Abstract
Estimation risk occurs when individuals form beliefs about parameters that are unknown. We examine how auditors respond to the estimation risk that arises when they form beliefs about the likelihood of client bankruptcy. We argue that auditors are likely to become more conservative when facing higher estimation risk because they are risk-averse. We find that estimation risk is of first-order importance in explaining auditor behavior. In particular, auditors are more likely to issue going-concern opinions, are more likely to resign, and charge higher audit fees when the standard errors surrounding the point estimates of bankruptcy are larger. To our knowledge, this is the first study to quantify estimation risk using the variance-covariance matrix of coefficient estimates taken from a statistical prediction model.
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Notes
Our assumption that auditors are risk averse is consistent with risk-averse individuals self-selecting to enter the auditing profession (Davidson and Dalby 1993). It is also consistent with analytical models in which auditors are assumed to be risk averse (Baiman et al. 1987; Balachandran and Ramakrishnan 1987; Baiman et al. 1991).
In Section 2, we explain that insurance and diversification are unlikely to render auditors completely risk neutral.
There is evidence that audit firms use bankruptcy prediction models to assess companies’ financial health (Eidleman 1995; Johnstone et al. 2016, p. 677). Even if an audit firm does not formally use a bankruptcy prediction model, we expect that the point estimates and standard errors are likely to correlate with auditors’ rational beliefs about the expected likelihood of bankruptcy and the uncertainty that surrounds this likelihood.
Research shows that the point estimates of bankruptcy risk are highly significant in explaining the auditor’s decision to issue a going-concern opinion (Mutchler 1985; Dopuch et al. 1987; Carcello and Neal 2000; DeFond et al. 2002; Carcello et al. 2009) or to resign from the engagement (Krishnan and Krishnan 1997; Ghosh and Tang 2015).
The case of zero estimation risk does not mean that the auditor knows whether the company will go bankrupt. It only means that the auditor knows the ex ante probability of bankruptcy. Therefore bankruptcy risk exists even in the absence of any estimation risk.
While an audit firm would want its partners to act in the best interests of the firm, in practice, many decisions are delegated to individual partners because audit firms cannot perfectly monitor the actions of individual partners. Consistent with firms delegating key decisions to partners, empirical research finds that audit outcomes are significantly affected by the characteristics of individual partners (Gul et al. 2013; Knechel et al. 2015). Moreover, partners are compensated based on the outcomes of their own audits as well as the audits of the entire firm (Knechel et al. 2013). Therefore audit outcomes are likely to be shaped by partners’ own risk preferences as well as the risk preferences of their firms.
X n is a 1 × k vector while \( {\widehat{V}}_{\widehat{\alpha}} \) is a k × k matrix, where k corresponds to the number of X variables in the bankruptcy prediction model. In Stata, the values of SE(\( {\widehat{B}}^{*} \)) are obtained using the command: “predict [varname], stdp” after estimating the bankruptcy prediction model. For further details, see www.stata.com/statalist/archive/2004-04/msg00752.html.
To compute DD, we follow the approach outlined in Bharat and Shumway (2008) (which is also consistent with Correia et al. 2012). In particular, we generate the DD measure by solving the following equation:
$$ DD=\frac{ \ln \left[\frac{\mathrm{E}+\mathrm{D}}{\mathrm{D}}\right]+\left({r}_{it-1}+0.5{\sigma}_V^2\right)T}{\sigma_V\sqrt{T}}, $$where E = the market value of equity; D = the face value of debt (computed as the sum of short-term debt and half of the reported value of long-term debt); rit-1 is past year equity returns; σ V = total volatility of the firm computed as \( \frac{\mathrm{E}}{\mathrm{E}+\mathrm{D}}{\sigma}_E+\frac{\mathrm{D}}{\mathrm{E}+\mathrm{D}}{\sigma}_D \) where σ E is the volatility of firm equity and σ D is the volatility of firm’s debt; σ E is calculated using the standard deviation of stock returns in the past one year; and σ D is calculated as 0.05 + 0.25*σ E .
In some studies, bankruptcies are predicted using a hazard model (Shumway 2001; Beaver et al. 2005). The hazard model can be written as follows: h(t| X) = h 0(t) × exp (αX), where h(t| X) is the hazard rate in year t, conditional on the values of X, h 0(t) is the baseline hazard, while α are the model parameters. The hazard model is semi-parametric because the baseline hazard, h 0(t), is left unestimated (Cleves et al. 2004). As h 0(t) is not estimated, it is not possible to obtain point estimates or standard errors for the dependent variable, h(t| X). Accordingly, the hazard model is not suitable for examining estimation risk. In contrast, the logit model is fully parametric, and it is straightforward to obtain point estimates and standard errors. Accordingly, we follow bankruptcy prediction studies that use logit (e.g., Campbell et al. 2008).
The Altman (1968) and Ohlson (1980) bankruptcy models report pseudo R2s of 7% and 10% respectively. Likewise Campbell et al. (2008) obtain a pseudo R2 of 11.4% in a model that predicts bankruptcy 12 months into the future (see their Table 4). Campbell et al. (2008) obtain higher pseudo R2s, ranging from 26% to 31%, when the bankruptcy horizon is just one month (see their Table 3). In our study, the bankruptcy horizon is 15 months rather than one month because an auditor is required to consider the likelihood of failure for a period of up to one year and the audit report can be issued up to three months after the fiscal year-end.
Our results are similar if we estimate Eq. (3) without the ZGC variables.
In an untabulated test, we estimate an alternate version of model 1 by including all of the bankruptcy predictor variables (X) in the going-concern reporting model. In this specification, we are forced to drop the point estimate (\( {\widehat{B}}^{*} \)), as it is a linear function of the X variables, i.e., there is perfect multicollinearity between \( {\widehat{B}}^{*} \) and the X variables. The coefficients on estimation risk (SE(\( {\widehat{B}}^{*} \))) remain positive and highly significant. Therefore our results are robust to replacing \( {\widehat{B}}^{*} \) with the X variables.
We obtain very similar results if we estimate Eq. (4) without the ZR variables.
References
Aharony, J., Jones, C. P., & Swary, I. (1980). An analysis of risk and return characteristics of corporate bankruptcy using capital market data. The Journal of Finance, 35, 1001–1016.
Altman, E. (1968). Financial ratios, discriminant analysis, and the prediction of corporate bankruptcy. The Journal of Finance, 23, 589–609.
Baiman, S., Evans, J. H., & Noel, J. (1987). Optimal contracts with a utility-maximizing auditor. Journal of Accounting Research, 25, 217–244.
Baiman, S., Evans, J. H., & Nagarajan, J. (1991). Collusion in auditing. Journal of Accounting Research, 29, 1–18.
Balachandran, B. V., & Ramakrishnan, R. T. S. (1987). A theory of audit partnerships: audit firm size and fees. Journal of Accounting Research, 25, 111–126.
Baum, C. F. (2006). An introduction to modern econometrics using Stata. College Station: StataCorp LP.
Beaver, W. H., Correira, M., & McNichols, M. (2012). Do differences in financial reporting attributes impair the predictive abilty of financial ratios for bankruptcy? Review of Accounting Studies, 17, 969–1010.
Beaver, W. H., McNichols, M., & Rhie, J.-W. (2005). Have financial statements become less informative? Evidence from the ability of financial ratios to predict bankruptcy. Review of Accounting Studies, 10, 93–122.
Bharat, S. T., & Shumway, T. (2008). Forecasting default with the Merton distance to default model. Review of Financial Studies, 21, 1339–1369.
Campbell, J. Y., Hilscher, J., & Szilagyi, J. (2008). In search of financial distress. The Journal of Finance, 63, 2899–2939.
Carcello, J. V., & Neal, T. L. (2000). Audit committee composition and auditor reporting. The Accounting Review, 75, 453–467.
Carcello, J. V., & Palmrose, Z.-V. (1994). Auditor litigation and modified reporting on bankrupt clients. Journal of Accounting Research, 32, 1–30.
Carcello, J. V., Vanstraelen, A., & Willenborg, M. (2009). Rules rather than discretion in audit standards: going-concern opinions in Belgium. The Accounting Review, 84, 1395–1428.
Chava, S. (2014). Environmental externalities and cost of capital. Management Science, 60, 2223–2247.
Chava, S., & Jarrow, R. A. (2004). Bankruptcy prediction with industry effects. Review of Finance, 8(4), 537–569.
Cleves, M. A., Gould, W. W., & Gutierrez, R. G. (2004). An introduction to survival analysis using Stata. College Station: Stata Corporation.
Correia, M., Richardson, S., & Tuna, I. (2012). Value investing in credit markets. Review of Accounting Studies, 17, 572–609.
Davidson, R. A., & Dalby, J. T. (1993). Personality profiles of Canadian public accountants. International Journal of Selection and Assessment, 1, 107–116.
DeAngelo, L. (1981). Auditor size and audit quality. Journal of Accounting and Economics, 3, 183–199.
DeFond, M. L., Raghunandan, K., & Subramanyam, K. R. (2002). Do non-audit service fees impair auditor independence? Evidence from going-concern audit opinions. Journal of Accounting Research, 40, 1247–1274.
Dopuch, N., Holthausen, R. W., & Leftwich, R. W. (1987). Predicting audit qualifications with financial and market variables. The Accounting Review, 62, 431–454.
Eidleman, G. (1995). Z-scores – a guide to failure prediction. CPA Journal, 65(2), 52–53.
Firth, M. (1990). Auditor reputation: the impact of critical reports issued by government inspectors. RAND Journal of Economics, 21, 374–388.
Francis, J. R., & Krishnan, J. (2003). Evidence on auditor risk-management strategies before and after the private securities litigation reform act of 1995. Asia-Pacific Journal of Accounting and Economics, 9, 135–157.
Francis, J. R., & Yu, M. D. (2009). Big four office size and audit quality. The Accounting Review, 80, 1521–1552.
Gerakos, J., Hahn, R., Kovrijnykh, A., & Zhou, F. (2016). Prediction versus inducement and the informational efficiency of going concern opinions. Chicago Booth working paper.
Ghosh, A., & Tang, C. (2015). Auditor resignation and risk factors. Accounting Horizons, 29, 529–549.
Gul, F., Wu, D., & Yang, Z. (2013). Do individual auditors affect audit quality? Evidence from archival data. The Accounting Review, 88(6), 1993–2023.
Hanoch, G., & Levy, H. (1969). The efficiency analysis of choices involving risk. Review of Economic Studies, 36(3), 335–346.
House of Lords (2011). Auditors: market concentration and their role. Select committee on economic affairs. 2nd report of session 2010–2011. London: The Stationery Office Limited.
Hribar, P., Kravet, T., & Wilson, R. (2014). A new measure of accounting quality. Review of Accounting Studies, 19, 506–538.
Huang, Y., & Scholz, S. (2012). Evidence on the association between financial restatements and auditor resignations. Accounting Horizons, 26, 439–464.
Johnstone, K., Gramling, A., Rittenberg, L., (2016). Auditing: A risk based-approach to conducting a quality audit, 10th Edition. Cengage Learning.
Klein, R. W., & Bawa, V. S. (1976). The effect of estimation risk on optimal portfolio choice. Journal of Financial Economics, 3, 215–231.
Krishnan, J., & Krishnan, J. (1997). Litigation risk and auditor resignations. The Accounting Review, 72, 539–560.
Knechel, W. R., Niemi, L., & Zerni, M. (2013). Empirical evidence on the implicit determinants of compensation in big 4 audit partnerships. Journal of Accounting Research, 51(2), 349–387.
Knechel, W. R., Vanstraelen, A., & Zerni, M. (2015). Does the identity of engagement partners matter? An analysis of audit partner reporting decisions. Contemporary Accounting Research, 32(4), 1443–1478.
Larcker, D. F., & Richardson, S. A. (2004). Fees paid to audit firms, accrual choices, and corporate governance. Journal of Accounting Research, 42, 625–658.
Lys, T., & Watts, R. L. (1994). Lawsuits against auditors. Journal of Accounting Research, 32, 65–93.
Mutchler, J. (1985). A multivariate analysis of the auditor’s going-concern opinion decision. Journal of Accounting Research, 23, 668–682.
Ohlson, J. A. (1980). Financial ratios and the probabilistic prediction of bankruptcy. Journal of Accounting Research, 18, 109–131.
Palmrose, Z.-V. (1987). Litigation and independent auditors: the role of business failures and management fraud. Auditing: A Journal of Practice & Theory, 6, 90–103.
Shumway, T. (2001). Forecasting bankruptcy more accurately: a simple hazard model. Journal of Business, 74, 101–124.
U.S. House of Representatives. (1985). Hearings before the subcommittee on oversight and investigations of the committee on energy and commerce. No. 99–17. February 20 1985. Washington, D.C.: Government Printing Office.
U.S. House of Representatives. (1990). Hearings before the subcommittee on telecommunications and finance of the committee on energy and commerce. No. 101–196. August 2, 1990. Washington, D.C.: Government Printing Office.
Venkataraman, R., Weber, J. P., & Willenborg, M. (2008). Litigation risk, audit quality and audit fees: evidence from initial public offerings. The Accounting Review, 83, 1315–1345.
Von Neumann, J., & Morgenstern, O. (1967). Theory of games and economic behavior. Princeton University Press.
Waymire, G. (1985). Earnings volatility and voluntary management forecast disclosure. Journal of Accounting Research, 23, 268–295.
Weber, J., Willenborg, M., & Zhang, J. (2008). Does auditor reputation matter? The case of KPMG Germany and ComROAD AG. Journal of Accounting Research, 46, 941–972.
Weil, J. (2001). Going concerns: did accountants fail to flag problems at dot-com casualties? The Wall Street Journal, 9, C1.
Zmijewski, M. (1984). Methodological issues related to the estimation of financial stress prediction models. Journal of Accounting Research, 22, 59–82.
Acknowledgements
This paper has benefited from the helpful comments and suggestions made by Richard Sloan (the editor), two anonymous reviewers, Neil Bhattacharya, Qiang Cheng, Elisabeth Dedman, Bin Ke, April Klein, Oliver Li, Richard Taffler and participants and discussants at the European Accounting Association 2013 annual meeting, the 2013 Tri-School Conference in Singapore, and Warwick Business School. Asad Kausar gratefully acknowledges the financial support provided by the Ministry of Education, Singapore (Grant RG58/12). We are responsible for all remaining errors and omissions.
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Lennox, C.S., Kausar, A. Estimation risk and auditor conservatism. Rev Account Stud 22, 185–216 (2017). https://doi.org/10.1007/s11142-016-9382-y
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DOI: https://doi.org/10.1007/s11142-016-9382-y