Forecasting the distribution of multi-step inflation: do macro variables matter?

The evidence in the inflation forecasting literature suggests that simple time series models are typically hard to outperform in predicting the dynamics of the first moment, and that using information about indicators of economic activity does not lead to out-of-sample forecasting gains. While most of the earlier literature focused on the ability of leading indicators (via the Phillips Curve PC models) to forecast the central tendency of future inflation, our aim is to examine their role in driving the changes of the complete inflation distribution. The second moment is particularly relevant in policy-making as it can help address the question: is the uncertainty about inflation constant over time or does it respond to the state of economy? The recent trend in monetary policy is to view its role as that of balancing risks to price and output stability. In this framework, the distribution of inflation is a necessary tool to evaluate such risks in the form of probability statements. In this paper we introduce a simple semi-parametric approach that characterizes the distribution of inflation forecasts. The approach is structured such that the quantiles of the multi-step forecast errors of the baseline autoregressive models are defined as functions of leading indicators of economic indicators. To evaluate the value added of the approach, we conduct an extensive comparative study with existing time series models under different distributional assumptions for the multistep forecast errors. We forecast (out-of-sample) the distribution of inflation for 3, 6 and 12 months ahead for the period 1985:1 to 2007:12 and evaluate the performance of the models in two sub-samples (1985:1 to 1995:6 and 1995:7 to 2007:12). To evaluate the distribution we use the tests recently proposed by Hong, Li and Zhao (2007) and Amisano and Giacomini (2007). We consider four measures of inflation: CPI, PCE and their respective core versions. Summarizing, we find that for some inflation measures (PCE and core PCE) conditioning the dynamics of the predictive distribution on some of the leading indicators (in particular, output and income gap and housing starts) provide more accurate forecasts compared to the case of assuming that the distribution (around the conditional mean forecast) is constant. Also, aggregating predictive densities conditional on the leading indicators provide densities that outperform the time series forecasts at all horizons, and for all measures of inflation. This is also a robust finding as it holds in all the sub-periods considered for forecast comparison.