INSTRUMENTAL VARIABLE ESTIMATION OF A THRESHOLD MODEL
针对存在内生变量但阈值变量外生的阈值模型，提出了两阶段最小二乘和广义矩估计方法，证明了估计量的一致性和渐近分布，蒙特卡洛模拟验证了方法的适用性。
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.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.