The correlation between shocks to output and the price level: evidence from a multivariate GARCH model.

• Author: Cover, James Peery
• Position: Generalized Autoregressive Conditional Heteroskedasticity

1. Introduction

   In what way has The price level in the United States been related to the level of output? At one time it was generally believed that the correlation between the price level and output is positive and to be useful a macroeconomic model should be able to predict a positive price-output correlation. (1) Hence, Mankiw (1989, p. 88) criticizes real business cycle theory because it cannot explain the fact that "inflation tends to rise during booms and fall during recessions." This general belief in procyclical prices began to change in the early 1990s after several authors reported finding that detrended measures of the price level and output have a negative correlation during the postwar period. One important early study is that of Kydland and Prescott (1990, p. 17), who conclude that "any theory in which procyclical prices figure crucially in accounting for postwar business cycle fluctuations is doomed to failure. The facts we report indicate that the price level since the Korean War moves countercyclically." (2) This apparent change in the sign of the price-output correlation has resulted in a literature on the cyclical behavior of the price level. Although this literature is concerned largely with measuring the correlation between fluctuations in the price level (or inflation) and fluctuations in output (the price-output correlation), it is also concerned with what determines whether an economy has a positive or a negative price-output correlation.

   This paper contributes to the literature on the cyclical behavior of prices by presenting time-varying estimates of the price-output correlation. The motivation for this research is the dependence of the estimated price-output correlation on sample period. The difference between pre- and postwar estimates is only one example. There also appears to be some disagreement about when the change in the sign of the correlation occurred. For example, Cooley and Ohanian (1991) report a negative correlation for their entire post-1945 sample, Kydland and Prescott (1990) argue that it has been negative since the end of the Korean War, but Wolf (1991) presents evidence that it did not become negative until after 1973. (3) One advantage of our methodology is that it can estimate when the change in the sign occurred. Another is that it is capable of finding other changes in the sign of the correlation that until now have not been reported in the literature.

   Although the previous literature clearly recognizes that the price-output correlation is sample dependent, the typical study implicitly assumes that the correlation is fixed over any given sample period. By focusing only on the constant correlation within arbitrarily chosen periods, one may be losing important information about the dynamics of the comovement of output and the price level within and across regimes. Furthermore, there is a risk that the regimes might have been misspecified. This paper therefore presents time-varying estimates of the price-output correlation for the United States. This is done by estimating a two-variable vector autoregression (VAR) model in which it is assumed that the disturbances follow a bivariate generalized autoregressive conditional heteroskedasticity (GARCH) process. In the GARCH process, the conditional variance-covariance matrix of the residuals changes over time, allowing quarterly estimates of the contemporaneous price-output correlation coefficient. These estimates allow the identification of periods during which the price-output correlation was generally positive, those during which it was essentially zero, and those during which it was generally negative. It also allows a comparison of whether the price-output correlation is systemically different during periods of recession than it is during periods of recovery. (4)

   This paper defines the price-output correlation to be the contemporaneous correlation coefficient between unexpected changes in output and the price level, a definition supported by the work of den Haan (2000). Assuming a fixed residual variance-covariance matrix, he shows that the forecast errors from a VAR can be used to obtain consistent estimates of the price-output correlation as long as the number of lags in the VAR is sufficient to cause the disturbance to be stationary. It does not matter whether the variables in the VAR are stationary and what filter is used to detrend the data.

   This paper finds that the price-output correlation is usually positive before 1945 and nearly always close to zero from 1945 through 1963. Beginning in 1963, the frequency of negative correlations increases dramatically. In addition, we find that a zero (or at least statistically insignificant) price-output correlation has been much more common than realized by previous writers. For the entire sample period (1876:IV-1999:IV), this paper reports a statistically insignificant price-output correlation 57% of the time. For the post-1944 part of the sample, the correlation is zero 70% of the time, significantly positive only 11% of the time, and significantly negative only 19% of the time. The results are supportive of macroeconomic models in which both aggregate demand and aggregate supply shocks can be important in both the short and the long run--that is, models that allow the price-output correlation to be positive, negative, or zero for extended periods of time at forecast horizons up to four years in the fut ure.

   Section 2 explains why one should expect the price-output correlation to be time-varying and in doing so offers a brief survey of previous literature on the price-output correlation. Section 3 describes the data and presents the methodology employed by this paper. Section 4 presents and discusses the results, while section 5 offers some conclusions.

2. Reasons for a Time-Varying Price-Output Correlation

   There is some value in asking why one should expect the price-output correlation to be time-varying. The simplest possible explanation for a time-varying price-output correlation is that the relative frequency and sizes of shocks to aggregate supply and aggregate demand change. In a model with flexible prices, during periods when shocks to aggregate supply dominate, the correlation is negative, while during those when shocks to aggregate demand dominate, the correlation is positive.

   Several writers, however, confront such a naive connection between the sign of the price-output correlation and the relative importance of supply and demand shocks. Chada and Prasad (1993), Ball and Mankiw (1994), and Judd and Trehan (1995) show that sticky-price models with only demand shocks can yield a negative price-output correlation. (5) These models therefore imply that the price-output correlation could be time varying because the degree of price stickiness changes over time, den Haan (2000), however, shows that models with only a demand shock are not capable of generating the pattern of price-output correlations across different forecast horizons that he obtains. Hence, his results imply that a changing degree of price stickiness by itself cannot be the only cause of a time-varying price-output correlation.

   A more interesting explanation for a time-varying price-output correlation comes from the observation that monetary policy affects the price-output correlation. Cover and Pecorino (2003) and Pakko (2000) present models in which monetary policy can change the sign of the price-output correlation. (6) Since monetary policy is likely to be systematically different during recessions and expansions, their models imply that the price-output correlation is time varying.

   Pakko (2000) obtains his results by simulating a shopping time monetary model with endogenous monetary policy. He finds that the price-output cospectrum is negative at all frequencies in response to a productivity shock if there is a constant growth money rule. But if it is assumed that monetary policy is implemented in a way that makes the money stock procyclical, then Pakko finds that the price-output cospectrum can be made positive at all frequencies. Since the degree to which monetary policy is procyclical changes with economic conditions, Pakko's model implies a time-varying price-output correlation.

   Cover and Pecorino (2003) examine the effect of optimal monetary policy on the price-output correlation in an IS-LM model augmented with an upward-sloping aggregate supply curve. They find that the more successful monetary policy is in offsetting aggregate demand shocks, the less likely it is that the price-output correlation is positive. Whether or not successfully offsetting aggregate demand shocks causes the price-output correlation to be close to zero or to become negative depends on how the monetary authority responds to supply shocks. The greater the degree to which the monetary authority allows supply shocks to affect output, the more likely it is that the correlation is close to zero. But if the monetary authority tries to prevent temporary supply shocks from affecting output, the more likely it is that the price-output correlation is negative, if the degree to which the monetary authority has been successful at offsetting aggregate demand shocks, as well as the degree to which the monetary authority has allowed temporary supply shocks to affect output has changed over time, then Cover and Pecorino's model implies that the price-output correlation is time varying.

3. Data and Methodology

   The U.S. quarterly time-series data on real gross domestic product (GDP) and nominal GDP are from the U.S. Department of Commerce for the period 1959:I-1999:IV and Balke and Gordon (1986) for the period 1875:I-1959:I. The data sets were spliced together so that the quarterly growth rates of real and nominal GDP through the first quarter of 1959 are equal to those in the Balke-Gordon data, while those beginning with the second quarter of 1959 are equal to those in the Department of Commerce data. (7) The price...