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DSGE Model Identification

DSGE Model Identification - Dynamic Identication of DSGE...

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Dynamic Identification of DSGE Models Ivana Komunjer * Serena Ng September 2009 Preliminary: Comments Welcome Abstract This paper studies identification of the parameters of a DSGE model using the entire au- tocovariance structure of the data. Classical results for identification of structural parameters do not apply because some reduced form parameters in DSGE models cannot be identified. We use the parameter restrictions that two models with identical spectrum must satisfy to obtain the rank and order conditions for identification. Both conditions depend on the parametrization of the model alone, and should be checked before any observations are considered. The results are established in a general set up that allows fewer shocks than endogenous variables. Three examples are considered to illustrate the results. * University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093. Email: [email protected] Columbia University, 420 W. 118 St. MC 3308, New York, NY 10027. Email: [email protected] This paper was presented at the 2009 NBER summer institute, as well as the econometrics seminar at UC Davis. We thank Roger Farmer, Frank Schorfheide, Giuseppe Ragusa, and Leon Wegge for helpful comments. Part of this work was done while the first author was visiting Columbia University whose warm hospitality is gratefully acknowledged. The second author acknowledges financial support from the National Science Foundation (SES-0549978).
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1 Introduction Dynamic stochastic general equilibrium (DSGE) models have now reached the level of sophistication to permit analysis of important policy and theoretical macroeconomic issues. Whereas the param- eters in these models used to be calibrated, numerical advances in the last two decades have made it possible to estimate models with as many as a hundred parameters. Researchers are, however, aware that not all deep or structural parameters of DSGE models can be consistently estimated due to identification problems. A DSGE model is identifiable whenever changing the values of the model parameters induce a variation in the reduced form parameter that is not observationally equivalent to its original value. In spite of the recognition of this problem, a procedure has yet to be developed that tells us in a systematic manner how many parameters are identifiable, and if so which ones. This is not a trivial problem because unlike in the classical setup, the reduced form parameters of DSGE models are generally not identifiable. The contribution of this paper is to propose rank and order conditions for identification of parameters of interest. These can either be the deep parameters of the optimizing model, or the structural parameters of the log-linearized model. Hereafter, we will let θ denote the parameter vector of interest. Given that these models are dynamic, identification is obtained from the autocovariance structure (spectral density) of the observables. The results are new and not yet seen in the literature.
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