Instrumental variable estimation of a threshold model. (English) Zbl 1071.62115

Summary: 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 [B. E. Hansen, Econometrica 68, No. 3, 575–603 (2000; Zbl 1056.62528)], 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.


62P20 Applications of statistics to economics
62L12 Sequential estimation
62E20 Asymptotic distribution theory in statistics
65C05 Monte Carlo methods
62J05 Linear regression; mixed models
62F05 Asymptotic properties of parametric tests


Zbl 1056.62528
Full Text: DOI


[1] DOI: 10.1007/BF00536298 · Zbl 0326.60053
[2] DOI: 10.1017/S0266466602183113__S0266466602183113
[3] DOI: 10.1162/003465397557132
[4] DOI: 10.2307/2951753 · Zbl 0815.62033
[5] DOI: 10.2307/1427090 · Zbl 0585.62151
[6] DOI: 10.1214/aos/1176347498 · Zbl 0703.62063
[7] DOI: 10.1162/003465398557564
[8] DOI: 10.1111/1468-0262.00124 · Zbl 1056.62528
[9] DOI: 10.1016/S0304-4076(99)00025-1 · Zbl 0941.62127
[10] DOI: 10.2307/2171789 · Zbl 0862.62090
[11] DOI: 10.1086/317670
[12] DOI: 10.2307/2534426
[13] DOI: 10.2307/2335690 · Zbl 0362.62026
[14] DOI: 10.1214/aos/1176349040 · Zbl 0786.62089
[15] DOI: 10.1016/0304-4076(87)90015-7 · Zbl 0618.62040
[16] DOI: 10.1016/S0304-3932(98)00028-2
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.