ALTERNATIVE P* MODELS OF INFLATION FORECASTS

I. INTRODUCTION Inflation forecasts play a key role in monetary and macroeconomics. During the past three decades, dramatic changes in the inflationary environment have stimulated a wealth of studies on the relative accuracy of alternative models of inflation forecasts. In particular, Mehra [1988], Stockton and Glassman [1987], and Reichenstein and Elliott [1987] found varying performance in traditional models, including the term structure, Phillips curve, and typical monetarist models, across postwar periods. Against this background, Hallman, Porter, and Small [1991] (HPS) introduced a model called P-star ([P.sup.*]) as inflation forecasters' "holy grail." The [P.sup.*] framework is built on the general perception that inflation over the long run is a monetary phenomenon. However, as Christiano [1989] argued, [P.sup.*] entails no practical implication for shorter-run horizons that are of primary interest to inflation forecasters. He further pointed out that, for the period of 1970-89, one- to three-year ahead forecasts from [P.sup.*] are not meaningfully more accurate than those from traditional models. The usefulness of [P.sup.*] as an anchor for the price level also suffers from another limitation - the assumption that velocity, which is the ratio of nominal GDP to a monetary aggregate, is stable over the long run. HPS justified the validity of this hypothesis based on postwar (1955-88) data for the broad monetary aggregate M2 used in their model. During the early 1990s, however, the growth rate of M2 apparently slowed down relative to that of GDP, leading to a sharp rise in M2 velocity. This consequently caused [P.sup.*] to persistently underpredict actual inflation. Duca [1995a] has provided a detailed discussion on plausible sources of this instability in velocity. The literature has also offered plausible solutions to correct [P.sup.*] models for the observed structural change, ranging from redefining the relevant monetary aggregate to directly accounting for a trend break in velocity. While evidence supports that these individual methods improve upon the original [P.sup.*] formulation, there is a lack of research comparing their performance, especially in periods other than the early 1990s. The first objective of the present study, therefore, is to fill this void. The second objective of this paper is to reevaluate the robustness of earlier findings regarding the relative performance of HPS's original [P.sup.*] model. To this end, we divide the full out-of-sample forecast period of 1970-96 into three subsamples. Our results reveal a pattern of switching forecast performance between money-based and output-based models across recent periods. The fragility of these models highlights the extent of temporal instability in the inflation generating process. This paper proceeds as follows. The next section describes alternative [P.sup.*] model specifications and other inflation forecast models. Section III discusses the forecast results. Section IV summarizes and concludes. II. MODEL SPECIFICATIONS The [P.sup.*] Model The benchmark of the [P.sup.*] model is the quantity theory of money, which relies on the equation of exchange: (1) [P.sub.t] [equivalent to] [M.sub.t] [V.sub.t] / [Y.sub.t] where P is the price level, M is a measure of money supply, V is the velocity of money, Y is the level of output (real GDP), and a time subscript denotes the current value of a variable. It follows that if [V.sub.t] and [Y.sub.t] reach their long-run equilibrium levels at [Mathematical Expression Omitted] and [Mathematical Expression Omitted], respectively, then the current equilibrium price level, [Mathematical Expression Omitted], can be determined as: (2) [Mathematical Expression Omitted] According to HPS, [Mathematical Expression Omitted] is measured by the historical mean of [V.sub.t], and [Mathematical Expression Omitted] by the level of potential GDP. …