Money, Income and Dynamic Lag Patterns

Abstract

In traditional vector autoregression (VAR) models, a fixed lag length is imposed on all variables and across all observation periods. This practice, however, is prone to potential model misspecifications. More specifically, underparameterization (due to too short lag lengths) results in estimation bias, while overparameterization (due to too long lag lengths) results in a loss of degrees of freedom and thus estimation efficiency. The significance of such problems can be exemplified by recent results of money-income causality tests based on conventional VAR methodology. The empirical relationship between money and income during the postwar period has long been found fragile by Litterman and Weiss [7], and Sims [8]. Recently, Friedman and Kuttner [3] argued that since the late 1970s, monetary aggregates have ceased to predict real income in a four-lag VAR system including an interest rate variable. Further, by extending the sample period from 1985 to 1988, they [4] weakened Stock and Watson's [9] statistical support for money-income causality. The robustness of Friedman and Kuttner's findings, however, has been questioned.' For example, Thoma [10] documented subsample instability in causality statistics, particularly in the 1980s. Becketti and Morris [1] argued for longer lag lengths in the VARs. Webb [11] further suggested that two lag lengths--one for the dependent variable and another for all independent variables-be considered in each equation. The objective of this paper is to provide some explanations for these puzzles. First, the marginal significance levels, or p-values, of money-income Granger causality tests are shown to vary remarkably over subsamples as well as different lag specifications. Second, as an extension to the standard VAR estimation strategy, a lag selection procedure is applied to determine the optimal lag structure that can vary across both variables and observation periods. The empirical results suggest that previous findings on the collapse of the money-income causal relationship is attributable to lag length misspecification, especially for money. The rest of the paper is organized as follows. The next section discusses temporal instability in causality test statistics. Section III outlines a new lag selection method, and Section IV presents