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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.
JEL-Codes: C12, C22, C52
Keywords: Threshold effects; Integrated processes; Nonlinear cointegration; Weak identi…cation


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