THE ECONOMETRICS OF MACROECONOMIC MODELLING

Model performance

The model (9.5)-(9.13) is a small econometric model for Norway, which is characterised by the inclusion of labour market effects in addition to effects of aggregated demand and the exchange rate. The motivation for the extended model is given in the preceding chapters: in order to capture the effects of monetary policy in general and on inflation in particular, it is essential to include the workings of the labour market.

Figure 9.6 gives an overview of the transmission mechanism in the model, focusing on the relationship between interest rates and inflation. The most direct effect on inflation from a rise in the interest rate is an exchange rate appreciation which feeds into lower consumer price inflation with a time lag. This delayed ‘pass-through’ of exchange rates into consumer price inflation is well known in empirical work and reflects inter alia that price setters may find it difficult to distinguish between permanent and temporary shocks to the

image193

Figure 9.6. Interest rate and exchange rate channels

exchange rate. Other interest rate effects work through their effects on aggregate demand which in turn affect output growth and the rate of unemployment. Both indicators affect domestic wage and price growth and hence inflation.

There is a link between Figure 9.6 and Figures 1.1 and 1.2. The small econo­metric model we are studying here captures the effect of Figure 1.1 through the aggregate demand channel and of Figure 1.2 through the exchange rate channel.

In order to take account of all implied feedback links, the model is completed with the necessary set of identities for the equilibrium-correction terms, real wages, the real exchange rate, the real bond rate, and so forth. With these new equations in place it is possible to estimate the model simultaneously with full information maximum likelihood (FIML). Doing so does not change the coefficient estimates of the model much.

As it stands, the system is fundamentally driven by the following exogenous variables:

• real world trade (weighted GDP for trading partners), ywt, and real public expenditure (gt)

• nominal foreign prices pwt measured as a trade-weighted index of foreign consumer prices

• the price of Brent Blend in USD (oilt)

Подпись: Inflation Подпись: Real wages 84 86 88 90 92 94 96 98 00

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180 170 160 150 140 130 120

• the monetary policy instrument, that is the short-term interest rate, represented through the money market interest rate (RSt).[100]

Figure 9.7 shows the tracking performance of the model when we simu­late from 1984(1) to 2001(1). The variables (listed row-wise from upper left to bottom right) are annual headline CPI inflation ((Pt/Pt-4) — 1), the real wage level (Wt/Pt), the nominal and real exchange rate Vt and Vt(PWt/Pt), respect­ively, unemployment rate (Ut) and real interest rate on bank loans (RL — 4Ap)t. The dotted lines are 95% confidence intervals. The model tracks headline CPI inflation fairly well over the period, but it should be noted that dummies are used to represent active price - and wage-policies during some periods in the 1970s and 1980s.

Figure 9.8 shows the model’s forecasting properties for the period 1999(1)- 2001(1). The variables (listed row-wise from upper left to bottom right) are quarterly wage inflation, Awt, quarterly headline CPI inflation, Apt, deviation from PPP, [v — (p — pw)]t, quarterly import price inflation, Apit, annual head­line CPI inflation, A4pt, unemployment, ut, mainland output, yt, annual output growth, A4yt, and the nominal exchange rate, vt. The model parameters are estimated on a sample that ends in 1998(4). These dynamic forecast are con­ditional on the actual values of the non-modelled variables (ex post forecasts). However, the model has a high degree of endogeneity as all important variables describing the domestic economy are explained within the model. The model exhibits good forecasting properties and the quarterly inflation rate Apt is in particular accurately forecasted. However, there is a slight overprediction in each quarter, and when we look to the annual inflation A4pt the effect accumu­lates over the period. The same is the case for annualised output growth A4yt over the last 4 quarters (i. e. in 2000). The predicted nominal exchange rate is constant and tends not to capture the observed changes in vt.

Figure 9.8 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.

However, forecast uncertainty appears to be much smaller than similar results for the United Kingdom: Haldane and Salmon (1995) estimate one standard error in the range of 3 to 41 percentage points, while Figure 9.8 implies a standard error of 1.0 percentage points 4-periods ahead, and 1.2 percentage points 8-periods ahead. One possible explanation of this marked differences is that Figure 9.8 understates the uncertainty, since the forecast is based on the actual short-term interest rate, while Haldane and Salmon (1995) include a policy rule for interest rate.

In Bardsen et al. (2003) an attempt is made to control for this difference. To make their estimate of inflation uncertainty—which is nearly of the same order of magnitude as the estimated uncertainty in Figure 9.8—comparable to Haldane and Salmon (1995), they calculated new forecasts for a model that includes an equation for the short-term interest rate as a function of the lagged rates of domestic and foreign annual inflation, of nominal exchange rate depre­ciation, and of the lagged output gap. The results showed a systematic bias in the inflation forecast, due to a marked bias in the forecasted interest rate, but the effect on forecast uncertainty was very small. Hence it appears that the difference in forecast uncertainty stems from the other equations in the mod­els, not the interest rate policy rule. For example, Haldane and Salmon (1995) use a Phillips curve equation for the wage growth, and the other equations in their model are also in differences, implying non-cointegration in both labour and product markets. In contrast, Bardsen et al. (1998) (see Section 6.7.2) find that a core wage-price model with equilibrium-correction terms give very simi­lar results for Norway and the United Kingdom. Hence it is clearly possible that

111 in

Подпись: -3.0 - -3.5 -4.0 -Подпись: - - Forecasts — Aw Подпись: -- Forecasts — A4p

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image201 image202

x±l I

Подпись: ■ - Forecasts — Au
Подпись: 2000
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2000

2000

Forecasts — y

Forecasts — A4 y

Forecasts — v

Figure 9.8. Dynamic forecasts over 1999(1)-2001(1): from top left to bottom
right: quarterly wage inflation, Aw, quarterly headline CPI inflation, Ap,
deviation from PPP, [v — (p — pw)], quarterly import price inflation, Api,
annual headline CPI inflation, A4p, unemployment, u, mainland output, y,
annual output growth, A4y, and the nominal exchange rate, v. The bars show
prediction intervals (±2 standard errors)

a large fraction of the inflation forecast uncertainty in Haldane and Salmon’s study is a result of model mis-specification.

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