Production, Sales and the Change in Inventories: An Identity that Doesn't Add Up

In this paper we examine two different measures of monthly production that have been used by economists. The first measure, which we refer to as IP, is the index of industrial production constructed by the Board of Governors of the Federal Reserve. This measure is used extensively in empirical work on the business cycle, as well as by policymakers and others to assess the current state of the economy. The second measure, which we refer to as Y4, is constructed from the accounting identity that output equals sales plus the change in inventories. Sales and inventory data are reported by the Department of Commerce. This measure of output is frequently used to estimate models of inventory accumulation. Theoretically, these two series measure the same underlying economic variable -- the production of goods by firms during the month. We show here that the time series properties of these two series are radically different. We examine means, variances, and serial correlation coefficients of the log growth rates, and show that these statistics differ substantially between the two series. In addition, the cross-correlations between the two seasonally adjusted series range from .7 to .0 and are in most cases less than .4. We then demonstrate the significance of these differences in two ways. First, we estimate a model of white noise measurement error for the two series. The estimates indicate that in 15 out of 20 2-digit industries measurement error accounts for over 40% of the variation in the monthly growth rates of seasonally adjusted industrial production data. Second, we show that the variance bounds results of Blinder’s (1986) study of inventory behavior are partially reversed when the IF rather than the Y4 output measure is used.