d)Simon Kuznets, who won the Nobel Prize in economics, collected data on consumption expenditures and national income from 1869 to 1938 and found, using overlapping period averages, that the APC was relatively constant over this period. To reconcile this finding with the regression results, Milton Friedman, who also won the Nobel Prize, formulated the "permanent income" hypothesis. In essence, Friedman hypothesized that both actual consumption and income are measured with error, $\overline { C _ { t } } = C _ { t } + v _ { t }$ and $\bar { Y } _ { t } = Y _ { t } + w _ { s }$ where $C _ { t }$ and $Y _ { t }$ were called "permanent" consumption and income, respectively, and $v _ { t }$ and $w _ { t }$ , the two measurement errors, were labeled transitory consumption and income. Friedman hypothesized that the transitory components were purely random error terms, uncorrelated with the permanent parts.
Let permanent consumption and income be related as follows: $C _ { t } = k \times Y _ { p d t } + u _ { t }$ so that the APC and MPC are the same and constant over time. Furthermore, let both transitory and permanent income be independent of the error term. Show that by regressing actual consumption on actual income, the MPC will be downward biased, and the intercept will be greater than zero, even in large samples (to simplify the analysis, assume that permanent income and all of the errors are i.i.d. and mutually independent).