Prediction of Financial Vulnerability to Funding Instability

Abstract

Financial vulnerability of nonprofit organizations arising from governmental funding instability is examined using hazard analysis. Funding instability is characterized by time-at-risk, and vulnerability is expressed by hazard rate measuring the speed of nonprofit organizations closure. The analysis provides estimation of instantaneous probability of a nonprofit organization failure at a given point in time. Drawing on 2,660 Israeli nonprofit organizations, we found that the relationship between hazard rate and time-at-risk has an inverted U–shape curve; hazard rate increases with time-at-risk, reaches a maximum then descends.

Keywords

financial vulnerability nonprofit prediction hazard rate government grants risk

Introduction

Nonprofit organizations (NPOs) play a significant role in the global economy and in most societies worldwide (Anheier, 2009). Most developed market economies have seen an increase in the economic importance of NPOs as providers of wide ranging services.

Investigators face the challenge of adequately classifying types of NPOs that have proliferated in post-modern societies (Galnoor, 2011). NPOs can be classified in terms of size and age, where size is often assessed in terms of the number of paid employees (Hall, Jonson, & Haas, 1967). As to fields of activity, the situation is more complex. Three major classifications are currently used though not all are NPO unique: the International Standard Industrial Classification of All Economic Activities (ISIC); the Statistical Classification of Economic Activities in the European Community (NACE); and the International Classification of NPOs (ICNPO) developed by the Johns Hopkins Comparative Nonprofit Sector Project. Noteworthy is that though NPOs need to be private, they are not fully categorized in either the public or private sectors, but in the third sector.

The Israeli welfare state is unique in several respects. Characteristically, NPOs were developed as part of the civil society of an existing nation (i.e., the state preceded NPOs). By contrast, Israel’s largest NPOs (e.g., the Jewish Agency and the Jewish National Fund) preceded the formation of the state. These NPOs were instrumental in the creation of the state and were crucial in the formation of Israel’s first governments (Gidron, Bar, & Katz, 2004). Second, independent organizations were established to carry out state functions such that ministries and local authorities even created NPOs (Galnoor, 2011). Third, in the realm of state budgets, funds were transferred to private bodies and NPOs to provide services on a contractual basis. These include chronic care that the state must provide by law. This led to a blurring of the boundaries between the government and these NPOs in terms of funding and delivery of services that persist to-date (Galnoor, 2011). Consequently, these “national institutions” are not “private” (i.e., are not institutionally separate from government), and hence, fail NPOs’ definitions. Indeed, Israel Central Bureau of Statistics (CBS) categorizes the national institutions separately. Consequently, CBS data on NPOs exclude national institutions, but include NPOs that receive government funding, which the CBS classifies according to the Johns Hopkins ICNPO categories. Public funding in Israel constitutes more than half of the NPOs’ total income (Table 1). Grants are provided to NPOs as ministerial support and bequest funds, support for special objectives, and National Insurance Institute allowances. These support grants are transferred to NPOs expecting them to “further the policy” of granting ministries. In addition, government transfers money to NPOs through local authorities and national institutions. Table 1 shows that the percentage of NPO income attributable to government transfers increased yearly between 2004 and 2010. The large sums transferred illustrate the high dependence of the third sector on public support.

Table 1.

Government Transfers to Israeli NPOs as a Percentage of Total NPO Income.

	2004	2005	2006	2007	2008	2009	2010
Total Israeli NPOs	51.2	51.7	53.4	53.1	53.3	53.3	53.3

Source. Israel Central Bureau of Statistics.

Note. This table reports the percentage of NPO income attributable to government transfers. Government transfers include current and capital transfers from government ministries, current transfers from local authorities, and national institutions. NPO = nonprofit organization

In this study, we use hazard analyses to longitudinally examine NPOs’ financial vulnerability arising from governmental funding instability. Specifically, our research question probes the nature of the relationship between hazard rates and state funding instability overtime in a population of Israeli NPOs. Funding instability is characterized by a generalized time-at-risk measured in conditional years; five different definitions of time-at-risk are suggested and used. We found that the relationships between HR and time-at-risk have an inverted U shape rather than monotonic and that these HR versus time-at-risk curves are qualitatively similar for the various definitions of time-at-risk used (but differ quantitatively in the values of the maximum HR). These results imply that whenever an NPO is faced with a funding instability, there is some “critical” period (in terms of time-at-risk) when a probability of the NPO closure is maximal—after this period, NPOs’ financial vulnerability decreases. Irrespective of the time-at-risk definition used, NPOs engaged in education have the longest time-at-risk while health and social work NPOs are characterized by the shortest time-at-risk before reaching their maximum failure. Overall, the results show that the longer the time-at-risk until reaching the maximum HR, the higher the value of the maximum HR, regardless of the system of classification of NPOs with respect to their field of activity. It is found that younger NPOs are more vulnerable to funding instability irrespective of the definition of time-at-risk used. A somewhat unexpected finding, commensurate with the liability of adolescence theory (Fichman & Levinthal, 1991), is that the largest NPOs, following a long period of funding volatility, may become even more vulnerable than mid-sized NPOs. The robustness of the results (and the possibility of using them for predicting financial vulnerability) was tested by comparing the results of the HR calculations on two subsets of the set of 2,660 NPOs obtained by dividing it into two approximately equivalent samples. It is found that the HR–time-at-risk curve is almost identically reproduced on the two samples which indicates that such a curve can be used for predicting the financial vulnerability to funding instability.

Related Literature and Subject of Research

The extensive theoretical domain of business and organizational failure pertain to several measures that may be used to timely identify failure thus attenuate or even avert the threat of bankruptcy defined as a legal proceeding involving a business or person that is unable to repay outstanding debts (Weiss, 1990).

In what follows, we first discuss bankruptcy forecasting, then extend on relevant aspects of business failure at large.

Government Support and Consistency in Funding Stream

Owing to the benign relationships between NPOs and governments, states provide support for NPO’s projects aimed at delivering public services to citizens on behalf of governments (Rushton & Brooks, 2007). This support, however, rarely comes without strings, one of which is the continuation of financial support following political changeover. Steadiness of governmental support therefore determines to a great extent NPO’s resource munificence. Steadiness of NPOs’ governmental funding depends significantly on NPOs’ accountability and projects compatible with incumbent governments’ policies (Hager, Galaskiewicz, & Larson, 2004). That said, older and younger publicly funded NPOs are equally likely to survive or fail, though older organizations devoid of government funding are less likely to close.

Bankruptcy Forecasting

Bankruptcy forecasting has been addressed by economists and accountants for decades. Beaver (1966) was the first to use financial ratios to predict financial failure in distinguishing failed firms from non-failed ones using comparisons of means of various financial ratios. Altman (1968) followed with the z score, based on predictors with the highest predictive power in a multivariate discriminant analysis model where the probability of bankruptcy increases as the z score decreases. Ohlson (1980) and Zmijewski (1984) used multinomial choice techniques, including probit and maximum likelihood logit. Ohlson’s 1-year prediction model is based on an O-score that uses coefficients as proxies for financial distress. These studies were undertaken in the context of the for-profit sector.

Tuckman and Chang (1991) developed a theory specifically designed to assess NPOs’ financial vulnerability. Accordingly, an NPO should be considered financially vulnerable if it is liable to curtail its services instantaneously when it experiences a financial shock such as the loss of a major donor or an economic downturn (Tuckman & Chang, 1991). Greenlee and Trussel (2000) developed a model to predict NPOs’ financial distress by applying for-profits prediction methodologies. Hager (2001), Trussel (2002), and Trussel and Greenlee (2004) followed by using accounting ratios to estimate NPOs’ financial distress. The above models for predicting financial distress and bankruptcy are mostly predicated on single-period or cross-sectional data (Duffie, Saita, & Wang, 2007). As Greenlee and Trussel (2000) stated, these models generally use financial data as their financial vulnerability predictor variables, financial information pertaining to at least 1 year prior to the onset of financial vulnerability. According to Shumway (2001), the hazard bankruptcy model involves a survival analysis (Balcaen & Ooghe, 2006) rather than a cross-sectional design. By ignoring the fact that firms change overtime, cross-sectional models produce biased bankruptcy probabilities (Bauer & Agarwal, 2014) and inconsistent estimates of the probabilities that they approximate (Shumway, 2001).

Organizational Failure Rate, Size, and Age

Brüderl and Schüssler (1990) showed that depending on the initial firm’s resource endowments, death risk peaks between 1 and 15 years after founding. They indicate that large for-profit organizations generally have better survival chances than smaller ones owing to resource munificence. Thus, larger for-profit organizations have lower and later maximum risk than smaller ones akin with the liability of adolescence theory (Brüderl & Schüssler, 1990; Fichman & Levinthal, 1991) though small for-profit organizations show the lowest survival probability. The liability of adolescence theory asserts that risks rise for an early period of an organization’s existence and subsequently decline.

Capital, members’ commitment, entrepreneurial skills, and legitimacy are key to adolescent firms (Henderson, 1999). Initial endowment of assets shields the organization from early failure. Sunk costs, however, epitomized by initial mobilization of resources often leads to an escalation of commitment (Brockner, 1992) in the face of failure despite buffers provided by this early endowment and the psychological commitment related to sunk costs (Fichman & Levinthal, 1991). Therefore, adolescent organizations poorly fitted with their environments are more likely to fail. A similar picture emerges for NPOs. Fernandez (2008) found that smaller NPOs dissolve at a younger age. This phenomenon relates to a “liability of smallness,” for example, in contrast to larger organizations, smaller organizations face problems accessing resources (Grilli, Piva, & Lamastra, 2010). Recent findings concerning U.S. NPOs also indicate the existence of a “liability of bigness,” in that instability concerning government funding is more problematic for large NPOs compared with small and medium-sized ones (Boris, Leon, Roeger, & Nikolova, 2010). They note that government funding varies according to NPO size. NPOs that rely primarily on governmental contracts and grants are more likely to be larger than NPOs that count on government as their single largest source of funding.

Overtime, numerous studies have studied the dependence of failure rate on organizational age. Stinchcombe (1965) coined the term “liability of newness” for the comparatively higher death rates of newly formed organizations relative to older ones. Studies (Halliday, Powell, & Granfors, 1987; Le Mens, Hannan, & Pólos, 2011) showed that organizational failure rate (death risk) declines monotonically with age. In addition, the dependence of failure rates on organizational age is not monotonic, and hazard plots follow a strikingly non-monotonic pattern. Carroll and Huo (1986) identified two maxima in the death process in a late 19th-century labor union. Singh, House, and Tucker (1986) observed an absolute hazard peak after the sixth year of existence of Canadian NPOs. In these cases, an empirically established period of initially rising risks defies a monotonic decline interpretation of the liability of newness. Noteworthy is that most evidence against a monotonic risk pattern and the liability of newness was obtained from analyses of NPOs (Chen, 2014). Hager et al. (2004) found that government-supported NPOs are more vulnerable than those dependent on other funding sources. In addition and unexpectedly, it appears that the closure rate for the government-supported NPOs is hardly dependent on age. Levinthal and Fichman (1988) and Brüderl and Schüssler (1990) introduced the concept of a “liability of adolescence.” This concept proposes an inverted U–shaped risk pattern for business organizations (Fichman & Levinthal, 1991) for the dependence of death rate on age and has been corroborated more recently (Oertel & Walgenbach, 2011). Hager et al. (2004) found that for nonprofits with government funding, the hazard rate is virtually not dependent on their age. Overall, research concerning the relationship between key NPO characteristics (size, age, and government funding) and the likelihood of organizational survival has yielded inconsistent results, and the nature of the relationships between proneness to financial failure and size has yet to be fully explored. For Israeli NPOs, the dependence of failure rate on age has only been marginally studied. In Katz, Gidron, and Limor (2009), the rate of survived organizations is investigated but there exists no age categorization. All NPOs established prior to 1981 are batched as if they all were founded in 1981. However, as time elapsed, organizations grew older, so some dependencies on the age are possibly reflected in this series.

Research Purpose

The purpose of our research is to investigate the financial vulnerability of Israeli NPOs using a hazard analysis methodology. The research focuses on financial vulnerabilities that arise specifically from funding instability. Only one funding source is considered, ministerial support grants, as these are the major central-government funding mechanism of relevance to Israeli NPOs.

Specific Research Objectives

The research had four objectives: (a) to statistically characterize the degree of funding instability and vulnerability to financial failure due to funding instability faced by Israeli nonprofits that obtain financial support through ministerial grants; (b) to study the relationship between Israeli NPOs’ vulnerability to financial failure and funding instability; (c) to investigate the relationship between vulnerability to financial failure and funding instability for different classes of NPOs; and (d) to assess the relationships (standard curves) that can be used for prediction of financial vulnerability of Israeli NPOs to funding instability.

Data

CBS data on NPOs were used. The CBS entrusted a copy of its NPO data set to the Israeli Centre for Third Sector Research (ICTR). For each NPO, the ICTR database provides information on foundation date, paid employees, field of activity (12 ICNPO categories excluding data on Israel’s national institutions); the size of any annual ministerial grant obtained for the 1997-2007 period; NPO’s function; and NPO’s status (solvency, insolvency) and status change date.

The reason underlying the choice of solely one form of governmental support is that public funding of Israeli NPOs takes two major forms: contracts and ministerial support grants. Although these supports are not necessarily the main source of income, still they constitute an essential income source because they are flexible in terms of being used for various purposes including current expenses. In addition, for many NPOs’, they constitute the main source of income.

ICTR database was amended to extract a sample meeting the needs of the present study. First, only NPOs that had obtained governmental funding through a ministerial support grant at least once during an 11-year period (1997-2007) inclusive were selected (6,216 NPOs). Next, NPOs that did not undergo funding instability were excluded. It is also evident that NPOs closed before 1997 should be excluded from the sample (meaning, NPO failures in the sample could begin only from 1998). Initially, we aimed at both privately owned and governmentally funded NPOs. Because data about non-governmental funding are unavailable and when they rarely are, it is impossible to account for consecutively registered longitudinal data. Hence, and for the sake analyzing solely NPOs for which we could obtain sequential (yearly) data, we resorted to governmentally funded NPOs exclusively.

Variables

We examined four variables: NPO size, NPO field of activity, NPO function, and NPO age.

NPO Size

NPO size was determined by the number of paid staff employed in 1997 as recorded in the ICTR database. Four size categories were then defined (Table 2).

Table 2.

NPO Size Categories.

NPO size category	N of employees
1	>50 employees
2	11-50 employees
3	3-10 employees
4	0-2 employees

Note. NPO size was determined by the number of paid staff employed in 1997 as recorded in the ICTR database. Four size categories were then defined. NPO = nonprofit organization; ICTR = Israeli Centre for Third Sector Research.

NPO Field of Activity

Three classification systems of NPO field of activity were examined: ISIC, NACE, and modified ICNPO system. It was necessary to modify the ICNPO categories, because following the exclusions described, few NPOs remained in some of the original ICNPO categories that had been used to classify the ICTR database. Consequently, following Gidron et al. (2004), the 12 ICNPO categories were rearranged into five new categories that reflect the five main fields of activity in the modified database (religion; education and research; philanthropy; welfare and social work; culture and recreation).

NPO Function

Three NPO functions, as defined by the NPOs (mission statement) were obtained from Gidron et al., 2004. The NPOs in the data set were sorted into one of these three functions; service provision, advocacy, and grant bestowal. Gidron et al. (2004) defined these three categories only for civil society NPOs. We applied these categories to all NPOs (“integrated within the welfare state system” [IWSS] and “Civil Society Organisations” [CSOs]).

Age

Two age groups were defined: older NPOs aged 8 to 25 years in 1997 and younger NPOs aged <8 years in 1997. Importantly, Group 1 formed the larger category (1,575 older compared with 1,085 younger NPOs). NPOs aged >8 years in 1997 did not experience the early 1980s economic crisis (Mandelkern & Shalev, 2010), as opposed to older NPOs (<8 years) who proved more resilient hence, survived this crisis.

Method

Operationalization of Financial Vulnerability and Finding Instability

Financial vulnerability is expressed by the hazard rate that measures the speed of NPO closure, and a level of funding instability is characterized by time-at-risk.

Hazard Analysis

Hazard analysis concerns the occurrence and timing of events. It is ideal for a study of organizational closure, because it was designed for failures and requires longitudinal data on the occurrence of events.

The procedure’s main objective is to quantify the instantaneous risk that an organization will close at time t. Because time is continuous, the probability that closure will occur at exactly t is zero. However, there exists an observable probability that the event will occur in the interval (a full year in the present case) between t and t + Δt. The probability is conditional on the firm surviving to t, becuase firms that have closed are no longer at risk of failure. The hazard function captures this relationship. The hazard rate (or hazard function) h(t) expresses the probability that an organization will fail within a specific time period as follows:

h (t) = \lim_{Δ t \to 0} \frac{\Pr (t < T < Δ t | T > t)}{Δ t},

where T is a nonnegative random variable denoting the time to an organizational death (failure).

Model

The Cox proportional hazards model (Cox, 1972) asserts that the hazard rate (HR) for the ith subject in the data is

h_{i} (t | x_{i}) = h_{0} (t) e x p (x_{i} β_{x}),

where the regression coefficients, β_x , are to be estimated from the data. The baseline hazard function h₀(t) is

h_{i} (t | x) = 0 .

From Equation 1, h_o(t correspond with the overall hazard when x_i = 0. The term baseline hazard refers “the hazard function when all covariates are equal to zero.”

In our research, we estimated the baseline hazard solely. Although the Cox model produces no direct estimate of the baseline hazard, one may obtain estimates of the baseline survivor function corresponding to a baseline hazard, the baseline cumulative hazard function, and the baseline hazard contributions that may then be smoothed to estimate baseline hazard itself (Appendix A).

Methods for Time-at-Risk Estimation

Time-at-risk is a key variable in hazard analysis. Various ways to estimate time-at-risk are addressed by the extant literature (Hager et al., 2004), but they do not reflect the variety of situations encountered by organizations. Hager et al. (2004) estimated time-at-risk as the number of years after exiting from the panel. We introduced the concept of generalized time-at-risk (in units of conditional years), which measures the “level of funding instability.” The time-at-risk variable represents the duration and timing of funding instability until organizational failure or the last available data point. We examined five formal definitions of generalized time-at-risk suggested: T₀, T₁, T₁_M, T₂, and T₃ (Appendix B).

Using the Findings to Predict Financial Vulnerability

This possibility was tested by dividing the sample of 2,660 NPOs into two approximately equivalent samples in terms of size, field of activity, function, and age distributions. Predicated on these data, a standard curve was formed with the view of predicting NPOs’ financial vulnerability. The second sample was used for prediction purposes. Whenever calculations on the second sample provided results close to those predicted using the “standard” curve obtained on the first sample, the curve may be considered robust for prediction purposes.

Findings

Financial vulnerability is characterized by the hazard rate (HR) that measures the speed of NPO closure or, what is approximately the same, a risk of given NPO closure within a current year. The results present the dependence of HR and time-at-risk that measures a level of funding instability. Meaning, the results provide different aspects of influence of funding instability on financial vulnerability.

Relationship Between Hazard Rate and Time-at-Risk

We found that the relationships between HR and time-at-risk have an inverted U shape rather than monotonic. Figure 1 presents typical plots of the HR estimate versus time-at-risk for NPOs obtained using the five definitions of time-at-risk: T₀, T₁, T₁_M, T₂, and T₃. It is apparent that these HR versus time-at-risk curves are qualitatively similar for the various definitions of time-at-risk used but differ quantitatively notably in the values of the maximum HR (Figure 1). These results imply that whenever an NPO is faced with a funding instability, there is some “critical” period (in terms of time-at-risk) when a probability of the NPO closure is maximal—after this period, NPOs’ financial vulnerability decreases. Noteworthy is that to the best of our knowledge, this is the first inverted U–shaped relationship to be established between HR and NPOs’ time-at-risk (or for any other organization).

Figure 1.

The relationship between the hazard rate and time-at-risk (entire sample).

Hazard Rate and the Size

Figure 2 presents the plots of the HR estimate versus time-at-risk for NPOs’ of different sizes obtained when time-at-risk has been defined as T_0. The size categories are defined in Table 2.

Figure 2.

Hazard rate versus time-at-risk for NPOs in different size categories (entire sample).

Figure 2 shows that HR rises toward a maximum value for all four size categories, but the HR values, slope of the rising curve, maximum values, and time-at-risk values corresponding to the maximum are different for different NPO sizes. Commonly, the larger NPOs exhibit a lower HR than the smaller NPOs, with the exception that the HR for Category 1 of NPOs (>50 employees) rises above that of Category 2 NPOs (11-50 employees) at 5 conditional years, and above that of Category 3 NPOs (3-10 employees) at 8 conditional years. Thus, in general, small NPOs are more vulnerable to funding instability than the larger ones (as expected). However, a somewhat unexpected result is that the largest NPOs, after a rather long period of funding instability, may become even more vulnerable than mid-sized NPOs.

When time-at-risk is defined as T₀, T₁, or T₁_M, the maximum HR usually occurs at lower time-at-risk values for medium- and small-sized NPOs (Size Categories 2, 3, and 4; 5-50 employees, respectively) than for large NPOs (Category 1), with the former facing their maximum HR when time-at-risk is 5 to 8.75 conditional years compared with 9 to 10 conditional years for the latter. When time-at-risk is defined as T₂, the pattern changes somewhat, with both Categories 1 and 2 NPOs being subject to a maximum HR at a time-at-risk of 10 to 10.75 conditional years, while the smaller Categories 3 and 4 NPOs face their maximum HR at a lower time-at-risk of 9 to 10 conditional years. When time-at-risk is defined as T₃, the time-at-risk associated with the maximum HR is similar for all but the smallest NPOs. Thus, NPOs in Size Categories 1, 2, and 3 face a maximum failure HR when time-at-risk is 5.75 to 6.25 conditional years compared with a slightly larger time-at-risk value of 7 conditional years for Category 4 NPOs.

Hazard Rate and the Field of Activity

Irrespective of the time-at-risk definition used, NPOs engaged in education have the longest time-at-risk (7-12.5 conditional years) before reaching their maximum failure HR (of 0.014-0.023 failures/year). Health and social work NPOs are characterized by the shortest time-at-risk (5.25-8 conditional years) until they reach their lower maximum failure HR (of 0.005-0.010 failures/year).

The T₀ and T₃ definitions of time-at-risk produce very similar values for the time-at-risk associated with maximum HR in each ISIC field of activity category. The T₁, T₁_M, and T₂ definitions of time-at-risk also produce time-at-risk values that are similar to each other, but that are 4 to 5.5 conditional years longer than the corresponding values produced by the other two definitions of time-at-risk. When the ISIC classification was used, it was observed that the T₀ and T₃ definitions of time-at-risk produce very similar values for the time-at-risk associated with maximum hazard in each ISIC field of activity category, and these values are shorter than the corresponding values produced by the T₁, T₁_M, and T₂ definitions of time-at-risk, which are also similar to each other. Thus, certain trends are retained across both the ISIC and NACE classifications (the NACE fields of activity are recreation and culture, education, health and social work, research and development and other community, social, and personal services), with health and social work NPOs reaching their maximum failure HR first. Furthermore, the two classification systems also agree with respect to the absolute values for time-at-risk and maximum HR.

Irrespective of the time-at-risk definition, education and research NPOs have the longest time-at-risk (7-12.5 conditional years) before reaching their maximum HR (of 0.014-0.024 failures/year). These results are commensurate with those obtained using the ISIC and NACE, both of which show that education NPOs have the longest time-at-risk before reaching their maximum failure HR. The three classification systems also agree regarding the time-at-risk value associated with the maximum HR (7-12.5 conditional years under all three classifications) and produce similar values for the size of the maximum HR (of 0.014-0.023 using ISIC; 0.015-0.022 using NACE; and 0.014-0.024 failures/year using the modified ICNPO). Philanthropic NPOs are characterized by the shortest time-at-risk (5-8 conditional years) until they reach their lower maximum failure HR (of 0.005-0.009 failures/year). Religion-oriented NPOs have an only slightly longer time-at-risk (5.8-9.3 conditional years) than philanthropic NPOs. Only the modified ICNPO includes these two fields of activity, and therefore, it is impracticable to compare with the results obtained using other classifications.

Overall, the results show that the longer the time-at-risk until reaching the maximum HR, the higher the value of the maximum HR, regardless of classification system. A qualitative comparison of the three classifications appears in Table 3, which presents the fields of activity in descending order according to the time-at-risk value associated with the maximum HR. The tendencies reflected by Table 3 do not depend on the definition of time-at-risk.

Table 3.

Fields of Activity of NPOs Arranged in Order of Decreasing Values of the Time-at-Risk Associated With the Maximum Hazard Rate(HR).

Magnitude of time-at-risk associated with maximum HR	Field of NPO activity as per different classification systems
Magnitude of time-at-risk associated with maximum HR	ISIC	NACE	Modified ICNPO
Longest time-at-risk	Education	Research and development	Education and research
	Other community, social, and personal activities	Other community, social, and personal services	Philanthropy religion
	Health and social work	Education	Philanthropy religion
		Recreation and culture	Culture and recreation
Shortest time-at-risk		Health and social work	Welfare and social work

Note. NPO = nonprofit organization; ISIC = International Standard Industrial Classification of All Economic Activities ; ICNPO = International Classification of NPO.

Hazard Rate and the Function

NPOs engaged in different functions share similar values for time-at-risk until maximum HR is reached within each definition of time-at-risk. However, different results are produced by different definitions of time-at-risk, with T₀ and T₃ producing results that are similar to each other but lower than those produced by the other three definitions of time-at-risk.

Hazard Rate and the Age

Figure 3 presents graphs of the smoothed hazard estimate for NPOs from different age categories for different definitions of time-at-risk.

Figure 3.

Hazard rate versus time-at-risk for NPOs in different age categories.

It is seen that younger NPOs are more vulnerable to funding instability. This finding does not depend on the definition of time-at-risk. The HR is always higher for younger NPOs for all definitions of time-at-risk. Moreover, for younger NPOs, the HR achieves its maximum earlier than for older ones, for all definitions of time-at-risk (older NPOs, aged 8-25 years in 1997; younger NPOs, aged <8 years in 1997).

Prediction of Financial Vulnerability

The results were obtained using a relatively large data set. They are statistically robust and may be used for prediction of NPOs financial vulnerability (typical distributions of NPOs, for example, size, age, field of activity, and major functions). To test the robustness of these results (and the possibility of using them for predicting financial vulnerability), the set of 2,660 NPOs was divided into two approximately equivalent samples. The HR–time-at-risk curves based on these two samples were compared. We expected the curves based on the two samples to be rather close to each other. The closer these curves are to one another, prediction is more accurate. If curves practically merge, prediction is most accurate and enables the use of the curve based on the first sample for prediction.

We found that the HR–time-at-risk curves obtained on two samples are fairly close to each other and to that obtained for the whole sample. Figures 4 and 5 show the results obtained using T₀ and T_{1_}M as the time-at-risk definitions. Although the difference is evident from the graphs, to make a more consistent comparison, we compared the results obtained with different definitions of time-at-risk on the basis of two criteria. First, differences between the maximum hazard rates, and second, the standard deviations (SD) between the curves.

Figure 4.

Validation of reliability, Time-at-risk T_0.

Figure 5.

Validation of reliability, Time-at-risk T₁_M.

Thus, since the HR–time-at-risk curve is almost identically reproduced on the two samples, such a curve can be used for predicting the financial vulnerability to funding instability.

Conclusion

In this study, we strived to refine our understanding of the nature of the general relationship between HR and time-at-risk. We extend the common methodological scope of the hazard theory in terms of survival and time-at-risk.

A principal finding shows that hazard of failure increases and then declines.

Our findings corroborate the postulation that small firms have lower survival chances than larger ones (Grilli et al., 2010) that has been firmly established in the literature. When time-at-risk is defined as T₀, the HR rises toward a maximum value for all four size categories, but the HR values, the slope of the rising curve, and the time-at-risk corresponding to the maximum tends to differ for different NPO sizes. For most values of time-at-risk, larger NPOs exhibit a lower HR than the smaller ones, with the exception that the HR for Category 1 NPOs (>50 employees) rises above that of Category 2 NPOs (11-50 employees) at 5 years and above that of Category 3 NPOs (3-10 employees) at 8 years. Thus, as expected, small NPOs are more vulnerable to funding instability than larger ones (Smith, 2008). However, a somewhat unexpected finding, commensurate with the liability of adolescence theory is that the largest NPOs, following a long period of funding instability, may become even more vulnerable than mid-sized NPOs. Noteworthy is that the time passed from the beginning of our data period has no relevance to funding instability and age. Funding instability is characterized by time-at-risk that depends on an interruption of government support so that Years 5 and 8 are not the years that elapsed the beginning of the data period. The same applies to age. Different NPOs have different ages at the beginning of the data period.

We therefore corroborated both the liability of smallness and likewise liability of adolescence theories (Brüderl, Preisendörfer, & Ziegler, 1992; Henderson, 1999) and confirmed that both are applicable to NPOs. The liability of smallness theory holds that hazard functions for populations comprising of larger organizations have lower and later risk peaks than those comprising of small ones (Brüderl & Schüssler, 1990). In addition, the hazard peak should be lower for organizations with more resources. This is because resource munificence should not only extend the time organizations can endure initially, but should also serve as a buffer against financial distress (Miner, Amburgey, & Stearns, 1990). Usually, initial size (number of employees) is a good proxy for the amount of initial resources available (Brüderl & Schüssler, 1990). In supporting this theory, our findings corroborate earlier findings regarding NPOs’ liability of smallness (Fernandez, 2008; Wollebaek, 2009).

In the United States, instability in funding from grants is more problematic for large NPOs because, plausibly, larger NPOs are more likely to depend on governmental contracts and grants for revenue (Boris et al., 2010). When time-at-risk is defined as T₃, our results validate Boris et al.’s (2010) findings. By contrast, when time-at-risk is defined as T₀ and T₂, our findings indicate that larger NPOs face a lower HR than small- and medium-sized ones. Commensurate with the ICTR database, size was defined in terms of the number of paid employees. We therefore failed to accurately capture NPOs that rely primarily on volunteers while being staffed by only a few employees. Such NPOs are considered “small” or at most “mid-sized” in our study, even though the total number of paid and voluntary staff may actually be very large.

We utilized three classifications for organizational field of activity: ISIC, NACE, and a modified version of the ICNPO. Our findings indicate that education- and R&D-oriented NPOs are the most viable or able to survive the longest in an unstable grant environment regardless of the time-at-risk definition or field of activity classification used. The next most viable are religion- and philanthropy-oriented NPOs, followed by recreation and culture NPOs. Health and social work NPOs are least viable according to all three classifications.

Interestingly, when the time-at-risk value associated with the highest HR occurs, more viable NPOs actually face a higher hazard rate conforming to the liability of adolescence theory (i.e., the peak of the time-at-risk vs. HR curve is higher for more viable NPOs than for less viable ones). For instance, Israeli schools in independent educational networks form a significant percentage of NPOs within the education category. These NPOs are highly dependent on ministerial grants, which may explain why, when they experience funding instability, their HR rises concurrently.

Three major NPO functions were considered: service provision, advocacy, and funding. Findings indicate that the time-at-risk values and maximum HRs are broadly the same for NPOs engaged in different functions. This consistency across different functions probably stems from the functions’ definitions. NPOs’ key functions were determined by analyzing NPOs’ goals, as stated by the founders (Gidron et al., 2004) rather than by studying their actual activities. Possibly, NPOs’ actual activities differ from those formulated by their founders, which would introduce significant inaccuracies into the classifications used. We corroborated the liability of newness theory. Younger NPOs (aged 0-8 years) reach their maximum HR earlier than do older ones (aged 9-25 years) and face a higher absolute HR, for all definitions of time-at-risk.

Hager et al. (2004) found that for nonprofits with government funding (which are a subject of our study), the hazard rate is rarely age dependent. Although this finding seems contradictory with our results, in fact, it is our results that can explain this strange feature. The point is that Hager et al. (2004) collected nonprofits data from the same sample (with a natural removal of closed organizations from the panel) at different years. They separated NPOs by several factors and notably, by the dependence on government funding. They did not, however, follow a history of funding for each NPO (as we did) and so could not introduce such a characteristic as time-at-risk. Nevertheless, it is evident that in general, among older NPOs with government funding, a percentage of NPOs with higher values of time-at risk should be also larger. Thus, the two factors, increase in organization age (which makes NPOs less vulnerable) and increase in time-at-risk values (which makes NPOs more vulnerable) while influencing the hazard rate should compensate each other. Additional important finding by Hager et al. (2004) is that the NPOs dependent on government funding are more vulnerable than those existing at the expense of other funding sources. This supports our focus on studying vulnerability of NPOs with government funding.

We also aimed at generating the relationships (standard curves) for the prediction of financial vulnerability of NPOs to funding instability. The possibility of using the research results for predicting financial vulnerability was tested by dividing the set of 2,660 NPOs into two approximately equivalent samples and by comparing the calculations based on the two samples with each other, and with those for the whole sample. Whenever calculations on the second sample provide results close to those predicted using the “standard” curve obtained on the first sample, the curve may be considered robust for prediction purposes.

We found that the HR–time-at-risk curves obtained on two samples are fairly close to each other and to that for the whole sample. Hence, such a curve may be used for predicting NPOs’ financial vulnerability to funding instability. Having time-at-risk gleaned from the data on the previous history of the NPO, the HR and the probability of its financial failure can then be calculated. Noteworthy, however, is that such a “standard” curve has been obtained using data with some (typical) NPOs’ distribution with respect to size, age, field of activity, and major functions. Hence, we may expect that it can be applied for predicting statistical properties of organizational mortality for large sets of NPOs.

It can be seen that the results obtained on the samples of the whole sample accentuate the definition of time-at-risk as T₀. However, plausibly, for a sample with NPOs of specific type, the results obtained on samples could better concur with another definition of time-at-risk.

Noteworthy is that for NPO’s from different fields, the proportion of governmental support of the total income may be different. Because we could not obtain other income data, this may well be a topic for future studies. However, though the governmental support component is likely to differ, these support grants constitute a substantial part of NPO’s income. In addition, our findings are predicated on a relatively large population (2,660 NPO’s); hence, they are invariably statistically robust. Importantly, splitting our research population into two samples did not affect the main finding (inverted U shape), although the division was not based on the proportional part of governmental supports of the total income, but predicated on different criteria.

An important course of future research would be to extend the scope by including NPOs from different nations. National culture characteristics could prove most useful as additional predictors. Moreover, the extension of predictability by constructing of “standard” HR–time-at-risk curves to the international level would evidently add new insights and enrich our knowledge vis-à-vis financial vulnerability as a universal or else as national phenomenon. In this vein, hierarchical linear modeling, a form of multilevel analysis, would be most appropriate. A different and theoretically important research orientation can draw on the extant organizational decline literature, specifically by conjoining financial vulnerability and various decline phases.

The findings are relevant to central-government planners and policy makers tasked with improving the efficiency of government spending allocations. Specifically, in making grant allocation decisions, thereby also reducing NPOs’ financial vulnerability. Alter, Shoemaker, Tuan, and Emerson (2001) recommended that governments adopt an NPO exit strategy and essentially practice what they term “venture philanthropy” (Alter et al., 2001). We provide specific tools, in the form of relevant at-risk and HR relationships, by which to implement this recommendation. The HR–time-at-risk curves obtained on a large set of data with a normal distribution of NPOs may be used for predicting NPO mortality. In the case of a specific field of activity, the “standard” curve could be adopted from the results related to that particular field. Also, in making decisions regarding allocation grants to specific NPOs, their financial stability and possible vulnerability may be assessed using “standard” curves specified according to NPOs’ profile. In light of the findings regarding governmental funding of NPOs, established NPOs and primarily nascent ones appear most susceptible to discontinued remittances. Hence, governments should maintain consecutiveness in supporting these NPOs even though governmental assistance (in Israel) is almost exclusively politically oriented rather than age dependent.

Footnotes

Appendix A

Appendix B

Acknowledgements

The authors thank Yona Rubinstein and Uri Ben Zion for useful advices. The authors are thankful to the anonymous reviewers for their comments and suggestions that considerably improved the presentation of the article. The authors express their gratitude to the directors of the Israeli Center for Third Sector Research (ICTR) Benjamin Gidron and Hagai Katz for permission to use the data of the center for this research. The first author acknowledges the PhD scholarship from the Israel National Institute for Health Policy Research.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Author Biographies

Gila Burde received her PhD from the Ben-Gurion University of the Negev in 2012. Currently, she is a teaching fellow at the Ben-Gurion University of the Negev, Department of Management. Her research interests include financing policy, financial risk, and risk management.

Ahron Rosenfeld is a senior lecturer in finance, Ben-Gurion University of the Negev. He received his PhD in finance from the University of Rochester. His research and teaching interests are in corporate governance, including mergers and acquisitions, related-party transactions, and the performance of nonprofit organizations.

Zachary Sheaffer is an associate professor of strategic management and organizational behavior at Ariel University, economics and business administration department. He received his PhD from Waikato University, New Zealand. His research interests include crisis management, organizational decline and crisis, unlearning failure, and leadership.

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