RDP 2003-12: The Real-Time Forecasting Performance of Phillips Curves 2. Recent Literature

The ability of Phillips curves to forecast inflation has been the focus of much recent research. In this section, we briefly review the relevant literature.

Stock and Watson (1999) consider year-ahead forecasts for US inflation obtained from Phillips curves based on an unemployment gap – the difference between the unemployment rate and the estimated Non-Accelerating Inflation Rate of Unemployment (NAIRU). They then assess the accuracy of these, relative to predictions from both univariate autoregressive models and from a ‘no change’ assumption.^[6] They interpret their results as being generally positive regarding the ability of such Phillips curves to forecast inflation. However, the outperformance by their Phillips curve-based forecasts is sometimes only marginal, with the mean squared errors (MSEs) of these forecasts little different from those of their alternative forecasting methods, for certain periods or measures of inflation.

There are two characteristics of the Phillips curve specifications estimated by Stock and Watson (1999) which mean that their results may not be directly applicable to Australia. First, they assume that the NAIRU is constant through time, over their sample period from 1959 to 1997. While this may be an appropriate assumption for the US, the work of Gruen, Pagan and Thompson (1999) suggests that, for Australia, there are likely to have been sizeable movements in the NAIRU over recent decades.^[7] Secondly, they omit supply-side variables, such as import and oil prices, from their Phillips curve specifications. Such variables were found by Gruen et al (2002) to be important for modelling inflation in Australia – a result which is unsurprising given that Australia is a small, open economy.

In contrast to Stock and Watson's broadly positive endorsement, several recent papers have questioned the usefulness of Phillips curves for forecasting inflation. For example, Atkeson and Ohanian (2001) estimate alternative versions of the Phillips curves in Stock and Watson (1999) and find their performance to be no better than a naive alternative.^[8] However, Sims (2002) argues that Atkeson and Ohanian's results are sensitive to the sample they use (1984:Q1 to 1999:Q3), so that the poor Phillips curve performance they report may not be instructive.^[9]

The paper with the most direct relevance to our own study is the recent work by Orphanides and van Norden (2003), who examine inflation forecasts derived from output-gap-based Phillips curves. They consider the wide array of different output-gap series estimated, using real-time US GDP data and both univariate and multivariate techniques, in Orphanides and van Norden (2002). To forecast inflation, they place each of these alternative output-gap series – a dozen in all – in a separate ‘forecasting relationship’, namely a simple Phillips curve with a constant, lags of inflation and lags of the output gap. In a procedure similar to Stock and Watson (1999), they re-estimate each forecasting relationship (including choice of lag lengths) for each forecast period, using only data available up to that date. They then compare the forecasts generated by these relationships with those from an alternative, autoregressive model of inflation.

Orphanides and van Norden (2003) find that, while several of their Phillips curves yield more accurate forecasts over their full sample, the improvement is typically not statistically significant, and is frequently reversed when the analysis is restricted to one or other half of their evaluation period. Moreover, this finding of little or no consistent improvement in forecast accuracy is found to be robust to a wide array of variations to their general framework for assessing the forecast performance of their Phillips curves and alternative output-gap estimates.^[10] In all, they conclude that while ‘a historical Phillips curve is suggested by the data, and ex post estimates of the output gap are useful for understanding historical movements in inflation … our simulated real-time forecasting experiment suggests, instead, that [their] predictive ability is mostly illusory’ (p 24).

One possible explanation for these disappointing results is that Orphanides and van Norden's use of such a simple Phillips curve framework, with no role for supply side influences, may be limiting the performance of their Phillips curve-based inflation forecasts.^[11] Moreover, for their multivariate filter-based output-gap estimates, their use of separate ‘forecasting relationship’ Phillips curves to generate their inflation forecasts is somewhat counterintuitive, given that the derivation of these gap estimates used different Phillips curves, embedded in the multivariate filtering.^[12]

Orphanides and van Norden's approach, however, simply reflects their somewhat different overall goal from our own. They use their framework to assess the value, for Phillips curve-based inflation forecasting, of a wide range of alternative output-gap estimates. Their use of a common, simple framework to do this allows them to readily test the sensitivity of their results to various plausible variations to this framework, such as to the method for selecting lag lengths in their forecasting Phillips curves in real time.

By contrast, our aim is to focus on only one suite of Phillips curves and associated output-gap data vintages – those assessed by Gruen et al (2002) to be the best performed from a range of alternatives considered there. We then assess the real-time forecasting performance of these Phillips curves when coupled with corresponding optimally-specified equations for forecasting the output gap. We thus aim to assess the real-time inflation forecasting performance of Phillips curves for Australia, when care has been taken to try to make these Phillips curves and output-gap equations as well and richly specified as possible.

Footnotes

This comparison is made on a real-time basis: for each period, Stock and Watson estimate their various models based on data up until that period, then calculate forecasts for the year ahead, and then repeat this process for the next period. Since the US unemployment rate only gets revised though seasonal re-analysis, the effect of which is small, the real-time data for this series in each period is essentially equivalent to the final data up until that period. [6]

Gruen et al (2002) find that it is important that the possibility of corresponding large shifts in the growth rate of potential output over time be allowed for, in any output-gap-based Phillips curve specifications for Australia. [7]

Atkeson and Ohanian's Phillips curves are more restricted than those of Stock and Watson, in the sense that they allow only one lag at a time of the monthly change in inflation, and of the level of the unemployment gap, in their specifications (although they do examine the effect of varying the lengths of these lags, up to one year, on the forecasts). They also do not allow a contemporaneous unemployment gap in their Phillips curve specifications, which the results in Gruen et al (2002) suggest would be an undesirable restriction for Australia. [8]

When this sample is extended back only slightly, to 1979, so as to incorporate a period when US inflation was more volatile, Sims finds that Phillips curve-based forecasts do outperform the naive model over this longer sample. [9]

Orphanides and van Norden's long evaluation period for forecasts is 1969:Q1 to 1998:Q4. Splitting this sample into two, their latter sub-sample is 1984:Q1 to 1998:Q4, comparable to that used in Atkeson and Ohanian (2001). [10]

Orphanides and van Norden note, in this regard, that ‘the forecasting problem faced by policymakers in practice is more complex than the one we consider. One obvious and important difference is that the information set available to policy-makers is much richer’. They argue, however, that ‘it is therefore possible that output gaps might improve on simple univariate forecasts of inflation but not on forecasts using a broader range of inputs. For this reason, we feel that the experiment we perform may actually overstate the utility of empirical output gap models’. Certainly, the comparison exercise they conduct prevents both their Phillips curves and competing univariate models from using additional information which might naturally be incorporated into inflation forecasts – such as data on oil and import prices. In this sense, their comparison is designed to isolate what, if any, real-time benefit is gained solely through the addition of estimates of the output gap to a univariate inflation-forecasting framework. [11]

The Phillips curves incorporated in these multivariate filters were, however, relatively simple – for example, they also did not include any supply-side variables. Orphanides and van Norden's ‘forecasting relationship’ Phillips curves may therefore not be a bad approximation to them. [12]