Constrained estimation using penalization and MCMC

We study inference for parameters defined by either classical extremum estimators or Laplace-type subject to general nonlinear constraints on the parameters. show that running MCMC penalized version of problem offers a computationally attractive alternative solving original constrained optimization problem. Bayesian credible intervals are asymptotically valid confidence in pointwise sense, providing exact asymptotic coverage functions allow nonadaptive and adaptive penalizations using ℓp p⩾1 penalty functions. These methods motivated include as special cases model selection shrinkage such LASSO its versions. A simulation validates theoretical results. also provide an empirical application estimating joint density U.S. real consumption asset returns Euler equation CRRA pricing model.