Moderate regulations are optimal for HOs' program expense allocations: Findings from the combination of mechanism design and k-means clustering

2.1 Definitions of NFP and HO

NFP can be defined as an organization that focus on fulfilling a specific mission rather than generating profits. An NFP has different natures from profit-oriented entities in organizational goals, financial resources, human resources, and leadership and governance. Obtaining financial resources is one of challenges for NFPs. NFPs have less restrictions on board structured than profit-oriented entities, while NFPs executives are more responsible for accountability than financial performance. NFPs are accountable not only to contributors but also to beneficiaries (Gee et al., 2023). HO is a specific type of NFPs.

HO can be defined as an organization fulfills all of three requirements below (Egger and Schopper, 2022);

2.2 Program expense allocations

Prosocial activities are a common topic in finance. For example, Walker et al. (2023) wrote about finance for these types of activity. Tariq et al. (2023) assert that the funding of HOs is not only insufficient but also volatile.

There is also an extensive literature on expense allocations. Dang and Owens (2020) indicated that approximately 25% of British NFPs are financially misreported. Cyr et al. (2022) indicate that regulations influence how executives of Canadian NFPs recognize expense allocations. Cyr et al. (2022) indicates sanctions on NFPs’ taxation status even trigger NFP executives’ program expense allocations. Ling and Roberts (2023 and 2025) and Allen et al. (2024) explain expense allocations in the U.S. and ways to prevent inflated expense allocations. There is prior literature on the limitations of the contributors. Caviola et al. (2020) revealed that contributors have limited ability to understand the effectiveness of NFPs. According to Yang and Northcott (2021), one method for regulators to build public trust is to investigate public concerns about “wrongdoing” at NFPs. Chan and Zhang (2021) focused on sanctions for misreporting NFPs.

2.3 Agency theory is sometimes not suitable

Many scholars have been conducting research related to accountability of NFPs.

Harris and Neely (2021) regard transparency as value added because transparency attracts contributors. In agency theory, it is one of fundamental themes to make agents report financial information to principles honestly. Harris and Neely (2021) seem correct from agency theory. Meanwhile, Dethier et al. (2023) specifies the dark side of NFPs’ transparency as a research orientation. Dethier et al. (2023) says transparency also produces its undesirable outcomes in various aspects.

Yasmin and Ghafran (2021) said needs are competing among NFP stakeholders including beneficiaries. However, competing needs can make the interest of contributors as principles and the interest of beneficiaries divert. Beneficiaries of HOs have imminent needs and it can be a reason for NFP executives to prioritize beneficiaries. This prioritizing is for beneficiaries and different from NFP executives’ personal purposes, while it is almost obvious that regulators should take strict actions against funds misused by NFP executives for personal purposes (Noor, 2025). Although it is from another perspective, it is known that agency theory is sometimes not suitable for NFPs (Zoukoua, 2025). NFPs are regarded to promote well-being of beneficiaries rather than make profits (Rouault and Albertini, 2022).

2.4 Trade-off is not only around agency theory itself

Some prior studies cast doubt on the current accounting norms of NFPs. Muller (2018) criticized not only program expense ratios, but also various metrics. Goncharenko and Khadaroo (2020) warned that accounting regulations may restrict NFP activities based on Russian law.

Bénassy-Quéré et al. (2019) explain the shapes of economic policy and describe it as a succession of trade-offs. Regulators were also included in the public sector. Fowler (2023) depicted the ambiguity of the public sector as a double-edged sword and showed practical trade-offs. The concept of trade-offs is discussed in Section 6 of this paper.

There is ambiguity as to whether inflated expense allocations are deliberate falsification, and these distorted expenses are often lawful and may even be justifiable in some circumstances. Sandel (2010) separated lies from other kinds of misinformation and suggested that certain falsehoods are more justifiable than lies. Finlayson (2005) describes psychologist Kohlberg’s theory as influenced by philosopher Habermas, which posits that even though laws must usually be complied with, sometimes they ought to be disobeyed.

2.5 Mechanism design for optimization

Rasmusen (2007) is a textbook of game theory and includes explanations of agency theory. The players’ utility is frequently considered. Financial reporting is also within the scope of this study. In addition, the labor market is discussed by dividing the supply side into “serious” and other applicants.

Mechanism design is a theme of game theory and is a form of optimization. As Viljoen et al. (2021) lists as a goal, social welfare can be a goal for a mechanism designer. Viljoen et al. (2021) underlines mechanism design is useful when the mechanism designer lacks information that would allow optimal allocations to be specified in advance. This can be paraphrased that mechanism design is useful when a market is necessary for the mechanism designer. Koster et al. (2022) describes mechanism design can tell a mechanism designer the way to control the flow of information among incentivized players by regulating markets.

NFPs’ executives and contributors are in the charitable giving market (Schmitz, 2021).

2.6 K-means clustering

K-means clustering is a classic statistical method. For example, Kopec (2019) explained k-means clustering in a recent textbook. If an analyzer knows how many groups are in a dataset, K-means clustering can proceed grouping of samples in a dataset. Hsu et al. (2021) adopted k-means to analyze the finances of NFPs but did not combine k-means with game theory.

3.1 Research question

The identified research gap is lying down around HOs. Transparency also has the dark side and stakeholders have competing interest, while transparency is usually necessary for NFPs to be accountable. This research gap may not be critical for many NFPs but may be critical for HOs aiding beneficiaries with imminent needs.

The research question in this paper is to match a model based on mechanism design to the regulators’ real decision-makings by verification based statistical data. This research question aims to find optimized accounting regulations for HOs. If the analysis on statistical data is consistent with the model, this paper supposes that Californian regulators are intentionally adopting moderate regulations.

3.2 Modelling

This paper is not based on agency theory so much but aims to find a way to optimize regulations for beneficiaries rather than contributors as principles. However, agency theory Rasmusen (2007) explained is still insightful for building a theory.

Decisions by executives at NFPs rely on expected decisions by contributors to NFPs; therefore, game theory is a suitable framework for analysis. NFPs’ expense allocations can be regarded as an issue in the mechanism design for messages. Regulators can influence financial reporting as messages from NFPs through mechanism design. NFP executives want to be trusted by contributors through their messages (financial reporting), even though their financial reporting has sometimes been manipulated.

The NFPs mentioned here have program expense ratios, both in actual terms and in terms of fundraising needs. Program expense allocations are unnecessary for NFPs with good program expense ratios and NFPs without fundraising requirements. Notably, if an NFP is an HO and the utility of its executives reflects the utility of its beneficiaries whose lives are at risk, fundraising success strongly influences the utility of executives. The von Neumann–Morgenstern utility is often adopted in game theory. Thus, this study adopted this utility.

Symbols mean here:

p: population of contributors

r_c: ratio of serious contributors

r_s: ratio to be imposed sanctions

a: dummy variable if serious contributors contribute

b: dummy variable if non-serious contributors contribute

d_i: average contribution amount by a serious contributor

d_j: average contribution amount by a non-serious contributor

Under conditions in which there are no sanctions by regulators, donation revenue can be formulated as follows:

Here, true means the contributors are triggered to make contributions and false means the contributors are not triggered to make contributions.

If an NFP’s financial reporting is honest, a simple formula is:

Serious contributors understand administrative expenses are necessary and are triggered to make contributions even if the program expense ratio is low. Other contributors do not understand the necessity and are not triggered to make contributions.

Generally, contributors want financial transparency from the NFPs. As such, even serious contributors who are eager to see an NFP reach their goals will not approve of inflated expense allocations. If serious contributors do not allow these types of expense allocations and there are no sanctions by regulators, the manipulated financial report that brings donation revenue is as follows:

Serious contributors doubt inflated expense allocations and refuse to make contributions. Other contributors are not mentioned inflated expense allocations and are triggered to make contributions.

Under the assumption that the funding of HOs is volatile, after sanctions by regulators are introduced:

In this simplified model, the sanctioned NFP goes bankruptcy, and contributors do not want to make contributions in vain. Monitoring by regulators dissolve serious contributors doubt on inflated expense allocations and contributors are triggered to make contributions, if inflated expense allocations is not revealed through sanctions.

If the actual data show (5) as a positive value, there is a negative incentive to allocate expenses. Thus, there is no space for expense allocations and no regulations are necessary.

If (5) is not a positive value, an NFP decides whether to manipulate following (6).

It is useful to calculate how (7) is achieved using the actual data. Of course, there may be differences between an individual NFP and a third sector as a whole. However, even a simplified analysis will bring a blueprint to the third sector.

If r_s is sufficiently low, regulators can easily prevent all inflated expense allocations. Since there are frequently these types of expense allocations by NFPs all over the U.S., including California, it can be assumed that regulators intentionally keep regulations on NFPs moderate. However, if r_s is high, there is a different presumption concerning regulators. However, if they decided to impose these sorts of sanctions on all inflated expense allocations, the cost for regulators would be prohibitive, and they simply could not prevent all misstatements.

4.1 Combination of mechanism design and k-means clustering

This paper adopts a combination of mechanism design and k-means clustering as the research methodology. This research methodology needs to be quantitative in order to answer the research question set in the previous section.

4.2 The dataset

It is well known that the total amount of contribution in the U.S. and the U.K. is large. While ample statistical data exist concerning the financial statements of NFPs in both countries, California is somehow not the case when it comes to audited financial statements (Waymire and Mechanick, 2023). Raw data for contributors are rare. However, there are raw data for contributors with large sample sizes in Japan, which have been paying attention to the legal system for NFPs in California since the last part of the 20th century. Japanese raw data are suitable enough to investigate states and countries influence by California.

The Japan Fundraising Association (JFRA) provides a dataset of Japanese contributors in 2020 for each fee. The dataset was used as the data source for this study. The association collected statistical data through the Nationwide Survey on the Reality of Donations (Zenkoku Kifu Jittai Chosa). Its respondents stand at 5,678. JFRA have experiences to conduct surveys and validity and reliability of this statistical data look high, though the details of the sample selection and the sampling technique are not disclosed by JFRA. Because only anonymized datasets are provided by the association, IRB review is unnecessary for this study.

How processed by summing up various categories of contributions, consistency with Giving USA was brought to each sample of this dataset (IUPUI Lilly Family School of Philanthropy, 2023). This is the sum from NQ2_1_8 to NQ2_1_19 which mean NFPs for the numbering of the dataset. Subcategories of the third sector classified in Giving USA and the Nationwide Survey are as Table 1. Based on subcategories, the third sectors of the U.S. and Japan consist of similar organizations except for “Religion”. NQ2_1_4 is “Religion” and this numbering is apart from the chunk between NQ2_1_8 and NQ2_1_19. JFRA excludes religious organizations from the third sector in the statistics. Because so-called contributions to religious organizations in Japan sometimes have traits different from contributions to NFPs in the U.S., this paper agrees JFRA’s exclusion of religious organizations in Japan from NFPs.

Because the annual income of each respondent is recorded only as a range and not as a precise figure, the annual income of each respondent is substituted by the midpoint of each respondent’s annual income category. Samples that did not make any contribution can be assumed to be not or only slightly influenced by the culture of the U.S. donation market. Then, the setting up of k-clustering was completed by removing samples that did not make any contributions. Next, Equation (5) was calculated. Finally, if (5) is not a positive value, (6) is calculated.

4.3 Computer applications

Setting up the above steps are preceded by a spreadsheet. IBM SPSS, which is popular in the social sciences, is a statistical application used for counting and k-means clustering. The input for the number of clusters was two. The mathematical application used for calculations and building a figure from the formula is Wolfram|One, which is reliable.

6.1 Findings

The main finding is that it is supposed that regulators are intentionally adopting moderate regulations in California and states or countries influenced by the state. This is because the analysis on statistical data of Japan, a country with California-influenced regulations on NFPs, is consistent with the model in the section 4. This main finding is supported by small findings described below.

The mean of annual income in Table 2 is near the average taxable income in Japan. It is assumed that non-response bias in the data by JFRA is small and the data is therefore reliable.

The scarcity of serious contributors was revealed by k-means clustering. Serious contributors were only 37 cases. If there were many serious contributors, sanctions by regulators are meaningless from the starting point. In real world, many contributors do not understand necessity of administrative expenses and this lack of understanding ought to cause program expense allocations.

The application of the statistical data into the model showed the optimal regulations. Regulators could hypothetically use sanctions to prevent all inflated expense allocations, an amount that is less than approximately 34% of all expense allocations, which appears to be an achievable goal (7). In the real world, there are frequent expense allocations by NFPs across the U.S., including California. This leads the finding described in the top of this section.

6.2 Academic implications

This paper can be positioned in the one of research orientations, the dark side of transparency, Dethier et al. (2023) introduced. This paper fulfills the research gap identified in the section 4 a little.

Some sanctions are necessary to maintain mutual trust within the donation market, and maintaining the market is the point of decision. However, regulators do not want to impose sanctions on all inflated expense allocations. To achieve the objectives of HOs, fundraising through inflated expense allocation is sometimes required. Complete prevention would harm the beneficiaries of some NFPs, especially of HOs. Allowing inflated expense allocations is a possible option. Through imperfect sanctions, regulators make HOs navigate through a series of obstacles.

In terms of obstacles for NFPs, HOs are particularly volatile and have imminent fundraising needs, as Tariq et al. (2023) state. As Rouault and Albertini (2022) says NFPs promote well-being of beneficiaries. Yasmin and Ghafran (2021) said needs are competing. Bénassy-Quéré et al. (2019) also explained that regulators are confronted with trade-offs, though the trade-off described by the textbook is in a context other than HOs. According to Sandel (2010) and Finlayson (2005), it can be assumed that there is a space where these types of imperfect sanctions are permitted.

Incidentally, the scarcity of serious contributors is consistent with the findings of Caviola et al. (2020). This finding on serious contributors is meaningful, because the cluster center for serious contributors is 160,581 and the cluster center for other contributors is 9,343 in JPY. Both cluster centers are quite different from each other and cannot be ignored.

6.3 Practical implications

This paper is contradicting with CharityWatch, a vigorous rating agency on NFPs.

Regulators who recognize the goals of NFPs intentionally adopt moderate regulations. This is not because of potential costs for regulators, but because of the burdensome implementation challenges for NFPs, especially for HOs. This result is consistent with the decisions made by California’s governor and the attorney general, as described in the Introduction. Regulatory decisions can be interpreted from the perspective of mechanism design.

The California governor’s and attorney general’s decisions seem less than optimal for preventing all inflated expense allocations, but optimal in terms of maximizing the utility of HOs’ stakeholders, including beneficiaries. Bonta (2019) and Senate Judiciary Committee (2021) were reasonable in this meaning.