Taxation with Mobile High-Income Agents: Experimental Evidence on Tax Compliance and Equity Perceptions

Abstract

In a laboratory experiment on tax compliance, we model a situation in which high-income taxpayers can leave a tax system that finances a public good. We compare low-income taxpayers’ compliance decisions and equity perceptions across treatments in which they are informed or not informed about the mobility option of high-income taxpayers. This allows us to test if low-income taxpayers regard the mobility option as a rationale for implementing a regressive tax schedule. To investigate if a potential ‘justification effect’ of the mobility option depends on the causes of income heterogeneity, we also varied whether income was allocated based on relative performance in a prior ability task or at random. Interestingly, although the performance-based allocation itself was judged to be fairer, we observed higher compliance under the random allocation mechanism. However, compliance and equity perceptions did not significantly differ by the information treatment variation, regardless of the source of income inequality. The results indicate that the threat of losing high-income taxpayers’ contributions does not lead low-income taxpayers to view the regressive tax schedule more favorably. This suggests that taking the differential mobility options as given and altering tax schedules accordingly may not be perceived as an adequate policy response.

1. Introduction

In a world in which high-income taxpayers are more responsive to taxation than low-income taxpayers, governments are compelled to lower taxes on high-income taxpayers compared to what would otherwise be seen as a socially desirable tax schedule. One response margin that may underlie ‘higher responsiveness’ is actual relocation of the taxpayer to a different jurisdiction. While mobility for labor is typically not as high as for capital, there is evidence that individual mobility increases with skill [1] and is sensitive to tax rates [2], especially for top professionals [3,4]. Countries may then perceive competitive pressures to attract or retain mobile high-income individuals and effectively be compelled to lower taxes on them [5,6]. Denmark, for example, offers new immigrants with high income a preferential tax rate of nearly half the rate for domestic workers, a scheme which [7] found to be very effective at attracting highly paid workers. According to an OECD report from 2011, 15 other OECD countries had introduced tax concessions for high-skilled workers. Although ‘obvious’ tax concessions are often confined to foreigners, similar competitive pressures exist for domestic high-income taxpayers. As [8] write in their survey article on international tax competition, ‘the reduction in top marginal rates of personal taxation (…) [is] reflecting the mobility of high earners and (…) tax avoidance opportunities (…)’.

At the same time, a widely held normative belief is that those who can afford to carry a higher share of the tax burden should do so.1 Such equity principles may be in conflict with the logic of lowering taxes on mobile high-income taxpayers. The OECD report, for instance, states that ‘tax concessions will create equity concerns by treating differently high-skilled and less-skilled workers’ ([9], p. 124).2 Equity perceptions, in turn, are believed to influence tax compliance [10,11], raising the possibility that compliance is adversely affected by a preferential tax treatment of high-income taxpayers. In what follows, we generically refer to the possibility of legally avoiding taxation (e.g., by relocating abroad) as ‘outside option’.3 Because reliable information on tax compliance and equity perceptions is difficult to obtain simultaneously with exogenous variation in outside options, we conducted a laboratory experiment.

In this experiment, we focus on a closely related situation. In our set-up, high-income taxpayers are offered a preferential tax rate so that they do not leave the ‘domestic’ tax system. We investigate if low-income taxpayers’ equity perceptions and compliance behavior are susceptible to the logic of offering high-income taxpayers preferential tax treatment because of their outside options. We are particularly interested in this situation because it may create a conflict of interest among low income-taxpayers who are better off if the high-income taxpayers do not opt out but may resent the preferential tax rate. Thus, we compare the tax compliance and tax equity perceptions of experimental participants with low income and high tax rates across conditions in which they do or do not know about an outside option for participants with high income and a low tax rate.4 Because we suspected that a potential ‘justification effect’ of an outside option might depend on the perceived equity of the initial income inequality, we conducted this treatment comparison under two different allocation conditions: one in which high and low incomes were allocated at random and one in which they were allocated according to relative performance in a prior cognitive ability task, with the latter allocation arguably carrying some connotation of ‘desert’ or ‘merit’.

Our main result is that regardless of the source of income inequality, compliance and perceptions do not react favorably to the exogenously provided reason for preferential tax treatment of high-income taxpayers. In terms of policy, this suggests that governments would find it difficult to increase (but also would not harm) tax compliance by communicating the existence of outside options as rationale for taxing high-income taxpayers at lower rates. It may also be taken to suggest that taking differential outside options as given and altering tax schedules accordingly is not perceived as an adequate policy response. Our second finding shows that random allocation of advantages led to higher tax contributions than the performance-based allocation mechanism. A possible interpretation is that being in the position of a low-income taxpayer through worse cognitive performance is particularly unpleasant and thereby not conducive to cooperative behavior.

The remainder of this chapter is organized as follows. In the next section, we review the literature that the present study relates to. Section 3 explains the experimental design. Section 4 briefly states predictions and hypotheses. The results are presented and discussed in Section 5. The final section concludes.

2. Related Literature

Our study thematically relates to the experimental literature on tax compliance and in particular the nexus between tax compliance and equity perceptions. As we construe taxation and compliance as a cooperative endeavor, it also connects with certain experimental studies of general aspects of other-regarding behavior and cooperation, i.e., studies that are not specifically motivated and framed in the context of taxation. We begin by giving a brief overview of the experimental literature on tax compliance and point out connections to other experimental studies at the end of this section.

The experimental literature on tax compliance owes its existence and breadth largely to the fact that with observational data, tax compliance is difficult to measure and exogenous variation in independent variables of interest can be hard to find (see [14], for an overview of methods to measure tax non-compliance). In contrast, laboratory experiments offer a way to easily measure compliance and induce exogenous variation by design, although at the cost of raising concerns with regards to the external validity of the results.5 Some, in particular earlier studies, have directly implemented simple experimental analogues of Allingham and Sandmo’s [16] influential [1972] model of tax compliance as an individual decision under risk. While some of its main comparative static results—higher audit probabilities and fines increase compliance—have by and large been confirmed (see e.g., [17,18]), several authors have argued that observed levels of compliance are too high to be explained only by aversion to the risk of being fined (e.g., [19,20,21]).6 Partially in response to the debate about the merits and demerits of the Allingham-Sandmo model, partially as independent efforts to understand the determinants of tax compliance, experimental designs have tended to become more involved, introducing inter alia public good elements (e.g., [17,19,23,24]), heterogeneous and earned income [23,25,26], richer tax schedules [26,27,28] or endogenous audit rules [29,30]. Other studies haven taken up psycho-social factors like the role of persuasion [31], moral constraints [32,33] and emotions [33,34], and still others investigated design factors such as the role of framing (e.g., [19,25,35]) or income source [25,36].7 Importantly for the current investigation, several studies found that equity concerns affect the compliance decision [10,11,37]. Interpreting taxation as a cooperative endeavor and non-compliance as free-riding, such influence of equity concerns is reminiscent of ‘conditionally cooperative’ behavior, as it has been observed in public good experiments [38]. We are, however, not aware of a study that addresses the potential equity-mediated interaction between outside options, tax schedules and tax compliance. Our study specifically tests whether an outside option is accepted as a rationale for tax concessions by comparing equity perceptions and compliance behavior across treatments in which participants do and do not know about the existence of this outside option.8 In other words, within the experimental literature on tax compliance, our study appears to be the first to investigate if constraints to more equitable taxation—through their potential effects on equity perceptions—affect compliance behavior. Prima facie evidence for the possibility of such a ‘justification effect’ of constraints that might induce a change in cooperative behavior through a change in perceptions comes from ultimatum game experiments: [39] and [40] report that outside options affected the distribution of offers and rejections by changing the fairness perception of a given offer. Ref. [40], for instance, finds that when responders had an outside option, offers were higher and given offers were also rejected more often. While the tax game of the present study is different from an ultimatum game, the underlying idea in common is that outside options influence how players perceive and evaluate a given situation and that this evaluation could ultimately affect behavior. The next section describes how we implemented this idea in the context of the tax compliance experiment.

3. Experimental Design

We study the compliance decisions and tax equity perceptions of taxpayers in a laboratory environment with heterogeneous income, differential outside options and a regressive tax schedule. The main dependent variable of interest was compliance behavior of low-income taxpayers in a one-shot multi-player tax game, which we will describe in detail below. One treatment variation lay in the knowledge low-income taxpayers had about the existence of an outside option for high-income taxpayers. The idea behind this treatment variation was to test if knowledge about the outside option leads low-income taxpayers to view a reduced tax rate for high-income taxpayers less negatively and if such ‘justification by constraints’ (i.e., the outside option threat) materializes in higher compliance behavior by low-income taxpayers. Because we suspected that such an effect might depend on the causes of income heterogeneity, we also varied whether roles were allocated based on relative performance or at random. In the first six experimental sessions, a prior cognitive performance contest motivated the allocation of different roles and in particular incomes: high-income taxpayer positions were given to those participants with the highest relative performance in the earnings stage. In the six remaining experimental sessions, role allocation was random (but the earnings stage was retained for comparability).9

Table 1. Treatment overview (2 × 2 design).

Performance-based allocation (PBA), without information	Performance-based allocation (PBA), with information
Random allocation (RA), without information	Random allocation (RA), with information

displays the four treatment conditions that result from the between-subjects combination of outside option information and role allocation mechanism treatments. Figure 1 provides a visual overview of the main stages and features of the experimental design.

We proceed now in chronological manner, explaining first the earnings stage, then an intermediate stage in which the outside option information treatment variation occurred, and then the tax game. All elements except the intermediate stage containing the outside option were explained in the instructions that were read aloud before the experiment started.10 These instructions were using tax language, but were otherwise framed as neutrally as possible.11 The experiment concluded with a questionnaire on tax equity perceptions and risk preferences.

Stage 1: Earnings stage.

Participants had 15 min to answer nine multiple choice questions taken from the Graduate Management Admission Test (GMAT).12 In the performance-based role allocation condition, relative performance on these GMAT questions determined role allocation, with the best-performing participants being granted ‘role A’ (high income) and the remainder being allocated to ‘role B’ (low income).13 In the randomized role allocation condition, role allocation was random and hence independent of GMAT performance. Participants in role A earned 500 experimental points as their initial income in the tax game. Participants in role B earned 100 points. Each participant was privately informed about his or her resulting role on the computer screen immediately after stage 1.

Stage 2: Outside option decision by high-income taxpayers.

After stage 1, participants in role A were given the opportunity to opt out of the succeeding tax game. More precisely, they could either participate in the tax game or take a fixed fraction (95%, i.e., 475 points) of their earned income as final earnings instead. The fraction was chosen such that given the tax rates and compliance rules in the following tax game, it would always be weakly profitable for them not to opt out.14 This ensured that an interpretation that the tax rate was low enough to prevent the flight of high-income taxpayers was independent of beliefs.15 If a participant in role A decided to participate, she would form a group of four players with three participants in role B in the following tax game. If a role A participant opted out instead, the three participants in role B would form a group of three players in the tax game.

The information treatment difference lay in the information that low-income taxpayers were given about the outside option. In treatments with no information, low-income participants were unaware about the existence of the outside option. They had only been instructed that they could be in a group of three low-income taxpayers or a group of three low-income and one high-income taxpayer in the subsequent tax game.16 In treatments with information, low-income taxpayers were informed about the outside option of high-income taxpayers and that the composition of their group depended on the high-income taxpayer’s decision.17

During this stage, all taxpayers had to calculate the minimum and maximum earnings for high-income taxpayers in the tax game explained next. In addition, low-income taxpayers had to calculate the minimum and maximum earnings for high-income taxpayers under a counterfactual tax rate of 50% for both high and low-income taxpayers. While for all participants these questions may have appeared like standard control questions, their purpose was to make it explicit to informed low-income participants that the outside option for high-income taxpayers was not profitable under the given tax rates, but would be under a counterfactual tax schedule with a higher rate on high income. To gain information on whether participants had understood this connection between the tax rate for high-income taxpayers and the outside option, we also asked informed low-income taxpayers about their belief as to whether the high-income taxpayer in their group would opt out, and if they themselves would opt out if they were in the situation of a high-income taxpayer under the given and under the counterfactual tax rate regime.18

Stage 3: Tax game.

In stage 3, the actual tax game interaction, participants’ income from stage 1 was subject to tax. High-income (‘role A’) taxpayers were taxed at rate ${\tau }^H=0.1$ and low-income (‘role B’) taxpayers at rate ${\tau }^L=0.5$. Taxes paid amounted to a public good: collected taxes were multiplied by 2 and shared equally among the members of a group. While group members had the possibility to contribute less than their due amount—namely any integer between 0 and their tax liability of 50 points—paying less entailed the risk of being audited and fined. More precisely, high-income participants were audited with certainty while for low-income participants, the audit probability was 5%. For high-income participants, non-compliance within the tax game was hence not a viable option.19 If audited and found to have contributed less than the due amount, participants had to pay their full tax liability and additionally a fine in the amount of their tax contribution gap.20

As explained above, participants could either be in a group of one high-income and three low-income participants or in a group of three low-income participants only. With $V_i\in \{0,1,2,\dots ,50\}$ denoting pre-audit contributions, ${𝟙}_i$ an indicator function for the occurrence of an audit, post-audit contributions $C_i=(1-{𝟙}_i)·V_i+{𝟙}_i·50$ and $n\in \{3,4\}$ group size, the following payoff functions summarize the tax game:

$$\begin{array}{cc}\hfill {\pi }_i^H& =\left\{\begin{array}{cc}500-C_i+{\displaystyle \frac{2}{4}}·{\sum }_{j=1}^4{C}_j-{𝟙}_i·(50-V_i)\hfill & \mathrm{if}\mathrm{outside}\mathrm{option}\mathrm{not}\mathrm{taken}\hfill \\ 475\hfill & \mathrm{if}\mathrm{outside}\mathrm{option}\mathrm{taken}\hfill \end{array}\right.\hfill \\ \hfill {\pi }_i^L& =100-C_i+{\displaystyle \frac{2}{n}}·\sum _{j=1}^n{C}_j-{𝟙}_i·(50-V_i)\hfill \end{array}$$

Further details. After the instructions were read out aloud, participants had to answer control questions about payoffs and the rules of the game. Stage 1 began when all participants had answered these correctly. We also asked participants for their beliefs about others’ compliance decisions.21

The experiment was computerized using z-Tree [42] and conducted at the Laboratory for Experimental Research at the University of Erlangen-Nuremberg. Participants were recruited from the laboratory’s student participant pool using ORSEE [43]. In total, 348 students participated in 12 sessions.22 Participants were paid a show-up fee of 4 Euro, plus the points from the experiment, converted at a rate of 25 experimental points = 1 Euro. On average, participants earned 12.75 Euro for a session of 65 min. Experimental sessions were run between May and November 2015.

Table 2. Number of observations and average earnings by session type and player type.

	All		Low-Income Player		High-Income Player
	N	Avg. Earnings	N	Avg. Earnings	N	Avg. Earnings
PBA, without information	93	€12.82	72	€9.43	21	€24.43
PBA, with information	93	€12.69	72	€9.29	21	€24.34
RA, without information	85	€12.64	66	€9.24	19	€24.47
RA, with information	77	€12.90	60	€9.57	17	€24.64
All sessions	348	€12.75	270	€9.38	78	€24.46

Notes: PBA = Performance-based allocation. RA = Random allocation. N refers to the number of observations. Earnings include a show-up fee of €4. The first column refers to session types (not actual information status with regards to the outside option, compare footnotes 16 and 17).

shows that while the average earnings for different session types were very similar, participants in role A (high-income taxpayers) earned substantially more than participants in role B (low-income taxpayers): across all sessions, the mean earnings were 24.46 Euro for high-income taxpayers and 9.38 Euro for low-income taxpayers respectively.

4. Predictions

It can easily be verified that low-income taxpayers maximize their expected payoff by contributing zero and high-income taxpayers by contributing in full.23 Furthermore, given the low enforcement threats for low-income taxpayers, risk aversion is an unlikely explanation for positive compliance levels.24 In other words: a standard expected utility model of behavior would predict zero tax contributions for low-income taxpayers. Conversely, observed positive tax compliance choices can be interpreted to reveal preferences over ‘something else’ than the financial stakes involved for the decision-maker herself—where ‘something else’ could be anything from social preferences along the lines of [44] to a perceived ‘duty-to-comply’ in taxation contexts [45] or with social norms more generally. Furthermore, it is worth noting that because the financial incentives are the same for informed and uninformed taxpayers, any model of utility based purely on financial outcomes (including outcome-based social preference models) predicts no treatment difference with regards to information. Alternatively, if compliance depends on equity perceptions and the low tax rate for high-income taxpayers is seen as more acceptable when ‘justified’ by the outside option, one would expect more contributions in the treatment conditions with information. Because we conjectured the performance-based allocation to be viewed as more fair than the random type allocation, we expected less of a ‘justification effect’ of information in the treatments with performance-based allocation compared to the effect in the random allocation conditions.25 We state these two predictions with regards to the role of information about the outside option as hypotheses:

Hypothesis 1 (Justification effect):

Compliance of low-income taxpayers in groups of four is higher when they are informed about the outside option of high-income taxpayers.

Hypothesis 2 (Justification effect interaction with allocation type):

The justification effect is smaller in treatments with performance-based allocation of taxpayer types (compared to treatments with random allocation).

5. Results

Before the analysis of compliance choices and equity perceptions, we first establish that participants understood the basic incentive structure of the experiment. We then analyze the effect of the information and the allocation treatment dimension on compliance choices. The lack of a positive effect of information about the outside option on compliance and the negative effect of performance-based allocation are then further interpreted in light of the stated equity perceptions and tax preferences.

5.1. Manipulation Checks

Over 90% of high-income taxpayers (72 out of 78) chose the weakly dominant strategy of not opting out and then contributing fully in the tax game interaction.26 More than 80% of informed low-income taxpayers (93 out of 114) stated the corresponding rational belief that high-income taxpayers would in fact not take their outside option. Moreover, over 70% of informed low-income taxpayers (81 out of 114) also stated they would not opt out themselves if they were in the position of a high-income taxpayers under the prevailing tax structure, but would do so under a counterfactual tax rate of 50% for high-income taxpayers. Hence most participants seemed to understand the basic incentive structure of the experiment; in particular the majority of informed participants understood that the outside option was not financially attractive for high-income taxpayers under the prevailing tax scheme, but would become attractive if the tax rate on high-income taxpayers were as high as the factual tax rate for low-income taxpayers. The subsequent results on compliance choices are qualitatively robust to excluding the participants who, based on their stated beliefs and intentions, appear to have been ‘confused’ about the incentive structure.27

5.2. Compliance Choices and Treatment Effects

We now proceed to analyzing compliance choices, focusing on the compliance choices of low-income taxpayers in groups of four.28 Figure 2 plots the corresponding distributions of compliance rates by treatment.29

We briefly take note that across all treatments, a majority of low-income taxpayers (62%) chose positive contribution levels, i.e., did not make an expected payoff-maximizing choice. This suggests that their compliance choices were not exclusively guided by financial considerations.30 This is also consistent with the fact that contributions strongly correlate with stated beliefs about others’ contributions (see Appendix A

Table A3. Information treatment regressions (OLS) with covariates.

DV: Compliance Rate	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)
		PBA	RA		PBA	RA		PBA	RA		PBA	RA
Informed	−4.10	−13.09 *	7.60	−8.93 *	−8.30	−9.75	−3.35	−9.14	6.43	−8.86 **	−11.09 *	−3.76
	(5.80)	(7.16)	(9.05)	(4.77)	(6.10)	(7.97)	(6.19)	(7.94)	(9.78)	(4.47)	(5.83)	(7.39)
Risk pref.	−6.13 ***	−7.15 ***	−6.07 ***							−4.89 ***	−4.85 ***	−5.68 ***
	(1.01)	(1.24)	(1.51)							(0.86)	(1.21)	(1.20)
Belief				1.52 ***	1.49 ***	1.51 ***				1.43 ***	1.34 ***	1.44 ***
				(0.11)	(0.15)	(0.19)				(0.12)	(0.16)	(0.19)
GMAT							−2.46	-1.74	−5.02 *	−0.24	0.85	−2.40
							(1.90)	(2.63)	(2.55)	(1.34)	(1.75)	(2.01)
Constant	79.85 ***	81.34 ***	84.26 ***	13.94 ***	12.24 **	17.45 **	64.96 ***	57.36 ***	84.44 ***	40.34 ***	34.02 **	59.07 ***
	(6.13)	(7.54)	(9.76)	(4.47)	(5.76)	(7.57)	(11.64)	(16.13)	(15.15)	(10.52)	(13.94)	(16.72)
N	216	126	90	216	126	90	216	126	90	216	126	90
$R^2$	0.13	0.19	0.13	0.39	0.42	0.32	0.0094	0.014	0.037	0.47	0.50	0.44

Robust standard errors in parentheses. * $p<0.10$, ** $p<0.05$, *** $p<0.01$.

,

Table A4. Information treatment regressions (OLS) with covariates—excluding ‘confused’.

DV: Compliance Rate	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)
		PBA	RA		PBA	RA		PBA	RA		PBA	RA
Informed	−0.11	−10.41	13.28	−7.99	−7.65	−8.48	0.38	−6.25	12.74	−7.41	−10.45	0.65
	(6.49)	(8.20)	(9.54)	(5.28)	(6.75)	(8.88)	(6.89)	(8.86)	(11.29)	(4.97)	(6.45)	(8.33)
Risk pref.	−5.91 ***	−6.93 ***	−6.04 ***							−4.73 ***	−4.86 ***	−5.52 ***
	(1.10)	(1.32)	(1.65)							(0.96)	(1.32)	(1.35)
Belief				1.53 ***	1.50 ***	1.53 ***				1.45 ***	1.36 ***	1.44 ***
				(0.12)	(0.16)	(0.21)				(0.13)	(0.17)	(0.21)
GMAT							−2.19	−0.94	−5.51 *	0.36	2.18	−2.60
							(2.10)	(3.06)	(2.92)	(1.58)	(2.22)	(2.22)
Constant	78.83 ***	80.27 ***	84.16 ***	13.53 ***	12.02 **	16.77 **	63.47 ***	52.87 ***	87.18 ***	35.58 ***	25.98	59.39 ***
	(6.42)	(7.83)	(10.19)	(4.67)	(6.02)	(7.90)	(12.75)	(18.50)	(16.97)	(11.73)	(16.19)	(18.39)
N	184	107	77	184	107	77	184	107	77	184	107	77
$R^2$	0.12	0.18	0.12	0.39	0.41	0.33	0.0057	0.0057	0.048	0.46	0.49	0.44

Robust standard errors in parentheses. * $p<0.10$, ** $p<0.05$, *** $p<0.01$. Estimations exclude participants classified as ‘confused’. These are the informed participants who indicated a belief that the high-income taxpayer will opt out, or a hypothetical intention to do so themselves (compare Footnote 27).

,

Table A13. Allocation treatment regressions (OLS) with covariates.

DV: Compliance Rate	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)
	Pooled	Inf.	Uninf.	Pooled	Inf.	Uninf.	Pooled	Inf.	Uninf.	Pooled	Inf.	Uninf.
PBA	−18.28 ***	-28.93 ***	−7.99	−5.12	−4.05	−5.67	−16.02 **	−22.71 **	−8.76	−8.94 *	−13.26 *	−5.57
	(5.77)	(7.62)	(8.54)	(5.15)	(7.76)	(7.08)	(6.17)	(8.78)	(8.81)	(4.81)	(6.85)	(6.88)
Risk pref.	−6.46 ***	−6.77 ***	−6.61 ***							−5.07 ***	−6.13 ***	−4.20 ***
	(0.97)	(1.34)	(1.39)							(0.87)	(1.08)	(1.38)
Belief				1.47 ***	1.52 ***	1.48 ***				1.36 ***	1.45 ***	1.33 ***
				(0.12)	(0.17)	(0.16)				(0.12)	(0.18)	(0.18)
GMAT							−3.11 *	−2.31	−4.54	−0.77	−1.59	0.14
							(1.82)	(2.41)	(2.78)	(1.32)	(1.71)	(2.09)
Constant	90.00 ***	95.58 ***	86.79 ***	13.64 ***	7.35	18.20 **	76.37 ***	74.03 ***	81.77 ***	46.82 ***	52.02 ***	40.54 **
	(6.34)	(7.96)	(9.37)	(5.18)	(7.55)	(7.04)	(11.40)	(16.05)	(16.39)	(11.10)	(14.25)	(16.91)
N	216	108	108	216	108	108	216	108	108	216	108	108
$R^2$	0.17	0.21	0.16	0.38	0.39	0.39	0.038	0.059	0.032	0.47	0.53	0.44

Robust standard errors in parentheses. * $p<0.10$, ** $p<0.05$, *** $p<0.01$. Inf. = Informed, Uninf. = Uninformed.

and

Table A14. Allocation treatment regressions (OLS) with covariates—excluding ‘confused’.

DV: Compliance Rate	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)
	Pooled	Inf.	Uninf.	Pooled	Inf.	Uninf.	Pooled	Inf.	Uninf.	Pooled	Inf.	Uninf.
PBA	−17.75 ***	−31.91 ***	−7.99	−5.49	−4.32	−5.67	−15.46 **	−23.73 **	−8.76	−9.09 *	−15.37 *	−5.57
	(6.32)	(8.94)	(8.54)	(5.55)	(9.40)	(7.08)	(6.75)	(11.01)	(8.81)	(5.25)	(8.40)	(6.88)
Risk pref.	−6.25 ***	−6.51 ***	−6.61 ***							−4.95 ***	−6.35 ***	−4.20 ***
	(1.05)	(1.54)	(1.39)							(0.97)	(1.32)	(1.38)
Belief				1.48 ***	1.57 ***	1.48 ***				1.38 ***	1.56 ***	1.33 ***
				(0.13)	(0.21)	(0.16)				(0.13)	(0.21)	(0.18)
GMAT							−2.85	−1.60	−4.54	−0.38	−1.22	0.14
							(2.01)	(3.14)	(2.78)	(1.56)	(2.50)	(2.09)
Constant	90.72 ***	100.03 ***	86.79 ***	14.75 **	6.88	18.20 **	76.44 ***	74.02 ***	81.77 ***	45.03 ***	51.27 **	40.54 **
	(7.01)	(8.85)	(9.37)	(5.69)	(9.55)	(7.04)	(12.89)	(22.30)	(16.39)	(12.84)	(19.83)	(16.91)
N	184	76	108	184	76	108	184	76	108	184	76	108
$R^2$	0.16	0.20	0.16	0.38	0.39	0.39	0.033	0.059	0.032	0.46	0.53	0.44

Robust standard errors in parentheses. * $p<0.10$, ** $p<0.05$, *** $p<0.01$. Inf. = Informed, Uninf. = Uninformed. Estimations exclude participants classified as ‘confused’. These are the informed participants who indicated a belief that the high-income taxpayer will opt out, or a hypothetical intention to do so themselves (compare Footnote 27).

), in line with the public goods structure of the tax game and prior evidence of ‘conditionally cooperative behavior’ in such situations [38]. We also note that compliance choices were concentrated at the boundaries of zero and full compliance.31 This bipolar distribution of compliance rates is consistent with prior experimental evidence and available field data on compliance rates for taxpayers with self-reported income [15].

The compliance choice distributions displayed in Figure 2 reveal that there is no indication at all that being informed about the outside option increased compliance levels.

Table 3. Information treatment regressions (OLS).

DV: Compliance Rate	(1)	(2)	(3)	(4)	(5)	(6)
	Pooled	PBA	RA	Pooled	PBA	RA
Informed	−3.76	−8.89	3.42	−0.55	−6.26	7.22
	(6.20)	(7.91)	(9.72)	(6.86)	(8.83)	(10.56)
Constant	51.20 ***	47.62 ***	56.22 ***	51.20 ***	47.62 ***	56.22 ***
	(4.37)	(5.53)	(7.09)	(4.38)	(5.54)	(7.11)
N	216	126	90	184	107	77
$R^2$	0.0017	0.010	0.0014	0.0000	0.0048	0.0060

Robust standard errors in parentheses. * $p<0.10$, ** $p<0.05$, *** $p<0.01$. Columns (1)–(3): All low-income taxpayers in groups of four. Columns (4)–(6): Excluding participants classified as ‘confused’ (compare Footnote 27). PBA = Performance-based allocation, RA = Random allocation.

shows the corresponding statistical results of OLS regressions of compliance choices on the treatment indicator for information.32 Whether collapsing the two allocation conditions or analyzing them separately: the coefficient on the information treatment indicator does not even come close to reaching a 10-percent significance level (and in case of the performance-based allocation, its sign is even negative).33 This pattern does not change if ‘confused’ participants are excluded from the analysis (see columns (4)–(6) in Table 3). The results are also qualitatively robust to adding stated risk preferences, beliefs about others’ contributions and GMAT performance as covariates to the regressions (see Table A3 and Table A4 in the Appendix A). Moreover, the coefficient on the information treatment indicator is also not significantly different between performance-based and random role allocation (see

Table A10. Treatment interaction regressions (OLS).

DV: Compliance Rate	(1)	(2)	(3)	(4)
	All		Excl. Confused.
PBA	−8.60	−8.72	−8.60	−8.72
	(8.99)	(8.84)	(9.01)	(8.85)
Informed	3.42	5.41	7.22	10.51
	(9.70)	(9.65)	(10.54)	(10.80)
PBA x Informed	−12.31	−14.78	−13.47	−16.76
	(12.52)	(12.52)	(13.76)	(14.02)
GMAT		−3.32 *		−3.29
		(1.83)		(2.10)
Constant	56.22 ***	74.89 ***	56.22 ***	74.71 ***
	(7.08)	(12.03)	(7.09)	(13.27)
N	216	216	184	184
$R^2$	0.032	0.045	0.029	0.041

Robust standard errors in parentheses. * $p<0.10$, ** $p<0.05$, *** $p<0.01$. Columns (1) and (2) estimate the treatment effects and their interaction on the full sample of low-income taxpayers in groups of four (without and with controlling for GMAT performance). Columns (3) and (4) exclude taxpayers classified as ‘confused’ (compare Footnote 27). The coefficient on the treatment interaction is never significant.

and

Table A11. Treatment interaction regressions (Tobit).

DV: Compliance Rate	(1)	(2)	(3)	(4)
	All		Excl. Confused
PBA	−40.32	−40.80	−41.33	−41.95
	(39.89)	(39.71)	(41.14)	(41.01)
Informed	21.28	29.13	41.33	57.31
	(43.19)	(43.23)	(49.39)	(50.28)
PBA x Informed	−65.00	−76.44	−78.47	−96.23
	(56.64)	(56.84)	(64.73)	(65.63)
GMAT		−16.20 *		−17.86 *
		(8.81)		(10.31)
Constant	84.77 ***	176.85 ***	85.69 ***	187.29 ***
	(30.99)	(59.88)	(31.98)	(68.08)
N	216	216	184	184

Standard errors in parentheses. * $p<0.10$, ** $p<0.05$, *** $p<0.01$. Columns (1) and (2) estimate the treatment effects and their interaction on the full sample of low-income taxpayers in groups of four (without and with controlling for GMAT performance). Columns (3) and (4) exclude taxpayers classified as ‘confused’ (compare Footnote 27). The coefficient on the treatment interaction is never significant.

in the Appendix A). If the true effect of being aware of the outside option is indeed negative and small as in the data, many more observations would be needed to ‘confirm’ this statistically (i.e., reach conventional statistical significance).34 Bayesian updating of the prior probability of Hypothesis 1 lead us to believe that this does likely not hold given the data observed. We essentially conclude that the true effect must be small and may even be negative.

Looking at participants’ post-experimentally stated equity perceptions (Figure 3), we note that awareness of the outside option did not affect these perceptions. In particular, whether knowledgeable about the outside option or not, low-income taxpayers rated the tax schedule as equally unfair and the lower tax rate for high-income taxpayers as not justified.35 Moreover, informed low-income taxpayers expressed a preference for non-regressive tax rates in spite of the outside option, for increasing the tax rate for high-income taxpayers, and limited agreement to a statement that the risk of the high-income taxpayers opting out ‘justifies’ the lower tax rate (see

Table A5. Informed low-income taxpayers’ judgements and stated tax preferences regarding the outside option (groups of four).

	RA (median/mean)	PBA (median/mean)
Would you favor a tax increase for participants in role A (even if this could make it more likely that they take the outside option)? (1 = Yes, 0 = No)	1 / 0.58	1 / 0.59
The low tax for participants in role A is justified because a higher tax rate would increase the likelihood of participants taking the outside option (1 = Do not agree at all, …, 7 = Completely agree)	4 / 3.6	5 / 4.5
If it were not for the outside option, tax rates on participants in role A should be at least as high as those for participants in role B (1 = Do not agree at all, …, 7 = Completely agree)	6 / 5.2	6 / 5.5
Despite potential outside options participants with higher income should not pay a lower tax rate than participants with low income (1 = Do not agree at all, …, 7 = Completely agree)	7 / 5.5	6 / 5.3

in the Appendix A).36 The hypotheses that the existence of an outside option might provide a compliance-enhancing ‘justification’ for the low tax rate on high-income taxpayers (Hypothesis 1) and that this effect would be larger in treatments with performance-based allocation (Hypothesis 2) are therefore not confirmed in the experimental set-up and data.

Result 1 (Irrelevance of outside option):

Being informed about the outside option of high-income taxpayers did not affect low-income taxpayers’ compliance choices nor their expressed equity perceptions.

The distributions displayed in Figure 2 do suggest, however, that compliance is higher when player types are allocated randomly rather than based on relative performance. In fact, this visual impression bears out in nonparametric and parametric statistical tests.

Table 4. Allocation treatment regressions (OLS).

DV: Compliance Rate	(1)	(2)	(3)	(4)	(5)	(6)
	Pooled		Informed		Uninformed
PBA	−14.76 **	−16.02 **	−20.91 **	−22.71 **	−8.60	−8.76
	(6.25)	(6.17)	(8.71)	(8.78)	(8.99)	(8.81)
GMAT		−3.11 *		−2.31		−4.54
		(1.82)		(2.41)		(2.78)
Constant	57.93 ***	76.37 ***	59.64 ***	74.03 ***	56.22 ***	81.77 ***
	(4.83)	(11.40)	(6.63)	(16.05)	(7.08)	(16.39)
N	216	216	108	108	108	108
$R^2$	0.026	0.038	0.051	0.059	0.0088	0.032

Robust standard errors in parentheses. * $p<0.10$, ** $p<0.05$, *** $p<0.01$. PBA = Performance-based allocation (omitted reference category: random allocation).

presents the results of OLS regressions of compliance rates on an indicator for performance-based player type allocation, with and without controlling for performance in the earnings stage itself. Compliance rates are significantly lower under the performance-based player type allocation.37 Restricting the analysis to participants who do not exhibit signs of confusion yields very similar results (see

Table A7. Allocation treatment regressions (OLS)—excluding ‘confused’.

DV: Compliance Rate	(1)	(2)	(3)	(4)	(5)	(6)
	All		Informed		Uninformed
PBA	−14.17 **	−15.46 **	−22.07 **	−23.73 **	−8.60	−8.76
	(6.79)	(6.75)	(10.43)	(11.01)	(8.99)	(8.81)
GMAT		−2.85		−1.60		−4.54
		(2.01)		(3.14)		(2.78)
Constant	59.22 ***	76.44 ***	63.44 ***	74.02 ***	56.22 ***	81.77 ***
	(5.25)	(12.89)	(7.82)	(22.30)	(7.08)	(16.39)
N	184	184	76	76	108	108
$R^2$	0.024	0.033	0.057	0.059	0.0088	0.032

Robust standard errors in parentheses. * $p<0.10$, ** $p<0.05$, *** $p<0.01$. Estimations exclude participants classified as ‘confused’. These are the informed participants who indicated a belief that the high-income taxpayer will opt out, or a hypothetical intention to do so themselves (compare Footnote 27).

). The overall difference appears to stem chiefly from informed taxpayers, but the coefficient on the performance-based allocation indicator is not significantly different between informed and uninformed taxpayers (see Table A10 and Table A11 in the Appendix A).

It should be noted that by construction, the composition of low-income taxpayers differs between random and performance-based allocation treatments in terms of their performance on the GMAT questions in the earnings stage. Because performance in the earnings stage itself is negatively correlated with compliance (see

Table A12. Association between Graduate Management Admission Test (GMAT) performance and compliance.

	Pooled	RA, Uninformed	RA, Informed	PBA, Uninformed	PBA, Informed
Spearman’s rho (p-value)	−0.10 (0.15)	−0.38 (0.01)	−0.00 (0.99)	0.04 (0.75)	−0.18 (0.15)
N	216	45	45	63	63

Only low-income taxpayers in groups of four are included. RA = random allocation, PBA = performance-based allocation.

) and performance-based allocation treatments have worse-performing low-income taxpayers than random allocation treatments by construction ($p<0.1$, Mann-Whitney U test), it is unsurprising that the allocation type effects become somewhat larger when GMAT scores from the earnings stage are added as a covariate to the regressions. The results are also qualitatively robust to the inclusion of further covariates such as stated risk preferences (Table A13 and Table A14). We therefore conclude that the random allocation of taxpayer types increased compliance compared to the performance-based mechanism.

Result 2 (Main effect of allocation type):

Compliance levels were higher in treatment conditions with random rather than performance-based allocation of taxpayer types.

This occurred despite the fact that participants (including low-income participant) judged the performance-based mechanism to be fairer than random allocation in the post-experimental questionnaire, consistent with the meritocratic element of performance-based allocation.38 If compliance behavior is positively influenced by fairness perceptions, this would raise the question why contributions were not lower in the random allocation. One plausible interpretation is that the competitive element of our performance-based allocation treatment reduced participants’ pro-social orientation.39 Such an explanation appears consistent with studies on giving behavior [53,54,55]. Ref. [53] found that providing information about relative ability decreased the amount of giving to unknown recipients.40 Ref. [54], in turn, documented that participants gave more to third-parties when their income was uniform and independent of prior absolute performance on GMAT questions, with the difference stemming from the ‘increased generosity of low performers’ under the ‘egalitarian’ vis-à-vis the ‘meritocratic’ treatment.41 While in the first study by Riyanto and Zhang the difference in pro-social behavior appears to be driven exclusively by social comparisons of ability, in the second study it apparently stemmed from the different allocation rules themselves. We also note that negative feedback about one’s relative performance on a cognitive ability task (rather than ‘pure’ spontaneous effort), in combination with the allocation of advantages based on this performance, may have been particularly unpleasant.42 Precisely because the performance-based allocation mechanism contains elements of ‘desert’, it may have created enhanced feelings of envy or inferiority among the lower performers.43 An alternative interpretation places the result in the context of ‘house money’ or entitlement effects: having earned the income in the performance-based allocation condition may also have contributed to decreased compliance (cf. Footnote 39). Although plausible, there is no full consesus in the literature on the effect of income sources on tax compliance decisions. As pointed out by [56], ‘research on the impact of effort on decisions under uncertainty allows for directly opposed predictions’. For a more recent review on earned income and increased vs. decreased compliance in laboratory environments see [25], who themselves do not find a significant impact of income source on compliance.

Either way, the performance-based allocation mechanism was not conducive to cooperative compliance behavior. Disentangling the precise cognitive and emotional mechanisms underlying the behavioral differences in performance-based versus random allocation treatments could be an interesting topic for future research.

6. Discussion and Conclusions

In the experimental tax compliance game, we did not find evidence that an outside option for high-income taxpayers provides a justification for low-income taxpayers to accept low tax rates for high-income taxpayers, neither on the level of stated equity perceptions and tax preferences, nor on the level of compliance behavior. The lack of judgmental and behavioral differences is particularly noteworthy given that the experiment had been designed so as to maximize the saliency of the relation between the outside option and the correspondingly large tax concession. While it could be that equity considerations did not affect participants’ compliance choices at all, precluding the hypothesized mechanism from equity perceptions to compliance behavior in the first place, this explanation for the lack of a compliance response is unlikely in face of the evidence that the player type allocation mechanism did influence perceptions and behavior. In fact, the lack of a compliance response to the information about the outside option seems more readily explainable by the observation that the participants’ equity perceptions seemed unaffected by the information about the outside option.

In light of the evidence that participants in fact understood that a higher tax rate for high-income taxpayers would render the outside option financially attractive, this leaves us with the question why information about the outside option did not affect equity perceptions and tax preferences. For one thing, one might note that upholding one’s viewpoint about what is desirable (e.g., as to what constitutes a fair tax schedule) even in the face of alleged or real constraints on feasibility, is a sensible normative position. One model of tax competition makes this explicit by considering equity norms as a constraint on tax competition and finding empirical support for the importance of such constraints [57]. On the other hand, anecdotal and prior experimental evidence (e.g., [40]) suggest that people do modulate their normative viewpoints and other-regarding behavior in accordance with what is feasible. Besides, it also appears questionable that normative viewpoints be completely disconnected from the constraints encountered in reality.

The question, then, appears to be at what costs differential constraints and freedoms can be brought to a level playing field. It is possible that the experimental participants questioned that the lower tax rate on high-income taxpayers is an adequate policy response to the latters’ outside option by asking themselves why an outside option existed in the first place. In terms of public policy, this leads us to a debate about what ‘outside options’ exist for different taxpayers, why, and to what extent and at what cost these could be modified. Pointing to their existence alone does not seem to make taxpayers accepting of preferential tax treatment. Future research could incorporate voting and deliberation mechanisms on the tax rate as a means of capturing policy preferences. Laboratory environments can also be used to assess the potentially important dynamic aspects and convergence properties of the behavioral, perceptional and policy outcomes. These aspects constitute interesting starting points for future research on how income-graded freedoms and constraints affect tax policy and behavior in an international environment, both positively and normatively.