Mehmet Caner and Bruce E. Hansen
"Instrumental Variable Estimation of a Threshold Model"

Econometric Theory, (2004), 20, 813-843.


Threshold models (sample splitting) models have wide application in economics. Existing estimation methods are confined to regression models, which require that all right-hand-side variables are exogenous. This paper considers a model with endogenous variables but an exogenous threshold variable. We develop a 2SLS estimator of the threshold parameter and a GMM estimator of the slope parameters. We show that these estimators are consistent, and derive the asymptotic distribution of the estimators. The threshold estimate has the same distribution as for the regression case (Hansen, 2000), with a different scale. The slope parameter estimates are asymptotically normal with conventional covariance matrices. We investigate our distribution theory with a Monte Carlo simulation which indicates the applicability of the methods.

We apply our methods to the term structure model of interest rates. In several bi-variate cointegrating VECMs, we find strong evidence for a threshold error-correction model.

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Some of the above material is based upon work supported by the National Science Foundation under Grants No. SES-9022176, SES-9120576, SBR-9412339, and SBR-9807111. Any opinions, findings, and conclusions, or recommendations expressed in this material are those of the author(s), and do not necessarily reflect the views of the NSF.