A Gibbs sampling approach to the estimation of linear regression models under daily price limits

In this paper, we propose a Bayesian approach using the Gibbs sampler to estimate linear regression models in which the dependent variable, the stock return, is subject to a price limit regulation. Assuming that the underlying 'true' stock price process is not affected by the price limits, we show that the observed stock returns are serially correlated when the sample contains limit stock prices. The linear model is shown to be a variant of the two-limit Tobit model subject to some form of censoring rule, and a Gibbs sampling approach is proposed to estimate the model. Examples based on real data as well as simulated data are presented.