Propensity Score Matching in Accounting Research and Rosenbaum Bounds Analysis for Confounding Variables

Abstract

Propensity score (PS) matching is becoming an increasingly popular method of estimating treatment effects. However, a major limitation relative to two-step Heckman procedures is that it does not control for potential unobserved selection bias. This paper employs a new method - Rosenbaum bounds - which enables researchers to assess the robustness of their PS matched estimates against the effects of potential unobserved ‘confounding’ variables. We provide an evaluation of PS matching and a comprehensive exposition of the Rosenbaum method and illustrate its properties and parameters with reference to auditor premiums for the standard dichotomy of big 4 versus non-big 4 auditors, together with new evidence relating to big 4 versus the next four largest (mid-tier) auditors, and the latter versus smaller auditors. Inter alia, our findings indicate that hidden bias would have to be large and influential in order to account for the big 4 premium generally, but only a comparatively small confounding unobserved covariate is required to negate the premium relative to leading mid-tier auditors. The Rosenbaum method also provided consistent estimates when covariates were omitted which were known ex ante to have either a large or small impact on the outcome. We conclude that the Rosenbaum technique provides researchers with a valuable tool to assess the sensitivity of causal inferences under bounded uncertainty and one which makes explicit the degree of hidden bias required to neutralise treatment effects estimated with the method of PS matching.An extended version of this paper, including simultaneous multi-sample PSM and quantile regression estimates, was published in Journal of Business Finance & Accounting, 39(5) & (6), 2012; entitled: Differential Audit Quality, Propensity Score Matching and Rosenbaum Bounds for Confounding Variables.