NPO Financial Statement Quality: An Empirical Analysis Based on Benford’s Law

Abstract

In order to assess the accuracy of the figures reported in NPOs’ financial statements, I perform a digital analysis on Belgian non-profit organizations’ financial statements for accounting years 2007 up to 2012. Specifically, I compare observed frequencies for digits in the second-from-the-left position with expected frequencies based on Benford’s Law. Results based on the full sample indicate that observed frequencies strongly conform to Benford’s Law (and thus suggest a high degree of accuracy of the figures reported in NPOs’ financial statements). Nevertheless, I note statistically significant deviations from Benford’s Law (both for the entire distribution and at the individual digit level). The largest deviation is noted for zeroes in the second position (i.e., a significantly positive deviation), which can be explained based on humans’ reliance upon so-called cognitive reference points. Considering different sub-samples, I note that observed deviations from Benford’s Law are largest for the smallest non-profits and those non-profits that rely most heavily on grants and/or donations.

Résumé

Afin d’évaluer l’exactitude des chiffres indiqués dans les états financiers des organisations à but non lucratif, j’effectue une analyse numérique des états financiers des OBNL belges pour les exercices 2007 à 2012. Plus précisément, je compare les fréquences observées des chiffres en deuxième position en partant de la gauche avec les fréquences attendues sur la base de la loi de Benford. Les résultats établis sur l’ensemble de l’échantillon indiquent que les fréquences observées sont fortement conformes à la loi de Benford (et semblent donc indiquer un degré élevé d’exactitude des chiffres déclarés dans les états financiers des OBNL). Néanmoins, je constate des écarts significatifs du point de vue statistique par rapport à la loi de Benford (tant pour toute la répartition qu’au niveau des chiffres individuels). Le plus grand écart se reconnaît par des zéros en deuxième position (soit un écart positif significatif), qui peut s’expliquer par le recours des humains à ce que l’on appelle les repères cognitifs. Compte tenu des sous-échantillons différents, je remarque que les écarts observés par rapport à la loi de Benford sont plus grands pour les petites organisations à but non lucratif et pour celles qui dépendent le plus des subventions ou des dons.

Zusammenfassung

Mittels einer digitalen Analyse der Jahresabschlüsse belgischer gemeinnütziger Organisationen für die Geschäftsjahre 2007 bis 2012 prüfe ich die Richtigkeit der in den Jahresabschlüssen dieser Organisationen ausgewiesenen Zahlen. Ich vergleiche insbesondere die beobachtete Häufigkeit der Ziffern an der zweiten Stelle von links, wobei für die erwartete Häufigkeit das Benfordsche Gesetz angewandt wird. Die Ergebnisse aus der gesamten Stichprobe zeigen, dass die beobachtete Häufigkeit dem Benfordschen Gesetz starkentspricht (und somit auf ein hohes Maß an Richtigkeit der in den Jahresabschlüssen der gemeinnützigen Organisationen ausgewiesenen Zahlen schließen lässt). Trotzdem gibt es statistisch große Abweichungen vom Benfordschen Gesetz (sowohl bei der gesamten Verteilung als auch bei individuellen Ziffern). Die größte Abweichung wird bei Nullen an der zweiten Stelle festgestellt (d. h. eine bedeutend positive Abweichung), die sich dadurch erklären lässt, dass sich Menschen auf sogenannte kognitive Referenzpunkte veralssen. Betrachtet man verschiedene Unterstichproben, findet man die größten beobachteten Abweichungen vom Benfordschen Gesetz bei den kleinsten gemeinnützigen Organisationen und den Organisationen, die sehr von Zuschüssen bzw. Spenden abhängig sind.

Resumen

Con el fin de evaluar la precisión de las cifras notificadas en los estados financieros de las organizaciones sin ánimo de lucro (OSL/NPO), realizo un análisis digital de los estados financieros de organizaciones sin ánimo de lucro belgas para los años contables 2007 a 2012. Específicamente, comparo las frecuencias observadas para los dígitos en la posición segunda desde la izquierda con las frecuencias esperadas basadas en la Ley de Benford. Los resultados basados en la muestra completa indican que las frecuencias observadas cumplen considerablemente con la Ley de Benford (y de este modo sugieren un elevado grado de precisión de las cifras notificadas en los estados financieros de las OSL/NPO). No obstante, observo desviaciones estadísticamente significativas de la Ley de Benford (tanto para la distribución entera como a nivel del dígito individual). La desviación más grande se observa en los ceros en la segunda posición (es decir, una desviación significativamente positiva), que puede explicarse en base a la confianza de los humanos en los denominados puntos de referencia cognitivos. Considerando las diferentes submuestras, señalo que las desviaciones observadas de la Ley de Benford son más grandes para las organizaciones sin ánimo de lucro más pequeñas y para aquellas organizaciones sin ánimo de lucro que confían en mayor medida en las subvenciones y/o donaciones.

摘要

为了评估非营利性机构在财务报表中披露的数据的准确性,本人对比利时非盈利性机构2007至2012年的会计年的财务报表进行了数据分析,具体而言,本人将观察到的左二位置的数字的频率和根据本福德定律预期的频率进行了比较,建立在全样本基础上的结果说明, 观察到的频率非常符合本福德定律(因此说明非营利性机构在财务报表中中披露的数据的准确性很高),但是,本人(在整个分布和单个数字层面)发现了具有统计学意义的本福德定律的偏离,最大的偏离是第二个位置上的0(即,显著正偏离),这可以根据人类对所谓的认知参考点的依赖性进行解释。本人在考虑到不同的子样本的情况下,发现规模最小的非盈利性机构和严重依赖拨款和/或捐助的非盈利性机构对本福德定律的偏离程度最大。

要約

NPO法人の財務諸表における報告数値の精度を評価するために、会計年度2007年から2012 年までのベルギーの非営利組織の財務諸表のデジタル解析を実施する。具体的には、ベンフォードの法則に基づいて予想される周波数から、左から2番目の位置での数字の周波数観測を比較する。完全なサンプルに基づく観測された発生頻度の結果は、ベンフォードの法則(NPOの財務諸表から精度の高い数字を示唆)を示している。そのため、ベンフォードの法則(全体の配布用と個々の数字レベルの両方)では統計的に有意な偏差に注目する。最大偏差ゼロで2番目の位置(すなわち有意な正の偏差)を説明することができるが、人間のいわゆる認知的な基準点に対する依存度が説明できる。別の準標本を考えると、ベンフォードの法則で観測された偏差は、規模が最大および最小の非営利団体が、助成金および/または寄付金に最も依存することがわかった。

ملخص

من أجل تقييم مدى دقة الأرقام التي أعلن عنها في البيانات المالية للمنظمات الغير ربحية (NPO) ، وإجراء تحليل رقمي على المنظمات الغير هادفة للربح البلجيكية القوائم المالية للسنة المحاسبية 2007 حتى عام 2012. وعلى وجه التحديد، أقارن الترددات المرصودة للأرقام في ثاني من اليسار مع التكرارات المتوقعة على أساس قانون (Benford). النتائج التي تستند على عينة كاملة تشير إلى أن الترددات المرصودة مطابقة بقوة لقانون (Benford) (وبالتالي تشير إلى وجود درجة عالية من دقة الأرقام التي أعلن عنها في البيانات المالية للمنظمات الغيرربحية(NPO)). مع ذلك، ألاحظ أن الإنحرافات ذات دلالة إحصائية من قانون (Benford) (سواء لتوزيع كامل وعلى مستوى أرقام فردية). يلاحظ أكبر إنحراف عن أصفار في المرتبة الثانية (أي إنحراف إيجابي كبير)، التي يمكن تفسيرها على أساس الإعتماد البشري على ما يسمى النقاط المرجعية المعرفية. النظر في عينات فرعية مختلفة، ألاحظ أن الإنحرافات الملحوظة من قانون (Benford) هي أكبر لأصغر المؤسسات الغير ربحية وتلك المؤسسات الغير ربحية التي تعتمد بصفة أساسية على المنح و/ أو الهبات.

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Notes

  1. 1.

    Verbruggen et al. (2011) rely on an index to assess compliance with existing accounting regulation. Specifically, their compliance index consists of quantifiable measures related to four accounting principles (i.e., objectivity, quality of information, periodicity, and prudence) that are directly observable in the FS. As an illustration, they check the presence of debtors and creditors in the balance sheet, as this is typical under accrual accounting (and can thus be considered as being related to quality of information). As such, Verbruggen et al. (2011) assess the formal compliance of the FS. That is, the mere presence of debtors and creditors does not imply that the reported figures are accurate.

  2. 2.

    It is important to acknowledge that Newcomb (1881) reports the same factual observation several years prior to Benford (1938). However, Benford does not refer to Newcomb’s article and ever since the publication of Benford’s article, the law of anomalous numbers is known as Benford’s Law.

  3. 3.

    More specifically, Benford examined 20 different datasets that were neither too restricted in numerical range nor too conditioned in some way. Examples of datasets studied by Benford include: Arabic figures appearing in front page news item of a newspaper; all figures (except for dates and page numbers) appearing in an issue of Reader’s Digest; figures appearing in mathematical tables from engineering handbooks, etc.

  4. 4.

    See www.benfordonline.net for a comprehensive bibliography with regard to (empirical applications of) Benford’s Law.

  5. 5.

    “(…) analytical review procedures compare expected relationships among data items to actual observed relationships. If the actual relationships are not consistent with the expected relationships further audit investigation is required to explain the unexpected results.” (Busta and Weinberg 1998, p. 356) Examples of traditional analytical review procedures include ratio analysis and trend analysis.

  6. 6.

    It is important to add that NPO size is no longer significant in the model when controlling for the presence of an external FS audit. However, because NPO size and the presence of an external FS audit are strongly correlated (i.e., I refer to the correlation matrix presented in Verbruggen et al. (2011)), the presence of an external FS audit (partially) captures the size effect.

  7. 7.

    The financial reporting lag (or financial reporting delay) is the period that elapses between the closing date of the accounting year and the date of making the FS public. Because timeliness is recognized to be of vital importance to the usefulness of FS information (Ismail and Chandler 2003), a short(er) financial reporting lag implies more useful FS.

  8. 8.

    Balsam and Harris (2014) distinguish between ‘service oriented’ and ‘charitable’ NPOs, which essentially comes down to the same classification.

  9. 9.

    Belgian NPOs have to file their FS within 7 months after the closing date of the accounting year (subject to legal sanctions).

  10. 10.

    Bureau van Dijk’s Belfirst database contains FS data for Belgian and Luxembourgian firms and organizations.

  11. 11.

    Belgian accounting legislation imposes a standardized format for the FS. Three models exist (i) the complete format; (ii) the abbreviated format; and (iii) some alternative formats (that are used/prescribed in specific industries). A limitation of the Belfirst database is that it only includes data from FS that have been filed according to a format prescribed by law, being (i) and (ii) (because information in the Belfirst database is presented according to these templates). As the name already suggests, the complete format of the FS is more detailed and provides more information than the abbreviated format of the FS. For example, while the complete format counts 52 pages, the abbreviated format counts 30 pages. Specific examples of differences between both formats are that, on the balance sheet, the abbreviated format contains less detailed information with respect to financial fixed assets, inventories, investments, and long-term debt. In the abbreviated format of the income statement, operating revenues (e.g., turnover) may be merely expressed as a gross margin, whereas detailed information on both operating revenues and expenses is mandatory in the complete format. Finally, far less information (and detail) is required in the notes for the abbreviated format of the FS. Importantly, regardless of the FS format used, the organization is obliged to disclose all information contained in that type of format. Size criteria determine whether the complete or the abbreviated format of the FS has to be filed. The complete format is mandatory for very large NPOs and allowed for large and small NPOs on a voluntary basis. The abbreviated format is mandatory for large NPOs, unless they choose to file the complete format, and allowed for small NPOs on a voluntary basis. Very large NPOs exceed at least two of the following criteria: (i) total assets of 3,125,000 EUR, (ii) total incoming resources of 6,250,000 EUR, and/or (iii) 50 employees (expressed as full-time equivalents). NPOs with at least 100 full-time equivalent employees are always considered to be very large. Large NPOs exceed at least two of the following characteristics: (i) five full-time equivalent employees; (ii) total assets of 1,000,000 EUR, and/or (iii) total incoming resources of 250,000 EUR. All other NPOs are considered to be small. Note that for small NPOs there is no obligation to file FS.

  12. 12.

    NPOs are assigned to deciles for each sample year separately.

  13. 13.

    I refer to Table 2 Descriptive statistics for additional detail.

  14. 14.

    Reported figures are based on winsorized data (at the 1 and 99 percent level).

  15. 15.

    Results based on the MAD and the Chi-squared statistic might appear to contradict each other. That is, the MAD indicates strong conformity, whereas the Chi-squared statistic is highly significant (indicating non-conformity). As discussed earlier, goodness of fit tests usually produce statistically significant results when based on large sample sizes, while the MAD is not affected by sample size. Given the large sample employed in the current study, small deviations attain statistical significance because of sample size. While the MAD indicates strong conformity, it is important to note that the observed deviation for zeroes in the second position is quite substantial (regardless of sample size). That is, about 8.2 percent of the observed zeroes in the second position is ‘unexpected’ (cf. infra). Nevertheless, deviations for all other digits are modest, which explains the low value for the MAD.

  16. 16.

    A cognitive reference point can then be defined as “(…) a stimulus (…) which other stimuli are seen in relation to” (Rosch, 1975: 532). Worded differently, a cognitive reference point is a member of a category that acts as a natural benchmark for comparing other members of that category (Bowdle and Gentner, 1997).

  17. 17.

    Results reported by Hinrichs et al. (1982) and Poltrock and Schwartz (1984) support the idea that multiples of ten serve as cognitive reference points. Both studies examine the way humans process multi-digit numbers.

  18. 18.

    This is clearly expressed in the so-called ‘$1.99’or ‘odd pricing’ phenomenon (i.e., the observation that an abnormally large quantity of retail prices fall just below a round number). Several studies in marketing (see e.g., Twedt, 1965; Holdershaw et al., 1997) demonstrate the prevalence of this phenomenon. Whereas several alternative explanations have been offered for this phenomenon (see e.g., Schindler and Kibarian, 1996; Holdershaw et al., 1997), results lend support for the ‘underestimation mechanism’ hypothesis (see e.g., Schindler and Wiman, 1989; Schindler and Kibarian, 1996). That is, Schindler and Wiman (1989) show that leftmost digits are most likely to be accurately recalled and recall errors on odd prices are therefore more likely to be underestimates than on even prices (i.e., prices ending in zeroes). Results by Schindler and Kibarian (1996) show that the odd pricing phenomenon really induces a sales effect and that this effect is attributable to the fact that humans tend to underestimate odd prices. Brenner and Brenner (1982) argue that this is due to the fact that humans are flooded with numerical data (e.g., in advertising brochures, financial statements, etc.) and that first rounding numbers would result in an additional inordinate load on humans’ information processing capabilities. Accordingly, humans merely store the most important bits of information (i.e., first digits of large numbers).

  19. 19.

    Auditing standards require auditors to provide reasonable assurance that FS are free of material misstatements. Nevertheless, auditing standards do not provide detailed materiality guidelines (i.e., the assessment of materiality is considered to be a matter of professional judgment). Frequently mentioned cut-off levels for assessing materiality in the auditing literature are 0.50 percent of total assets; 5 percent of net income; and 0.50 percent of operating income. From this, it should be clear that materiality is typically determined in terms of quantitative measures. As such, it is possible that the observed rounding behavior is not quantitatively material.

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Correspondence to Tom Van Caneghem.

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Van Caneghem, T. NPO Financial Statement Quality: An Empirical Analysis Based on Benford’s Law. Voluntas 27, 2685–2708 (2016). https://doi.org/10.1007/s11266-015-9629-4

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Keywords

  • Non-profit organizations
  • Financial reporting
  • Financial statements
  • Benford’s Law
  • Digital analysis