Does the MA(1) process prove that the forward solution applies?

Assume that the true model is

Apt = bp1^pt-1 + £pt: bpl < 1

and the the following model is estimated by means of instrumental variables

Apt = bpiApt+i + £pt – What are the properties of efptl

£pt = APt – bpiAPt+i-

Assume, as is common in the literature, that we find that bfpi и 1. Then
£fpt и APt – APt+i = – A2Pt+i

= — [£pt+i + (bpi — 1)^pt + ••• ]•

So we get a model with a moving average residual, but this time the reason is not forward-looking behaviour but mis-specification.

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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 empirica...

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Four groups of interest rate rules

The rules we consider are of the type

RSt = ш RSt_i + (1 — шr )(n* + RR*) + Шп (fit+в — n*)

+ шу (A4 Vt+K — 3*y) + Wealzreal, t + ^openzopen, t?

where RSt denotes the short-term nominal interest rate, RR* is the equilibrium real interest rate, fit+e is a model-based forecast of inflation (i. e. A4pu) в periods ahead, n* is the inflation target for A4put, A4yt+K is a model-based forecast of output growth к periods ahead, gy is the target output growth rate, zrealt denote real-time variables and zopen t denotes open economy variables (typically the real exchange rate). When the target horizons в and к are set to zero, the rules are based on contemporary values of output and inflation. In Section 10.3...

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The New Keynesian Phillips curve

We estimate a hybrid NPCM as described in Section 8.5.3 (cf. Chapter 7 for further details). Using the instruments of Gall et al. (2001)[77]—five lags of infla­tion, Apt, and two lags in the wage share, wst, and output gap (gap)—we are able to replicate the results for the hybrid model in Chapter 7, which in turn are representative for the empirical results reported in Gall et al. (2001). We have chosen to estimate a small simultaneous model where the inflation lead Apt+1 and the wage share wst are specified as functions of the instruments and full information maximum likelihood estimation[78] then yields the following inflation equation:

Apt = — 0.0008 + 0.72Apt+1 + 0.31Apt_ 1 + 0.002 + dummies (0.006) (0.07) (0.07) (0.008)

a = 0.00232 (8.22)


Single equation diagnos...

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A large-scale EqCM model and four dVAR type forecasting systems based on differenced data

Section 11.2.1 brought out that even for very simple systems, it is in general difficult to predict which version of the model is going to have the smallest forecast error, the EqCM or the dVAR. While the forecast errors of the dVAR are robust to changes in the adjustment coefficient a and the long-run mean Z, the dVAR forecast error may still turn out to be larger than the EqCM forecast error. Typically, this is the case if the parameter change (included in the EqCM) is small relative to the contribution of the equilibrium-correcting term (which is omitted in the dVAR) at the start of the forecast period.

In the following, we generate multi-period forecasts from the econometric model RIMINI, and compare these to the forecasts from models based on dif­ferenced data...

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An encompassing representation

The main alternatives to the NPCM as models of inflation are the Standard Phillips Curve Model (PCM) and the Incomplete Competition Model (ICM). They will therefore be important in suggesting ways of evaluating the NPCM from an encompassing perspective. To illustrate the main differences between alternative specifications, consider the following stylised framework—see also Bardsen et al. (2002a). Let w be wages and p consumer prices; with a as productivity, the wage share ws is given as real unit labour costs: ws = ulc — p = w — a —p; u is the unemployment rate, and gap the output gap, all measured in logs. We abstract from other forcing variables, like open economy aspects. A model of the wage-price process general enough for the present purpose then takes the form

Aw = aApe — fiw...

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