"Life Cycle" Hypothesis of Saving: Aggregate ... - Arabictrader.com

58 The Life-Cycle Hypothesis
The constrained estimation results in the equations reported in rows (3) and
(5) of table 2.2. A comparison of row (1) and row (3) shows that this procedure
leads to estimates which are more nearly of the order of magnitude suggested by
our model. Unfortunately the serial correlation is still so high that the reliability
of the estimate is open to serious question. From row (5) it also appears that the
addition of the variable
Y L E
is again not very helpful. Though its contribution is somewhat more significant,
it again lowers the coefficient of A, and the serial correlation remains high.
A common procedure in time-series analysis when serial correlation of errors
is high is to work with first differences. In the present instance this procedure
also serves to reduce drastically the degree of multicollinearity and provides a
more meaningful test for the adequacy of the hypothesis as a causal explanation
of consumption. The results, reported in rows (6) and (9) and in figure 2.1, appear
quite favorable to the hypothesis. The multiple correlation remains quite high and
the coefficient of net worth is highly significant. Also the Durbin-Watson statistic
improves considerably and there is no longer any reason to suspect that the
reliability of the estimate is seriously affected by serial correlation of residuals.
A comparison of row (6) with row (3) reveals that the coefficient of A remains
essentially unchanged, while the coefficient of Y is reduced from 0.64 to 0.55.
On the other hand, comparison of rows (5) and (9) shows that, for hypothesis II,
estimates of all parameters remain essentially unchanged under the two estimation
methods.
These results seem to be readily explainable. When we deal with actual values
the movements of all variables are dominated by their trend. On the other hand,
when dealing with first differences as in (6) and (9), we are primarily focusing
on short-run cyclical variations. In this light, the results of row (6) suggest that
consumption is less responsive to purely cyclical and temporary fluctuations in
labor income than the estimate of row (3) would imply. The close agreement
between (5) and (9) tends to support this interpretation, since the presence of the
variable Y(L/E)—which is cyclically more stable than Y—accounts for the relative
stability of expected labor income over current labor income. It should be
remembered in this connection that according to our model consumption depends
largely on expected rather than current labor income. At the same time the fact
that both Y(L/E) and A perform a similar function in stabilizing consumption with
respect to short-run variations in Y helps to explain why the addition of the latter
variable generally tends to reduce not only the coefficient of Y but also that
of A. 16