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Constrained estimation using penalization and MCMC
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DOI：10.1016/j.jeconom.2021.02.004.png)
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Abstract
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We study inference for parameters defined by either classical extremum estimators or Laplace-type estimators subject to general nonlinear constraints on the parameters. We show that running MCMC on the penalized version of the problem offers a computationally attractive alternative to solving the original constrained optimization problem. Bayesian credible intervals are asymptotically valid confidence intervals in a pointwise sense, providing exact asymptotic coverage for general functions of the parameters. We allow for nonadaptive and adaptive penalizations using the l(p) for p >= 1 penalty functions. These methods are motivated by and include as special cases model selection and shrinkage methods such as the LASSO and its Bayesian and adaptive versions. A simulation study validates the theoretical results. We also provide an empirical application on estimating the joint density of U.S. real consumption and asset returns subject to Euler equation constraints in a CRRA asset pricing model. (C) 2021 Elsevier B.V. All rights reserved.
Keywords:
Penalized estimation
MCMC
Laplace-type estimators
Bayesian LASSO
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