A Consolidation of Instrumental Variable Approaches to Endogeneity in Fractional Regression Models

Modeling bounded outcomes in the form of a fraction or proportion is tricky in the face of endogeneity. Reviewing SMJ articles from 2007-2016 that included the modeling of a fractional outcome, I found that just seven out 43 papers employed an instrumental variable approach to adjust for endogeneity. All of the seven papers used a linear approach risking biased results and nonsensical predictions. In this paper, I seek to bring methodological developments concerning fractional regression models with endogenous regressors to strategic management scholars. I do this by consolidating the material on instrumental variable approaches to endogeneity in fractional regression models into a single, practical source. I present and compare three useful approaches: the quasi-limited information maximum likelihood, control function and transformation regression approach. To improve the methodological practice in strategic management, I present clear guidelines a long with advice on estimation in Stata and R.