Continuous Record Laplace-based Inference about the Break Date in Structural Change Models

TL;DR

This paper introduces a Laplace-based (Quasi-Bayes) method for estimating and constructing confidence sets for the break date in structural change models, offering improved accuracy and inference over traditional methods within a continuous record asymptotic framework.

Contribution

It develops a novel Laplace-type inference procedure for structural break dates, utilizing a Quasi-posterior distribution for more precise estimation and valid confidence sets.

Findings

Lower MAE and RMSE compared to least-squares estimates

Confidence sets achieve better coverage and shorter length

Method performs well for both small and large break sizes

Abstract

Building upon the continuous record asymptotic framework recently introduced by Casini and Perron (2018a) for inference in structural change models, we propose a Laplace-based (Quasi-Bayes) procedure for the construction of the estimate and confidence set for the date of a structural change. It is defined by an integration rather than an optimization-based method. A transformation of the least-squares criterion function is evaluated in order to derive a proper distribution, referred to as the Quasi-posterior. For a given choice of a loss function, the Laplace-type estimator is the minimizer of the expected risk with the expectation taken under the Quasi-posterior. Besides providing an alternative estimate that is more precise|lower mean absolute error (MAE) and lower root-mean squared error (RMSE)|than the usual least-squares one, the Quasi-posterior distribution can be used to construct asymptotically valid inference using the concept of Highest Density Region. The resulting Laplace-based inferential procedure is shown to have lower MAE and RMSE, and the confidence sets strike the best balance between empirical coverage rates and average lengths of the confidence sets relative to traditional long-span methods, whether the break size is small or large.