# Category THE ECONOMETRICS OF MACROECONOMIC MODELLING

## Model specification and forecast accuracy

Forecasters and policy decision-makers often have to choose a model to use from a whole range of different models, all claiming to represent the economy (or the part of it that is the focal point of the forecasting exercise). The current range of wage and price models that can be used for inflation forecasting pro­vides an example. As we have discussed earlier, in Chapter 9, inflation targeting implies that the central bank’s conditional forecast 1-2 years ahead becomes the intermediate target of monetary policy. Consequently, there is a strong linkage between model choice, forecasting, and policy analysis in this case.

The statistical foundation for a conditional forecast as an operational target is that forecasts calculated as the conditional mean are unbiased and no other predictor (...

## Testing against richer dynamics

In the case of the NPCM, the specification of the econometric model used for testing a substantive hypothesis—forward and lagged endogenous variable— incorporates the alternative hypothesis associated with a mis-specification test (i. e. of residual autocorrelation). Seeing residual correlation as corroborating the theory that agents are acting in accordance with NPCM is invoking a very

strong ceteris paribus clause. Realistically, the underlying cause of the residual correlation may of course be quite different, for example, omitted variables, wrong functional form or, in this case, a certain form of over-differencing. In fact, likely directions for respecification are suggested by pre-existing results from several decades of empirical modelling of inflation dynamics...

## The nominal exchange rate vt

The nominal exchange rate affects wages and prices via import prices pit. Let pft be an index of import prices in foreign currencies. Then, as a first step in the completion of the model, we make use of the identity

pit = Vt + pft

and attempt to model the (log) of the trade weighted exchange rate index vt. In doing so, we follow Akram (2004), who models the exchange rate as equilibrium-correcting to the real exchange rate, which means that it is determined by PPP in steady state,

ecmv, t = vt + pwt – pt,

where pwt is the log of a trade-weighted index of foreign consumer prices. Figure 9.4 shows the time-series properties of ecmv, t, together with the cor­responding term ecmy, t from the aggregate demand equation developed later.

 Figure 9.4...

## An example

As an example, and in the process of illustrating different techniques, we will work out the dynamic properties of the wage-price model of Section 9.2.2. This involves evaluating the stability of the model, and the long-run and dynamic multipliers. Disregarding taxes and short-run effects, the systematic part of the model is on matrix form.

w

P

a

u

РЧ t

Steady-state properties from cointegration The long-run elasticities of the model are, from the cointegration analysis.

w = p + a — 0.1u p = 0.7(w — a)+ 0.3pi,

so the long-run multipliers of the system should be easily obtained by solving for wages and prices. For wages:

0.7(w — a) + 0.3p + a — 0.1u —0.7a + 0.3pi + a — 0.1u

0.3 0.1

— a——— u + pi

0.3 0.3 [118] a — 0.33u + pi.

Then for prices:

p = 0.7(w — a)+ 0...

## Monetary effects in the inflation equation?

We find no effect of inflation in the money demand equations for Norway. Hence it does not make sense to interpret the money demand functions as inverted inflation equations. We have, however, experimented with a model where we consider money in real terms (mt — pt), the real interest rate on money and the yield spread as potential explanatory variables for inflation. These are the variables that enter the cointegrating relationship of the money demand equation in Eitrheim (1998), cf. Table 8.3.

This gives us a model which has several aspects in common with the inverted money demand relationship for the Euro area in Section 8.3.2. In addition to

6 Test statistics marked * and ** indicate significance at the 5% and 1% level.

Table 8.5

The MdInv model of inflation, including variables (in...

## Data input for interest rate rules

Figure 10.2 shows the variation in the variables we use in the different interest rate rules over the period 1995(1) to 2000(4). Underlying inflation A4put is headline inflation corrected for changes in excise duties and energy prices, and is clearly less volatile than headline CPI inflation during the 1990s, cf. Figure 10.2(a). Output growth picked up towards the end of the 1990s, and during 1997-98 we see from Figure 10.2(b) that the four-quarter output growth rate shifts rather abruptly. Figure 10.2(c) shows the development in three variables used in the ‘real-time’ rules, that is, the rate of unemployment, ut, annual wage growth, A4wt, and annual growth in nominal domestic credit A4ncrt...