A Gaussian Approximated Least Squares Estimator for Linear Threshold Models
26 Pages Posted: 24 Jul 2022
Date Written: June 16, 2022
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
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