Applications of Fractional Response Model to the Study of Bounded Dependent Variables in Accounting Research

by Susanna Gallani, Ranjani Krishnan & Jeffrey M. Wooldridge

Overview — This paper discusses key features of the fractional response mode developed by economists Leslie E. Papke and Jeffrey M. Wooldridge.

Author Abstract

Bounded dependent variables are frequently encountered in settings of interest for accounting researchers. The econometric modeling of these variables presents particular challenges. Linear estimation methods (e.g. OLS) are often inadequate in the study of bounded dependent variables and may produce predicted values that lie outside the unit interval. Established nonlinear approaches such as logit and probit transformations, or censored and truncated regressions may attenuate the shortcomings of linear regressions. However these approaches are not suitable in settings where a material portion of the observations is at the boundaries. Nonlinear methods use restrictive distributional assumptions and employ ad-hoc transformations for observations at the boundaries. The fractional response model (FRM) (Papke and Wooldridge 1996, 2008) overcomes many limitations of established linear and non-linear econometric solutions in the study of bounded data. In this study, we review the econometric characteristics of the FRM and propose its applicability to a wide range of phenomena of interest for accounting scholars. We provide examples of accounting research that routinely uses bounded dependent variables, present results from Monte Carlo simulations to highlight the advantages of using the FRM relative to conventional models, and conduct an archival extension that compares the results from a traditional OLS model and the FRM to the study of managerial compensation. We conclude that the FRM provides an improved methodological approach to the study of bounded dependent variables.