The chicken or the egg: An experimental study of democracy survival, income, and inequality

Transcription

1 The chicken or the egg: An experimental study of democracy survival, income, and inequality Dmitry Ryvkin and Anastasia Semykina February 21, 2015 Preliminary draft: Please do not distribute Abstract Many empirical studies have found a positive association between economic development and democracy survival across countries; however, establishing a causal link between the two with naturally occurring data is problematic. We address this question in a laboratory experiment with democracy defined in a narrow sense as the ability of citizens to invest freely in profitable projects and vote on redistributive income taxation. The level of economic development is measured as the productivity of investment. In the alternative regime autocracy efficient investment levels and equitable redistribution are implemented exogenously, but there is a risk of resources being partially expropriated. Citizens can voluntarily switch from democracy to autocracy by a majority vote. Using a 2 2 between-subject design, we explore how the likelihood of such switches, referred to as democracy breakdown, varies with economic productivity and inequality in initial endowments. We find, consistent with theoretical predictions, that democracy breakdown increases with the degree of inequality. However, contrary to theoretical predictions, the likelihood of democracy breakdown does not vary with productivity. The results suggest that the causal link in the association of democracy survival and development is directed from democracy survival to development but not the other way around. Keywords: democracy breakdown, economic productivity, inequality, voting, experiment JEL classification codes: D72, P48, C92 Corresponding author: Department of Economics, Florida State University, Tallahassee, FL , USA; dryvkin@fsu.edu; tel.: Department of Economics, Florida State University, Tallahassee, FL , USA; asemykina@fsu.edu. 1

2 1 Introduction Since the year of 1980, 81 countries emerged as new democracies or experienced a transition from a non-democratic regime to democracy. Yet, during the same period 33 countries transitioned from democracy to nondemocracy at least once. 1 What causes such transitions? What factors contribute to the likelihood that once a country becomes a democracy, it will retain its democratic rule in the future? In this paper, we attempt to answer these questions using a laboratory experiment. Building upon the existing literature, our focus is on the role of economic advancement and income (re)distribution. A relationship between democratization and economic development has long been of interest to political scientists and economists. Numerous studies have documented a strong positive correlation between the level of democratization and per capita income (Acemoglu et al. 2008, Burkhart and Lewis-Beck 1994, Epstein et al. 2006, Londregan and Poole 1996, for example). However, thus far there has been no consensus on why this positive association exists, and whether a causal link in this relationship can be established. Until recently, the modernization hypothesis has been the leading theory for explaining the positive correlation between democratization and economic development, building upon a fundamental idea that economic progress and rising incomes induce an increased desire for democratic institutions (Lipset 1959). This theory prevailed largely uncontested until the work by Przeworski and his colleagues (Przeworski et al. 2000, Przeworski et al. 1996, Przeworski and Limongi 1997) who argued that democratization is positively associated with income due to a higher chance of democracy survival in wealthier countries. Indeed, several studies have found that democracy consolidation was more likely in highly developed countries and argued that higher incomes helped to alleviate social tension and social unrest, which in turn reduced the risk of democracy breakdown (Bernhard et al. 2001, Przeworski et al. 1996). 2 The idea that desire for redistribution is an important determinant of political transitions has found support in the literature. Deriving from historical experiences of particular regions or countries, several studies relate economic inequality to political instability and higher probability of institutional breakdown (Przeworski et al. 1996, Savoia et al. 2010, Thorbecke and Charumilind 2002). Moreover, it is argued that democratization helps to 1 Results were obtained using the Polity IV data for years ( org/inscrdata.html). A country is classified as a democracy if the polity score (polity2 variable) is 6 or higher. 2 Several studies find that democracy survival is less likely in poor countries that experience a negative shock to economic growth (Bernhard et al. 2001, Garsiorowski 1995, for example). Moreover, Bruckner and Ciccone (2011) find evidence suggesting that negative economic shocks make autocratic regimes less stable. 2

3 reduce economic inequality through voting and redistribution, which should make democratic regimes more stable (Acemoglu and Robinson 2001, Savoia et al. 2010). However, the latter argument is only partially supported by empirical evidence, especially in the case of developing countries (Muller 1995, Savoia et al. 2010). Because inequality often arises as an important issue in policy debates, learning more about the role of democratic institutions in limiting inequality would be useful. Empirical studies investigating the link between income, inequality, and political institutions have recently been criticized for their inability to adequately account for crosscountry differences in historical factors, political institutions, and the possibility of reverse causality (Acemoglu et al. 2008, Bollen and Jackman 1985, Gates et al. 2006, Goldstone et al. 2010, Persson and Tabellini 2009). Although several studies have attempted to address these issues, the results are at times contradictory, 3 suggesting that more research is needed. Given the difficulties in causal inference inherently present in observational data, a laboratory experiment employed in this paper serves as an alternative, and complementary, research methodology. It allows us to measure the effects of truly exogenous variation in economic productivity and inequality on democracy breakdown in a laboratory democracy. The laboratory democracy is implemented through voting on a redistributive tax rate on subjects investments. In every period, subjects decide how much of their endowment to invest into a project that yields a fixed return. The returns from projects are taxed at the rate determined by the median voter mechanism, and the taxes collected are redistributed back to subjects. 4 Democracy breakdown is implemented as a possibility for subjects to switch, by a majority vote, to an autocratic regime in which fully efficient investment and full redistribution are imposed exogenously, but there is a risk that resources are partially expropriated. Thus, democracy breakdown occurs through a democratic process; citizens vote to forfeit their rights to make investment decisions and vote for taxes. To explore the role of economic productivity and inequality, in different treatments we vary the return on investments and allocation of initial endowments. Our paper contributes to the growing experimental literature on endogenous institutions (see, e.g., a review by Dal Bó 2010). Most studies so far have explored the effects of voting for formal sanctions as a way to increase efficiency in social dilemma settings (e.g., Ertan et al. 2005, Putterman et al. 2011). Dal Bó et al. (2010) found that sanctions introduced through a democratic process are more effective than those same sanctions 3 For example, Londregan and Poole (1996) found that income had a significant positive effect on democratization even after country-specific fixed effects were included in the regression, while the fixedeffects estimation performed by Acemoglu et al. (2008) produced no significant effects. 4 A similar median tax voting mechanism has been used, e.g., by Esarey et al. (2012) and in the direct democracy treatment of Agranov and Palfrey (2014). Holcombe (1977) describes a referendum on property tax rates for public school funding in Florida that uses the same median tax voting rule. 3

4 imposed exogenously, due partly to selection and partly to the direct effect of democracy on the propensity to follow rules. There have been several recent experimental studies of voting-based redistribution in the presence of inequality generated exogenously as well as via investment of resources or a market mechanism. In the experiment of Esarey et al. (2012), subjects perform a real-effort task and are compensated at differential piece rates, either randomly assigned or earned. In the process, subject vote for a tax rate to be used to redistribute postproduction earnings. Esarey et al. (2012) find that tax votes are determined primarily by subjects relative income positions and are largely independent of their political affiliations and preferences. Grosser and Reuben (2013) let subjects trade in a double-auction market and then vote for one of two candidates proposing binding redistributive tax rates, with or without a possibility of transfers from voters to the candidates. The experiment is designed so that the median voter is poor, which leads to very high predicted, and observed, tax rates. Agranov and Palfrey (2014) investigate the effect of inequality on tax votes in a labor market-like environment where subjects characterized by different randomly assigned productivities (piece rates) choose a level of labor supply. The costs of labor are quadratic, which leads to interior optimal tax rates for subjects. In a 2 2 design, the authors vary the degree of inequality and the type of political institution (direct democracy, i.e., the median tax voting mechanism, or representative democracy with two candidates similar to Grosser and Reuben(2013)). The observed average tax rates are close to theoretical predictions, and increase in the degree of inequality. While the studies discussed above study various democratic redistribution mechanisms, our study is the first experiment, to the best of our knowledge, in which democracy itself is an endogenous institution that subjects can shut down through majority voting. 5 Using a simple theoretical framework based on self-interested payoff-maximizing behavior, weakly dominant sincere voting and backward induction, we predict that democracy breakdown increases in the degree of inequality and decreases in the level of economic productivity (return on investment). Consistent with the predictions, we find a strong positive effect of the degree of inequality in initial endowments on the likelihood of democracy breakdown; however, contrary to the theoretical predictions, we do not identify any effect of productivity. We find that subjects behavior exhibits significant deviations from rationality and show that the data patterns are described reasonably well by the Quantal Response Equi- 5 In a somewhat related study of Hamman et al. (2011), subjects individually choose whether or not to participate in a representative democracy governing allocation of resources to a public good. In the endogenous delegation treatment of their experiment, each group member decides whether to contribute to a public good on her own or to delegate the contribution decision to an allocator who is elected among those group members who opted in for the delegation institution. 4

5 librium framework of McKelvey and Palfrey (1995). Such deviations from rationality do not affect the comparative statics of democracy breakdown with respect to inequality. However, the effect of productivity on democracy breakdown is more sensitive to fully rational behavior and does not survive. The rest of the paper is organized as follows. In Section 2, we present a theoretical model and predictions that inform our experimental design and hypotheses. Section 3 presents experimental design and procedures. Section 4 presents the results, and Section 5 provides concluding remarks. 2 Theoretical model and predictions 2.1 Democracy Consider a society of n 2 risk-neutral players with initial endowments w i > 0, i = 1,..., n. The game consists of two stages. At stage 1, the players simultaneously and independently submit their votes, τ i [0, 1], for the revenue tax rate. The median of the tax votes submitted, τ = med{τ 1,..., τ n }, is used to tax revenue at stage 2. At stage 2, the median tax rate τ is revealed, and the players simultaneously and independently choose investment levels, x i [0, w i ]. Investment x i generates revenue µx i to player i, with µ > 1. The investment revenues are taxed at rate τ and the collected taxes are equally redistributed back to the players. The players also keep the uninvested remainder of their endowment. Thus, player i s payoff is π i = w i x i + (1 τ)µx i + µτ n n x j. (1) j=1 As seen from Eq. (1), for a given τ at stage 2, player i s strictly dominant strategy is to invest x i = 0 (respectively, x i = w i ) if τ > τ (respectively, τ < τ), 6 where τ = n(µ 1) (n 1)µ. (2) In what follows, we assume that τ < 1. The corresponding equilibrium payoff of player i is π i = w i if τ > τ and π i = µ[w i τ(w i w)] if τ < τ. Here, w = (1/n) n i=1 w i is the average endowment. As is typical for games with voting, multiple configurations of tax votes at stage 1 can be supported in equilibrium. In what follows, we restrict the set of equilibria to those arising as a result of sincere voting. Under the median voter mechanism, sincere voting 6 When τ = τ, players are indifferent among all investment level in [0, w i ]. 5

6 (i.e., voting for the tax rate the player believes is the best tax rate for herself) is a weakly dominant strategy. For our purposes, we focus on configurations of endowments mimicking income distribution in a generic society. These distributions are typically positively skewed, i.e., the majority of the population has income below average. First, note that if τ < τ in equilibrium, the players whose endowment is above (respectively, below) average prefer the lowest (respectively, highest) possible tax rate. Second, the players whose endowment is below average prefer the equilibrium with full investment for any τ. These two observations imply that a tax rate at or just below τ is individually preferred by all players with w i < w. Thus, assuming that the majority of players have endowments below average, a tax rate close to τ should emerge as the equilibrium tax rate under sincere voting. In the experiment, we manipulate the environment along two dimensions. First, we change the distribution of initial endowments between (relatively) weak and strong inequality. Second, we change the investment productivity parameter µ between a (relatively) low and high productivity. The above observations lead to the following comparative statics predictions. Prediction 1 In democracy, (a) Taxes are the same under weak and strong inequality as long as w med < w, where w med = med{w 1,..., w n }. (b) Taxes are higher under high productivity than under low productivity. (c) For a given tax rate, investment is higher under high productivity than under low productivity. Prediction 1(b) follows from the fact that the upper bound of equilibrium taxes, τ, increases in µ, cf. Eq. (2); therefore, we expect an upward shift in tax votes. For the same reason, Prediction 1(c) follows because the inequality τ < τ is more likely to hold the higher µ is. 2.2 Autocracy We model autocracy as the rule of an exogenous dictator 7 that can be of two types. With probability ρ [0, 1], the dictator is a law-abiding representative of the majority who sets all players investments to efficient levels, x i = w i, and implements full redistribution with tax rate τ = 1. With probability 1 ρ, the dictator is corrupt: she still implements 7 An alternative, albeit more complex, design would allow citizens to elect a dictator. We decided in favor of exogenous dictatorship because we wanted the vote for or against regime change to represent a choice between institutions that would not be confounded with a decision to vote for a particular candidate. 6

7 efficient investment and full redistribution but only allows players to retain a proportion α [0, 1] of their wealth while the rest is expropriated. Thus, each player i s expected payoff in autocracy is exogenous and given by π aut = µ w[ρ + α(1 ρ)]. (3) 2.3 Regime change Players start by voting for one of the two regimes democracy or autocracy to proceed with. In the experiment, democracy is always the status quo regime that subjects start with, and thus the regime choice vote is formulated as a decision whether or not to switch from democracy to autocracy. Such a switch, if it occurs, will be referred to as democracy breakdown. If democracy is chosen by the majority, the game proceeds as described in Section 2.1, while if the majority votes for autocracy, the institution described in Section 2.2 applies. Assuming the median voter s endowment is below average, w med < w, the equilibrium with τ at or just below τ and full investment will realize in democracy. The switch to autocracy, therefore, will occur if π aut > πmed, where π aut is given by Eq. (3) and πmed is the equilibrium payoff of the player with median endowment at τ = τ, i.e., µ w[ρ + α(1 ρ)] > µ[w med τ(w med w)]. This gives w med w ρ + α(1 ρ) τ <. (4) 1 τ The ratio w med / w is a measure of inequality. The lower this ratio the stronger the degree of inequality is, and the more likely it is, ceteris paribus, that condition (4) is satisfied. Furthermore, the right-hand side of condition (4) decreases in τ which in turn increases in the productivity parameter µ, cf. Eq. (2). This implies that, ceteris paribus, condition (4) is less likely to hold the higher µ is. following comparative statics predictions. Prediction 2 With the possibility of regime change, These considerations lead to the (a) The likelihood of democracy breakdown increases in the degree of inequality. (b) The likelihood of democracy breakdown decreases with productivity. 7

8 Treatment µ w τ w med / w RHS(4) Sessions Subjects Indep. Obs. LM/WI 1.4 (140,80,80) HM/WI 2.4 (140,80,80) LM/SI 1.4 (220,40,40) HM/SI 2.4 (220,40,40) Table 1: Summary of treatments and parameters. 3 Experimental design and procedures 3.1 Treatments and parameters The experiment consisted of four treatments following a 2 2 between-subject design. The number of subjects in a group, n = 3, was the same in all treatments. To explore the effects of economic productivity and inequality on democracy breakdown, we varied the economic productivity parameter µ (return on investment) and the vector of initial endowments w = (w 1, w 2, w 3 ). Specifically, in the high productivity (HM) treatments µ = 2.4, while in the low productivity (LM) treatments µ = 1.4; in the weak inequality (W I) treatments w = (140, 80, 80), while in the strong inequality (SI) treatments w = (220, 40, 40). Twelve experimental sessions, three sessions per treatment, were conducted as summarized in Table 3.1. We set the probability that the dictator is law-abiding to ρ = 2/3, and the proportion of subjects wealth to be retained in autocracy if the dictator is corrupt to α = 0.75 in all treatments. Note that the average endowment, w, is 100 in all treatments, while the median endowment, w med, is 80 in the WI treatments and 40 in the SI treatments. These parameters produce equilibrium tax rate τ, ratio w med / w and the right-hand side of condition (4) in each treatment as shown in Table 3.1. As seen from Table 3.1, it is predicted that regime change will occur in both low productivity treatments and will not occur in both high productivity treatments. However, the sharpness of these predictions depends on the level of inequality because in treatments LM/WI and HM/SI the switch condition (4) is much closer to indifference than in treatments HM/WI and LM/SI. 3.2 Procedures Using the online announcement system ORSEE (Greiner 2004), we recruited 228 subjects (47.4% female) from the population of more than 3,000 undergraduate students at Florida State University who pre-registered as potential experimental participants. The experiment was implemented using z-tree (Fischbacher 2007) and conducted at the XS/FS 8

9 laboratory at FSU. Upon arrival to the laboratory, subjects were seated at visually separated computer terminals. After the formal consent procedure, written instructions were distributed to subjects and read out loud by the experimenter. 8 Subjects were informed that the experiment consists of several parts, and that instructions would be provided separately at the beginning of each part. Each subject participated in one session. The sessions lasted around 100 minutes, with average earnings of $25.29 per subject, including a $10.00 participation fee. Each session started with the elicitation of subjects risk preferences using the method of Holt and Laury (2002), 9 and of subjects social preferences using the four distributional decisions similar to Bartling et al. (2009). 10 The realizations of random draws and earnings from these tasks were not shown to subjects until the end of the experiment. Next, subjects were randomly divided into groups of three and participated in a realeffort competitive task. Subjects were informed that the winner of the task in their group will be able to earn more money than other participants in the subsequent parts of the experiment, but no other details were provided at that point. 11 The task involved counting how many numbers there are in a random string of 20 numbers and letters. 12 When a subject submitted an answer, the next random string was generated. The winner in each group was the subject who submitted the most correct answers in 180 seconds. 13 Ties were broken randomly. The winner of each group then received the high endowment while the other two subjects received the low endowment in each treatment, cf. Table 3.1. These endowments were fixed for the duration of the experiment. In what follows, we will refer to the high-endowment subjects as rich and to the low-endowment subjects as poor. The main part of the experiment consisted of 36 decision periods divided into six decision sequences of six periods each. At the beginning, subjects were randomly divided into large groups of six in such a way that there were exactly two rich and four poor 8 Sample instructions are provided in Appendix A. 9 Subjects made choices between two lotteries, A = ($2.00, $1.60; α, 1 α) and B = ($3.85, $0.10; α, 1 α), with α changing from 0.1 to 1 in increments of 0.1. One of the choices was selected randomly and played for actual earnings. 10 Each subject was randomly matched with an anonymous other in the session and made four choices between two allocations, A and B, of the form (money to self, money to other). Allocation A was always ($1.00, $1.00). Allocation B varied so that the choice of A would capture pro-sociality, B = ($1.00, $0.50), costly pro-sociality, B = ($1.50, $0.50), envy, B = ($1.00, $2.00), and costly envy, B = ($1.50, $2.50). One of the four choices was selected randomly and implemented. For details, see Bartling et al. (2009). 11 The goal of letting subjects earn their right to high endowment was to minimize other-regarding behavior, cf., e.g., Hoffman et al. (1994) and Durante et al. (2014). 12 We intentionally chose a dull and boring task, performance in which is determined largely by effort and not as much by skill or cognitive ability. 13 We observed substantial variation in performance. The number of correct answers ranged between 8 and 37, with mean 23.9 and standard deviation

10 subjects in each large group, and stayed within those large groups for the entire time. Thus, every large six-person group provides us with one independent observation, cf. Table 3.1. At the beginning of each sequence, two groups of three subjects were formed within each large group, with one rich and two poor subjects in one group. These groups stayed fixed during the sequence of six periods and then were randomly rematched. Each of the six possible matchings was used exactly once. 14 Each sequence of six periods was divided into two half-sequences of three periods each. In the first period of each half-sequence, i.e., in periods 1 and 4 of the sequence, subjects started by submitting their revenue tax votes. The median revenue tax vote was calculated and shown to subjects. That revenue tax rate was fixed during the three periods of the half-sequence. Given the tax rate, subjects decided each period how many points of their endowment to invest into a project. Payoffs in each period consisted of the part of the endowment that was not invested, investment revenue (the invested amount times µ) less the tax, and 1/3 of the total tax collected in the group, cf. Eq. (1). After each period, subjects were informed about the tax votes, investments and payoffs of all members of their group. Sequence payoffs were calculated as a total of all six periods in the sequence. The exchange rate was $0.01 per point. Recall that there were six six-period sequences in each session. The first two sequences allowed subjects to experience the two available institutions democracy and autocracy. In the first sequence, subjects participated in democracy. Democracy was implemented as described above, with two unrestricted revenue tax votes, in periods 1 and 4, and with six unrestricted investment decisions. In the second sequence, subjects participated in autocracy. Autocracy was implemented as follows. At the beginning, subjects were informed whether their dictator was law-abiding or corrupt, 15 and that they were only allowed to vote for a tax rate in the range % and to choose an investment in the range % of their endowment. Except for these restrictions on decisions, the autocracy institution followed exactly the same procedures as democracy, with tax votes in periods 1 and 4 and investment decisions in every period. This implementation was chosen for two reasons. First, subjects in autocracy still had some decisions to make and thus would not simply be sitting and waiting for the sequence to end; second, it was impossible for any subject to infer, by looking around, how many other subjects in the room were in autocracy. The latter point is important for the following sequences where 14 In a group of six subjects indexed 1,2,3,4,5 and 6, with subjects 1 and 4 designated as rich, there are six possible matchings: (1,2,3 4,5,6), (1,2,5 4,3,6), (1,2,6 4,3,5), (1,3,5 4,2,6), (1,3,6 4,2,5) and (1,5,6 4,2,3). Subjects were told, without going into details, that they will be randomly re-matched with other subjects after each sequence. 15 The instructions were formulated using neutral language. Terms such as dictator, corruption, democracy or autocracy were not used. Law-abiding dictators were referred to as type 1 and corrupt as type 2. See Appendix A. 10

11 average tax, % average investment, % endowment half-sequence half-sequence LM/WI HM/WI LM/SI HM/SI Figure 1: Average tax rate (left) and investment as a share of endowment (right) under democracy, by treatment. The dashed lines in the left panel show the equilibrium tax rates of 42% in the LM treatments and 87% in the HM treatments. subjects could switch between the two regimes. In the remaining four sequences (3 through 6), subjects started the first half-sequence under democracy. Then, in period 4, subjects voted to either continue with democracy or switch to autocracy. If the majority voted to continue with democracy, the sequence proceeded the same way as the first sequence. If the majority voted to change the regime, the second half-sequence proceeded under autocracy: the dictator type was randomly realized and the restrictions on revenue tax votes and investments were imposed on all members of the group. The experiment ended with a short questionnaire based on the World Values Survey, see Appendix B. Only after all subjects submitted answers to the questionnaire were the payoffs from all parts of the experiment summarized and final earnings shown to subjects. 4 Results 4.1 Aggregate treatment effects Recall that subjects went through two half-sequences of democracy and two half-sequences of autocracy at the beginning to get experience with both institutions. From sequence 3 onward, they started with democracy in the first half-sequence and then either continued with democracy or switched to autocracy in the second half-sequence. In what follows, we only use data from sequences 3-6 for the analysis. Figure 1 shows the average implemented tax rate (left) and average investment as a 11

12 regime change frequency LM/WI LM/SI HM/WI HM/SI half-sequence Figure 2: The frequency of regime changes from democracy to autocracy, by treatment. percent of endowment (right) in democracy in every half-sequence. Note that in odd halfsequences democracy is imposed exogenously in all groups, while in even half-sequences it is selected endogenously only by some groups. The dashed lines in the left panel of the figure also shows the equilibrium tax rates 42% in the LM treatments and 87% in the HM treatments. As seen from Figure 1, implemented taxes appear to be higher in the HM treatments, as compared to the LM treatments, under both weak and strong inequality. Taxes also appear to be higher under strong inequality than under weak inequality, for both values of the productivity multiplier. It is also evident from Figure 1 that, on average, taxes are below the predicted equilibrium levels τ in all treatments. Average investment, shown in the right panel of Figure 1, is everywhere below the equilibrium (and efficient) level of 100% of endowment. At the beginning, investment is higher in the HM treatments, as compared to LM, and also is higher under weak inequality as compared to strong inequality. However, investment increases over time in the LM/WI treatment and decreases in the HM/SI treatment, while it remains relatively stable in the HM/WI and LM/SI treatments, so that by the end of the experiment the two weak inequality treatments produce nearly the same average investment levels and so do the two strong inequality treatments. These dynamics of investment are consistent with the dynamics in implemented tax rates shown in the left panel of the figure. Figure 2 shows the average frequency of regime change by treatment (recall that regime change is only possible in even half-sequences). As seen from the figure, regime change is substantially more likely under strong inequality, for both values of the multiplier, and there appears to be no difference in the frequency of regime change between the two productivity levels, under both weak and strong inequality. 12

13 Tax Investment Regime Change (1) (2) (3) (4) SI 18.04*** ** * 0.36** (5.16) (8.19) (6.13) (0.13) HM 21.54*** 9.08** 21.17*** (6.85) (4.36) (4.03) (0.132) SI HM (10.70) (9.89) (7.53) (0.191) Tax *** (0.053) Intercept 16.38*** 80.33*** 89.52*** (2.14) (2.95) (2.49) N Clusters R-squared Table 2: Regressions showing aggregate treatment effects. Columns (1), (2) and (3) report OLS coefficient estimates, while column (4) reports probit marginal effects. Robust standard errors adjusted for clustering at the large group level are in parentheses. Significance levels: *** 1%, ** 5%, * 10%. Table 2 presents the results of regressions providing formal statistical tests for the treatment effects suggested by Figures 1 and 2. The independent variables in the regressions are SI (=1 in the SI treatments, 0 in the WI treatments), HM (=1 in the HM treatments, 0 in the LM treatments), their interaction, and the implemented tax rate T ax. Columns (1) and (2) show the results of OLS regressions of tax rates and investment levels, respectively, on the treatment dummies. In column (3), a control for tax is added to the regression for investment. Column (4) shows the marginal effects of a probit regression for regime change. Standard errors in the regressions are clustered at the large group level. The following results summarize the aggregate treatment effects. Result 1 In democracy, (a) implemented tax rates are higher under strong inequality than under weak inequality; (b) implemented tax rates are higher under high productivity than under low productivity. Support for Result 1(a) is the positive and significant coefficient on SI and a positive and significant sum of coefficients on SI and SI HM (p = , F-test) in column (1). Support for Result 1(b) is the positive and significant coefficient on HM and a positive and significant sum of coefficients on HM and SI HM (p = , F-test) in column (1). 13

14 Result 2 In democracy, (a) investment is lower under strong inequality than under weak inequality; however, this result is driven primarily by higher taxes under strong inequality. When taxes are controlled for, there is no effect of inequality on investment; (b) investment is higher under high productivity than under low productivity. Support for Result 2(a) is the negative and significant coefficient on SI and a negative and significant sum of coefficients on SI and SI HM (p = , F-test) in column (2), but only a marginally significant coefficient on SI in column (3) and an insignificant sum of coefficients on SI and SI HM (p = 0.32, F-test) in column (3). Support for Result 2(b) is the positive and significant coefficient on HM and a positive and significant sum of coefficients on HM and SI HM (p = , F-test) in column (3). Result 3 The likelihood of democracy breakdown (a) is higher under strong inequality than under weak inequality; (b) is independent on productivity. Support for Result 3(a) is the positive and significant coefficient on SI and a positive and significant sum of coefficients on SI and SI HM (p = , F-test) in column (4). Support for Result 3(b) is the insignificant coefficient on HM and an insignificant sum of coefficients on HM and SI HM (p = 1.000, F-test) in column (4). 4.2 Discussion and further analysis With the exception of Result 1(a), Results 1 and 2 are in line with the predicted comparative statics for behavior in democracy. Result 1(a) can be explained by a simple model of other-regarding preferences, as voting for higher taxes would be a natural way for the poor to reduce the distance in payoffs between themselves and the rich under strong inequality. We now turn to the analysis of the main results regarding the frequency of democracy breakdown. Result 3(a) is in line with the predictions and confirms that there is a strong effect of inequality on the likelihood of regime change. If indeed higher taxes under strong inequality are due to other-regarding preferences, the presence of the latter would only exacerbate the effect because, unable to reduce inequality via taxation in democracy, the poor will switch to autocracy even if it is not worth doing so from a selfish payoff maximization perspective. We conclude that the effect of inequality on democracy breakdown is robust to, and in fact can be enhanced by, the presence of other-regarding preferences. At the same time, Result 3(b) does not support the prediction regarding the effect of productivity, even though the effects of productivity on taxation and investment (Results 1(b) and 2(b)) are directionally as predicted. It appears that the basic monotonicity of 14

15 % endowment invested LM/WI poor rich tax, % 100 % endowment invested HM/WI poor rich tax, % 100 % endowment invested LM/SI poor rich tax, % % endowment invested HM/SI poor rich tax, % Figure 3: Average investment as a function of taxes under exogenous democracy (first half-sequences of sequences 3-6). The vertical dashed lines show the equilibrium tax rates of 42% in the LM treatments and 87% in the HM treatments. taxation and investment with respect to productivity (higher taxes and higher investment in HM as compared to LM) does not generate sufficient differences in payoffs to affect the likelihood of regime change. In what follows we will analyze subjects decisions in more detail in order to understand why this may be happening. Under democracy subjects vote for taxes and then, given the median tax rate, decide how much to invest. Consider first the second-stage investment decision. Recall that, for a given tax rate τ, it is a dominant strategy to invest the entire endowment (respectively, zero) if τ > τ (respectively, τ < τ). Thus, the optimal investment profile is a step function switching from 100% of endowment to zero at τ = τ. Figure 3 shows the average second-stage investment as a function of taxes. We divided the implemented tax rates into ranges 0-10%, 11-20%,..., %, and averaged subjects investments in the first half-sequences of sequences 3-6 for each tax range, separately for poor and rich subjects. 15

16 The vertical dashed lines in Figure 3 show the equilibrium tax rates τ for each treatment. As seen from Figure 3, subjects deviate substantially from dominant strategies. While investment generally declines with taxes, the decline is not abrupt at τ as predicted. It is also evident that the rich react to taxes stronger than the poor and invest less, in relative terms, for a given tax rate. 16 Looking at the distribution of investment by treatment, we found that the poor (respectively, the rich) invested their entire endowment 50.8% (52.1%) of the time in LM/WI, 71.5% (65.8%) of the time in HM/WI, 42.4% (43.1%) of the time in LM/SI and 55.1% (37.0%) of the time in HM/SI. Given that, on average, the implemented tax rates are well below τ, we conclude that overall subjects underinvested substantially as compared to the second-stage equilibrium. Importantly, the rich underinvested more than the poor, in relative terms, in both HM treatments. We now turn to analyzing first-stage decisions, i.e., tax votes. Recall that in the subgame-perfect equilibrium with sincere voting the poor should vote for a tax close to τ. Figure 4 shows the cumulative distributions of tax votes for each treatments, separately for the poor and for the rich. As seen from the figure, the tax votes of the poor are dispersed substantially, with a lot of 0% votes (23.1% in LM/WI, 15.6% in HM/LI, 20.1% in LM/SI and 5% in HM/SI) and 100% votes (3.8% in LM/WI, 24.4% in HM/LI, 18.1% in LM/SI and 34.0% in HM/SI). As expected the rich voted for much lower taxes than the poor. The tax votes votes of the rich are dispersed mainly between 0 and τ, which is consistent with the equilibrium predictions. The patterns of tax votes of the poor (which matter for the implemented tax rates) and investment of both the poor and the rich deviate substantially from the equilibrium predictions and exhibit a lot of heterogeneity, both within and between subjects. 17 Such behavior is consistent with experimentation and random deviations from best response in a complex environment and can be understood theoretically using the Quantal Response Equilibrium (QRE) framework proposed by McKelvey and Palfrey (1995). 4.3 QRE predictions Let T denote the set of available tax rates a subjects can vote for, and let X p and X r denote the sets of available investment levels for the poor and rich subjects, respectively. In the second stage when implemented tax rate τ T is revealed, subject i chooses 16 This is confirmed by adding variables Rich and Rich T ax to the specification (3) in Table 2. The coefficient estimate on the interaction Rich T ax is (p = 0.000), i.e., the rich reduce their investment stronger by 0.28 percentage points than the poor for every percentage point increase in the tax rate. 17 Investment as a share of endowment has a between-subject standard deviation of 0.24 and the average within-subject standard deviation of Tax votes have a between-subject standard deviation of 32.9% and the average within-subject standard deviation of 15.2% 16

17 cdf 40 cdf LM/WI poor rich tax vote, % HM/WI poor rich tax vote, % cdf 40 cdf LM/SI poor 20 HM/SI poor rich tax vote, % rich tax vote, % Figure 4: The cumulative distributions of tax votes in the first rounds of sequences 3-6. The vertical dashed lines show the equilibrium tax rates of 42% in the LM treatments and 87% in the HM treatments. 17

18 an investment level x X according to a mixed strategy p (i) 2 (x, τ) determined by the following system of equations: p (i) 2 (x, τ) = π (r) e2 (x, τ) = π (p) e2 (x, τ) = ( (i) π e2 (x, τ) ) λ ( (i) x X i π e2 (x, τ) ) λ, i = r, p, (5) π r (x, x, x, τ)p (p) 2 (x, τ)p (p) 2 (x, τ), x,x X p x X r, x X p π p (x, x, x, τ)p (r) 2 (x, τ)p (p) 2 (x, τ). Here, π r (x, x, x, τ) is the payoff of a rich subject given her investment x, the investments x and x of the two poor subjects and the tax rate τ. Similarly, π p (x, x, x, τ) is the payoff of a poor subject given her investment x, the investments x of the rich subject and x of the other poor subject, and the tax rate τ. Both payoffs are given by Eq. (1). Parameter λ determines the level of noise, or the intensity of subjects errors, with the limits λ 0 corresponding to a completely random behavior and λ to the Nash equilibrium. 18 Given the second-stage mixed strategies p (i) 2 (x, τ) and expected payoffs π (i) e2 (x, τ) satisfying (5), subjects choose first-stage tax votes τ T according to mixed strategies p (i) 1 (τ) satisfying the system of equations p (i) 1 (τ) = π (r) e1 (τ) = π (p) e1 (τ) = ( (i) π e1 (τ) ) λ ( (i) τ T π e1 (τ ) ) λ, i = r, p, (6) π (r) e2 (x, med{τ, τ, τ })p (r) 2 (x, med{τ, τ, τ })p (p) 1 (τ )p (p) 1 (τ ), x X r, τ,τ T x X p, τ,τ T π (p) e2 (x, med{τ, τ, τ })p (p) 2 (x, med{τ, τ, τ })p (r) 1 (τ )p (p) 1 (τ ). For computational experiments, we used the space of tax rates T = {0, 0.05, 0.1,..., 1} and the spaces of investment X i = {0, 0.05w i, 0.1w i,..., w i }, i = r, p. The systems of equations (5) and (6) were solved in two stages, with the system (5) solved first for all τ for both types, and the results then used to solve (6). Figure 5 shows the QRE results using the noise parameter λ = 30. The top four panels in Figure 5 show the expected QRE investment as a function of 18 In most specifications, QRE mixed strategies are written in a logit form. This is, to some extent, arbitrary because the true functional form depends on the error-generating process, which is unknown. We have chosen the functional form (5) because, unlike the logistic function, it is homogeneous of degree zero. This is important in our case because changes in the productivity parameter µ lead to changes in the scales of payoffs, which would make the results for the same level of noise difficult to compare across the LM and HM treatments. 18

19 % endowment invested % endowment invested QRE, =30 LM/WI 20 poor 0 0 rich tax, % QRE, =30 LM/SI 20 poor 0 0 rich tax, % % endowment invested % endowment invested QRE, =30 HM/WI 20 poor 0 0 rich tax, % QRE, =30 HM/SI 20 poor 0 0 rich tax, % cdf cdf QRE, = LM/WI poor rich tax vote, % QRE, = LM/SI poor rich tax vote, % cdf cdf QRE, = HM/WI poor rich tax vote, % 1.0 QRE, = HM/SI poor rich tax vote, % Figure 5: Top four panels: Expected second-stage investment as a function of the implemented tax rate, by treatment and type, in the QRE with λ = 30. Bottom four panels: Cumulative distributions of first-stage tax votes, by treatment and type, in the QRE with λ =

20 taxes, x (i) QRE(τ) = x X i xp (i) 2 (x, τ), for rich and poor subjects in each treatment. The QRE investment profiles are smooth downward-sloping functions, similar to the observed ones in Figure 3. Interestingly, the QRE investments of rich subjects are higher for taxes below τ but lower for taxes above τ, as compared to the investments of the poor. This is in partial agreement with the observed behavior where the investment of the poor is higher than that of the rich for high taxes but not for relatively low taxes. The bottom four panels in Figure 5 show the cumulative distributions of first-stage tax votes predicted by the QRE. The patterns are remarkably similar to those in Figure 4. The poor vote for higher taxes than the rich, and the gap between the two increases both with productivity and with the degree of inequality. The only substantial difference between the QRE distributions of tax votes and the observed ones is the presence of large masses of zero and 100% tax votes in the latter. It is well-known, however, that QRE typically fails to capture bunching at the boundaries of a strategy space. Given that the QRE model captures the observed patterns and comparative statics across treatments and types much better than the subgame-perfect Nash equilibrium predictions, it is natural to explore the predictions of QRE regarding regime change. Of main interest is the comparison of expected payoffs of the poor following from the QRE model in democracy to the payoffs in autocracy. The expected payoffs in autocracy, π aut, are in the LM treatments and in the HM treatments. 19 The expected payoffs of the poor following from the QRE model with λ = 30 are in LM/WI, in HM/WI, 67.3 in LM/SI and in HM/SI. The first observation is that the expected QRE payoffs of the poor are lower than π aut in all treatments. The second observation is that the distance between the QRE payoffs and π aut (19.8 in LM/WI, 22.0 in HM/WI, 61.0 in LM/SI and 56.2 in HM/SI) does not decrease noticeably with productivity. In contrast, the distance does increase substantially with the level of inequality. Of course, the QRE predictions depend on the noise parameter λ and approach the Nash equilibrium predictions as λ becomes larger. The value of λ = 30 we chose for the illustration is reasonable because it leads to approximately the same variation in QRE tax votes as the one observed in the data. These results imply that the predicted comparative statics regarding the effect of productivity on the likelihood of democracy breakdown are not robust to deviations from equilibrium behavior. The predicted effect hinges on the positive dependence of the threshold tax rate τ on productivity µ, but also on the ability of subjects to play dominant strategies at the second stage (i.e., invest their entire endowments for any implemented tax rate up to τ) and to backward-induct (i.e., for poor subjects to vote for a tax rate just 19 These payoffs are calculated under the assumption of full investment and redistribution and are independent of types and the level of inequality. 20

21 below τ). Deviations from both of these strategies lead to payoffs that are lower π aut in all treatments and eliminate the differential effect of productivity on the incentives to switch to autocracy. In contrast, the effect of inequality is robust to off-equilibrium behavior. 4.4 Individual and group-level analyses In this section, we present a more detailed analysis of individual behavior, controlling for subjects types, characteristics and history. Taxes and Investment Table 4 reports estimated coefficients and standard errors from tax vote and investment regressions, where only decisions under democracy are considered. Because a significant fraction of individual and group outcomes is censored (25.9% at zero and 10.8% at 100 for the individual tax vote, 17.4% at zero and 3.8% at 100 for the median tax rate, and 8% at zero and 49.5% at 100 for the percent of endowment invested), we employ a two-sided Tobit estimator. Standard errors are adjusted for clustering at the big group level. In addition to treatment dummies all regressions include an indicator for rich subjects, a female dummy, an experimental measure of risk aversion, and various measures of social preferences. 20 The treatment effects reported in Table 4 are in line with the aggregate results reported earlier, so here we focus on other factors. Column (2) in Table 4 displays results from a regression that includes a dummy for the second half of the sequence (periods 4-6) and its interaction with Rich dummy. As seen from the Table, individual tax vote among poor subjects tends to be lower in the second half of the sequence, while there is no change for the rich (the effect is small and not statistically significant). This finding does not necessarily imply that poor subjects modify their choices after the first few rounds of decision making. Instead, it might demonstrate that experiment participants who choose 20 Economic growth is important is an indicator equal to one if when answering the question about this country s goals for the next ten years the subject chose A high level of economic growth as either the most important or second most important. Stable is important is an indicator equal to one if when choosing from a list of possibly important things the subject chose A stable economy as either the most important or second most important. More say in government is important is a dummy equal to one if when answering the question If you had to choose which one of the things below would you say is most important? the subject chose Giving people more say about important government decisions. The variable Favor Income Inequality measures individual preferences for income inequality and takes on values from 1 = Incomes should be made more equal to 10 = We need larger income differences as incentives for individual effort. The variable Favor Self Responsibility also measures individual preferences and takes on values from 1 = The government should take more responsibility to ensure that everyone is provided for to 10 = People should take more responsibility to provide for themselves. RA is Holt and Laury (2002) measure of risk aversion. Variables P rosociality, Costly Prosociality, Envy, and Costly Envy measure subject s social preferences, as suggested by Bartling et al. (2009). See footnote 10 for a more detailed description of these measures. 21