Academic journal article Journal of Money, Credit & Banking

Trend Inflation, Taylor Principle, and Indeterminacy

Academic journal article Journal of Money, Credit & Banking

Trend Inflation, Taylor Principle, and Indeterminacy

Article excerpt

AVERAGE INFLATION IN the postwar period in developed countries was moderately different from zero and varied across countries. (1) Nonetheless, much of the extensive literature on monetary policy rules employed models approximated around the zero-inflation steady state (see, e.g., Clarida, Gali, and Gertler 1999, Gali 2003, Woodford 2003; see also Taylor 1999).

In this article we address this inconsistency by extending the basic small-scale New Keynesian dynamic stochastic general equilibrium (DSGE) model to allow for positive trend inflation. (2) We add a Taylor rule to describe the monetary authority's behavior and then examine to what extent the properties of the model economy change as trend inflation varies. We show that even moderate levels of trend inflation greatly modify the conditions under which the rational expectations equilibrium (REE) is determinate or unique.

Trend inflation has substantial effects on the well-known Taylor principle for the determinacy of the REE. This result is driven by the steady-state relative price distortions induced by trend inflation in the staggered adjustment mechanism a la Calvo (1983). As shown by Ascari (2004) and Yun (2005), the steady-state relation between output and inflation is highly nonlinear. The long-run Phillips curve is positively sloped around the zero-inflation steady state; however, as soon as trend inflation takes up even moderate positive values, the long-run Phillips curve inverts and becomes negatively sloped, reflecting the relative price distortions. In other words, the higher the trend inflation, the lower the level of output in steady state. In this article, we demonstrate that this feature of the model has remarkable implications for the celebrated Taylor principle. Therefore, a natural suspicion that many of the results in the literature are drawn from a case, namely, the zero-inflation steady state, which is both empirically unrealistic and theoretically special, arises.

Our key result is generalized and proved to be qualitatively robust to a number of checks: (i) different types of Taylor rules (contemporaneous, backward-looking, forward-looking, and hybrid nominal interest rate rules; see, e.g., Clarida, Gali, and Gertler 2000, Bullard and Mitra 2002), (ii) inertial Taylor rules for all the cases listed in (i), (iii) different price indexation schemes (see, e.g., Yun 1996, Christiano, Eichenbaum, and Evans 2005), and (iv) different calibration values.

In a nutshell, research in the field of monetary policy cannot neglect trend inflation, as both the theoretical model and the determinacy properties of Taylor rules are sensitive to low and moderate levels of positive trend inflation, as generally observed in Western countries.

The seminal analysis of Clarida, Gali, and Gertler (2000) can be taken as an example. Clarida, Gali, and Gertler were the first to estimate a Taylor rule on U.S. data. They found that during the pre-Volcker period the nominal interest rate reacted less than one to one in response to variations in inflation, while afterward the response of the policy rate was more than proportional Strictly speaking, U.S. monetary policy did not satisfy the Taylor principle in the first subsample, while it did in the second one. Thus, Clarida, Gali, and Gertler interpreted this as being responsible for the fact that inflation got out of control in the 1970s while getting back on track later. However, the data set used in Clarida, Gali, and Gertler features an average inflation of roughly 4% (see table II, p. 157, of their work). Yet, their analysis is based on a theoretical model that assumes zero trend inflation. When appropriately taken into account, positive trend inflation substantially changes the model structural equations and the determinacy region, so that one needs to account for trend inflation in order to label the REE as determinate. Indeed, using our benchmark parameters calibration in the standard New Keynesian DSGE model, the baseline estimates of the Taylor rule coefficients by Clarida, Gali, and Gertler would deliver indeterminacy in the pre-Volcker as well as the Volcker--Greenspan sample period. …

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