Modeling daily price limits

This paper characterizes the behavior of observed asset prices under price limits and proposes the use of two-limit truncated and Tobit regression models to analyze regression models whose dependent variable is subject to price limits. Through a proper arrangement of the sample, these two models, the estimation of which is easy to implement, are applied only to subsets of the sample under study, rather than the full sample. Using the estimation of simple linear regression model as an example, several Monte Carlo experiments are conducted to compare the performance of the maximum likelihood estimators (MLEs) based on these two models and a generalized method of moments (GMM) estimator developed by K. C. John Wei and R. Chiang. The results show that under different price limits and various distributional assumptions for the error terms, the MLEs based on the two-limit Tobit and truncated regression models and the GMM estimator perform reasonably well, while the naive OLS estimator is downward biased. Overall, the MLE based on the two-limit Tobit model outperforms the other estimators.