`::include_graphics('../picsfigs/subst_meta_cut.png') knitr`

# 3 Are charities in competition?

**Is the ineffective giving reducing effective giving?**

Are charitable gifts complements or substitutes; are charities rivals? Does one donation request (or donation itself) crowd out another, and if so when and by how much? This is critical to understanding the extent to which gains can be achieved by getting people to ‘switch’ from less to more effective charities. To the extent this crowding-out occurs, factors driving giving to the non-EA charities, especially local obligations (e.g., neighbors pressuring you to give to local organisations) themselves represent barriers to EA giving.

## 3.1 Theoretical framework and concerns

What does this question even mean? In a standard Economics framework we would consider joint optimization over “gifts to an ineffective charity” and “gifts to an effective charity”;* one doesn’t “respond” to the other.^{1}

Prices/ external changes shift each, but we can’t “force you to voluntarily give.” Furthermore, “prices” are unclear in this context (see Economics models of giving) and prices for one cause or charity rarely vary exogenously.

If we *could* shift the ‘meaningful giving’ \(\rightarrow\) we could use theory of Conditional Demand (Pollak 1969) \(\rightarrow\) “expenditure substitution” (D. A. Reinstein, n.d.). Still, the sign of the conditional demand effects are straightforward only under very restrictive conditions.

What we *can* measure in a straightforward way (in principle), is :

Does a promotion for a less-effective charity (such as Cancer Research UK) cause more or less giving to a presumably more-effective charity (such as Doctors Without Borders)? Most of the work discussed below focuses on this sort of estimate.

But this raises a more difficult question:

- Is the causality: Cancer Research UK (CRUK) promo \(\rightarrow\) give more to CRUK \(\rightarrow\) give less (more) to Oxfam? (see discussion in fold)

- Can we rule out
*direct*effects of the first promotion? (CRUK promo \(\rightarrow\) donations to Oxfam; see (Heckman and Pinto 2015) on “mediators”)

This is directly relevant for a *policymaker*. She might face a ‘shock’ that she knows or expects will lead to donations to charity A to rise by EUR 1,000,000 EUR. She will want to know ‘how much can we expect donations to charity B to fall?’

**What underlying causes might lead the effect to go in one direction or the other?**

The psychological ideas of “self-image management” and “moral-licensing” could also be expressed in terms of a utility function with particularly diminishing returns to total charitable giving; there may be a discount rate on the recency of the donation, as in a *perishable* good.

As previously noted, models from economics typically consider an individual maximizing her utility, including the utility she gets from her donations, directly or indirectly, quantified and formalized in terms of, e.g.,^{3}

“Public goods”: the total amount of ‘charity as a public good’ provided, no matter who provides it (sometimes referred to as ‘pure altruism’),

“Warm glow”: the amount the donor herself has sacrificed (in some depictions,

*even if it does no good at all, or completely crowds out others’ donations!*( Andreoni (1989), as interpreted by and others),the “Impact” a donor’s donation has on outcomes (Duncan 2004) (

*not*taking into account the effect of her donation on other donors) or on particular identified beneficiaries, (Atkinson 2009) and (Tonin and Vlassopoulos 2010)the donor’s prestige (Harbaugh 1998).

But see some critical notes on this in the fold

These models do not explicitly differentiate between gifts to different charitable causes. Still, the models can be generalized to yield varying predictions for expenditure substitution, as discussed in D. A. Reinstein (n.d.).

From an economics perspective, treating charitable giving like ‘any other good’ purchased by a donor (as a consumer), does not yield a clear prediction. Economists speak of goods being ‘complements and substitutes’, depending on how the price of one affects the number of units consumed of the other good. We can also consider how ‘expenditures on one good vary with shocks to expenditures on another’, referred to ‘expenditure substitution’ in D. A. Reinstein (n.d.). Here again, the prediction is ambiguous, but essentially it depends on the extent to which consumption of good (or charity) A satiates the desire for (diminishes the marginal utility of) good/charity B.^[(Scharf, Smith, and Ottoni-Wilhelm 2017) consider the intertemporal elasticity of a ‘warm glow’ component.]

### Expenditure substitution math

Assuming that utility is separable in own consumption and charitable gifts, and assuming an additive specific shock (\(\alpha\)), we can express utility as: \[U=f(x)+V(g_{1},g_{2}-\alpha )\] *where* the functions \(V\) and \(f\) are functions that represent utility from own-consumption and from charitable giving, repectively.

The budget constraint can be written as:

\[x+p_{1}g_{1}+p_{2}g_{2}\leq Y\] *where* \(Y\) represents total wealth, \(p_{1}\) and \(p_{2}\) are the prices of giving to charities one and two (per dollar the charity receives), and I normalize the price of own consumption to one.

Under this model, the marginal “indirect effect” of a shock (\(\frac{\partial g_{1}}{\partial \alpha })\) can be expressed simply as a function of the marginal “direct effect” of the shock (\(\frac{\partial g_{2}}{\partial \alpha }\)). Standard comparative statics of the optimal choices (assuming an interior solution and other standard regularity conditions) yields the total derivatives: \[\begin{aligned}
\frac{dx}{d\alpha } &=&\frac{\lambda _{\alpha }}{U_{xx}} \\
\frac{dg_{1}}{d\alpha } &=&\frac{\lambda _{\alpha }(p_{2}U_{12}-p_{1}U_{22})%
}{U_{12}^{2}-U_{11}U_{22}} \\
\frac{dg_{2}}{d\alpha } &=&1+\frac{\lambda _{\alpha
}(p_{2}U_{11}-p_{1}U_{12})}{-U_{12}^{2}+U_{11}U_{22}}\end{aligned}\] *where* \(\lambda (\alpha ,p_{1},p_{2})\) is the shadow value of the budget constraint, \(U_{IJ}\) \(\equiv \frac{\partial ^{2}U}{\partial I\partial J}\), \(\lambda _{\alpha }\equiv \frac{\partial \lambda (\alpha ,p_{1},p_{2})}{% \partial \alpha }\).

Hence

\[\frac{dg_{1}}{d\alpha }=(\frac{dg_{2}}{d\alpha }-1)\frac{% p_{2}U_{12}-p_{1}U_{22}}{p_{1}U_{12}-p_{2}U_{11}}\]

The sign of the marginal effect on \(g_{1}\) (relative to the marginal effect on \(g_{1}\)) can be either positive or negative, and will depend on the partial second derivatives of utility and the relative prices.

Looking at the discrete effect: \[g_{1}(\alpha _{1})-g_{1}(\alpha _{0})=\int_{\alpha _{0}}^{\alpha _{1}}[(% \frac{dg_{2}}{d\alpha }(g_{1,}g_{2})-1)\frac{% p_{2}U_{12}(g_{1,}g_{2})-p_{1}U_{22}(g_{1,}g_{2})}{% p_{1}U_{12}(g_{1,}g_{2})-p_{2}U_{11}(g_{1,}g_{2})}]d\alpha \label{integralgeneral}\]

With quadratic utility (defined in fold), the partial derivatives will be constants,

… and the *discrete* indirect effect, as well as the marginal effect, will be a simple linear function of the direct effect:

\[g_{1}(\alpha )=A+Bg_{2}(\alpha )\]

*where* \(A\) and \(B\) are constants.

Quadratic utility is often justified as a second-order approximation to any other utility function. With other utility functions the partial derivatives may vary at different consumption bundles, so the indirect effect may be a nonlinear function of the direct effect, but these should be solvable for a predictable functional form, which for estimation purposes, can be approximated to any desired accuracy by a polynomial function. o

## 3.2 Previous approaches and evidence^{5}

Observation of this ‘crowding out’ is difficult. There is a **lack of data** on donations at the individual-charity level; available data typically considers total individual giving in a year (especially via tax records), asks people to recall their recent donations, sometimes broadly differentiated by cause but not by specific charity (see, e.g., Wilhelm (2006)). There is also data on charity’s total revenues (reported to the government as well as independent surveys), and data on giving through specific platforms. However, there is no source of data on an individual’s lifetime giving broken down across modes and specific charities.

For identification: Lack of **independent observable variation** in price, shocks, or appeals.

**Intertemporal substitution** is an issue, and we typically **cannot observe ‘lifetime giving.’**

Even defining this issue is a challenge, as noted above. Furthermore, estimation of ‘Expenditure substitution’ (D. A. Reinstein, n.d.) is complicated by issues of extensive vs intensive margins, as well as heterogeneity.

### 3.2.1 Observational work

**Observational data** typically lacks shocks that are clearly *specific* to giving to one charity. Observational data on charitable giving (e.g., survey data or tax data) offers few variables that can be used to identify ‘specific’ shocks – shocks that alter giving to one charity but have no independent effect on giving to other charities. Most observable variables that are believed to increase giving to one charity will also increase giving to other charities, masking substitution effects.

#### Signing-the-bias approach

D. A. Reinstein (n.d.) using PSID/COPPS data finds some evidence of expenditure substitution, especially for large givers.

**Results, “bounding below” argument:**

He finds many negative significant correlations between residuals from fixed-effects regressions on donations to categories of charitable causes.

- This especially holds for larger (prior) donors and for certain paired cause categories.

Under what he argues to be plausible econometric assumptions (essentially, net positive correlations between the residuals of ‘propensity to donate to each cause’) implies that negative correlations are strong evidence of expenditure substitution.

**Interpretation:** He interprets these in terms of ‘heterogeneous motivations for giving’, arguing that large givers are more likely to have a sophisticated optimization over charities incorporating diminishing returns to each cause, and small givers more likely to be responding to temporary shocks and appeals.

**Limitations:** Even if one accepts the bounding assumptions, t hese findings are limited, even as a bounded result. The data is recall data, and charitable categories are not well defined in the PSID data; respondents may categorize the same donations into different groupings.

#### Observational data paired with ‘exogenous’ shocks

Deryugina and Marx (2015)**:**

**Results and interpretation:

Donations in a state affected by tornado increase 1.7-2 percent in that year and 1.9-2 percent in the 2 years after. The authors can only reject ‘full crowding out’.

Scharf, Smith, and Ottoni-Wilhelm (2017)**:**

These authors observe “CAF accounts”; for this particular group, they observe all donations over a substantial period.

*Author’s conclusions:*

They reject ‘full crowd-out’. They find a ‘tight zero’ long-run crowdout.

Non-disaster giving is pre-poned (!), especially for disaster/intl donors; they argue this is a “halo effect?”

Estimates: +.537 log donations to DEC-13, se .032; -0.008 log donations to ‘other charities’, se 0.017 \(\rightarrow\)

*Their interpretation…*

Consistent with… for (only) people responding to the DEC appeal … the disaster appeal increased the effectiveness with which donating to all charities, including other charities, produces warm glow utility—a halo effect

They argue that their data allows them to reject the “transactions cost” explanation because they see i. less bunching than usual, ii. shifts in amounts given and not just at the extensive margin and iii. a particular shift from certain categories.

*Limitations:*

- Specific CAF population
- disaster-specific context
- time-series variation issues (6 disasters=lumpy?)

Todo: add pictures of the relevant environments for these studies here

### 3.2.2 Simultaneous/proximate ‘lab’ experiments

A range of authors have asked ‘economics laboratory’ participants to make a sequence of real donation choices.

These include Reinstein (2006/11); ?filiz-ozbay and Schmitz (2016)

*Figures: Berkeley design, types*

Vary choice sets/prices, shocks \(\rightarrow\) crowd-out, esp. similar causes

*Figures: Berkeley line graphs*

(Reinstein, 2011) \(\rightarrow\) Strong “expenditure substitution” responses to shocks, esp for similar charities; approx 50% crowd-out; 2.59 cross-price-elasticity)

- Heterogeneity; mix of ‘fixed purse’, ‘flexible purse/never substitute’]

?Filiz-Ozbay2019 : Five paired choices, varying ‘rebate rate’ for one only; price-focus - ‘Stealing’ almost always - +0.35 net cross-price elast for ‘substitute’ charities

### 3.2.3 Lab/framed experiments with time gaps

Schmitz (2019) (ExpEcon, small time gap)

Vance-Mullen component of Reinstein et al

## 3.3 Field/natural experiments

Notes from previous paper (unfold)

- J. Meer (2014), Jonathan Meer (2017): DonorsChoose.org competition, matching campaigns

2017 paper: Finds increased funding for project, no significant impact on donations to other projects

J. Meer (2014): “increased competition reduces the likelihood of a project being funded”

Donkers, Diepen, and Franses (2017): Extra mailings to existing donors in a week, top-NL charities

- Extra mailings +1.81 EUR for charity,
- -0.10 EUR per ‘regular’ mailing for
*other*charity in*same week* - loss of 10% of revenues via competitive effects
- can’t reject zero-crowding, but wide CI’s

Adena and Huck (2019): Anticipated repetition \(\rightarrow\) 40% less “this year” (but also a *persistent* lower donation)

Cairns and Slonim (2011): *Anticipated* `2nd collection’ at Mass raised 7695 USD , reduced 1st collections by 1708 USD (22% “crowdout”)

Reinstein et al, 2020: First field-experiment to ask (or not ask) on multiple separate occasions with a significant delay, vary this delay time; find some crowding out but evidence on interaction with delay time is mixed. Possibly two channels: consistency versus fading of moral license/warm glow.

## 3.4 Synthesis (emerging)

“Proximate asks” and “clearly presented comparisons” \(\rightarrow\) expected crowding-out

However, the generalizability of this finding is limited by a particular set of issues: apparent contrast, “coherent arbitrariness” (Ariely, Loewenstein, and Prelec 2003), narrow brackets, framing (how people think they ‘should behave’ or how they behave when they are in a deliberative self-reflecting mode. This may characterize some giving decisions but it is probably not the most common.

With naturally-occurring, more time-separated shocks and asks, the results are more mixed, sometimes with much smaller, or no apparent substitution.

So “how proximate is proximate”? Evidence is still mixed.

In Reinstein et al, we are planning a meta-analysis of the above papers

or an optimization over ‘gifts to the causes these represent’.↩︎

I use DWB/MSF in the example here rather than a GiveWell charity like AMF because it is hard to discuss a massive ‘crowding out’ of giving to charities like AMF when there is little giving to these charities to begin with. … Certainly true from the PoV of a national policymaker.↩︎

I discussed this in the previous section; I intend to integrate these discussions to avoid repetition. (To do.)↩︎

This is largely drawn from the appendix of (D. Reinstein 2011)↩︎

The material in this section largely overlaps the literature review in Reinstein, Reiner and Vance-McMullen 202 ongoing, in the repository https://github.com/gerhardriener/CharitySubstitutionExperiment/, in the file lit-synth.Rmd↩︎