# Category THE ECONOMETRICS OF MACROECONOMIC MODELLING

## The wage-price model

We first model the long-run equilibrium equations for wages and prices based on the framework of Chapter 5. As we established in Section 5.4 the long-run equations of that model can be derived as a particular identifica­tion scheme for the cointegrating equations; see (5.19)-(5.20). Second, we incorporate those long-run equations as equilibrium correcting terms in a dynamic two-equation simultaneous core model for (changes in) wages and prices.

From equations (5.19)-(5.20), the variables that contain the long-run real wage claims equations are collected in the vector [wt pt at pit ut]’. The wage variable wt is average hourly wages in the mainland economy, excluding the oil produc­ing sector and international shipping...

## Estimation

Remember that the model is

APt = bp1Et APt+1 + bp1 APt —1 + bp2Xt + Zpt, which can be rewritten as

n = jEtnt+1 + SxH + vpt.

The model is usually estimated by means of instrumental variables, using the ‘errors in variables’ method (evm)—where expected values are replaced by
actual values and the expectational errors:

nt = Y^t+i + 5xt + vpt – YVt+i – (A.22)

The implications of estimating the model by means of the ‘errors in variables’ method is to induce moving average errors. Following Blake (1991), this can be readily seen using the expectational errors as follows.

1. Lead (A.15) one period and subtract the expectation to find the RE error:

3. Finally, re-express in terms of original variables, again using Apt = n + aApt-i:

Apt – aiApt-i = (— ) (Apt+i – aiApt) + ( ) xt + ( f— ) ...

## Monetary analysis of Euro-area data

8.3.1 Money demand in the Euro area 1980—97

In this section, we establish that money demand in the Euro area can be mod­elled with a simple equilibrium correction model. We base the empirical results on the work by Coenen and Vega (2001) who estimate the aggregate demand for broad money in the Euro area. In Table 8.1 we report a model which is a close approximation to their preferred specification for the quarterly growth

Table 8.1

Empirical model for Д(ш — p)t in the Euro area based on
Coenen and Vega (2001)

Дpant + Дpant і

— 0.36ДИЬ-_1 — 0.53 —-— t-1 — 0.01dum86t

(0.08) (0.050) 2 (0.002)

— 0.14[(m — p) — 1.140y + 1.462Дpan + 0.820(RL — RS)]t-2 (0.012)

0.23%

FAr(5, 55) =0.97[0.44]

Farch (4, 52) = 0.29[0.89]

X2cnmality(2) = 0.82[0.66]

Fhe...

## Evaluation of monetary. policy rules

We now relax the assumption of an exogenous interest rate in order to focus on monetary policy rules. We evaluate the performance of different types of reaction functions or interest rate rules using the small econo­metric model we developed, in Chapter 9. In addition to the standard efficiency measures, we look at the mean, deviations from targets, which may be of particular interest to policy makers. Specifically, we introduce the root mean squared target error (RMSTE), which is an analogue to the well known root mean squared forecast error. Throughout we assume that the monetary policy rules aim at stabilising inflation around an infla­tion target and that the monetary authorities also put some weight on stabilising unemployment, output, and interest rates...

## The P*-model

The estimation of the P*-model in Section 8.5.4 requires additional data relative to the AWM data set. We have used a data series for broad money (M3) obtained from Gerlach and Svensson (2003) and Coenen and Vega (2001), which is shown in Figure 8.8.[74] It also requires transforms of the original data: Figures 8.9 and 8.10 show the price gap (p — p*)t and the real money gap

 Figure 8.8. The M3 data series plotted against the shorter M3 series obtained from Gerlach and Svensson (2003), which in turn is based on data from Coenen and Vega (2001). Quarterly growth rate
 Figure 8.9. The upper graphs show the GDP deflator and the equilibrium price level (p*), whereas the lower graph is their difference, that is, the price gap, used in the P*-model

(rm — rm*)t along with ...

## Forecast errors of bivariate EqCMs and dVARs

In this section, we illustrate how the forecast errors of an EqCM and the corresponding dVAR are affected differently by structural breaks. Practical forecasting models are typically open systems, with exogenous variables. Although the model that we study in this section is of the simple kind, its properties will prove helpful in interpreting the forecasts errors of the large systems in Section 11.2.3.

A simple DGP This book has taken as a premise that macroeconomic time-series can be usefully viewed as integrated of order one, I(1), and that they also frequently include deterministic terms allowing for a linear trend. The following simple bivariate system (a first-order VAR) can serve as an example:

Vt = K + AlVt_1 + AXxt_1 + ey, t, (11.3)

xt = p + xt_i + ex, t, (11.4)

where the disturban...