Time-varying Analysis of Dynamic Stochastic General Equilibrium Models Based on Sequential Monte Carlo Methods

This paper proposes a new method to estimate parameters, natural rates, and business cycles of dynamic stochastic general equilibrium models simultaneously and consistently. It is based on the Monte Carlo particle filter and a self-organizing state space model. In our method, we estimate the parameters and the natural rates using the time-varying-parameter approach, which is often used to infer invariant parameters practically. In most previous papers on DSGE models, structural parameters of them are assumed to be "deep (invariant)." However, our method analyzes how stable structural parameters are. Adopting the TVP approach creates the great advantage that the structural changes of parameters are detected naturally. Moreover, we estimate time-varying natural rates of macroeconomic data: real output and an equilibrium real interest rate. In empirical analysis, we estimate a new Keynesian DSGE model using the US data. The analysis shows that the average of the growth of natural output is 3.02 and the average of inflation target is 2.46 from 1985 to 2007. From the late Volcker era to the early Greenspan era, the reaction coefficient to inflation in the Taylor rule is increasing, and from the mid Greenspan era to the early Bernanke era it is stable around 4.0. These results indicate that the behavior of the Fed had changed to realize the stability of inflation from the late Volcker era to the early Greenspan era. An equilibrium real rate is negative from the early 2000s to the mid-2000s because the Fed cuts policy rates to prevent deflation.