The Importance of Separating the Probability of Committing and Detecting Misstatements in the Restatement Setting

Abstract

This study demonstrates the importance of separating the probabilities of misstatement occurrence and detection when examining financial statement restatements. Despite the many benefits of examining the probability of restatements using traditional logistic models, interpretations of these models are clouded by partial observability—only subsequently detected misstatements are observable. We propose addressing this often overlooked issue by implementing a bivariate probit model with partial observability. We demonstrate the importance of separating these latent probabilities by re-examining three prior restatement studies and show the importance of separating the occurrence and detection probabilities. Our evidence suggests that future studies interested in restatements as a measure of accounting quality should consider implementing bivariate probit models as one way to address the partial observability inherent in this setting. This paper was accepted by Brian Bushee, accounting. Funding: B. P. Miller gratefully acknowledges financial support from the Sam Frumer Professorship. Supplemental Material: Data and the internet appendix are available at https://doi.org/10.1287/mnsc.2022.4627 .