Judgment and Decision Making, vol. 1, no. 1, July 2006, pp. 13-22.

Rebate subsidies, matching subsidies and isolation effects

Douglas D. Davis1
Department of Economics
Virginia Commonwealth University


In a series of recent experiments (Davis, Millner and Reilly, 2005, Eckel and Grossman, 2003, 2005a-c, 2006), matching subsidies generate significantly higher charity receipts than do theoretically equivalent rebate subsidies. This paper reports a laboratory experiment conducted to examine whether the higher receipts are attributable to a relative preference for matching subsidies or to an ``isolation effect'' (McCaffery and Baron, 2003, 2006). Some potential policy implications of isolation effects on charitable contributions are also considered.

Keywords: Experiments, charitable contributions, methodology.

1  Introduction

Voluntary charitable contributions play a large and ever-increasing role in supporting the social infrastructure of developed economics. In an effort to find ways to encourage private contributions, experimental economists have, in recent years, devoted considerable attention to the effects of alternative fundraising formats and mechanisms. (See, e.g., Davis and Isaac, 2006.) One branch of this general program regards the effects of different methods for subsidizing contributions. A series of recent experiments (e.g., Eckel and Grossman, 2003, 2005a-c, 2006, and Davis, Millner and Reilly, 2005) indicate that matching subsidies elicit considerably higher charity receipts than do comparable rebate subsidies.
The design for these experiments consists of one or more modified dictator games, similar to those used by Andreoni and Vesterlund (2001) and Andreoni and Miller (2002), where participants make "pass" and "hold" decisions under different endowment and price of contribution conditions. However, rather than changing directly the price of contributions, in the subsidy-format experiments subjects make pass/hold decisions under various matching subsidy and rebate subsidy conditions that alter the effective price of contributions.
Table 1 illustrates the design used as the control treatment in Davis, Millner and Reilly (2005), which is in many ways representative. Subjects are asked to make a series of decisions to hold for themselves, or pass to a charity portions of an endowment (in column 2) under the conditions shown in column (3). The sum of hold and pass entries must sum to the endowment. After making their choices, one randomly selected decision is implemented. For that decision, the subject receives as cash the amount they chose to hold (supplemented by rebates of passed amounts in the rebate conditions). The amount passed (supplemented by matching amounts in the matching conditions) is sent to a designated charity.
Table 1: Sample allocation decision problems for the control treatment.

(1) (2) (3) (4) (5)
Problem Endowment Condition Hold Pass
(for myself) (to charity)
1 $8 For every $1 you pass, the Charity will receive $1.
2 $8 For every $1 you pass, the Charity will receive $2: your $1 and a matching $1 provided by the experimenter.
3 $8 For every $1 you pass, the Charity will receive $1, and, the experimenter will refund to you $.50.
In general, a matching subsidy, sm, reduces the effective price of contributing $1 to charity to P = 1/(1+sm) and a rebate subsidy, sr, reduces the effective price of a $1 contribution to P = 1- sr. Thus, sm and sr induce the same effective price when sm = sr/(1-sr). However, Davis, Millner and Reilly observed substantially higher charity receipts under a matching subsidy than under a comparable rebate subsidy. For example, charity receipts were roughly twice as high under the 100% matching subsidy shown as problem 2 in Table 1 than under the 50% refund condition, shown as problem 3. This control treatment replicates results previously reported in Eckel and Grossman (2003). Eckel and Grossman also report very similar results in alternative laboratory designs where subjects make fewer allocative decisions (Eckel and Grossman, 2005a, 2006), and in field contexts (Eckel and Grossman 2005b, 2005c). In addition to their control treatment, Davis, Millner and Reilly (2005) report an "extra information" treatment where subjects received information prompting them about the net consequences of their choices. Extra information only reduced, but did not eliminate significant differences in net charity receipts.
The reason why changing subsidy formats so prominently affects charity receipts remains unclear. A failure on the part of subjects to understand the task at hand doubtfully drives results.2 The instructions are simple, and subjects report very high levels of understanding. Eckel and Grossman (2003), for example, observe that subjects strongly agreed with the statement that "instructions were clear." (Using a 5-point Likert scale, the mean subject response was 4.18).
One possible explanation for the higher charity receipts collected under a matching subsidy is that people find something psychologically appealing about matching subsidies. Eckel and Grossman (2003) suggest a sort of framing effect that might support such a preference for matching subsidies: the knowledge that the experimenter also contributes to the charity under a matching subsidy may create in subjects a "cooperation frame" that increases contributions relative to the "rewards frame" created by a rebate subsidy. At least some economists find this justification persuasive (e.g., Meier, 2005, p. 4).
Alternatively "isolation effects" discussed by McCaffery and Baron (2003, 2006) may explain the higher charity receipts generated with matching subsidies. The notion of isolation effects, which is closely related to, but distinct from the well known concept of mental accounting (Thaler, 1980, 1999), suggests that when given a multi-dimensional problem, people tend to disaggregate dimensions of the problem and focus on only those components that they control most directly or that affect them most directly.3 For example, given the problems shown in Table 1, people may focus on the direct consequences of giving away portions of their endowments, rather than on the indirect consequences for themselves or the charity that the various conditions imply. Harris and Joyce (1980) observed a similar result when they asked subjects to make a series of "fair" allocations among members in a partnership. When asked to divide profits, subjects tended to allocate profits equally among partners, despite very unequal profit contributions. When asked to divide expenditures, subjects again tended to use an equal-division rule, even though this time the rule resulted in a very unequal division of profits. Prompting subjects with information about the indirect consequences of their decisions reduced but did not eliminate the tendency to make equal allocations of the presented amounts.4
Preferences for matching subsidies and isolation effects carry distinct policy implications for charitable fundraising. If people simply prefer matching subsidies, governments and fundraising organizations might do well to switch from away from rebate schemes and toward schemes that feature matching contributions. In particular, replacing tax rebates with a government-sponsored matching contributions program would increase charitable contributions 5 However, to the extent that isolation effects explain the higher charity receipts generated with matching subsidies, policy-makers may encounter difficulties in implementing such a program, and even if implemented, may not find that such a program increases charity receipts.
Both potential difficulties follow from what people may isolate on as direct effects. For example, attempting to replace tax rebates with a combination of matching contributions and higher taxes might be difficult politically, since people may focus on the direct negative consequences of a personal tax increase rather than on the more indirect positive consequences of increased charitable contributions.6 Again, a matching subsidies program would increase charity receipts over the current tax refund subsidy policy only if people isolate more on the increased effectiveness of contributions induced by a matching subsidy than on other possible foci of attention, such as the reduction in obligations to a (sometimes resented) government that a (rebated) donation implies. The potential importance of isolation effects in these contexts remains a subject for future investigation.
This paper reports an experiment that focuses on the preliminary task of distinguishing between a preference for matching subsidies and isolation effects as an explanation for subsidy formatting effects. The idea of the experiment is straightforward. In addition to a previously-reported control treatment, conducted using the design shown in Table 1, I conduct a Maximum Possible Contribution ("MPC" ) treatment, where the allocation decisions are restructured so that the problem dimension presented most directly to subjects is the maximum amount that the charity may receive, rather than the maximum amount the subject may take home.
Although framing contributions in terms of charity receipts has few obvious parallels to natural contexts, it allows a clean distinction between simple preferences for matching subsides and isolation effects: to the extent that subjects simply prefer matching subsidies to rebates, matching subsidies will elicit higher net charity receipts than rebate subsidies in both the MPC and control treatments. On the other hand, to the extent that subjects isolate on the amount presented to be divided, net charity receipts under a matching subsidy will exceed those under a comparable rebate subsidy only in the control treatment. In the MPC treatment, charity receipts will increase equally with both rebate and matching subsidies, because subjects will divide maximum possible contributions between themselves and the charity in roughly the same way in all subsidy conditions. I summarize these observations as the following hypothesis, which I state in alternative form.
Hypothesis: Isolation effects drive the previously observed subsidy formatting effects. Shifting the direct effect of contributions from the amount of an endowment to donate to the maximum amount charity may receive eliminates the increased charity receipts elicited with matching subsidies over rebate subsidies.
By way of overview, experimental results are overwhelmingly consistent with isolation effects. The remainder of this paper is organized as follows. Section 2 explains the experimental design and procedures used to evaluate this hypothesis. Section 3 presents experimental results. A fourth section discusses some of potential policy implications of isolation effects on charity contributions.

2  Experiment design and procedures

2.1  Experiment design

Table 2 illustrates the MPC treatment. Subjects are given a cash account which is adjusted by the subsidy condition in column (3) to determine the maximum possible contribution, shown in column (2). Subjects decide how much of this MPC to pass (column 4) or hold for conversion to cash (column 5). Amounts passed and held must sum to the MPC. For the selected problem, the amount passed is sent to the charity, and the amount held is converted to cash by netting out the rebate or matching subsidy from the MPC.
Table 2: Sample allocation decision problems for the MPC treatment.

(1) (2) (3) (4) (5)
Problem Maximum possible Condition Dollars in MPC Dollars in MPC
contribution (MPC) to pass to the to hold for
charity conversion to
your cash
1 $8 No subsidy. Each $1 of the MPC represents $1 you donate to the charity from your cash account. Cash Account: $8
2 $16 100% Matching Subsidy: Each $1 of the MPC consists of $.50 you donate from your cash account and a $.50 matching contribution provided by the experimenter.
Cash Account: $8
3 $16 50% Refund Subsidy. Each $1 of the MPC consists of $1 you donate from your cash account, but with $.50 of this donation refunded back to your cash account by the experimenter. Cash Account: $8
To clarify decisions in the MPC treatment, consider possible choices for each of the decision problems in Table 2. In decision problem 1, subjects must decide how to divide $8 between themselves and the charity under a no subsidy condition. For this condition subjects are told that hold and pass decisions from the MPC are the same as making hold and pass decisions from their cash accounts. Thus, for example, if a subject passes $6 to charity and holds $2, the charity receives $6 and the subject receives $2.
In the 100% matching subsidy condition listed as problem 2, subjects must decide how much of a $16 MPC to pass to the charity or to hold for conversion to cash, under the condition that each dollar in the MPC reflects a combination of a $.50 donation from the subject and a $.50 matching contribution from the experimenter. Here subjects are told to view a decision to pass, say, $6 to charity as being equivalent to donating $3 from their cash accounts and keeping $5 (or, alternatively, keeping $16-$6 = $10 of their MPC and converting it to cash $10(1-.5)=$5). In the 50% refund subsidy condition shown as problem 3, each dollar a subject contributes from his or her cash account represents $1 passed to charity, but with $.50 of this contribution refunded back to his or her cash account by the experimenter. Here, the instructions tell each subject that passing $6 of the MPC to charity is the same as donating $6 from his or her cash account to the charity, and then getting a $3 refund. The charity receives $6, and the subject receives $5 (again, the subject keeps $16-$6 = $10 of their MPC, which is converted to cash $10(1-.5)=$5).
Notice in the rebate condition that the MPC exceeds the amount in a subject's cash account. Subjects may pass more than the amount in their cash account by passing portions of their refunds. To motivate this, the instructions present the example of passing $12 of the MPC to charity as equivalent to first passing the entire $8 in their cash account and then passing all of their $4 refund. Thus, the charity receives $12, while the subject takes home $2. Further iterations of contributions from rebates result in still higher maximum possible contributions.7

2.2  Experimental procedures

Decisions in the MPC treatment were collected in two separate sessions, one with 34 subjects and another with 27 subjects.8 I compare results to the decisions of 43 students in a control treatment previously reported by Davis, Millner and Reilly (2005) that used the decision format shown in Table 1. In all sessions subjects were undergraduate students enrolled in business and economics classes at a large university in the United States. Other than reframing the allocation questions, procedures and the sequence of decisions in the control and MPC treatments are essentially identical. In turn, except for some minor details, procedures closely follow those reported by Eckel and Grossman (2003).9
Procedures for this type of experiment are by now standard. For a more complete description, see Davis, Millner and Reilly (2005) or Eckel and Grossman (2003). In brief, subjects made a series of ten randomly ordered allocative decisions under complete combinations of two endowment conditions ($8 and $12) and five subsidy conditions (no subsidy, a 50% match, a 100% match, a 33% rebate and a 50% rebate).10 Subjects also completed a short survey of socioeconomic characteristics and a questionnaire regarding procedures. After all subjects completed their decisions, one randomly selected problem was implemented. For that problem, the experimenter converted to cash the amount held by each subject, and paid him or her. The experimenter also totaled the amounts passed to the charity, and wrote a check to the charity ("Feed the Children" ). Once all subjects were paid, the experimenter, along with a monitor and any interested subjects went to a mailbox and mailed the check.

3  Results

Responses of the 61 subjects to the procedural questionnaire in the MPC treatment parallel responses regarding procedures in the control treatment.11 The greatest difference across treatments is that the mean response to a question regarding the clarity of instructions question (3.63 out of 5) was slightly lower that that reported for the control treatment (3.81), reflecting perhaps the increased complexity of the presented problem. Importantly, however, the decisions of a small subset of subjects drive the lower mean response to the instructional clarity question in the MPC treatment. Eliminating the decisions of these subjects does not affect outcomes.12
Figure 1 provides an overview of results.13 The upper panel of the figure summarizes decisions for the control treatment. Mean charity receipts, shown as white bars, increase as the price of contributions falls under a matching subsidy, but not under a rebate subsidy. However, mean pass rates, shown as solid bars, remain essentially constant in all conditions, indicating that the matching subsidy rather than pass amounts drive the increased receipts.
Figure 1: Mean charity receipts and pass rates.


Results of the MPC treatment, shown in the bottom panel of Figure 1 suggest that switching the directly presented problem dimension from an endowment to the maximum amount a charity may receive eliminates any effect of matching subsidies on charity receipts. When people divide charity receipts (the hollow bars), contributions move directly with the effective price of contributions, regardless of whether a rebate subsidy or a matching subsidy induced the price reduction. Notice again that the pass rates in the MPC treatment remain roughly constant at all endowment levels and effective prices of contributions.
The charity receipt and pass rate data presented in Tables 3 and 4 allow a quantitative evaluation of the results suggested by Figure 1. Consider first charity receipts expressed as a percentage of endowments, shown in Table 3. In the table, the entries in column (3) list charity receipts in the no subsidy condition, while entries in columns (4) and (5) list charity receipts for comparable matching and rebate subsidy conditions. For example, as indicated by the entry in column (3) of row (a), given a $12 endowment mean charity receipts in the no subsidy condition of the control treatment equaled 38% of participants' endowments. Similarly, the entries in columns (4) and (5) of row (a1) indicate that given an effective contributions price of $0.67, and again a $12 endowment, mean charity receipts in the control treatment were 53% of participants' endowments under the (50%) matching subsidy, and 39% of participants" endowments in the comparable (33%) rebate condition.
Table 3: Charity receipts as a percentage of endowment ( p .001, p .05, one tailed).

(1) (2) (3) (4) (5) (6) (7) (8)
Mean CR (s.d.) t (matched pairs tests)
(lr)4-6 (lr)7-9 Price of $1 No
Endowment contribution subsidy Match Rebate M v. NS R v. NS M v. R
(a) $12 $1.000.38
(b)   $8 $1.000.39
(a1) $12 $0.67 0.53 0.39 5.09 0.30 5.15
(0.30) (0.23)
(a2)   $8 $0.67 0.63 0.41 6.55 0.96 8.60
(0.31) (0.23)
(b1) $12 $0.50 0.82 0.44 6.72                                       2.03 7.97
(0.46) (0.23)
(b2)   $8 $0.50 0.91 0.42 6.21 1.18 7.35
(0.57) (0.19)
(c) $12 $1.000.49
(d)   $8 $1.000.49
(c1) $12 $0.67 0.77 0.79 5.74 7.72 -0.85
(0.46) (0.46)
(c2)   $8 $0.67 0.80 0.83 7.73 9.26 -0.67
(0.47) (0.45)
(d1) $12 $0.50 1.10 1.16 10.61   10.59   -1.28
(0.60) (0.57)
(d2)   $8 $0.50 1.14 1.13 10.80   9.82 -0.27
(0.56) (0.62)
Inspection of the entries in columns (3), (4) and (5) of the control treatment reveal that mean contributions increase with matching subsidies, but not with rebate subsidies, an outcome consistent with both isolation effects and a preference for matching subsidies in the control treatment. Matched-pairs t test statistics, in columns (6), (7) and (8) easily confirm the statistical significance of the higher charity receipts generated with matching subsidies. As column (6) indicates, matching subsidies generate significantly higher receipts than the no subsidy condition. Further, matching subsidies elicit higher charity receipts than do comparable rebate subsidies, as indicated by column (8). In contrast, rebate subsidies, elicit significantly higher receipts than the no subsidy condition in only one of the four comparisons shown in column (7).
Results of the MPC treatment, shown in the bottom panel of Table 3, cleanly separate out isolation effects and preferences for matching subsidies. As can be seen from columns (3), (4) and (5), in the MPC treatment participants no longer exhibit any preference for matching subsidies. Rather, charity receipts move with the reductions effective price of contributions in both matching and rebate subsidy conditions. Again, these differences are easily significant at conventional levels of significance. As indicated by the t test statistics in columns (6) and (7), charity receipts in both match and rebate conditions significantly exceed charity receipts in the no subsidy condition. Further, as seen in column (8) the difference in charity receipts across subsidy types never approach significance.
The pass rate data summarized in Table 4, formatted as in Table 3, highlights the general insensitivity of pass amounts to subsidy type. Notice, in particular the t test statistics in column (8). Using conventionally accepted levels of significance, mean pass rates under a matching subsidy never exceed mean pass rates under a comparable rebate subsidy either in the control treatment or in the MPC treatment. Combined, the above results support the following finding.
Table 4: Pass amounts as a percentage of presented total ( p .05, one tailed).

(1) (2) (3) (4) (5) (6) (7) (8)
Mean CR (s.d.) t (matched pairs tests)
(lr)4-6 (lr)7-9 Price of $1 No
Endowment contribution subsidy Match Rebate M v. NS R v. NS M v. R
(a) $12 $1.000.38
(b)   $8 $1.000.39
(a1) $12 $0.67 0.35 0.39 -1.67       0.29 -1.99      
(0.20) (0.23)
(a2)   $8 $0.67 0.46 0.42   1.91 0.96 0.28
(0.29) (0.19)
(b1) $12 $0.50 0.41 0.44 0.73   2.03 -0.87      
(0.23) (0.23)
(b2)   $8 $0.50 0.42 0.41 1.50 1.18 0.86
(0.20) (0.23)
(c) $12 $1.00 0.49
(d)   $8 $1.00 0.49
(c1) $12 $0.67 0.50 0.53 0.31 1.14 -1.08
(0.30) (0.31)
(c2)   $8 $0.67 0.53 0.56 1.31   2.51 -0.83
(0.32) (0.30)
(d1) $12 $0.50 0.55 0.58 1.49   2.19 -1.48
(0.30) (0.29)
(d2)   $8 $0.50 0.56 0.56   1.86   1.93 -0.03
(0.29) (0.31)
Finding: In these environments isolation effects rather than a preference for matching subsidies drive the higher charity receipts generated under matching subsidies than under comparable rebate subsidies.
Prior to concluding this section, consider in more detail the effects of subsidies on mean pass rates. In stark contrast to the impressively large swings in charity receipts induced by subsidies shown in Table 3 -charity receipts increase by as much as 50 or 60 percentage points in some instances - subsidies affect pass rates relatively little. This is particularly true in the control treatment, where mean pass rates in any rebate or matching subsidy condition never exceed mean pass rates in the no subsidy condition by more than 7 percentage points. As seen in the upper panel of Table 4, using p .05, subjects passed significantly more in a subsidy condition than in a no subsidy condition only twice. Indeed, aggregating across all eight endowment/subsidy type/effective price combinations, participants passed only 2.75 percentage points more on average in the subsidy conditions than in the comparable baseline condition.14 I summarize the insensitivity of pass rates to changes in the effective price of contributions in the control treatment as the following comment.
Comment: In these environments, particularly in those like the control treatment, pass rates are very insensitive to changes in the effective price of contributions.

4  Discussion

The above results are interesting both for they imply and what they appear to imply about subsidizing charitable contributions. An apparent implication, suggested by the above comment, is that neither rebate nor matching subsidy schemes may increase charity receipts relative to a no subsidy condition. To see this, notice that net charity receipts are the sum of private contributions, and contributions by a subsidizing agency (in natural contexts, typically a big donor). If private contributors ignore the indirect consequences of rebates when making contributions decisions, then a rebate subsidy merely replaces private contributions with contributions from the subsidizing agency. The charity would enjoy a higher take by soliciting unsubsidized contributions from both the subsidizing agency and private contributors.
The consequences of matching subsidies are less clearly adverse, since expected net charity contributions with a matching subsidy equal those expected with unsubsidized (and unencumbered) contributions from both the subsidizing agency and private contributors. However, even in this case, risk aversion on the part of either the charity or the subsidizing agency would make an unsubsidized contributions scheme preferable.15 The almost complete insensitivity of subjects to rebate or subsidy formats in a number of laboratory experiments (e.g., Davis, Millner and Reilly, 2005, Eckel and Grossman, 2003, 2006) and in a field experiment (Eckel and Grossman 2005b), led me and my coauthors to stress that, to the extent these experiments had any practical external validity (a big if), results suggest that any subsidization of private charitable contributions is ineffective (Davis, Millner and Reilly, 2005).
However, results of other experiments, conducted both in the laboratory (Eckel and Grossman, 2005a), and in the field (Eckel and Grossman 2005d, Karlan and List, 2006 and Meier, 2005) indicate that environments do exist where people do respond at least partially to subsidy-induced reductions in contributions prices. These latter experiments are distinguishable from those mentioned in the preceding paragraph in that the scope of the problem was reduced, and in that the instructions emphasized the indirect consequences of contributions.16 Thus, the insensitivity of subjects to formatting effects in experiments like the control treatment suggests a methodological implication rather than a policy one: given sufficient task length or complexity, isolation effects may be anticipated almost trivially. We may expect to learn relatively little from such exercises, because the observed results are fully anticipatable, and because these effects may be more pronounced than would be observed in pertinent natural contexts. The more interesting insights in this line of research may be gained from examining the resilience of isolation effects in simple environments with close parallels to natural contexts, where the consequences of decisions are clearly emphasized.
In closing, we observe some interesting policy-relevant insights consistent with isolation effects that have emerged from recent field experiments by Karlan and List (2006) and Meier (2005). These field experiments involve matching (but not rebate) subsidies. Karlan and List (2006) report a large scale natural field experiment involving "a capital campaign for a liberal politically-oriented non-profit that focuses on social issues and civil liberties" (p. 3). Solicitations were conducted by mail, and in addition to a control (no-subsidy) condition, matching subsidies at varying rates (a $1 for $1 match, a $2 for $1 match and a $3 for $1 match). Karlan and List find that the announcement of a matching subsidy significantly increases both the likelihood of contributing (by 22%), and the amount given (by 19%). However, increasing the subsidy amount above the 1:1 match does not further affect contributions.17 While more research is needed, this result suggests that employers and charitable organizations may do well to reduce the depth and expand the width of their subsidy campaigns. That is, rather than matching private contributions at a 2 to 1 rate up to say a $1000 limit, a fundraising organization may more effectively increase contributions by matching contributions at a 1 to 1 rate up to a $2000 limit.18
Meier (2005) studies student contributions to a pair of social scholarship funds at a University in Zurich. At the outset of each semester, students are given the opportunity to check a box indicating that they would like to make a fixed contribution to one or both of two funds. In one semester, contributions were subsidized with a matching contribution for a randomly drawn subset of students. Unlike previous studies, Meier was also able to track contributions behavior in several semesters both prior and subsequent to the treatment. Meier reports that the matching subsidy significantly increased the incidence of contributions. However, once the subsidy was withdrawn, the group of subsidized contributors reduced their contributions rate below their pre-subsidy level. Results again are consistent with an isolation effect. Here contributors focused on the direct consequences of making a contribution. The inclusion of the subsidy made contributions a "better deal" and induced more people to check the contributions boxes. Once the matching subsidy is withdrawn, contributing is no longer such a good deal, and contributions fall. However, since individuals tend not to calculate precisely the effective price changes induced by the subsidy, it is not surprising that they contribute even proportionally less to the fund. The lesson here is that we should approach subsidy manipulations with care. To the extent that people take a binary view of contributions decisions, temporary manipulations may result in lower giving in the long run.


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1I thank without implicating Jonathan Baron, Glenn Harrison, Oleg Korenok, Edward Millner, Laura Razzolini, Robert Reilly and two anonymouss referee for useful comments. The usual disclaimer applies. Financial support from the National Science Foundation and the Virginia Commonwealth University Faculty Excellence Fund is gratefully acknowledged. The data, instructions and an appendix are available at http://www.people.vcu.edu/ dddavis. Author's address: Department of Economics, Virginia Commonwealth University, Richmond VA 23284-4000 USA, dddavis@vcu.edu.
2Noting the insensitivity of subjects to the different subsidy and rebate formats, I and my coauthors have argued that decisions are consistent with confusion or inattention (Davis, Millner & Reilly, 2005). However, the literature in cognitive psychology on isolation effects, discussed below, makes confusion an unlikely explanation.
3In contrast, decision errors attributable mental accounting occur when people fail to aggregate the consequences of a series of decisions. The notion of mental accounting is that people maintain separate mental ledgers for certain purchase or contribution decisions. Decisions that are anomalous (from a global perspective) can arise if people fail to aggregate the consequences of a series of separate decisions. Isolation effects are also distinguishable from the well documented tendency for individuals to value inordinately that which they think they own. Such "endowment effects" can cause a reluctance to trade (e.g., Kahneman et al. 1986). Here, however, the problem is not a reluctance to "pass" or make contributions, but rather an inattention to the differing consequences that subsidies make for such contributions.
4McCaffery and Baron (2003, 2006) also report similar results when they asked people to chose between alternative government fiscal policies. Subjects, for example, prefer an employer-paid payroll tax to an equivalent income tax, because an income tax more directly reduces their incomes.
5This is the position Eckel and Grossman advocate. For example Eckel and Grossman (2006) conclude "The findings reported in this paper, as well as those in [the other related papers] have implications for the government, non profit and for profit sectors of the economy. For government and the non profit sectors, the results suggest that replacing the current system of tax rebates with an equivalent matching subsidy system would increase contributions to charitable organizations."
6McCaffery and Baron (2006) make a closely related observation when discussing implications of isolation effects for fiscal policy.
7 Allowing subjects to pass iteratively out of their rebates represents a necessary asymmetry between the MPC and control treatments. Had I reduced the MPC in the rebate condition to the cash account then the tendency for subjects to divide a constant amount of a presented amount would again result in increased contributions under matching subsidies, as is possible in the control treatment. On the other hand, if I increased the cash account in the rebate condition to the MPC, then the design would confuse higher contributions elicited in the rebate condition of the MPC treatment with a larger endowment.
8Procedures in the two MPC sessions differed slightly in that instructions for the second session explained in somewhat greater detail the relationship between the cash account and the MPC (the extra text is italicized in the instructions). Allocative decisions in the two sessions were virtually identical and for that reason I pool them here.
9The control and MPC treatments differ from Eckel and Grossman primarily in the respects that (a) the set of rebate and subsidy conditions presented to subjects differed slightly and (b) contributions were directed to a single charity, rather than allowing subjects to choose from a menu of charitable alternatives.
10In the MPC treatment, the MPC varies from $8 to $24 and is determined by dividing the endowment by the effective price of contributing $1 to charity.
11As in the previous studies, subjects generally agreed that procedures preserved their anonymity (4.02 on a 5 point Likert scale), that the charity was deserving of their support (4.67) and that contributions would actually be sent to the charity (4.58)
12For example, deleting from the sample the four individuals who responded to the question on procedural clarity with a 1 (on a 5 point scale) raises the mean response to 3.83. However, deleting the decisions of these subjects does not affect any of the results reported below. Details of this comparison are available in an unpublished data appendix.
13Notice in figure 1 than decisions are pooled across endowment levels. I make this aggregation for purposes of presentational clarity. I disaggregate decisions for the quantitative analysis reported below in Tables 3 and 4.
14As inspection of the bottom panel of Table 4 suggests, subsidy-induced reductions in the effective price of contributions increase pass rates at least marginally more in the MPC treatment. In four of the eight subsidy type/endowment/effective price treatment cells in the MPC treatment pass rates in the subsidy condition significantly exceeded pass rates in the no subsidy condition. Further, averaging mean increases over the eight treatments cells, in the subsidy conditions were 5.6 percentage points higher than in the no subsidy condition. I focus on the control treatment in the text, as the decisions in this context more closely parallel natural circumstances.
15With a matching subsidy, the charity stands exposed to the possibility that private contributions do not meet expectations, resulting in a smaller than intended contribution from the subsidizing agency. Similarly, under a matching subsidy, the subsidizing agency stands exposed to the possibility that private contributions may force the agency to contribute more to the charity than it had intended to give.
16In Eckel and Grossman (2005a) rebate and matching decisions were divided, so subjects faced either a series of allocations involving matching subsidies, or a series allocations involving of rebate subsidies. Participants in each of the field studies (Eckel and Grossman (2005c), Karlan and List (2006) and Meier (2005) made only a single decision, and a flier announcing the subsidy stressed the indirect consequences of the decisions. These three field experiments differ from an initial field experiment by Eckel and Grossman (2005b), where the indirect consequences of contributions were not heavily stressed (and where contributors clearly focused only on the direct consequences of their donations).
17As Karlan and List observe, this result is similar to the scaling effect reported by Kahneman and Knetsch (1992). Scaling effects may critically undermine willingness to pay elicitations in contingent valuation studies. People, for example, report the same willingness to pay to clean up Lake Ontario as to clean up the entire Great Lakes.
18Interestingly, this result may also suggest that reductions in the top marginal tax rates may not affect charitable contributions elicited with tax rebates. Again, additional research would be needed to confirm this hypothesis.

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