Robust Estimation and Inference for Threshold Models with
Integrated Regressors

Haiqiang Chen

Econometric Theory 31, 2015, 778–810.

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This paper studies the robust estimation and inference of threshold models with integrated regres-
sors. We derive the asymptotic distribution of the pro led least squares (LS) estimator under the
diminishing threshold e¤ect assumption that the size of the threshold e¤ect converges to zero. Depend-
ing on how rapidly this sequence converges, the model may be identi ed or only weakly identi ed and
asymptotic theorems are developed for both cases. As the convergence rate is unknown in practice, a
model-selection procedure is applied to determine the model identi cation strength and to construct
robust con dence intervals, which have the correct asymptotic size irrespective of the magnitude of
the threshold e¤ect. The model is then generalized to incorporate endogeneity and serial correlation
in error terms, under which, we design a Cochrane-Orcutt feasible generalized least squares (FGLS)
estimator which enjoys e¢ ciency gains and robustness against di¤erent error speci cations, including
both I(0) and I(1) errors. Based on this FGLS estimator, we further develop a sup-Wald statistic to
test for the existence of the threshold e¤ect. Monte Carlo simulations show that our estimators and
test statistics perform well.