RDP 2010-03: Modelling Inflation in Australia 1. Introduction

Central banks in most advanced economies now operate with some form of either explicit or implicit inflation target, with the Reserve Bank of Australia (RBA) operating under such a framework since 1993. A natural result of this change has been an increased interest among central banks and academics in research about the inflation process.

These efforts have resulted in a large number of different models for inflation, which vary in terms of scale, and in terms of the variables assumed to drive inflation (including the output gap, unemployment rate or unit labour costs). At the RBA, a variety of approaches are used to model inflation, including singleequation models (such as that in de Brouwer and Ericsson 1995), VAR models (Gerard and Nimark 2008), factor models (Gillitzer and Kearns 2007; Gerard and Nimark 2008) and DSGE models (Jääskelä and Nimark 2008). While there are advantages to systems approaches to modelling inflation, single-equation models can also be very useful due to their simplicity. This paper outlines the broad structure of three types of single-equation models that are used as part of an array of models at the RBA: a standard Phillips curve; a New-Keynesian Phillips curve; and a mark-up model.

We find that the single-equation model approach has performed relatively well in terms of both modelling and forecasting inflation over the past two decades, with equal or better in-sample and out-of-sample performance than some standard benchmarks and VAR models. The standard errors surrounding the model predictions have also fallen since the introduction of inflation targeting. However, it is notable that the explanatory power – in terms of adjusted R-squared – of these equations has also declined over this time as inflation has become more stable. Of the three models studied, the standard Phillips curve has performed best over this time but the results from an expectations-augmented mark-up model are broadly comparable. In contrast, the New-Keynesian Phillips curve model fits the data relatively poorly, although most of this reflects issues with the use of generalised method of moments (GMM) to instrument for expected inflation, and the model fits reasonably well when we use a direct measure of inflation expectations instead. Our results show that either the unemployment rate alone, or a combination of growth in unit labour costs and the output gap help to explain the deviation of inflation from measures of inflation expectations in Australia, once we have controlled for import price shocks. After controlling for the variables discussed above, we find little role for some other variables – notably commodity prices, excess money growth – that have sometimes been suggested as important determinants of inflation.

A concern with these single-equation models, however, is that they do not impose many of the theoretical restrictions that would be standard in any structural model of inflation. For example, we find that imposing a restriction to ensure that the long-run Phillips curve is vertical results in a significant deterioration of fit for samples estimated since 1990. While there may be empirical issues or theoretical considerations that might explain this, such a result highlights the fact that reduced-form models such as those estimated in this paper are unlikely to perform well if inflation ever deviated persistently and substantially from target. Accordingly, it is appropriate to supplement the single-equation approach with results from more structural econometric models such as the Jääskelä-Nimark DSGE.

The remainder of this paper is structured as follows. The various models are introduced in Section 2, the empirical estimation is discussed in Section 3 and the results are presented in Section 4. In Section 5 we assess the role of various additional variables and coefficient restrictions that are suggested by the existing literature. Section 6 assesses the stability of these models over time and Section 7 concludes.