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Review of Accounting Studies
Published in: Review of Accounting Studies 1/2020

10-01-2020

Entropy-balanced accruals

Authors: Jeff L. McMullin, Bryce Schonberger

Published in: Review of Accounting Studies | Issue 1/2020

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Abstract

This study assesses whether the accrual-generating process is adequately described by a linear model with respect to a range of underlying determinants examined by prior literature. We document substantial departures from linearity across the distributions of accrual determinants, including measures of size, performance, and growth. To incorporate non-linear relations, we employ a recently developed multivariate matching approach (entropy balancing) to adjust for determinants in place of relying on a linear model. Entropy balancing identifies weights for the control sample to equalize the distribution of determinants across treatment and control samples. In simulations drawing random samples from deciles where a linear model displays poor fit, we find that entropy balancing significantly improves accrual model specification by reducing coefficient bias relative to linear and propensity-score matched models. Consistent with entropy balancing retaining sufficient power, we find that its estimates detect seeded accrual manipulations and explain variation in accruals around equity issuances.
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Appendix
Available only for authorised users
Footnotes
1
Jones’s (1991) discretionary accrual study is cited more than 8100 times, according to Google Scholar, as of December 2018.
 
2
In addition, multivariate matching avoids the two-step estimation concerns raised by Chen et al. (2018) for studies using residuals from a first-stage linear model in a second-stage regression. These authors document that this two-step approach results in biased estimates (inflation, attenuation, or sign change) that lead to type I and type II errors.
 
3
Consistent with the ease of implementing entropy balancing, we provide an online appendix with detailed Stata code and examples.
 
4
Similarly, Nikolaev (2017) and Bloomfield et al. (2017) model accruals using a general method of moments approach and by modeling the extent to which accrual innovations map into future cash flows, respectively.
 
5
We estimate this difference in a multiple regression to control for any remaining difference after matching, as this approach is shown to produce the least biased estimate (Rubin 1973).
 
6
Hainmueller (2012) notes that entropy balancing is a generalization of propensity-score weighting (Hirano et al. 2003). In addition, it is in essence a large-sample version of the synthetic controls method developed by Abadie and Gardeazabal (2003) and Abadie et al. (2010). Synthetic controls are designed to examine case studies by comparing a single treated case with a weighted sample of control cases (e.g., examining the effect of a cigarette tax on cigarette consumption in California or the effect of terrorism on a specific region’s economic output).
 
7
These latter samples will not converge when using only positive control sample weights (e.g., a treatment sample of large firms is compared to a control sample of small firms, such that there is limited or no overlap in their distributions).
 
8
In addition to these advantages, Hainmueller (2012) notes that entropy balancing is in a class of matching methods called “equal percent bias reducing,” which guarantee that covariate imbalance after matching will be lower than before matching, and Zhao and Percival (2016) note that entropy balancing is “doubly robust with respect to linear outcome regression and logistic propensity score regression.” See work by King et al. (2011) for a discussion of propensity-score matching’s shortcomings.
 
9
Similarly, research on audit quality finds that estimates of Big N auditor effects are sensitive to changes in propensity-score-matching assumptions (DeFond et al. 2017).
 
10
This dataset is available through the University of California at Berkeley’s Haas School of Business and is current through August 31, 2012. AAERs typically take at least three years for the SEC to file. As a result, AAERs are considered for a subsample of observations over the 1987–2009 period.
 
11
In untabulated tests, we find nearly identical results using the standard Jones (1991) model that includes a control for ROAt (Kothari et al. 2005) in place of this normal accrual model.
 
12
In the case of the EPt-1 sort, we include EPt-1 as a control in place of ROAt-1. Results are qualitatively unchanged if we include ROAt-1 instead.
 
13
While this tolerance for entropy balancing does prevent some random samples out of the 1000 from converging (due to a lack of covariate overlap, collinearity in covariates, or both), the number of unconverged iterations never exceeds 2%.
 
14
The 95% confidence interval for binomial tests, using rejection rates computed according to the test statistic from the ordinary least squares-estimated coefficient, ranges from 3.5% to 6.7% for the 1000 independent draws. Rejection rates outside of these bounds are consistent with an abnormal accrual measure that is biased for (rejection rates above 6.7%) or against (rejection rates below 3.5%) the hypothesis of no earnings management. Because samples are randomly drawn from a sample of observations that is pooled across years and industries, clustering concerns are not expected to be present within the simulated data. We verify that clustering by firm and year does not alter results.
 
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Metadata
Title
Entropy-balanced accruals
Authors
Jeff L. McMullin
Bryce Schonberger
Publication date
10-01-2020
Publisher
Springer US
Published in
Review of Accounting Studies / Issue 1/2020
Print ISSN: 1380-6653
Electronic ISSN: 1573-7136
DOI
https://doi.org/10.1007/s11142-019-09525-9

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