THE ECONOMETRICS OF MACROECONOMIC MODELLING

Inversion may lead to forecast failure

Assuming that the monetary authorities can control the stock of money balances in the economy, it would be appealing if one could obtain a model of inflation from the established money demand relationship above. We follow Hendry and Ericsson (1991) and invert the empirical money demand relationship in Table 8.1 to a model for quarterly inflation Дpt. Since the model

2 The Euro-area data are seasonally adjusted.

Figure 8.1. Estimation of money demand in the Euro area,
1985(4)-1997(2)—recursive residuals and Chow tests

in Table 8.1 explains quarterly changes in real money holdings, we can simply move Amt to the right-hand side of the equation and re-estimate the rela­tionship over the selected period 1980(1)-1992(4), saving 20 observations for post-sample forecasts.

Recalling the empirical findings of Hendry and Ericsson (1991) and the fact that we started out with a money demand relationship with stable parameters over this period, one might expect to see a badly specified inflation relationship with massive evidence of model mis-specification including clear evidence of parameter non-constancy—at least enough to indicate that there is little to learn about the inflation process from this relationship.

The results in Table 8.2 are surprising: it turns out that the inverted rela­tionship is fairly stable over the selected sample period as well, and it is well specified according to the tests reported in the table. Figure 8.2 shows that the inflation model has stable parameters and, except in one quarter (1987(2)), recursive Chow tests indicate that the model is reasonably constant. So, the non-invertibility of the money demand relationship reported in Hendry and Ericsson (1991) does not seem to apply for the Euro area in this period. The model has significantly positive effects on inflation from real money growth and from changes in output growth, AAyt. Also, lagged changes in long-term interest rates have a positive effect on inflation, while changes in short interest rates have a negative impact.

The picture changes completely when we test the model outside the selected sample: Figure 8.3 shows one-step forecasts from this model over the period from 1993(1) to 1998(4). The model seems to provide a textbook illustration of forecast failure.[67] The forecast failure is caused by parameter instability which

Table 8.2

Inverted model for Apt in the Euro area based on Coenen and Vega (2001)

Apant + Apant 1

+ 0.30ARLt_ 1 + 0.46 - — + 0.004Adum86t

(0.073) (0.039) 2 (0.002)

+ 0.17[(m - p) - 1.140y + 1.462Apan + 0.820(RL - RS)lt_2 (0.011)

0.16%

Diagnostic tests

Far(i-4)(4, 37) =1.02[0.41] Farch(i-4)(4, 33) = 0.39[0.81] x2ormaiity(2) = 0.53[0.77]

Fhetx^ (14, 26) = 1.12[0.38]

Freset(1, 40) = 5.96[0.02]*

Figure 8.2. Inverted money demand equation for the Euro area
1985(4)-1992(4)—recursive residuals and Chow tests

takes the form of a structural break as the Euro-area inflation rate starts to fall in the early 1990s. This is demonstrated by the plots of recursive residuals and Chow tests in Figure 8.4 which are obtained when we re-estimate the model over the entire sample until 1997(2). The sample evidence for the entire period thus shows that while we find a constant empirical relationship for money conditional on prices, the inverse relationship is all but stable and we have established non - invertibility. Hence, as pointed out in Hoover (1991), these results indicate that

Figure 8.3. Post-sample forecast failure when the inverted money demand equation for the Euro area is used to forecast inflation 1993(1) to 1998(4)

1.00 t - 0.75 0.50 0.25

— Nup Chow statistics — 1%

1985 1990 1995 1985 1990 1995 Figure 8.4. Instabilities in the inverted money demand equation for the Euro area after 1993—recursive residuals and Chow tests

causality runs from prices to money rather than from money to prices also in the case of the Euro area.