Econometric Theory


Mehmet  Caner  a1 c1 and Bruce E.  Hansen  a2 c2
a1 University of Pittsburgh
a2 University of Wisconsin

Article author query
caner m   [Google Scholar] 
hansen be   [Google Scholar] 


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 two-stage least squares estimator of the threshold parameter and a generalized method of moments estimator of the slope parameters. We show that these estimators are consistent, and we derive the asymptotic distribution of the estimators. The threshold estimate has the same distribution as for the regression case (Hansen, 2000, Econometrica 68, 575–603), 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 that indicates the applicability of the methods. a

c1 Address correspondence to Mehmet Caner, Department of Economics, WW Posvar Hall 4S01, Pittsburgh, PA 15260, USA; e-mail:
c2 Or address correspondence to Bruce E. Hansen, Department of Economics, 1180 Observatory Drive, Madison, WI 53706, USA; e-mail:


a We thank the two referees and co-editor for constructive comments. Hansen thanks the National Science Foundation for financial support. Caner thanks University of Pittsburgh Central Research Development Fund for financial support.