A semiparametric type II Tobit model for time-to-event data with application to a merger and acquisition study

ABSTRACT

Merger and acquisition is an important corporate strategy. We collect recent merger and acquisition data for companies on the China A-share stock market to explore the relationship between corporate ownership structure and speed of merger success. When studying merger success, selection bias occurs if only completed mergers are analyzed. There is also a censoring problem when duration time is used to measure the speed. In this article, for time-to-event outcomes, we propose a semiparametric version of the type II Tobit model that can simultaneously handle selection bias and right censoring. The proposed model can also easily incorporate time-dependent covariates. A nonparametric maximum likelihood estimator is proposed. The resulting estimators are shown to be consistent, asymptotically normal, and semiparametrically efficient. Some Monte Carlo studies are carried out to assess the finite-sample performance of the proposed approach. Using the proposed model, we find that higher power balance of a company is associated with faster merger success.

KEYWORDS:

• Power balance
• frailty model
• right censoring
• selection bias
• time-dependent covariates

Acknowledgements

The authors thank two referees for their insightful and helpful comments that have significantly improved the original manuscript. The authors also thank Professor Michael E. Sobel for the suggestions and great help on improving the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of Ming Zheng was supported by the National Natural Science Foundation of China [grant number 11771095]. The research of Wen Yu was supported by the National Natural Science Foundation of China [grant number 11671097].