PREDICTING INFLATION: DOES THE QUANTITY THEORY HELP?

I. INTRODUCTION Inflation forecasting has played a key role in recent U.S. monetary policy, and this has led to a renewed search for variables that serve as good indicators of future inflation. One frequently used indicator, based on the Phillips curve, is the unemployment rate or a similar measure of the output gap, as in Gerlach and Svensson (2003), Clark and McCracken (2003), Mankiw (2001), and Gali and Gertler (1999). The Phillips curve is believed by many to be the preferred tool for forecasting inflation (see, e.g., Mankiw 2001; Stock and Watson 1999a; Blinder 1997) though as argued by Sargent (1999) its use in formulating monetary policy is not without controversy. Another approach, based on the quantity theory of money, uses monetary aggregates to predict inflation. Despite the strong theoretical motivation for this approach, though, there is little evidence that measures of the nominal money supply are useful for predicting inflation relative to a conventional unemployment rate Phillips curve model; see Stock and Watson (1999a) for a detailed analysis of the forecast performance of popular inflation indicators. Stock and Watson's results indicate that even simple univariate time-series models generally forecast about as well as models that include measures of the money supply, so that it is hard to make the case that nominal money supply data have any predictive content for inflation. (1) This article evaluates inflation forecasts made by models that allow for prices, money, and output to be cointegrated, and in the process reexamines the question of whether monetary aggregates have marginal predictive content for inflation. Our work is motivated in part by economic theory, as the presence of a cointegrating relationship among the series we look at corresponds to an implicit assumption that prices, the money supply, and output "hang together" in the long run, an implicit feature of most analyses based on the quantity theory. From a statistical point of view, a system with cointegrated regressors does not have a finite-order vector autoregressive (VAR) representation, so that a VAR in differences will be misspecified and may not forecast well regardless of the relevance of the included variables. Our analysis is therefore focused on the questions, "Are there gains, in terms of forecast accuracy, from imposing the restriction that prices, money, and output are cointegrated?", "Does it matter whether cointegrating restrictions are imposed a priori based on economic theory, or can they be estimated?", and "Do models imposing cointegration among prices, money, and output forecast inflation as well as the Phillips curve and other alternative models?" The econometric framework that we employ is similar to that of Stock and Watson (1999a) but differs from theirs in two ways. First, Stock and Watson (1999a) consider one-year horizon inflation forecasts, whereas we consider forecast horizons of up to five years. This is potentially important in our context, as we include versions of the quantity theory of money in our analysis, a theory that arguably may not yield substantive gains to forecasting in the short run. Additionally, future inflation at many horizons is in general of interest to policy makers (even if the weight attached to inflation at different horizons is a matter of individual preference), so that long-run predictions are only unuseful if and when they fail to have marginal predictive content for inflation. (2) A second difference between our work and that of Stock and Watson (1999a) is that some of our models differ from theirs, including those that impose quantity theory-based cointegrating restrictions, for example. In these types of models we (1) impose a cointegration restriction derived from the assumption of stationary velocity, and (2) estimate cointegrating restrictions. We also examine a fairly broad variety of (linear) models, including simple autoregressive (AR) models in levels and differences; conventional unemployment rate Phillips curve models; and VAR models in levels and differences with money, prices, and output. …