Topics in Nonlinear Econometrics

University Of Rochester, Rochester NY

Investigators

Abstract

This project contains three areas of research: the Generalized Method of Moments (GMM) with an infinity of moment conditions; Nonparametric estimation of a density when data are observed with measurement error; Parameter stability and unit-root tests against nonlinear alternatives. First, the project extends GMM with a continuum of moments to account for time-series and correlated moment conditions. An important application is the estimation of continuous-time models used in finance. While in such cases the likelihood does not have a closed-form expression, the characteristic function is often known or can be estimated via simulations. The characteristic function gives rise to a continuum of moment conditions which, if fully exploited, permit efficient estimation of the model. Special attention is devoted to the characterization of the moment conditions, which allow efficiency to be obtained in Markovian models. These results will also improve our understanding of how well efficiency can be approached in non-markovian cases. The second part of this project proposes a new nonparametric estimator of the density when data are measured with an additive error. The method consists in inverting an integral operator. It is shown that by imposing weak restrictions on the model, the estimator can achieve much faster rates of convergence than the usual estimators. The first two parts of this project draw from the statistical literature on integral operators and inverse problems. This research will highlight the usefulness of operator theory and contribute to make it popular in econometrics. Third, new methods are developed for testing when a nuisance parameter is not identified under the null hypothesis. This problem arises frequently in macro or financial econometrics. For example, in the presence of transaction costs, the real exchange rate is expected to behave in a nonlinear fashion. A natural specification is then a threshold model. In this context, testing whether the purchasing power parity holds consists in testing the null hypothesis of a unit root versus a stationary threshold alternative. The project proposes a test and derives its asymptotic distribution. This test should positively impact empirical work, as it is more powerful than existing tests.