Extensions and Applications of Efficient Method of Moments

University Of North Carolina At Chapel Hill, Chapel Hill NC

Investigators

Abstract

The proposed research to be undertaken will continue and extend a long-standing program of research in nonlinear econometric methods. The view is that an econometric specification is an approximation to the underlying data generating mechanism. In keeping with this view, methodologies have been developed that sequentially improve the approximation as information becomes available, and permit reliable inference at each intermediate stage of model evolution. These objectives have been accomplished at a level of generality that encompasses most nonlinear econometric inference procedures. The basic idea is to endow a procedure with nonparametric properties by replacing the structural model with a truncated series expansion, the error density with a truncated expansion, or both. By letting the truncation point grow adaptively with sample size, the approximation is accurate enough at each intermediate stage to permit reliable inference and ultimate convergence to the underlying data generating mechanism is assured. Tightly parameterized structural modeling can be carried out within this paradigm. The idea is to require that moments implied by the structural model match the scores of a model developed according to the methodology described above. This estimator has certain advantages. Estimates can be made as efficient as if maximum likelihood had been employed. Unlike maximum likelihood, the computational burden does not increase if the state vector is partially observed either because the structural model contains latent variables or because data is missing. Studentized scores serve as diagnostic tests and, because the scores correspond to identifiable features of data, failure to pass a diagnostic indicates which features of data a tightly parameterized structural model cannot explain. This is an invaluable aid to model development. The specific proposal is to establish that the advantages claimed above follow from assumptions that are more primitive than the high level assumptions used to date, to improve computational efficiency, and to continue an ongoing program of empirical work that exploits the new methodologies discussed above. Initial work will focus on the estimation of structural macro models with attention to the simultaneous use of time series and panel data. Reduced form applications will focus on methods for extracting the continuous time volatility process from discretely sampled asset prices and efficiently predicting functionals of the continuous time process such as integrated forward volatility.