Average inflation in the post-war period in developed countries was moderately different from zero and varied across countries.1 Nonetheless, most of the vast literature on monetary policy rules worked with models log-linearized around a zero inflation steady state (see e.g., Clarida et al., 1999, Galí, 2003, Woodford, 2003, or the book edited by Taylor, 1999). This paper aims to accomodate this clear inconsistency.
We generalize a standard Neo-Keynesian model with Calvo staggered price by taking a log-linear approximation around a general level of steady state inflation.2 Then we use a Taylor rule to close the model and address the question of how the properties of our economy change as the trend inflation level varies.
Our key finding is that trend inflation greatly affects the existing results in the literature. In particular moderate levels of trend inflation: (i) modify the determinacy region in the parameters space; (ii) alter the impulse response function of the model economy after a cost-push shock. As a consequence, trend inflation largely changes also the (unconditional) variances of key variables, such as inflation and output.
With respect to (i), we show that trend inflation substantially changes the well-known determinacy condition that the literature labelled the Taylor principle. This result is due to the distortions trend inflation causes in the long-run properties of the model and, particularly, in the steady state relationship between inflation and output, a surprisingly neglected issue in the literature. The long-run Phillips curve is highly non-linear in the Neo-Keynesian model: it is positively sloped in the inflation-output space, when steady state inflation is zero; but then the slope turns quite rapidly negative for extremely low value of trend inflation, because of the strong price-dispersion effect. We will show that this feature has significant implications on the celebrated Taylor principle. The results in most of the literature are therefore based on a case (i.e., zero steady state inflation) that is both empirical unrealistic and theoretically very special.
Our key result is then generalized and proved to be robust to: (i) different kinds of Taylor type rules proposed in the literature (contemporaneous, backward-looking, forward-looking and hybrid, see e.g., Clarida et al., 2000, Bullard and Mitra, 2002); (ii) inertial Taylor rules for all the cases in (i); (iii) indexation schemes (see, e.g., Yun, 1996 and Christiano et al., 2005); (iv) different parameter values.
In sum, this paper shows that the literature on monetary policy rules cannot neglect trend inflation both in the empirical and theoretical analysis, because the specification of the theoretical model (and so all the results) is very sensitive to low and moderate trend inflation levels, as empirically observed in western countries.
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Trend Inflation, Taylor Principle and Indeterminacy
