Estimation and Inference of Threshold Regression Models with Measurement Errors

An important assumption underlying standard threshold regression models and their variants in the extant literature is that the threshold variable is perfectly measured. Such an assumption is crucial for consistent estimation of model parameters. This paper provides the first theoretical framework for the estimation and inference of threshold regression models with measurement errors. A new estimation method that reduces the bias of the coefficient estimates and a Hausman-type test to detect the presence of measurement errors are proposed. Monte Carlo evidence is provided and an empirical application is given.