Essays on regime switching and DSGE models with applications to U.S. business cycle

This dissertation studies various issues related to regime switching and DSGE models. The methods developed are used to study U.S. business cycles. Chapter one considers and derives the limit distributions of likelihood ratio based tests for Markov regime switching in multiple parameters in the context of a general class of nonlinear models. The analysis simultaneously addresses three difficulties: (1) some nuisance parameters are unidentified under the null hypothesis, (2) the null hypothesis yields a local optimum, and (3) the conditional regime probabilities follow stochastic processes that can only be represented recursively. When applied to US quarterly real GDP growth rates, the tests suggest strong evidence favoring the regime switching specification over a range of sample periods. Chapter two develops a modified likelihood ratio (MLR) test to detect regime switching in state space models. I apply the filtering algorithm introduced in Gordon and Smith (1988) to construct a modified likelihood function under the alternative hypothesis of two regimes and I extend the analysis in Chapter one to establish the asymptotic distribution of the MLR statistic under the null hypothesis of a single regime. I also apply the test to a simple model of the U.S. unemployment rate. This contribution is the first to develop a test based on the likelihood ratio principle to detect regime switching in state space models. The final chapter estimates a search and matching model of the aggregate labor market with sticky price and staggered wage negotiation. It starts with a partial equilibrium search and matching model and expands into a general equilibrium model with sticky price and staggered wage. I study the quantitative implications of the model. The results show that (1) the price stickiness and staggered wage structure are quantitatively important for the search and matching model of the aggregate labor market; (2) relatively high outside option payments to the workers, such as unemployment insurance payments, are needed to match the data; and (3) workers have lower bargaining power relative to firms, which contrasts with the assumption in the literature that workers and firms share equally the surplus generated from their employment relationship