Constrained estimation using penalization and MCMC

A. Ronald Gallant, Han Hong, Michael P. Leung, Jessie Li

Research output: Contribution to journalArticlepeer-review


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 ℓp 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.

Original languageEnglish (US)
Pages (from-to)85-106
Number of pages22
JournalJournal of Econometrics
Issue number1
StatePublished - May 2022

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics


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