A smoothed least squares estimator for threshold regression models

• Published in: Journal of econometrics Vol. 141; no. 2; pp. 704 - 735
• Main Authors: Seo, Myung Hwan, Linton, Oliver
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.12.2007; Elsevier; Elsevier Sequoia S.A
• Series: Journal of Econometrics
• Subjects: Applications; Bootstrap mechanism; Econometric models; Econometrics; Error; Estimating techniques; Estimation; Exact sciences and technology; Index model; Insurance, economics, finance; Least squares method; Linear inference, regression; Mathematics; Parameter estimation; Parametric inference; Probability and statistics; Regression analysis; Sample splitting; Sciences and techniques of general use; Segmented regression; Smoothing; Statistics; Studies; Threshold estimation; Sample splitting; Segmented regression; C13; C12; Smoothing; C14; Index model; Threshold estimation; Data analysis; C12; C13; C14; Error estimation; Statistical estimation; Asymptotic convergence; Economic data; Statistical method; Statistical regression; Splitting; Index model; Sample splitting; Segmented regression; Smoothing; Threshold estimation; Consistent estimator; Regression model; Least squares method; Asymptotic normality; Bootstrap; Jackknife method; Econometrics; Resampling method
• ISSN: 0304-4076; 1872-6895
• DOI: 10.1016/j.jeconom.2006.11.002

We propose a smoothed least squares estimator of the parameters of a threshold regression model. Our model generalizes that considered in Hansen [2000. Sample splitting and threshold estimation. Econometrica 68, 575–603] to allow the thresholding to depend on a linear index of observed regressors, thus allowing discrete variables to enter. We also do not assume that the threshold effect is vanishingly small. Our estimator is shown to be consistent and asymptotically normal thus facilitating standard inference techniques based on estimated standard errors or standard bootstrap for the slope and threshold parameters.