Adaptive Elastic Net for Generalized Methods of Moments |
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Authors: | Mehmet Caner Hao Helen Zhang |
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Affiliation: | 1. Department of Economics, North Carolina State University,, 4168 Nelson Hall, Raleigh, NC 27518mcaner@ncsu.edu;2. Department of Mathematics, University of Arizona, Tucson, AZ 85718(hzhang@math.arizona.edu);3. Department of Statistics, North Carolina State UniversityRaleigh, NC 27695(hzhang@stat.ncsu.edu) |
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Abstract: | Model selection and estimation are crucial parts of econometrics. This article introduces a new technique that can simultaneously estimate and select the model in generalized method of moments (GMM) context. The GMM is particularly powerful for analyzing complex datasets such as longitudinal and panel data, and it has wide applications in econometrics. This article extends the least squares based adaptive elastic net estimator by Zou and Zhang to nonlinear equation systems with endogenous variables. The extension is not trivial and involves a new proof technique due to estimators’ lack of closed-form solutions. Compared to Bridge-GMM by Caner, we allow for the number of parameters to diverge to infinity as well as collinearity among a large number of variables; also, the redundant parameters are set to zero via a data-dependent technique. This method has the oracle property, meaning that we can estimate nonzero parameters with their standard limit and the redundant parameters are dropped from the equations simultaneously. Numerical examples are used to illustrate the performance of the new method. |
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Keywords: | GMM Oracle property Penalized estimators |
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