A Composite Likelihood Framework for Analyzing Singular DSGE Models

This paper builds upon the composite likelihood concept of Lindsay (1988) to develop a framework for parameter identification, estimation, inference and forecasting in DSGE models allowing for stochastic singularity. The framework consists of the following four components. First, it provides a necessary and sufficient condition for parameter identification, where the identifying information is provided by the first and second order properties of the nonsingular submodels. Second, it provides an MCMC based procedure for parameter estimation. Third, it delivers confidence sets for the structural parameters and the impulse responses that allow for model misspecification. Fourth, it generates forecasts for all the observed endogenous variables, irrespective of the number of shocks in the model. The framework encompasses the conventional likelihood analysis as a special case when the model is nonsingular. Importantly, it enables the researcher to start with a basic model and then gradually incorporate more shocks and other features, meanwhile confronting all the models with the data to assess their implications. The methodology is illustrated using both small and medium scale DSGE models. These models have numbers of shocks ranging between one and seven.