Dynamics of Inflation Rate: Comparison of New Keynesian Models via Simulated Density

We set up a variant of New Keynesian models for the dynamics of inflation, and discuss the relative importance of the expected inflation rate and past inflation rate. Many papers have studied the price decision rules in monopolistically competitive product markets. This paper employs a Calvo-type (1983) staggered price setting that has become a standard way to introduce nominal rigidities in the quantitative general equilibrium model. Firms that cannot optimize their prices set their prices with indexation to the past inflation rate. The "Canonical" and "Hybrid" New Keynesian models are without and with this indexation to the past inflation rate, respectively. Different degree of indexation is also considered for the Hybrid models. Rather than merely evaluating each of the alternative New Keynesian models, we compare different New Keynesian models (Canonical and Hybrid models) by constructing the test statistics between the distribution or density of empirical data and those of the simulated data from each theory model. Model parameters are calibrated and the reality check of White (2000) is applied to compare the models. The dynamics in inflation rate are compared for models with different degree of indexation. By comparing the simulated density or distribution to that of the empirical data, Hybrid New Keynesian models have better loss values, but the Canonical New Keynesian model can not be rejected with various degree of nominal rigidities. Moreover, we find that with a high degree of nominal rigidities, most firms follow the optimal pricing rule and indexing to past prices is suboptimal.