Parameter Bias in an Estimated DSGE Model: Does Nonlinearity Matter?
How can parameter estimates be biased in a dynamic stochastic general equilibrium model that omits nonlinearity in the economy? To answer this question, we simulate data from a fully nonlinear New Keynesian model with the zero lower bound constraint and estimate a linearized version of the model. Monte Carlo experiments show that significant biases are detected in the estimates of monetary policy parameters and the steady-state inflation and real interest rates. These biases arise mainly from neglecting the zero lower bound constraint rather than linearizing equilibrium conditions. With fixed parameters, the variance-covariance matrix and impulse response functions of observed variables implied by the linearized model substantially differ from those implied by its nonlinear counterpart. However, we find that the biased estimates of parameters in the estimated linear model can make most of the differences small.
Following the development of Bayesian estimation and evaluation techniques, many economists have estimated dynamic stochastic general equilibrium (DSGE) models using macroeconomic time series. In particular, estimated New Keynesian models, which feature nominal rigidities and monetary policy rules, have been extensively used by policy institutions such as central banks. Most of the estimated DSGE models are linearized around a steady state because a linear state-space representation along with the assumption of normality of exogenous shocks enables us to efficiently evaluate likelihood using the Kalman filter. However, Fern´andez-Villaverde and Rubio-Ram´ırez (2005) and Fern´andez-Villaverde, Rubio-Ram´ırez, and Santos (2006) demonstrate that the level of likelihood and parameter estimates based on a linearized model can be significantly different from those based on its original nonlinear model. Moreover, in the context of New Keynesian models, Basu and Bundick (2012), Braun, K¨orber, and Waki (2012), Fern´andez-Villaverde, Gordon, Guerr´on-Quintana, and Rubio-Ram´ırez (2015), Gavin, Keen, Richter, and Throckmorton (2015), Gust, L´opez-Salido, and Smith (2012), Nakata (2013a, 2013b), and Ngo (2014) emphasize the importance of considering nonlinearity in assessing the quantitative implications of the models when the zero lower bound (ZLB) constraint on the nominal interest rate is taken into account.