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

60 The Life-Cycle Hypothesis
All the estimates reported so far are based on the least-squares method applied
to a single equation. As is well known this method leads to estimates which are
biased, even in the limit, when one or more of the “independent” variables are
related to the dependent variable by other simultaneous relations. In the present
instance the variable A can be taken as predetermined, but the same is not true
of labor income which is related to consumption via total income. That is, the
true error component of the consumption function cannot be assumed to be
uncorrelated with Y, and hence the least-squares estimates of its parameters are
not consistent. Specifically, it can be shown that, asymptotically, the estimator
of the coefficient of Y is upward-biased and that of the coefficient of A
downward-biased. 17
The only really adequate way of resolving this difficulty would be to construct a
complete model of the U.S. economy and then apply an appropriate simultaneousequations
estimation procedure. This approach would lead at least to consistent
estimates, except to the extent that the model was incomplete or misspecified and
the exogenous variables were subject to errors of measurement. Furthermore, the
efficiency of the estimates might be reduced, particularly if the theory and data
relating to other sectors of the economy were less reliable than those relating to
the consumption sector. Whatever the merits of this approach, however, we regard
the specification of a complete model beyond the scope of this paper.
A compromise followed by some authors is to introduce an accounting identity
relating consumption, saving, and income, note that saving is equal to investment,
assume that investment is autonomous, and estimate the parameters of the
consumption function from the regression of consumption on saving [39] [43].
Now in our view this procedure is likely to lead to bias in the estimates of the
parameters which is more serious than that resulting from the conventional
regression on income. The arguments supporting this conclusion are developed
formally in Appendix section B and can be summarized here as follows:
1. When the “independent” variable is subject to errors of measurement, the
resulting estimate of the regression coefficient is biased toward zero, the more so
the greater the variance of the error of measurement of the independent variable
relative to its true variance. Now since personal saving is in the order of onetenth
of disposable income, it is reasonable to suppose that the variance of true
(as distinguished from measured) personal saving is a good deal smaller than the
variance of disposable income. At the same time, personal saving, as actually
measured in the national income accounts, represents the difference between
largely independent estimates of disposable income and of personal consumption.
Hence the error of measurement of personal saving is likely to be even larger
than that of disposable income. We can therefore be rather confident that the bias
toward zero due to errors of measurement will be a good deal more serious when