RDP 2003-12: The Real-Time Forecasting Performance of Phillips Curves 1. Introduction

Recent years have seen growing interest in the implications of real-time data issues for the use of output-gap estimates, and of Phillips curves based on these estimates, in policy analysis and macroeconomic modelling.^[1] This paper aims to contribute to that research, focusing on the real-time inflation forecasting performance of output-gap-based Phillips curves.

Analysts typically use a variety of techniques to forecast inflation, rather than rely upon a single method. One approach frequently used, especially over short horizons, is to adopt a ‘bottom-up’ perspective, using a combination of partial indicators, liaison with businesses and government, and judgment. Additionally, analysts may use a variety of econometric models of inflation, reflecting alternative methodologies or views about the structure of the economy.^[2],^[3]

One of these econometric approaches to inflation forecasting sometimes considered, particularly by academics and macroeconomic modellers, is the use of Phillips curves based on estimates of the output gap. These posit a relationship between the inflation rate and the level of capacity utilisation in the economy, as measured by the deviation of actual output (GDP) from the economy's potential level of output.^[4] However, a problem with this approach is that it requires estimation of an unobservable quantity, the level of potential output, and this must be done in real time, rather than with the benefit of hindsight.

There are several different aspects to the problem of reliably estimating the output gap in real time, and these are discussed in detail in Gruen, Robinson and Stone (2002). One is simply that GDP is revised over time as more information becomes available to the statistician.^[5] Recent work, however, has suggested that data revisions are not the primary source of problems in the real-time estimation of the gap (Orphanides and van Norden 2002). Rather, for Australia, the results of Gruen et al (2002) suggest that revisions to the output gap instead arise primarily from end-point problems associated with econometric methods used to estimate potential output. In this regard, Gruen et al find that the use of a Phillips curve relationship, to condition such estimates on observed inflation, can help to mitigate these end-point problems – allowing them to obtain real-time output-gap estimates which bear a fair resemblance to those obtained with the benefit of hindsight.

While the reliability of output-gap estimates is of interest to analysts in its own right, our focus in this paper is, however, on the accuracy of inflation forecasts from Phillips curves and output gaps estimated in real time. The accuracy of these forecasts provides an alternative metric by which the usefulness of output gaps and Phillips curves for policy analysis and forecasting can be assessed.

From this perspective, it is not enough to have a method for estimating potential output under which the ex post relationship between the output gap and inflation is strong. Rather, it must be possible to obtain real-time output-gap estimates and Phillips curves which provide a reliable guide to future inflation. Potential sources of error in such forecasts include the difficulties of determining both the correct specification of the Phillips curve in real time, and the correct coefficient estimates in this specification. They also include the direct impact of real-time errors which inevitably arise in estimating the output gap – notwithstanding the strong correlation which Gruen et al (2002) were able to obtain between their final and real-time gap estimates.

In this companion piece to Gruen et al (2002), we use the more than 120 vintages of Phillips curves and output gaps from that paper to investigate whether these obstacles are sufficient to undermine the usefulness of Phillips curves for forecasting inflation. We find that they result in inflation forecasts which, while unbiased, are excessively volatile. This makes their performance disappointing, relative even to simple alternatives such as univariate time-series models of inflation, or a ‘no change’ (random walk) assumption. Our results also suggest that it is the imprecision with which Phillips curve relationships can be estimated, in real time, which primarily undermines their usefulness for forecasting inflation.

In spite of their disappointing performance in isolation, however, it appears that Phillips curve-based forecasts do still contain some useful information about inflation, distinct from that available from other simple forecasting approaches. This appears to be especially so at the one-year-ahead forecasting horizon. Moreover, this added information can be used to improve the inflation predictions from these other forecasting approaches in real time – although the extent of the resulting improvement is only modest.

Footnotes

For example, a number of overseas central banks have been conducting research into these issues, including the US Federal Reserve (Orphanides et al 1999) and the Bank of England (Nelson and Nikolov 2001), amongst others. [1]

For example, mark-up models of inflation have been found to perform quite well for Australia – see de Brouwer and Ericsson (1998). [2]

Stevens (2001) provides a description of the policy formulation process employed by the Reserve Bank of Australia (RBA), and the roles of ‘bottom-up’ analysis, econometric models and judgment in this process. For a corresponding description for the US, see Reifschneider, Stockton and Wilcox (1997). [3]

Phillips curves based on other measures of aggregate activity, such as an unemployment gap, are also commonly used to model inflation. However, we do not consider these further here. [4]

Analysis for Australia by Stone and Wardrop (2002) suggests that, while the typical size of revisions to quarterly GDP growth has decreased over recent decades, sizeable changes do still occur, sometimes well after the initial data release for the period in question. [5]