Do interest rates lead real sales and inventories? A spectral analysis approach - Statistical Data Included

Business Economics, April, 2002 by Maurice Larrain

This paper uses spectral analysis to study aggregate sales, inventories, and interest rates from a macroeconomic perspective. We assume countercyclical Federal Reserve policy acts on economic growth, sales, and inventories with a time lag of unknown duration. Interest rate changes affect sales first, and through sales, they indirectly influence inventories. Viewed from this perspective, changes in interest rates may be expected to have a leading long-run negative statistical association with sales. In addition, attempts to maintain proportionality between inventories and sales may explain a cyclical lead by sales on inventories and a positive correlation between these two variables. In turn, the lagged response of sales to interest rates and the co-movement of sales and inventories may explain, albeit indirectly, why a moderate long-run negative statistical association of inventories to interest rates may also be expected.

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Forecasting business conditions is a critical function of many business economists, and there is a continuing quest for better tools to do this. This paper uses spectral analysis techniques to analyze nominal interest rates, real sales, and inventories from a macroeconomic perspective. Its primary purpose is to identify leads and lags between these three major and interrelated business cycle variables. A secondary outcome bears on the relative importance attached to inventories as compared to sales in business cycle analysis. In our view, the empirical role of inventories in recessions would be more complete if there were consideration of possible predictive leads by sales, which would make it easier for business to anticipate inventory behavior.

Spectral analysis is a statistical procedure that appears promising in business cycle analysis because it estimates cycles, correlations, lags, and turning points. It provides valuable diagnostics and complements other time series techniques. Its main objective is the decomposition of time series into their component frequencies. The analysis seeks to identify statistically significant cycles and lead-lag relationships that could be useful to applied economists.

Interest rate changes act on the economy with a time lag whose duration is to be determined. In turn, economic growth and changes in output are closely associated with changes in real sales, (1) and the latter are related to real inventories. There are two basic explanations for inventory behavior. One is known as the production-smoothing model. This theory asserts that the firm would be able to decrease costs if it meets temporarily high demand by smoothing production over several periods. This model makes three predictions: sales are negatively correlated to inventory investment over the short run, inventories are negatively correlated to interest rates, and sales are more variable than production. The other explanation for inventory behavior is based on accelerator models first proposed by Metzler (1941). In this view, if sales growth exceeds inventory growth there would be an ensuing inventory build-up to restore proportionality to the sales-inventory ratio. If, instead, sales growth were to be lower than inventory growth, then inventories would be liquidated, thus once again restoring proportionality. The model predicts that sales are positively correlated to inventories over the long run. Metzler's accelerator view was found to be important because it could generate business cycles in Keynesian models.

The results from this paper indicate that changes in interest rates have a leading long-run negative statistical association with sales growth. Furthermore, the results also indicate that sales appear to be positively correlated to, and lead, inventories. In turn, the lagged response of sales to interest rates and the likely co-movement of sales and inventories may help explain, albeit indirectly, why a moderate long-run negative statistical association of inventories to interest rates is to be expected. Though the actual relationship of sales to inventories is controversial, our results are consistent with the sales-inventory accelerator perspective, whereby sales and inventories are kept proportional to each other.

Our results are tentative on two counts. One count is usual: more studies are needed to confirm results. The second count is more serious: there is no agreement on uniform methods to estimate leads and lags with spectral analysis or even on whether such estimation is possible. However, in this paper we show that it is possible to make tentative estimates of lags. Thus, our application of spectral techniques indicates that interest rates are negatively correlated with sales and lead them by nearly twenty months. The inverse correlation presumably reflects the long-term effects of interest rate changes on economic activity. This would seem to imply that interest rates may be a leading indicator of real sales. Similarly, business sales appear to lead inventories by an average of ten months, which may lend some support to lagged accelerator models of inventory behavior.