Constrained estimation using penalization and MCMC

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.

Automated summary

This paper investigates inference for parameters subject to general nonlinear constraints using classical extremum estimators or Laplace-type estimators. By running MCMC on the penalized version of the problem, it offers a computationally attractive alternative to solving the original constrained optimization problem. Bayesian credible intervals are proven to be asymptotically valid confidence intervals for general functions of the parameters. Both nonadaptive and adaptive penalizations are allowed using the l(p) penalty functions for p >= 1. These methods are motivated by model selection and shrinkage methods such as LASSO and its Bayesian and adaptive versions. The theoretical results are validated through a simulation study and 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.