Dynamic Stochastic General Equilibrium Models Under a Liquidity Trap and Self-organizing State Space Modeling

This paper proposes a new method to estimate parameters of dynamic general equilibrium models under a liquidity trap based on the Monte Carlo particle filter, proposed by Kitagawa (1996) and Gordon et al. (1993), and a self-organizing state space model, proposed by Kitagawa (1998). This method is a natural extension of Yano (2009). In our method, we estimate the parameters using the time-varying-parameter approach, which is often used to infer invariant parameters practically. Our method is based on Bayesian statistics and nonlinear, non-Gaussian, and non-stationary state space modeling to estimate unknown parameters and states. In most previous papers on DSGE models, structural parameters of them are assumed to be "deep (invariant)." Our method, however, analyzes how stable structural parameters are. Adopting it creates the great advantage that the structural changes of parameters are detected naturally. The second advantage of our method is that we are able to estimate new Keynesian DSGE models under a liquidity trap (Krugman (1998)) because nonlinear,non-Gaussian, and non-stationary state space models allow model switching. In our method, the fit of a DSGE model is evaluated using the log-likelihood of it. Thus, we are able to compare the fits of DSGE models. Moreover, we estimate time-varying trends of macroeconomic data: real output, inflation rate, and real interest rate. Our method is an alternative to detrending methods based on the Hodrick-Prescott filter, the Baxter-King filter, the Christiano-Fitzgerald filter, and other filtering algorithms. In our framework, we emphasize that natural rates of macroeconomic data, time-varying parameters, and unknown states are estimated simultaneously. In empirical analysis, we estimate new Keynesian DSGE models under a liquidity trap using Japanese macroeconomic data which includes the "zero-interest-rate" period (1999-2006). The analysis shows that the growth rate of natural output declines in the late 1990s, but, becomes as high as about 2% in the mid-2000s. The target rate of inflation is too low in the 1990s and the 2000s, and it causes deflation in the Japanese economy.