An experimental investigation of intrinsic motivations for giving

Abstract

This paper presents results from a modified dictator experiment aimed at distinguishing and quantifying intrinsic motivations for giving. We employ an experimental design with three treatments that vary the recipient (experimenter, charity) and amount passed (fixed, varying). We find giving to the experimenter not to be significantly different from giving to a charity, when the amount the subject donates crowds out the amount donated by the experimenter such that the charity always receives a fixed amount. This result suggests that the latter treatment, first used by Crumpler and Grossman (J Public Econ 92(5–6):1011–1021, 2008), does not provide a clean test of warm glow motivation. We then propose a new method of detecting warm glow motivation based on the idea that in a random-lottery incentive (RLI) scheme, such as the one we employ, warm glow accumulates and this may lead to satiation, whereas purely altruistic motivation does not. We also provide bounds on the magnitudes of warm glow and pure altruism as motives that drive giving in our experiment.

Appendices

Appendix 1

Here, we add to (1) a warm glow component represented by the concave function $\gamma \left( \cdot \right)$. This captures the enjoyment the agent receives when contributing. Thus, preferences for a single allocation decision are represented by the following utility function:

$$\begin{aligned} U(x,g)=c\left( x\right) +\gamma \left( g\right) +\phi \left( g+\bar{g}\right) . \end{aligned}$$

(5)

In what follows, we study the decision of how much to contribute in a given treatment when this is faced in each of the three positions in the sequence. To simplify the exposition, we will look at treatment 1 (T1) and indicate the donations in the three positions as $g_{T1}^{DA}, \,g_{T1}^{DB}$, and $g_{T1}^{DC}$. When T1 is the last decision, an individual chooses his contribution by solving the following maximization problem, where we replaced $x$ using the budget constraint:

$$\begin{aligned} \max _{g_{T1}^{DC}}\gamma \left( g_{T1}^{DC}+\lambda g_{T2}+\rho g_{T3}\right) +\frac{1}{3}\left[ c\left( w-g_{T1}^{DC}\right) +\phi \left( g_{T1}^{DC}+\bar{g}_{T1}^{DC}\right) \right] . \end{aligned}$$

(6)

This characterization of the utility function captures the two properties of warm glow discussed in Sect. 4.1, namely that the warm glow component of utility is enjoyed even if a given allocation is not implemented and that, as a result, warm glow felt in each period may depend not only on the donation in that period but also on the donations in the previous periods. These two notions are captured by the fact that $\gamma \left( \cdot \right)$ is not multiplied by the probability of being implemented and that its argument is a weighted sum of the donation in the current treatment and donations in the previous two treatments, indicated as $g_{T2}$ and $g_{T3}$, with the weights given by $\lambda \ge 0$ and $\rho \ge 0$. We thus allow each treatment to have a different weight in the warm glow component of the utility function. After all, if I give $\pounds 5$ to a charity I may feel more generous than if I give $\pounds 5$ to the experimenters. Notice that the weights are specific to each treatment and not to a particular position in the sequence. Notice also that if warm glow does not accumulate, i.e., if $\lambda =0$ and $\rho =0,$ then Proposition 1 holds and we would expect donations in a given treatment to be the same regardless of the position in which the treatment is undertaken.

The f.o.c. is then given by

$$\begin{aligned} \gamma ^{\prime }\left( g_{T1}^{DC}+\lambda g_{T2}+\rho g_{T3}\right) =\frac{ 1}{3}\left[ c^{\prime }\left( w-g_{T1}^{DC}\right) -\phi ^{\prime }\left( g_{T1}^{DC}+\bar{g}_{T1}^{DC}\right) \right] . \end{aligned}$$

(7)

When facing the same treatment as the second choice, the maximization problem is given by

$$\begin{aligned} \max _{g_{T1}^{DB}}\gamma \left( g_{T1}^{DB}+\lambda g_{T2}\right) +\frac{1}{3 }\left[ c\left( w-g_{T1}^{DB}\right) +\phi \left( g_{T1}^{DB}+\bar{g} _{T1}^{DB}\right) \right] +V_{DB}, \end{aligned}$$

(8)

where $V_{DB}$ is the continuation value and, without loss of generality, we assume that T2 was the first decision in the sequence, so that $\lambda g_{T2}$ appears in the warm glow function. Different from the case of a purely altruistic individual discussed in Sect. 4.1, now the continuation value does depend on $g_{T1}^{DB}$, as the donation in this period has an impact on the warm glow component in the following period. If the individual does not take this fact into account, than the f.o.c. is

$$\begin{aligned} \gamma ^{\prime }\left( g_{T1}^{DB}+\lambda g_{T2}\right) =\frac{1}{3}\left[ c^{\prime }\left( w-g_{T1}^{DB}\right) -\phi ^{\prime }\left( g_{T1}^{DB}+ \bar{g}_{T1}^{DB}\right) \right] . \end{aligned}$$

(9)

Comparing (7) and (9), it follows immediately from the concavity of $\gamma \left( \cdot \right)$ that, as far as $\rho g_{T3}>0$, then the optimal donation in T1 is greater when T1 is undertaken in the second position in the sequence, than when it is undertaken in the third position in the sequence, so $g_{T1}^{DB}>g_{T1}^{DC}$.

If the individual takes into account the impact of a given donation on subsequent choices, then the f.o.c. is

$$\begin{aligned}&\gamma ^{\prime }\left( g_{T1}^{DB}+\lambda g_{T2}\right) +E_{DB}\gamma ^{\prime }\left( g_{T1}^{DB}+\lambda g_{T2}+\rho g_{T3}\right) \nonumber \\&= \frac{1}{3}\left[ c^{\prime }\left( w-g_{T1}^{DB}\right) -\phi ^{\prime }\left( g_{T1}^{DB}+\bar{g}_{T1}^{DB}\right) \right] , \end{aligned}$$

(10)

where $E_{DB}$ indicates expectations when in position DB, as donation in the third period, when T3 will be undertaken, is unknown. Because of the envelope theorem, we do not need to take into account the impact of $g_{T1}^{DB}$ on $g_{T3}$. Notice that compared to (9), in (10) there is an additional marginal benefit of a donation. So, also when the impact of a given donation on subsequent choices is taken into account, the optimal donation in T1 is greater when T1 is undertaken in the second position in the sequence, than when it is undertaken in the third position in the sequence, i.e., $g_{T1}^{DB}>g_{T1}^{DC}$.

Now, we look at the decision in the first position. An individual facing T1 in the first period maximizes

$$\begin{aligned} \max _{g_{T1}^{DA}}\gamma \left( g_{T1}^{DA}\right) +\frac{1}{3}\left[ c\left( w-g_{T1}^{DA}\right) +\phi \left( g_{T1}^{DA}+\bar{g} _{T1}^{DA}\right) \right] +V_{DA}, \end{aligned}$$

(11)

when the individual does not take the impact of the current choice on subsequent choices into account, the f.o.c. is

$$\begin{aligned} \gamma ^{\prime }\left( g_{T1}^{DA}\right) =\frac{1}{3}\left[ c^{\prime }\left( w-g_{T1}^{DA}\right) -\phi ^{\prime }\left( g_{T1}^{DA}+\bar{g} _{T1}^{DA}\right) \right] . \end{aligned}$$

(12)

By comparing (12) to (9), it is evident that as far as $\lambda g_{T2}>0$, then the donation in T1 when undertaken in the second position is less than the donation in T1 when undertaken in the first position, thus $g_{T1}^{DA}>g_{T1}^{DB}$. By comparing (12) to (7), it is also evident that $g_{T1}^{DA}>g_{T1}^{DC}$.

When the individual does take into account the impact of the current choice on subsequent choices, the f.o.c. is

$$\begin{aligned}&\gamma ^{\prime }\left( g_{T1}^{DA}\right) +E_{DA}\gamma ^{\prime }\left( g_{T1}^{DA}+\lambda g_{T2}\right) +E_{DA}\gamma ^{\prime }\left( g_{T1}^{DA}+\lambda g_{T2}+\rho g_{T3}\right) \nonumber \\&\quad =\frac{1}{3}\left[ c^{\prime }\left( w-g_{T1}^{DA}\right) -\phi ^{\prime }\left( g_{T1}^{DA}+\bar{g}_{T1}^{DA}\right) \right] . \end{aligned}$$

(13)

Without loss of generality, we assume that T2 is the second decision in the sequence and T3 is the last one. By comparing (13) to (7), it is evident that even when the individual does take into account the impact of the current choice on subsequent choices $g_{T1}^{DA}>g_{T1}^{DC}$. The comparison with (10) is more complex, as the expectation operator refers to two different positions in the sequence. However, as it is clearly the case that $\gamma ^{\prime }\left( g_{T1}\right) >\gamma ^{\prime }\left( g_{T1}+\lambda g_{T2}\right)$, then it follows that $g_{T1}^{DA}>g_{T1}^{DB}$ if $E_{DA}\gamma ^{\prime }\left( g_{T1}^{DA}+\lambda g_{T2}\right) +E_{DA}\gamma ^{\prime }\left( g_{T1}^{DA}+\lambda g_{T2}+\rho g_{T3}\right) >E_{DB}\gamma ^{\prime }\left( g_{T1}^{DB}+\lambda g_{T2}+\rho g_{T3}\right)$.

Thus, we have shown how a declining trend in donation arises if giving is motivated by warm glow and the warm glow felt in each period depends not only on the donation in that period but also on the donations in the previous periods. Notice that, as in Sect. 4.1, the above analysis holds even if the purely altruistic component of utility, $\phi \left( \cdot \right)$, is different in the three treatments.

Appendix 2

This section draws on Manski (2007). Indicate donation in T2 as $g_{2}$, while donation due to warm glow giving is $g_{w}$. There are three exhaustive and mutually exclusive groups in our population, identified by the variable $z$: non-givers in T2 ($z=1$), unreciprocals ($z=2$), and reciprocals ($z=3$). We are interested in mean donation due to warm glow motives, i.e., $E\left[ g_{w}\right]$. By the Law of Iterated Expectations

$$\begin{aligned} E\left[ g_{w}\right] \!=\!E\left[ g_{w}|z\!=\!1\right] P(z\!=\!1)+E\left[ g_{w}|z=2 \right] P(z=2)+E\left[ g_{w}|z=3\right] P(z=3), \end{aligned}$$

where $P(z=i)$ is the probability that $z$ equals $i=1,2,3$. The sampling process asymptotically reveals $P(z)$ and $E\left[ g_{w}|z=i\right]$ for $i=1,2$, as in this case $E\left[ g_{w}|z=i\right] =E\left[ g_{2}|z=i\right]$. However, $E\left[ g_{w}|z=3\right]$ is not revealed. Our identifying assumptions are

$$\begin{aligned} E\left[ g_{w}|z=3\right]&\le E\left[ g_{2}|z=3\right] \\ E\left[ g_{w}|z=2\right]&\le E\left[ g_{w}|z=3\right] . \end{aligned}$$

Hence, the identification region for $E\left[ g_{w}\right]$, indicated as $H\left\{ E\left[ g_{w}\right] \right\}$, is given by

$$\begin{aligned} H\left\{ E\left[ g_{w}\right] \right\} \!=\!\left[ E\left[ g_{2}|z\!=\!1\right] P(z\!=\!1)\!+\!E\left[ g_{2}|z\!=\!2\right] \left[ P(z=2)+P(z=3)\right] , E\left[ g_{2} \right] \right] . \end{aligned}$$