Estimation and Inference for Threshold Models with Measurement Errors

This project addresses the estimation and inference for threshold models when measurement errors exist in the threshold variable. With the presence of measurement errors:standard estimation procedure that does not recognize data imperfections in the threshold variable will lead to biased estimates because the data cannot be sorted properly by the true threshold variable;regime shifts are no longer deterministic jumps but become stochastic jumps governed by unobserved indicators, and the researcher can only infer regime shifts up to a probability; andthe test for measurement errors is non-standard because the parameter of interest (the variance of the measurement error) lies right on the boundary of the parameter space (zero) under the null hypothesis.In this project, the researchers adopt a Bayesian technique that involves the incorporation of a Bernoulli random variable to indicate the presence and absence of measurement errors in the threshold variable.