A reexamination of the consumption function using frequency domain regressions

Abstract

This paper reexamines the permanent income hypothesis (PIH) in the frequency domain. In contrast to some time domain tests, our frequency domain approach provides an explicit and natural test ofboth the permanentand transitory implications of the PIH for jointly nonstationary consumption and income data. Using a simple theoretical model, we demonstrate that the PIH implies the marginal propensity to consume (MPC) out of zero frequency income is unity. The PIHalso implies that the theoretical MPC out of transitory (or high frequency) income is smaller than the long-run MPC. These theoretical restrictions are natural implications of Friedman's hypothesis that agents consume out of permanent or low frequency income and (dis)save out of transitory or high frequency income.

We test this full set of restrictions directly using spectral regression techniques. Under our set of assumptions, the derived disposable income process is shown to have a unit root and to be cointegrated with consumption. We therefore employ a systems spectral regression procedure that accommodates stochastic trends in the consumption and income series as well as the joint dependence in these series. In view of the relatively recent development of these systems spectral estimators, we also conduct Monte Carlo simulations across both low and high frequencies to assess properties of the estimator relative to established single equation techniques. New empirical estimates of the consumption function and tests of the PIH based on systems spectral regression methods are reported for U.S. aggregate consumption and income data over the period 1948–1993. The empirical results provide some evidence for the theoretical implications of the PIH.