Tobit models in strategy research: Critical issues and applications

Mario Daniele Amore,Samuele Murtinu

doi:10.1002/gsj.1363

Abstract

AbstractResearch SummaryTobit models have been used to address several questions in management research. Reviewing existing practices and applications, we discuss three challenges: (a) assumptions about the nature of data, (b) apparent interchangeability between censoring and selection bias, and (c) potential violations of key assumptions in the distribution of residuals. Empirically analyzing the relationship between import competition and industry diversification, we contrast Tobit models with results from other estimators and show the conditions that make Tobit a suitable empirical approach. Finally, we offer suggestions and guidelines on how to use Tobit models to deal with censored data in strategy research.Managerial SummaryData on strategic decisions often exhibit certain features, such as excess zeros and values bounded within a given range, which complicate the use of linear econometric techniques. Deriving statistical evidence in such instances may suffer from biases that undermine managerial applications. Our study presents an extensive comparison of different econometric models to deal with censored data in strategic management showing the strengths and weaknesses of each model. We also conduct an application to the context of import penetration and industry diversification to highlight how the relationship between these two variables changes depending on the econometric model used for the analysis. In conclusion, we provide a set of recommendations for scholars interested in censored data.

Highlights

KEYWORDS data censoring, global strategy, latent variable, sample selection, Tobit modelMany strategic decisions are composed of two decisions: a “yes/no” choice about doing or not a certain activity and, in the case of a “yes,” a “how much” choice about the amount of resources to dedicate to such an activity
Contributing to this literature, we have provided a comprehensive assessment of censored data and Tobit models in strategy research
We have proposed an extensive set of guidelines and suggestions, collected in Table 3 and reported in the form of a decision tree in Figure 2, which will hopefully bring some clarity to deal with censored data in strategy research

Summary

| INTRODUCTION

KEYWORDS data censoring, global strategy, latent variable, sample selection, Tobit model. We identified two other critical issues: the idea that Tobit models could address problems of selection bias, and potential violations of Normality and homoscedasticity in the distribution of residuals As regards the former, Tobit models assume that the variables explaining whether or not the observed dependent variable is censored must explain the level of the variable when it takes positive values. We focused on identifying three main issues that may complicate the use and interpretation of Tobit models, namely: (a) potentially wrong assumptions about the nature of the data; (b) apparent interchangeability between censoring and selection bias; and (c) disregard of potential violations of Normality and homoscedasticity in the distribution of residuals These three insidious features cover the most fundamental aspects that can be commonly misinterpreted in regression methods: the nature of the data used to build the dependent variable, the specification of the regression model, and the structure of residuals. Two alternatives are the semiparametric trimmed least absolute deviation (LAD) estimator with fixed effects (Honoré, 1992), and the panel data regression model with two-sided censoring (Alan, Honoré, Hu, & Leth-Petersen, 2014)

| SUMMARY AND RECOMMENDATIONS

| CONCLUSION

Censoring versus selection bias

Findings

Non-normality and heteroscedasticity of residuals