Performance Matched Discretionary Accrual Measures
S.P. Kothari
Sloan School of Management
Massachusetts Institute of Technology
50 Memorial Drive, E52-325
Cambridge, MA 02142
kothari@mit.edu
Andrew J. Leone
William E. Simon Graduate School of Business Administration
University of Rochester, Rochester, NY 14627
hester.edu
Charles E. Wasley
William E. Simon Graduate School of Business Administration
University of Rochester, Rochester, NY 14627
hester.edu
First draft: October 2000
Current draft: May 2001
We gratefully acknowledge comments and suggestions of workshop participants at Arizona State University, the universities of Colorado and Rochester and especially from Wayne Guay and Jerry Zimmerman.  S.P. Kothari acknowledges financial support from Arthur Andersen and Andy Leone and Charles Wasley acknowledge the financial support of the Bradley Policy Research Center at the Simon School and the John M. Olin Foundation.
Abstract
Using discretionary accruals to test for earnings management and market efficiency is commonplace in the literature.  We develop a well-specified (rejects the null hypothesis, when it’s true, at the test’s nominal significance level) and powerful (rejects a false null hypothesis with high probability) measure of discretionary accruals.  A key feature of the discretionary accrual measure is that it is adjusted for the accrual performance of a matched firm where matching is on the basis of return on assets and industry.  We advocate matching to control for the impact of performance on accruals.  Our results suggest that performance matching is crucial to the design of well-specified tests based on discretionary accruals. Researchers will be able to draw more reliable inferences if they use a performance-matched discretionary accrual measure as proposed in this study.
Performance Matched Discretionary Accrual Measures
1.Introduction
Use of discretionary accruals in tests of earnings management and market efficiency is widespread (see, for example, Defond and Jiambalvo, 1994, Rees, Gill and Gore, 1996, Teoh, Welch, and Wong, 1998a and 1998b, and Kothari, 2001).  In an influential study examining the specification and power of commonly used discretionary-accrual models, Dechow, Sloan, and Sweeney (1995, p. 193) conclude t
hat “all models reject the null hypothesis of no earnings management at rates exceeding the specified test levels when applied to samples of firms with extreme financial performance.”  Unfortunately, there has been little research since Dechow et al. (1995) on the properties of discretionary accrual models.  Furthermore, and notwithstanding their conclusion above, the discretionary accrual models identified as misspecified continue to be used in research examining non-random samples (i.e., samples that firms self-select into by, for example, changing auditors).
Our objective in this paper is to develop a discretionary-accrual estimation approach that is both well specified and powerful.  Well-specified tests reject the null hypothesis, when it is true, at the nominal significance level of the test (e.g., 1% or 5%).  In the context of discretionary accrual models, power of a test refers to the likelihood that a test concludes non-zero discretionary accruals of a given magnitude (e.g., 1%, 2%, etc.) in a sample of firms.  Powerful tests reject the null hypothesis with high probability when it is false.  A key feature of our study is that we examine properties of discretionary accruals adjusted for a performance-matched firm's discretionary accrual, where performance matching is on the basis of a firm’s return on assets for the past year and industry membership.
Our results suggest that performance matching is crucial to designing well-specified tests of earnings management.  The critical importance of controlling for the effect of past
performance in tests of earnings management is not surprising.  The simple model of earnings, cash flows, and accruals in Dechow, Kothari, and Watts (1998) shows that working capital accruals increase in forecasted sales growth and earnings because of a firm’s investment in working capital to support growth.  Therefore, if a firm’s performance exhibits mean reversion or momentum (i.e., performance is not a random walk), then forecasted accruals would be non-zero. Firms with high growth opportunities often exhibit persistent growth patterns and accounting conservatism can produce earnings persistence in the presence of good news and mean reversion in the presence of bad news (B asu, 1997).  In addition, there is evidence of mean reversion conditional on extreme earnings performance (see Brooks and Buckmaster, 1976, for early evidence on mean reversion).  As a result, forecasted accruals of non-random samples of firms might be systematically non-zero.
The correlation between performance and accruals is problematic in tests of earnings management because commonly used discretionary accrual models (e.g., the Jones and modified-Jones models) are severely mis-specified when applied to samples experiencing non-random performance (see Dechow, et al., 1995).  Previous research therefore recommends and attempts to develop accrual models as a function of performance (see Kang and Sivaramakrishnan, 1995, Guay, et al., 1996, Healy, 1996, Dechow, Kothari, and Watts, 1998, Peasnell, Pope and Young, 2000, and Barth, Cram, and Nelson, 2001).
We control for the impact of performance on estimated discretionary accruals using a performance-matched firm’s discretionary accrual.  An alternative is to formally model accruals as a function of performance.  To do so requires imposing a specific functional form linking accruals to past performance in the cross-section.  Since a suitable way to do this is not immediately obvious, we develop a control for prior performance by using a performance-matched firm’s discretionary accrual.  Using a performance-matched firm’s discretionary accrual does not impose any particular functional form linking accruals to performance in a cross-section of firms.  Instead, the assumption underlying performance matching is that, at the portfolio level,
the unspecified impact of performance on accruals is identical for the test and matched control samples.  Results below suggest that tests using a performance-matched companion portfolio approach to estimate discretionary accruals are better specified than those using a regression-based approach (which imposes a linear functional form) to control for the effect of past performance on future accruals.
We also study discretionary accrual models’ properties over multi-year horizons, for a range of sample sizes, and for many types of non-random samples (e.g., large vs. small firms, growth versus value stocks, high vs. low earnings yield stocks, high vs. low past sales growth, etc.) and with and without co
ntrolling for potential survivorship biases.  These features are designed to mimic characteristics of typical research studies in accounting.  Previous research (e.g., Dechow et al., 1995, and Guay, Kothari, and Watts, 1996) does not simulate test conditions like multi-year horizons, different sample sizes, or survivorship biases.  Nor does it systematically examine properties of discretionary accruals adjusted for performance-matched firms’ discretionary accruals.  While adjustment of discretionary accruals for those of performance-matched samples is not uncommon in the literature, researchers choose from a wide range of firm characteristics on which to match without systematic evidence to guide the choice of a matching variable.  For example, previous research uses control firms matched on cash flows (Defond and Subramanyam, 1998), year and industry (Defond and Jiambalvo, 1994), industry and size (Perry and Williams, 1994), and control firm defined as the median performance of the subset of firms in the same industry with past performance similar to that of the treatment firm (Holthausen and Larcker, 1996) or median performance of the percentile of firms matched on return on assets (Kasznik, 1999).
Summary of results.  The main result from our simulation analysis is that discretionary accruals estimated using the Jones or the modified-Jones model and adjusted for a performance-matched firm’s discretionary accruals are quite well specified. We label these as performance-matched discretionary accruals.  Performance matching is on the basis of industry and past year’s
return on assets.1  Performance-matched discretionary accruals exhibit only a modest degree of mis-specification in certain non-random samples, but otherwise tests using them perform quite well.  We reach this conclusion on the basis of analyzing random as well as non-random samples of firms, one- and multi-year measurement intervals, a wide range of sample sizes, and tests for both positive and negative discretionary accruals.  We, however, caution the reader that non-random sample firms might be engaging in earnings management for contracting, political, and capital market reasons.  Therefore, the well-specified rejection rate of the performance-matched approach might in fact indicate under-rejection of the null hypothesis (see Guay et al., 1996). Our result that performance-matched measures are well specified is nevertheless helpful insofar as a researcher calibrates discretionary accruals relative to those estimated for a matched sample that has not experienced the treatment event (also see section 2).  Performance-matched measures’ superior performance compared to other measures of discretionary accruals parallels the result in the context of operating performance measures and long-horizon stock returns (see Barber and Lyon, 1996 and 1997, Lyon, Barber, and Tsui, 1999, and Ikenberry, Lakonishok, and Vermaelen, 1995).
Other aspects of our findings are that rejection rates are quite similar across different non-random samples and are moderately higher as the sample size increases and as the horizon increases from o
ne year to three or five years.  For example, when the sample size is 100 firms and discretionary accruals equal 2% of assets, the tests conclude significant abnormal accruals approximately 50% of the time.  The rejection frequency jumps to about 90% if the discretionary accruals are 4% of assets.  Our rejection rates are considerably higher than those reported in Dechow et al. (1995).  We believe that differences in research design account for the differences in the rejection rates reported in their versus our study.  Specifically, Dechow et al. report the
brooke fraser
1  While other performance matching variables are possible, performance matching on the basis of lagged return on assets follows the approach taken in Barber and Lyon (1996) in their study of detecting abnormal operating performance.  Barber and Lyon (1996) do not study accruals, discretionary or non-discretionary.