Abstract

Inflation dynamics are investigated by estimating a generalized version of the New Keynesian Phillips curve (NKPC) of Galí and Gertler (1999) using Bayesian GMM. US macroeconomic data suggests that the generalized NKPC (GNKPC) performs best in terms of quasi-marginal likelihood among those considered both during and after the Great Inflation period. The estimated GNKPC indicates that when trend inflation fell after the Great Inflation period, the probability of price change decreased and the GNKPC flattened, which is in line with findings by previous studies.

Introduction

The dynamics of inflation have long been the subject of intense investigation in macroeconomics. To describe inflation dynamics, the New Keynesian Phillips curve (NKPC) is often derived by assuming either zero trend inflation or price indexation to trend and lagged inflation.1 However, these assumptions in the canonical NKPC are at odds with empirical observations. Recent studies thus examine the effect of nonzero trend inflation on the NKPC, particularly without the indexation.2 The studies have shown that such a generalized NKPC (GNKPC) has substantially distinct features from the canonical NKPC, thereby generating important implications for policy and welfare. This finding raises the question as to which is a more plausible description of inflation dynamics, the GNKPC or the canonical NKPC.

This paper estimates and evaluates the GNKPC using a novel model selection procedure under the framework of limited-information Bayesian estimation. In the empirical literature on NKPCs, two main approaches have been adopted: limited-information (or single-equation) methods and full-information (or system) methods. For example, the GMM estimation of the NKPC in Galí and Gertler (1999) and the minimum distance estimation of the GNKPC in Cogley and Sbordone (2008) can be classified as limited-information methods. On the other hand, NKPCs in the estimated dynamic stochastic general equilibrium (DSGE) models of Christiano et al. (2005) and Smets and Wouters (2007) can be categorized as full-information methods. In a recent paper, Hirose et al. (2020) conduct a full-information Bayesian analysis to compare a GNKPC and an NKPC in an otherwise identical DSGE model, and show that the model with the GNKPC outperforms that with the NKPC in terms of marginal likelihood.

Empirical Results

This section presents the results of the model selection and accounts for the estimation results of the selected model.

۴٫۱ Comparison of Gal´ı-Gertler GNKPC, NKPC, and GNKPC with indexatioWe begin by comparing the empirical performance of the GNKPC (1), the NKPC (5), and the GNKPC with indexation. As noted in the preceding section, the performance is evaluated in terms of QML, which is computed with the two alternative modified harmonic mean estimators proposed by Geweke (1999) and by Sims et al. (2008). For each of the three, Table 3 reports log QML using the truncation parameter values of τ = ۰٫۵, ۰٫۹ for the estimator of Geweke (1999) and q = 0.5, 0.9 for that of Sims et al. (2008).

The third to fifth columns of Table 3 show that the GNKPC has higher QML than the NKPC and the GNKPC with indexation in all the three estimation periods for both estimators with both truncation parameter values. This result indicates that the GNKPC describes inflation dynamics better than the NKPC and the GNKPC with indexation both during and after the Great Inflation period as well as the full sample period. Moreover, the absence of the indexation, that is, retaining some unchanged prices in each quarter in line with micro evidence improves the GNKPC’s fit to the macroeconomic data. These findings coincide with those of Hirose et al. (2020). They conduct a full-information Bayesian analysis to compare a Gal´ı-Gertler GNKPC and NKPC in an otherwise identical DSGE model, and show that the model with the GNKPC outperforms that with the NKPC during both the Great Inflation and Great Moderation periods in terms of marginal likelihood. As noted in Introduction, recent studies have pointed out that GNKPCs possess substantially distinct features from canonical NKPCs, thereby generating important implications for policy and welfare. Therefore, our findings suggest that GNKPCs should be preferred to canonical NKPCs for the analysis of the Federal Reserve’s monetary policy.