A Composite Likelihood Framework for Analyzing Singular DSGE Models

This paper builds on the composite likelihood concept of Lindsay (1988) to develop a framework for parameter identification, estimation, inference, and forecasting in dynamic stochastic general equilibrium (DSGE) models allowing for stochastic singularity. The framework consists of 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 nonsingular submodels. Second, it provides a procedure based on Markov Chain Monte Carlo for parameter estimation. Third, it delivers confidence sets for structural parameters and 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. 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 1 and 7.