A Gaussian Approximated Least Squares Estimator for Linear Threshold Models

Abstract

Linear threshold models are popularly estimated by the least-squares (LS) method, but the resulted
threshold parameter estimator has a non-standard limiting distribution which makes statistical inference less straightforward. Seo and Linton (2007) introduce a smoothed least-squares (SLS) threshold parameter estimator, which has an asymptotic normality distribution at a cost of a slower convergence rate than the LS estimator. This paper proposes a two-step Gaussian approximated least squares (GALS) estimator and we show that the resulted threshold parameter estimator enjoys the normality limiting distribution, as well as obtains a convergence rate closer to the LS estimator than the SLS estimator. A small Monte Carlo study confirms our theory in finite samples.

Keywords: Estimation, Gaussian Approximation, Linear Threshold Model

JEL Classification: C13, C21, C51