Academic journal article
By Mitchell, James
National Institute Economic Review , No. 193
This paper has three aims. First, we summarise and thereby make readily available the historical time-series of quarterly density forecasts of year ahead RPIX (RPI excluding mortgage payments) inflation made by the National Institute for the period 1994Q1-2004Q4. Previous work has focused on those forecasts made in Q4 only. Secondly, we evaluate the quality of these density forecasts. Thirdly, with the benefit of hindsight we draw lessons for the future production and use of density forecasts.
Keywords: density forecasts; evaluating forecasts; inflation forecasting JEL classification: C53; E37
Increased attention is now given to providing measures of uncertainty associated with forecasts. Density forecasts capture this uncertainty fully. Accordingly since 1992Q3 the National Institute has, albeit in a sense implicitly, published density forecasts for inflation, in that this Review has contained the table 'Average Absolute Errors'. This table indicated the historical accuracy of National Institute forecasts by reporting the mean absolute error. Assuming normality, a 58 per cent confidence interval around the point forecasts corresponds to the point estimate plus/minus the mean absolute error. Since 1996Q1 the National Institute has explicitly published probability forecasts for inflation (and output growth too). These have taken the form of tabular histograms indicating the probability of inflation falling within a band, although these bands have changed periodically.
2. Quarterly density forecasts of inflation
Our focus is on the National Institute's quarterly forecasts of one-year ahead RPIX inflation (ONS code CHMK), the principal monetary policy target for much of the sample period. These forecasts were published in the Review. (1) The final projection for RPIX inflation, prior to the new target for inflation announced by the Chancellor in December 2003, was published in the 2003Q4 Review. By considering all RPIX forecasts until this date we are effectively examining a 'complete set' of forecasts.
National Institute density forecasts are centred on the point forecast published in this Review. This point forecast is produced by NiGEM, a large-scale macroeconometric model. In deriving the density forecasts, normality is assumed. This is because earlier work that analysed the historical errors (from 1984-95) made in forecasting RPI inflation could not reject normality; nor indeed could it reject unbiasedness (in fact rationality); see Poulizac et al. (1996). The variance of the density forecast is then set equal to the variance of the historical forecast error. Past forecast errors are commonly used as a practical way of forecasting future errors; e.g. see Wallis (1989), pp. 55-6. Given the backward looking and mechanistic nature of this method of determining the variance, it is important, as we see below, which historical sample period is chosen to estimate the variance.
Consistent with HM Treasury's focus in its regular comparison of independent forecasters when forecasting inflation, the Review focuses on density forecasting inflation in the fourth quarter of the current year and the fourth quarter of the next year. Therefore only the Q4 publication offers a one-year ahead density forecast. Previous work evaluating National Institute density forecasts, specifically Wallis (2004), has analysed these Q4 forecasts only. Naturally this leads to a very small available sample.
To increase the available sample and facilitate more reliable evaluation of National Institute density forecasts we first extract from back issues of the Review one-year ahead point forecasts for the other quarters. However, one is forced to make an assumption in order to infer uncertainty estimates.
We simply assume the density forecast is normal with standard deviation equal across the four quarters in a year. This assumption is sensible if we believe the National Institute only re-calibrated its forecast variances once a year. …