Accounting for uncertainty: an application of Bayesian methods to accruals models

Abstract

We provide an applied introduction to Bayesian estimation methods for empirical accounting research. To showcase the methods, we compare and contrast the estimation of accruals models via a Bayesian approach with the literature’s standard approach. The standard approach takes a given model of normal accruals for granted and neglects any uncertainty about the model and its parameters. By contrast, our Bayesian approach allows incorporating parameter and model uncertainty into the estimation of normal accruals. This approach can increase power and reduce false positives in tests for opportunistic earnings management as a result of better estimates of normal accruals and more robust inferences. We advocate the greater use of Bayesian methods in accounting research, especially since they can now be easily implemented in popular statistical software packages.

Using and Interpreting Fixed Effects Models

“…Such heterogeneity in the relation between $$X$$ and $$Y$$ is commonplace in accounting data and research. Popular accruals models, for example, allow for differences in accruals processes across industry‐years or even firms (e.g., Jones [1991], DeFond and Jiambalvo [1994], Chen, Hribar, and Melissa [2018], Breuer and Schütt [2023]). Similarly, Ball and Nikolaev [2022] allow for differences across firms in how various determinants map into firms' earnings.…”

Value investing via Bayesian inference

“…Since valuation models have specific data requirements and longer term event studies require a specification of a "normal" benchmark return and risk, misspecifications and data problems can limit the usefulness of the results. 2 Other studies emphasize the capability of Bayesian inference to intuitively and transparently resolve decision problems under uncertainty, like Cremers (2002), Goldstein (2006), Johnstone (2018Johnstone ( , 2021 or Breuer and Schütt (2021). 3 Fama and French (1992) demonstrated that including the difference in returns between firms with high and low B/P and Size as additional explanatory variables increases the explainability of cross-sectional returns.…”

“… 2 2 Other studies emphasize the capability of Bayesian inference to intuitively and transparently resolve decision problems under uncertainty, like Cremers (2002), Goldstein (2006), Johnstone (2018, 2021) or Breuer and Schütt (2021). …”

Access to Credit in Informal Economies: Does Financial Information Matter?

“…In that case, the model uses more information from the population to arrive at her parameter estimates, limiting the influence of outliers due to poor data. Recent empirical literature in finance and accounting has used Bayesian methods in various settings, for example, to predict stock returns (Shanken & Tamayo, 2012;Smith & Timmermann, 2021), to examine accruals-based earnings management and earnings quality (Breuer & Schütt, 2021;Du et al, 2020), and to study investor learning (Bernard et al, 2018;Neururer et al, 2016;Zhou, 2021).…”