Inflation Forecasting

Article excerpt

Forecasting inflation is one of the core responsibilities of economists at central banks and in the private sector, and models of inflation dynamics play a central role in determining monetary policy. In this light, it is not surprising that there is a long and rich literature on inflation dynamics and inflation forecasting.

A recurring theme in this literature is the usefulness--or not--of the Phillips curve as a tool for forecasting inflation. Phillips (1) originally documented an inverse relation between the rates of wage inflation and unemployment in the United Kingdom. Samuelson and Solow (2) extended "Phillips' curve" to U.S. data and to price inflation. The Phillips curve remains at the core of modern specifications, which additionally include expectations of inflation, often use activity variables other than the unemployment rate, and incorporate sluggish inflation dynamics. Indeed, the central price determination equation in modern dynamic stochastic general equilibrium models, the New Keynesian Phillips Curve, is a direct descendant of the original Phillips curve, augmented to incorporate forward-looking inflation expectations and with a real activity measure serving as a proxy for real marginal cost.

This research summary reviews our work of the past fifteen years on inflation forecasting using small, stand-alone models. Most of this work revolves around the use of real economic activity to forecast inflation, to which we refer broadly as Phillips curve models, although other forecasting frameworks (such as incorporating monetary aggregates) are also considered.

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Our research on inflation forecasting and inflation dynamics leads us to two broad conclusions. First, there are important regularities in the inflation-output relation. In particular, in the post-war United States, recessions are times of disinflation. This regularity was behind the deflation scares of 2002-3 and 2009-10. Figure 1 plots the rate of unemployment and the four-quarter rate of core PCE inflation for six U.S. slumps from 1960 to the present, labeled by the NBER-dated cyclical peak. The plotted rates are deviated from their values at the respective NBER-dated peak; the vertical axis is scaled so that all recessions have the same increase in the unemployment rate; and the horizontal axis is scaled so that the total time span is twice the time between the start of the recession and the peak of the unemployment rate. The mean paths of the unemployment rates and inflation are shown as dashed lines, and the dotted lines are [+ or -] one standard deviation bands (3). Over these six recessions and recoveries, by the time the unemployment rate peaks, inflation has fallen on average by 0.37 percentage points for each percentage point increase in the rate of unemployment.

Second, we conclude that despite this evident regularity, inflation dynamics and inflation forecasting models exhibit considerable instability. Such instability is unsurprising, given the substantial changes in monetary policy, unionization, globalization, and other aspects of the U.S. economy that are relevant to price-setting. Indeed, Figure 1 suggests one important aspect of this instability: the rate of inflation fell by less following the NBER-dated peaks of 2001Q1 and 2007Q2 than it did on average during earlier the previous five recessions. A leading explanation for the more muted response of inflation over the two recent recessions is that monetary policy has succeeded in anchoring inflationary expectations. However, because both disinflationary episodes started at low levels, another candidate explanation is resistance to nominal wage declines.

Time Variation in Inflation Forecasting Models

The first step towards handling instability is admitting that you have a problem. Providing formal statistical evidence of instability entails the use of a variety of methods, including tests for in-sample breaks, tests for breaks at the end of the sample, and pseudo out-of-sample forecast comparisons. …