The Cyclical Relationship between Output and Prices: An Analysis in the Frequency Domain
Pakko, Michael R., Journal of Money, Credit & Banking
THE CYCLICAL BEHAVIOR of the price level and its implications for evaluating macroeconomic models have recently been subjects of controversy. Dating at least as far back as Burns and Mitchell (1946), it has been taken as an established point of fact that the price level is procyclical. However, a number of recent studies have found that detrended measures of output and prices have displayed a negative correlation over the postwar period. Kydland and Prescott (1990) found both the CPI and the GNP deflator to be negatively correlated with real GNP. This finding was confirmed and shown to be robust to alternative detrending methods by Cooley and Ohanian (1991). Moreover, Backus and Kehoe (1992), Chadha and Prasad (1994), Fiorito and Kollintzas (1994), and Kim (1996) have shown that price fluctuations have also been countercyclical in a number of other countries over recent years.
This paper seeks to uncover additional information about the dynamic relationship between the price level and output in the United States by examining the relationship in the frequency domain: Cospectra of output and the prices for various sample periods are estimated to decompose the price-output correlation into frequency components. The purpose of this decomposition is to investigate whether the differences in price-output correlations across sample periods reflect shifts in the relative importance of various frequencies embedded within the correlation, or whether they reflect more fundamental changes in the entire spectral relationship.
The cyclicality of the price level has been attributed with having important implications for the evaluation of macroeconomic models. Cooley and Ohanian (1991) concluded that "much of the emphasis on developing models that feature a positive relationship between output and prices may have been unnecessary." Kydland and Prescott (1990) stated the case even more forcefully: "any theory in which procyclical prices figure crucially in accounting for postwar business cycle fluctuations is doomed to failure." On the surface, the finding lends support to flexible price, supply-driven models: In such a model, endogenous procyclical money demand fluctuations arising from supply-shock-induced movements in output produce inverse movements in the price level.
However, the price-output correlation has proven to be a less-than-perfect statistic for distinguishing among different classes of macroeconomic models. Hall (1995) and Judd and Trehan (1995) demonstrate that demand-driven models with sluggish nominal price adjustment can generate countercylical price behavior. Chadha and Prasad (1993) show that alternative demand-driven and supply-driven models are both capable of generating countercyclical prices. Gavin and Kydland (1999) suggest that endogenous money supply movements can affect the relationship between real and nominal variables, providing a channel through which changes in the behavior of the monetary authority can affect the price-output correlation.
In light of these considerations, I follow up the empirical section of the paper by evaluating the behavior of output and the price level in two representative models: the demand-driven Keynesian model of Judd and Trehan (1995) and a version of the shopping time model used by Gavin and Kydland (1999). The challenge posed by the empirical findings is that a model of price-output dynamics should be capable of generating both procyclical and countercyclical prices at different frequencies and over different sample periods. The simulations suggest that a model with at least two separate sources of exogenous shocks might be necessary to match the patterns in the cospectra of output and prices, particularly in the postwar era.
The remainder of the paper is structured as follows: Section 1 discusses the data and methodology used, section 2 presents the empirical results, and section 3 illustrates some model simulations. A brief conclusion is contained in section 4. …