Empirical Evidence on the Recent Behavior and Usefulness of Simple-Sum and Weighted Measures of the Money Stock

This 1994 Federal Reserve Bank of St. Louis Review paper by K. Alec Chrystal and Ronald MacDonald asks whether replacing simple-sum monetary aggregates with expenditure-weighted Divisia (or Rotemberg Currency Equivalent) aggregates actually improves money’s empirical usefulness for predicting nominal income and for detecting causal links with real activity, and it tests this question reduced-form, with no structural identification, across seven countries: the United States, United Kingdom, Australia, Germany, Switzerland, Canada, and Japan. The comparison runs on two tracks: modified St. Louis equations (regressing quarterly log-differenced GNP/GDP on current and four lags of log-differenced government spending and money, plus the Treasury bill rate for the US), scored with three non-nested test statistics (the Akaike Information Criterion, the Davidson-MacKinnon J-test, and the Fisher-McAleer JA-test) and exclusion F-tests; and a time-series causality track using Augmented Dickey-Fuller unit-root tests, Johansen cointegration analysis, and heteroskedasticity-robust Granger-type VECM exclusion tests, with country-specific quarterly samples spanning roughly the late 1960s/1970s through 1987-1992. The results are country-specific rather than uniform: for the US, Divisia dominates simple-sum for M2 and broader aggregates (Divisia M2’s F-test for exclusion is F(5,107)=4.73, p=0.001, versus simple-sum M2’s F(5,107)=4.43, p=0.001) but simple-sum still beats Divisia for the narrow M1/M1A aggregates; the UK and Australia show clearer, broader Divisia superiority (Australia is called “probably the clearest case” of Divisia dominance, especially for broad money); Germany and Switzerland show weak informational content for money generally; Canada shows strong Divisia dominance for M2, M3, and L; and Japan is an explicit outlier where simple-sum is favored by the information criterion yet no aggregate, weighted or unweighted, is significant in the F-tests. A US pre-1980 sub-sample (1960:1-1979:3) shows the Divisia advantage present but markedly weaker, consistent with the authors’ interpretation that Divisia’s edge stems from measurement error in simple-sum aggregates that is largest during the post-1980 period of rapid financial innovation. The authors are explicit that their St. Louis-equation results speak only to relative, not absolute, performance of competing money measures, and they conclude that the evidence for Divisia, while real in several countries, is not yet robust enough to recommend it as a direct policy-targeting variable.

K. Alec Chrystal | Macro Paper Warehouse

Empirical Evidence on the Recent Behavior and Usefulness of Simple-Sum and Weighted Measures of the Money Stock