The models above are estimated both for annual inflation (A4pt) and quarterly inflation (Apt) for all the inflation models, except for the NPCM where the forward-looking term on the right-hand makes the quarterly model the obvious choice. As with the Euro-area data, we shall seek to evaluate the different inflation models by comparing some of their statistical properties. In Table 8.17 we report p-values for mis-specification tests for residual autocorrelation, autoregressive conditional heteroskedasticity, non-normality and wrong functional form. With the exception of the normality tests which are x2(2), we have reported F-versions of all tests.
None of the models reported in the upper part of Table 8... Read More
To make the exposition self-contained, this appendix illustrates solution and estimation of simple models with forward looking variables—the illustration being the hybrid ‘New Keynesian Phillips curve’. Finally, we comment on a problem with observational equivalence, or lack of identification within this class of models.
A sufficiently rich data generating process (DGP) to illustrate the techniques are
Apt = bp1EtApt+i + 6p1Apt-i + bp2xt + £pt, (A.9)
xt = bxxt-1 + £xt, (A.10)
where all coefficients are assumed to be between zero and one. All of the techniques rely on the law of iterated expectations,
EtEt+kxt+j = Etxt+j, к < j,
saying that your average revision of expectations, given more information, will be zero.
A.2.1 Repeated substitution
This method is the brute force solutio... Read More
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... Read More
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... Read More
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 ... Read More
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
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... Read More