Measurement Error in Monetary Aggregates: A Markov Switching Factor Approach

Abstract

This paper compares the different dynamics of the simple sum monetary aggregates and the Divisia monetary aggregate indexes over time, over the business cycle, and across high and low inflation and interest rate phases. Although traditional comparisons of the series sometimes suggest that simple sum and Divisia monetary aggregates share similar dynamics, there are important differences during certain periods, such as around turning points. These differences cannot be evaluated by their average behavior. We use a factor model with regime switching. The model separates out the common movements underlying the monetary aggregate indexes, summarized in the dynamic factor, from individual variations in each individual series, captured by the idiosyncratic terms. The idiosyncratic terms and the measurement errors reveal where the monetary indexes differ. We find several new results. In general, the idiosyncratic terms for both the simple sum aggregates and the Divisia indexes display a business cycle pattern, especially since 1980. They generally rise around the end of high interest rate phases – a couple of quarters before the beginning of recessions – and fall during recessions to subsequently converge to their average in the beginning of expansions. We find that the major differences between the simple sum aggregates and Divisia indexes occur around the beginnings and ends of economic recessions, and during some high interest rate phases. We note the policy relevance of the inferences. Indeed, as Belongia (1996) has observed in this regard, "measurement matters."Measurement error; monetary aggregation; Divisia index; aggregation; state space; Markov switching; monetary policy; index number theory; factor models