A Bayesian approach for predicting material accounting misstatements

Abstract

In this paper, we develop prediction models of material accounting misstatements in a Bayesian framework. Outputs of the Bayesian approach are probabilistic descriptions for the propensity of conducting an accounting misstatement and for a riskiness comparison across different companies. The models are applied to a comprehensive sample of firms that have been subject to enforcement actions by the Securities and Exchange Commission for allegedly misstating their financial statements between 1982 and 2005. The results suggest that while maintaining a comparable Type-I error, out-of-sample predictions of the Bayesian models improve in terms of sensitivity and the Type-II error. This study provides a useful tool to assess material accounting misstatement risks.

Keywords:

• accounting misstatements
• prediction
• Bayesian
• MCMC

JEL classification:

• C11
• C15
• C53
• M42

Notes

1. The terms accounting misstatement, fraud, manipulation, and irregularity are used interchangeably throughout the paper. They all represent cases that have been subject to enforcement actions by the US Securities and Exchange Commission (SEC) for allegedly misstating financial statements.

2. The unconditional probability of misstatement is computed as the number of fraudulent firms divided by the total number of firms in the sample (including both fraud and non-fraud firms).

3. For example, SAS No. 99 requires brainstorming sessions on each audit to help auditors detect fraud.

4. There exist studies that rely on insider information to create red flags e.g. Loebbecke et al. (1989); Pincus (1989); and Asare and Wright (2004). Our paper focuses on studies based on publicly available information.

5. Not only the likelihood of the detection of distorted financial reporting, but also the incentives and abilities of managers to commit a fraud are usually included in such models.

6. Unlike Beneish (1997), Beneish (1999) excludes four variables and uses a sample of industry-matched firms instead of aggressive accruers.

7. This red flag benchmark is based on the assumption of relative costs of Type-I to Type-II errors of 10:1. The red flag benchmark may vary with the assumptions of relative error costs.

8. Our comprehensive sample has a size of 100,939, and a heterogeneous BLM model requires the computer program to simulate over 100,940 (including additional parameters and hyperparameter) additional random nodes. If we run MCMC simulation 10,000 times, there will be more than one trillion random values generated for the computer to memorize and analyze.