| Content | 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. |
