THE ECONOMETRICS OF MACROECONOMIC MODELLING

Forecast comparisons

Both models condition upon the rate of unemployment ut, average labour productivity at, import prices pit, and GDP mainland output yt. In order to investigate the dynamic forecasting properties we enlarge both models with relationships for these four variables, in the same manner as in Chapter 9.

Figure 11.5 illustrates how the ICM-based model forecast the growth rates of wages and prices, Awt and Apt. It is also instructive to consider the forecasts for the change in the real wage A(w—p)t and the annual rate of inflation, A4pt. The forecast period is from 1995(1) to 1996(4). The model parameters are estimated on a sample which ends in 1994(4). These dynamic forecasts are conditional on the actual values of the non-modelled variables (ex post forecasts). The quarterly inflation rate Apt only has one significant bias, in 1996(1). In that quarter there was a reduction in the excises on cars that explains around 40% of this particular overprediction. In the graphs of the annual rate of inflation A4pt this effect is naturally somewhat mitigated. The quarterly change in the wage rate Awt is very accurately forecasted, so the only forecast error of any importance for the change in real wages A(w — p)t also occurs in 1996(1). The forecasts for the rate of unemployment are very accurate for the first 5 quarters, but the reduction in unemployment in the last 3 quarters does not appear to be predictable with the aid of this model.

Figure 11.5 also contains the 95% prediction intervals in the form of ±2 standard errors, as a direct measure of the uncertainty of the forecasts. The prediction intervals for the annual rate of inflation are far from negligible and are growing with the length of the forecast horizon.

Next, Figure 11.6 illustrates how the model based on the Phillips curve forecast the same variables over the same period from 1995(1) to 1996(4). For most variables the differences are negligible. For the quarterly inflation rate Apt in particular, the Phillips curve specification seems to be no worse than the ICM as regards the point forecasts, although the prediction inter­vals are somewhat wider, due to the larger residual variances in wage - and price-setting.

However, in the graphs of the annual rate of inflation A4pt there is after all a clear difference between the predictions on this one-off comparison. A4pT+^imod is simply a 4-quarter moving average of the quarterly rates, and the same is true for the prediction errors, thus

3

Aypr+h - Л4РТ+h, mod = y^X^-PT+h-i - APT+h-i, mod),

i=0

mod = ICM, PCM.

Until 1995(4) there is zero bias in А^рт+н, pcm because all the preceding quarterly forecasts are so accurate. However, A4pT+h PCM becomes biased from 1996(1) and onwards because, after the overprediction of the quarterly rate in 1996(1), there is no compensating underprediction later in 1996. The ICM forecasts on the other hand achieve exactly that correction, and do not systematically overpredict inflation.

For the annualised inflation rate the uncertainty increases quite rapidly for both models, but markedly more so for the Phillips curve forecast. Indeed, by the end of the two-year period, the forecast uncertainty of the Phillips curve is about twice as big as the dynamic ICM. This effect is clearly seen when the annual inflation forecasts from the two models are shown in the same graph (Figure 11.7). The dotted lines denote the point forecasts and the 95% prediction bands of the dynamic ICM, while the solid lines depict the corresponding results from the forecasts of the Phillips curve specification. At each point of the forecast the uncertainty of the Phillips curve is bigger than for the ICM. Indeed, while the ICM has a standard error of 0.9 percent­age points 4 periods ahead, and 1.2 percentage points 8 periods ahead, the Phillips curve standard errors are 1.6 and 2 percentage points, respectively. Considering equation (11.56) it transpires that the explanation is not only that each Var[ApT+н - Арт+н, рсм] > Var[ApT+h - Арт+н, ісм], but also that the PCM quarterly prediction errors are more strongly positively autocorrelated than the ICM counterparts.