THE INTEREST ELASTICITY OF SAVINGS: AN ANALYSIS BASED ON EXPLICIT PRIORS
| Date | 01 November 1984 |
| DOI | http://doi.org/10.1111/j.1468-0084.1984.mp46004003.x |
| Author | Joachim Zietz |
| Published date | 01 November 1984 |
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 46,4 (1984)
0305-9049 $3.00
THE INTEREST ELASTICITY OF SAVINGS: AN
ANALYSIS BASED ON EXPLICIT PRIORS
Joachim Zietz*
INTRODUCTION
The interest elasticity of aggregate savings has received considerable
attention since Boskin's (1978) revival of the issue. This is not surpris-
ing given the central role of this parameter for a number of important
questions of economic policy (Boskin, 1978). What is unusual, however,
is the diversity of research results that are claimed to be consistent with
the data.
As the applied literature on non-nested tests in econometrics suggests
(e.g. Pesaran, 1982), one way to reduce the uncertainty regarding
certain economically relevant parameter estimates may be to test alter-
native model specifications against each other rather than just against
the data. However, a disadvantage of non-nested tests for the applied
researcher may be that, like all classical statistical inference they do not
offer a formal way to incorporate a priori knowledge in the statistical
test procedure. In light of that, the purpose of this paper is to demon-
strate how a Bayesian sensitivity analysis as suggested by Learner (1978)
can be usefully applied in such a situation. In particular, it is shown
how the posterior mean of the interest rate parameter, the focus coeffi-
cient in all studies on the interest elasticity of savings, changes with the
degree of confidence one has in the prior assumptions regarding the
model specification. Three non-nested model specifications of the
consumption function which have recently appeared in the literature
serve as alternative specification priors.
The results of the sensitivity analysis clearly demonstrate that the
data can support a wide range of values for the interest rate parameter,
both in the positive and negative range. Which of the values is ultimately
chosen for reporting purposes critically depends on the prior confidence
one has in a particular specification of the consumption function.
METIIODOLOG'r
The three alternative specifications of the consumption function con-
sidered in this study are the models by Boskin (1978), Gylfason (1981),
* The author wishes to thank the Economics Department at the American University in
Washington, D.C., for computational support. Anonymous referees provided helpful comments
on an earlier version of tise paper. The usual disclaimer applies.
311
312 BULLETIN
and Davidson et al. (1978). These specifications provide three distinct
yet viable approaches to modelling aggregate consumption behaviour.
The first step of the testing procedure consists of fitting an artificially
nested model to the data, using no parameter restrictions. The second
step employs a Bayesian-type framework based on explicit priors to
identify how the interest rate parameter varies with the degree of
certainty one has about the parameter restrictions associated with the
three models of the consumption function.
In what follows, the three alternative models of consumption
behaviours utilized in this study will be introduced.
The model used by Boskin (1978) for estimating purposes is of the
formlnC=a0 +a1lnY+a2lnY(-1)+a3lnW +a4inun +a5r +a6pe(2.1)
where the prefix in denotes the natural logarithm; C is consumption, Y
disposable income, and W beginning-of-period wealth; all of these
variables are measured in real per capita terms. The variable un repre-
sents the unemployment rate, r the expected real after-tax return on
capital and pe the expected rate of inflation. Lagged disposable income
is intended to proxy expected income. The variable un is supposed to
capture cyclical variations in consumption and pe a real balance effect
and/or the effect of uncertainty on consumption.
Similar to Boskin, Gylfason (1981) incorporates the real rate of
return into his model, although in its before-tax form and split up into
its two components, the nominal interest rate (rn) and the expected
rate of inflation. Gylfason derives his estimating equation by assuming
that the elasticities of C with respect to Y and W sum to unity. He also
postulates a partial adjustment process between the desired and the
actual average propensity to consume. For the sake of simplifying the
subsequent analysis Gylfason's original model specification will be
changed somewhat by replacing the nominal interest rate with r. the
real after-tax interest rate. Hence, the version of Gylfason's model used
here can be written as
in C = a0 + in Y + a ln(W/Y) + a2 ln C(l)/Y(l) + a3r + a4pe (2.2)
The third model to be analysed has been suggested by Davidson et al.
(1978) in their study of UK consumption behaviour. Unlike Boskin and
Gylfason, who explicitly concentrate on identifying the interest elasti-
city of savings, Davidson et al. are concerned with the general specifi-
cation issue as applied to consumption functions. In fact, their preferred
model for the UK does not even include an interest rate variable.
The version of their model used here is given by
ln C a0 + in C(-1) + a1(in Y - in Y(l)) + a2 In C(l)/Y(--1)
+a3r+a4pe (2.3)
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