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

*Alessandro Casini* () and
*Pierre Perron*

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Alessandro Casini: University of Rome Tor Vergata

No WP2020-014, Boston University - Department of Economics - Working Papers Series from Boston University - Department of Economics

**Abstract:**
Building upon the continuous record asymptotic framework recently introduced by Casini and Perron (2020a) 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 preciseâ€”lower mean absolute error (MAE) and lower root-mean squared error (RMSE)â€”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 a better 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.

**Keywords:** Asymptotic distribution; bias; break date; change-point; Generalized Laplace; infill asymptotics; semimartingale (search for similar items in EconPapers)

**JEL-codes:** C12 C13 C22 (search for similar items in EconPapers)

**Pages:** 53 pages

**Date:** 2020-05

**New Economics Papers:** this item is included in nep-ore

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http://www.bu.edu/econ/files/2020/05/CASINI_PERRON_Lap_CR_single_Inf-full.pdf

**Related works:**

Journal Article: Continuous record Laplace-based inference about the break date in structural change models (2021)

Working Paper: Continuous Record Laplace-based Inference about the Break Date in Structural Change Models (2020)

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**Persistent link:** https://EconPapers.repec.org/RePEc:bos:wpaper:wp2020-014

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