Category THE ECONOMETRICS OF MACROECONOMIC MODELLING

Models of money demand

8.2.1 The velocity of circulation

Models of the velocity of circulation are derived from the ‘equation of exchange’ identity often associated with the quantity theory of money (Fisher 1911) which on logarithmic form can be written:

mt + vt = pt + yt, (8.1)

where mt is money supply, vt is money velocity, yt is a scaling variable (e. g. real output), and pt is the price level. We define the inverse velocity of money as mt — yt — pt = – vt (small letters denote variables in logarithms). A simple

theory of money demand is obtained by adding the assumption that the velocity is constant, implying that the corresponding long-run money demand relation­ship is a linear function of the scaling variable yt, and the price level pt. The stochastic specification can be written as:

mt – yt – pt...

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Testing exogeneity and invariance

Following Engle et al. (1983), the concepts of weak exogeneity and parameter invariance refer to different aspects of ‘exogeneity’, namely the question of valid conditioning in the context of estimation, and valid policy analysis, respectively. In terms of the ‘road-map’ of Figure 9.1, weak exogeneity of the conditional variables for the parameters of the wage-price model Dy (yt | zt, Yt-1, Zt-1) implies that these parameters are free to vary with respect to the parameters of the marginal models for output, productivity, unemployment, and exchange rates DZl (z1t | z2t, z3t, Yt_i, Zt-1). Below we repeat the examination of these issues as in Bardsen et al. (2003): we follow Johansen (1992) and concentrate the testing to the parameters of the cointegration vectors of the wage-price model...

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The P*-model of inflation

In the P*-model (Hallman et al. 1991) the long-run equilibrium price level is defined as the price level that would result with the current money stock, mt, provided that output was at its potential (equilibrium level), y*, and that velocity, vt = pt + yt — mt, was at its equilibrium level v*:

pt = mt + vt — y*t. (8.14)

The postulated inflation model is given by

Apt = E(Apt I It-i) + ap(pt-i — p—1) + @zzt + £t, (8.15)

where the main explanatory factors behind inflation are inflation expectations, E(Apt | It-1), the price gap, (pt-1 — pt_ 1), and other variables denoted zt. Note that if we replace the price gap in (8.15) with the output gap, we obtain the NPCM (8.12) discussed in the previous section with the expectations term backdated one period.

In order to calculate the price ...

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Welfare losses evaluated by response surface estimation

Taylor (1979a) argues that the tradeoff between inflation variability and out­put variability can be illustrated by the convex relationship in Figure 10.6. In point A monetary policy is used actively in order to keep inflation close to its target, at the expense of somewhat larger variability in output. Point C

Подпись: ж

Подпись: y
image226

а

Figure 10.6. The Taylor curve

illustrates a situation in which monetary policy responds less actively to keep the variability of inflation low, and we have smaller output variability and larger inflation variability. Point B illustrates a situation with a flexible inflation target, and we obtain a compromise between the two other points...

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Summary of the findings—Norway vs. Euro area

The overall conclusion from the comparisons of inflation models for the Norwegian economy is that monetary measures do not play an important part in explaining and/or predicting Norwegian inflation. The preferred specifica­tions of money demand do not include inflation as a significant explanatory
variable and hence the money demand equation cannot be interpreted as an inverted inflation equation. An attempt to model an inflation equation as an inverted money demand function shows clear signs of mis-specification and the MdInv model is demonstrated to be inferior to all other competitors based on in-sample evaluations as well as in forecasting (Figure 8.19). Also the P*-model, which embody several aggregates which monetarist theorists predict would explain inflation, fails to do so...

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Undetermined coefficients

This method is more practical. It consists of the following steps:

1. Make a guess at the solution.

2. Derive the expectations variable.

3. Substitute back into the guessing solution.

4. Match coefficients.

We will first use the technique, following the excellent exposition of Blanchard and Fisher (1989: ch. 5), to derive the solution conditional upon the expected path of the forcing variable, as in Gall et al. (2001), so we will ignore any information about the process of the forcing variable.

In the following we will define

zt — bp2xt + &pt-

Since the solution must depend on the future, a guess would be that the solution will consist of the lagged dependent variable and the expected values of the forcing value:

Ж

Apt — aAp—i + 53 PiEtZt+i■ (A.19)

i=0

We now take the expectation o...

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