Likelihood ratio testing in linear state space models: An application to dynamic stochastic general equilibrium models

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This paper considers the problem of hypothesis testing in linear Gaussian state space models. We consider two hypotheses of interest: a simple null and a hypothesis of explicit parameter restrictions. We derive the asymptotic distributions of the corresponding likelihood ratio test statistics and compute the Bartlett adjustments. The results are non-trivial because the unrestricted state space model is not (even locally) identified. We apply our analysis to test the validity of the Dynamic Stochastic General Equilibrium (DSGE) models. A Monte Carlo exercise illustrates our findings and confirms the importance of Bartlett corrections at sample sizes typically encountered in macroeconomics.