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Motivation This paper Literature Model

Mission: Impossible? Diversity and economies of scale in the charitable sector

Sarah Sandford, London School of Economics and Kimberley Scharf, University of Warwick and CEPR NGO Workshop, London School of Economics 26th May 2012

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Motivation This paper Literature Model

Diversity in the charitable sector

Nearly 72,000 charities, or 44.5% of all UK charities (171,000), have annual income less than £10,000 Over 5,000 new charities created each year. Over 200 Refugee Community Organisations in London alone. (Source: Charity Commission & Evelyn Oldfield Unit)

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Motivation This paper Literature Model

Points of light, doing good?

“I have spoken of a thousand points of light, of all the community organizations that are spread like stars throughout the Nation, doing good.” (George Bush Senior, Presidential Inauguration Address, 1989) “The result of a big, strong society is that it will be administratively untidy. People will come together to do things in different ways and different places.” (Francis Maude, UK Minister for the Cabinet Office, 14th January 2011)

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Motivation This paper Literature Model

Diversity of missions: on the political agenda?

There is a lot of money in charity – $240 billion in the US (2002) Voluntary contributions are a key funding mechanism for health and education Budget cuts are leading to increased reliance on voluntary contributions to charities “Charitable donations an important source of government revenue” (Canadian Parliament, February 12, 2012)

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Motivation This paper Literature Model

Fixed costs: on the political agenda?

Fixed costs might include administration and accounting, fundraising activities, mortgage on premises Fixed costs are large - from 10% to 25% of charity’s income in Canada Meeting fixed costs is a major preoccupation of charities, and

• f governments concerned with their efficiency (eg, Institute

for Philanthropy, 2009) (Charity Commission, 2005), (Fiona Mactaggart MP, 2004) Government funds initiatives to encourage sharing of fixed costs, eg NCVO, SCVO.

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Motivation This paper Literature Model

Our Questions

Positive: How do economies of scale, preference diversity and income inequality affect diversity (number of charities, size of charities and missions of charities) in the charitable sector? Normative: Should we support diversity in the charitable sector when it has costs as well as benefits?

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Motivation This paper Literature Model

Answer has implications for efficiency and equity

Efficiency: Pareto-dominated equilibria with separate providers arise with nonprofit providers in contestable markets

Not so in private sector

Distributional implications: who chooses to donate and to whom makes a difference from a redistributive point of view

Agenda of missions is set by wealthy or numerous donor groups Number of missions affects who gets to distribute with whom

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Motivation This paper Literature Model

Some examples

Healthcare clinics: one in larger village A, one in smaller village B, or one inbetween? How close to village A? School system: more emphasis on Catalan language and history, or Castillian? Or two separate systems? Development banks: separate banks for East and West Africa,

• r one institution? With what focus?

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Motivation This paper Literature Model

Sketch of model

Model of private provision of collective goods Four types of individuals distinguished both by their income levels (high or low) and preference for variety of a public good (A or B) Variety is determined by provider’s mission Mission-specific fixed costs → mission diversity is costly Missions can serve the interests of group A only, group B

• nly, or both

Characterise the set of coalition proof Nash equilibrium missions

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Motivation This paper Literature Model

Constraints

Noncooperative giving outcomes are inefficient No bargaining possible because donations are about splitting costs of public good Different preferences for missions = ⇒ joint funding requires mission compromise

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Tradeoffs and outcomes

Deviation incentives in moving from a compromise mission: Mission more aligned to agent preferences Donations must cover fixed costs CPNE characterised by either: Mission compromise (single mission) Mission fragmentation (two missions)

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Motivation This paper Literature Model

Key positive predictions

Mission control: Rich or more numerous donor types exert more influence on the mission of “compromise” charitable projects Fragmented vs. centralised: the charitable sector is fragmented when fixed costs are low and centralised when fixed costs are high The effects of diversity: The number of charities is inverse U-shaped in diversity. Income growth: Income growth generally leads to greater fragmentation, income contraction creates centralisation

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Motivation This paper Literature Model

Normative Predictions: agreement on provision levels

Fragmented missions can occur in CPNE but this outcome may be less efficient than the compromise mission Happens when fixed costs are “intermediate”... ...and groups of donors with the same preferred mission have unequal numbers or total incomes Policies aimed at alleviating excess fragmentation, such as government grants towards compromise missions, can backfire

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Motivation This paper Literature Model

Normative predictions: Disagreement on provision levels

Compromise mission can occur in CPNE but it is less efficient than outcome with fragmented missions Happens when fixed costs are intermediate when groups of donors with the same preferred mission have equal numbers and incomes

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Motivation This paper Literature Model

Key normative predictions

Income growth

Income growth can create relatively inefficient fragmentation

Government policy

Relatively inefficient fragmentation can be overcome by non-targeted increases in charities’ fixed costs Inefficient centralisation can be tackled by non-targeted grants towards charities fixed costs

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Motivation This paper Literature Model

Literature

Diversity and public goods provision: Alesina, Baqir and Easterly (1999), Horstmann and Scharf (2009), Andreoni et al (2011), Algan, Hemet and Laitin (2011) Fixed costs in the charitable sector: Andreoni (1998), Scharf (2011) Expropriation of the rich by the poor: Olson (1965), Bardhan, Ghatak and Karaivanov (2006) Benefits from mission compromise: Ghosh, Karaivanov and Oak, (2007)

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Motivation This paper Literature Model Agreement on levels Disagreement on levels

Basics

Two groups, A and B, sizes NA and NB, respectively, both ∈ (0, ∞). There is a private good and “varieties” of a public good corresponding to charities’ “missions” The public good could correspond to the welfare of others A variety is represented by a single parameter γ ∈ [0, 1].

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Motivation This paper Literature Model Agreement on levels Disagreement on levels

Charities and missions

When γ = 1 the good is a local public good for those in community A Missions might correspond to religious ideology, or methodology (eg, 12-step vs CBT approaches to treating addiction), or a mixture of two goods (eg, primary and secondary edcuation). We assume that, for each variety γ ∈ [0, 1], there exists a charitable project that converts donations into that variety.

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Motivation This paper Literature Model Agreement on levels Disagreement on levels

Charities and missions ctd.

Charities who operate missions are strategically, black-boxed For each γ there exists a charity who will run a mission at γ Each mission incurs a fixed costs F Each has identical marginal costs of 1 Each faces a non-distribution constraint F + Pγ = Dγ

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Motivation This paper Literature Model Agreement on levels Disagreement on levels

Donors

Donors have incomes ∈ {m, m} with m > m. Donors have perfect information about the charities that exist. No transactions costs of giving No transfers between donors (not needed when donors agree

• n levels of giving)

Simultaneous move game played between donors Seek coalition-proof Nash Equilibria

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Motivation This paper Literature Model Agreement on levels Disagreement on levels

Preferences: the essentials

Public and private good are normal There is a sufficient degree of complementarity between the public and private goods The valuation of a mission does not fall away too quickly as we move away from a donors’ ideal

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Motivation This paper Literature Model Agreement on levels Disagreement on levels

Preferences: a convenient specification

A consumer i from community j has utility u(xi, Pj) = (xij)1/2(Pj)1/2 PA = 1 γPγdγ PB = 1 (1 − γ)Pγdγ

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Motivation This paper Literature Model Agreement on levels Disagreement on levels

Project size and the expropriation of the rich

Lemma Consider a group of size N in which all members have incomes ∈ {m, m} with m > m. Suppose that all donors give to the same mission. (i) Total provision is increasing in group size and total income. (ii) Rich donors give more than poor donors.....

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Project size and the expropriation of the rich ctd

Lemma ...(iv) If m − m is sufficiently large, only donors of income m give. Lower income donors find the level of public good provision too

• high. We call this disagreement on levels

(v) Otherwise all donors give and are satisfied with the levels of public good provision. We call this agreement on levels Olson (1965): “The systematic tendency for the “exploitation” of the great by the small”

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Motivation This paper Literature Model Agreement on levels Disagreement on levels

To keep in mind

Disagreement on levels is generated by m − m large: donors with the same preferences but different incomes can disagree

• n levels. Inequalities here may lead to inefficient

centralisation Disagreement on preferences is specified in the model. Income inequality across preference types can lead to inefficient fragmentation.

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Motivation This paper Literature Model Agreement on levels Disagreement on levels

Coalition Proof Nash Equilibria

Lemma A Coalition Proof Nash Equilibrium either consists of two separate missions, at γ = 0 and at γ = 1, or of a single compromise mission at γ ∈ [0, 1]. If it is profitable to deviate, it is most profitable to deviate to

• ne’s preferred mission.

Once fixed costs are met, donors give to the charity which

• ffers them the highest valuation.

No fixed costs = ⇒ no compromise mission is possible.

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Motivation This paper Literature Model Agreement on levels Disagreement on levels

Some notation

With Cobb Douglas preferences, the size of a compromise mission does not depend on the mission itself. Let qi be the size of the separate mission funded by community i relative to the size of the compromise mission. Let s be the the size of the fixed cost relative to the size of the compromise mission.

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Motivation This paper Literature Model Agreement on levels Disagreement on levels

Pareto improving compromise missions

In this section we assume that all donors would give to the compromise mission - we say that there is agreement on levels Lemma A compromise mission that is a Pareto improvement on separate missions must satisfy: q2

A ≤ γ ≤ 1 − q2 B

which exists iff: q2

B + q2 A ≤ 1

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Motivation This paper Literature Model Agreement on levels Disagreement on levels

Compromise mission CPNEs

Lemma Let m > Pjoint (i) A compromise mission γ exists in a CPNE if and

• nly if:

max

• qA,

qA qA +

s NA+1

2 ≤ γ ≤ 1 − max

• qB,

qB qB +

s NB+1

2 (ii) If a compromise mission exists as a CPNE, it is a Pareto improvement on separate missions. (iii) The set (qA, qB) defined in (i) where a compromise mission exists in a CPNE is strictly smaller than the set of pairs for which a compromise mission would be a Pareto improvement on separate missions.

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Motivation This paper Literature Model Agreement on levels Disagreement on levels

Where does the difference come from?

A remnant exists when one group makes contributions of more than F to the compromise mission The remnant charity exists when qi ≤ 1 −

s Ni+1

The no-deviation condition becomes: γ1/2 ≥ qi + γ1/2max

• 0, 1 − qi −

s Ni + 1

• Sandford, Scharf

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Motivation This paper Literature Model Agreement on levels Disagreement on levels

Welfare criterion

Lemma (i) Let donors agree on the level of provision at all missions.Then a compromise mission yields higher welfare than separate missions for all: NAqA + NBqB ≤ (N2

A + N2 B)1/2

(ii) The socially optimal compromise mission at γ∗ = N2

A

N2

A + N2 B

is only available as a CPNE when q2

A ≤ γ∗ ≤ 1 − q2 B

When there are no fixed costs, separate mission are preferred under a utilitarian social welfare function.

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Motivation This paper Literature Model Agreement on levels Disagreement on levels

Does this fit with the evidence?

Wealthy donors are greatly over-represented on governing boards and at high profile gatherings of supporters (Ostrower 1995) Only those who can make or raise large contributions are allowed to access policy-making positions (Oedendahl 1990) “Through their philanthropy wealthy donors come together with one another and sustain a series of organizations that contribute to the social and cultural fabric of upper class life” (Ostrower 1995) Large charities tend not to focus on the specific needs and concerns of minority groups (Third Sector 2011)

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Motivation This paper Literature Model Agreement on levels Disagreement on levels

An illustration: s=20, NA = NB = 50

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Motivation This paper Literature Model Agreement on levels Disagreement on levels

An illustration: s=5, NA = NB = 50

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Social budget constraint

(NA + 1)qA + (NB + 1)qB = 2N + 1 − s As fixed costs increase, this moves toward the origin.

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Motivation This paper Literature Model Agreement on levels Disagreement on levels

Where does the budget constraint lie?

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Motivation This paper Literature Model Agreement on levels Disagreement on levels

Communities of Equal Size

Lemma Assume NA = NB = N and agreement on levels (a) For equal distributions of income, a compromise mission is a CPNE ⇐ ⇒ it Pareto dominates separate missions. (b) For unequal distributions of income (i) There exists s such that the CPNE consists of separate missions and is Pareto dominated by a compromise mission. (ii) There exists an interval of s such that the CPNE is a separate missions equilibrium, but this acheives lower social welfare than some compromise mission.

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Motivation This paper Literature Model Agreement on levels Disagreement on levels

Some interpretation: the limits to expropriation

A compromise mission serves as a voluntary redistribution mechanism between groups A poorer group wants to redistribute with the rich community The richer group only consents when they gain too: when there is not too much income inequality between groups.

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Motivation This paper Literature Model Agreement on levels Disagreement on levels

Does the Pareto dominated case arise?

Income < $100,000 $100,000- 200,000 $200,000

• $1m

$1m + Total Religion 23.7 4.5 8.3 3.4 40 Combined 3.0 0.9 4.0 0.8 8.7 Basic needs 3.7 1.0 2.1 0.8 7.5 Health 1.2 0.4 1.9 5.1 8.7 Education 1.1 0.4 1.9 5.1 18.2 Arts 0.4 0.2 5.4 3.1 9.1 Other 2.4 0.5 2.9 1.9 7.8 Total 35.6 7.9 36.2 20.3 100 Indianapolis: Center on Philanthropy, 2007

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Motivation This paper Literature Model Agreement on levels Disagreement on levels

Communities of unequal size

Lemma Consider populations of sufficiently unequal sizes, NA

NB ≥ r∗ > 1,

equal distributions of income between groups and for which donors agree on levels. Then (i) there an interval of fixed costs for which separate missions is the CPNE, and for which separate missions is Pareto dominated by a compromise mission (ii) an interval of fixed such that separate missions is the only equilibrium, but for which a compromise mission would yield higher social welfare.

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Motivation This paper Literature Model Agreement on levels Disagreement on levels

Minorities and stability

Lemma Suppose that there is a fixed number of agents who have the same income m. Then for N > 1 and all NA

N ≥ r there exists a range of

fixed costs such that the socially optimal compromise mission is stable for NA

N but not for NA+1 N

. Corollary When there are two groups, the number of charitable projects is inverse-U shaped in the probability that two individuals are from the same ethnic group.

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Motivation This paper Literature Model Agreement on levels Disagreement on levels

Higher inequality between income types.

Lemma Suppose we have disagreement on levels and that max(c0, c1)m − F ≤ 0 Then there exist low across group income-inequality distributions

• f income, for which separate missions would generate higher social

welfare, but for which compromise mission equilibria also exist.

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Motivation This paper Literature Model Agreement on levels Disagreement on levels

Mission disagreement - a picture

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Increases in fixed costs/decreases in incomes

Increasing fixed costs is equivalent to a uniform reduction of incomes in this model. When there is agreement on levels increasing the fixed costs

• f all charities increases the stability of compromise mission

equilibria and can lead to welfare gains. When there is disagreement on levels, decreasing the fixed costs of all charities reduces the stability of compromise mission equilibria and can lead to welfare gains.

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