  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.
