PRIMAL AND DUAL REPRESENTATIONS OF THE ERROR IN SUMMATION MONETARY AGGREGATES

Abstract: We provide primal and dual representations for the tracking error in the official monetary aggregates published by the Federal Reserve System from the standpoint of monetary aggregation theory. We show that the tracking error will be zero if either all asset stocks or their prices change proportionally. This result implies that the squared tracking error is a function of the degree of non-proportionality in the changes in either asset stocks or their prices. We present two measures of the degree of non-proportionality that were originally developed by Theil (1967) and Allen and Diewert (1981). We first illustrate the interaction between the tracking error and these measures using simulated data. We next examine the available time series, which indicate that the degree of non-proportionality in monetary data changes over time and may increase systematically under certain monetary policy regimes. In particular, we show that the degree of non-proportionality for both asset stocks and their prices was very high during 1978-1982, when the Federal Reserve was targeting nominal monetary aggregates, contributing to a large error in the measurement of the underlying policy instrument