Vanishing leadership and declining reciprocity in a sequential contribution experiment.

Figuieres, Charles ; Masclet, David ; Willinger, Marc 等

I. INTRODUCTION

Contributing sequentially is a widespread practice for a large variety of public goods, ranging from dish washing in households to the ratification of international treaties by states. Academic research, free Wikipedia, and telethons are other popular examples. Contributions are not necessarily in monetary terms, but they share two important features: the amount of public good provided depends on some aggregation of individual contributions, and later contributors in a sequence can condition their contribution on previously observed contributions.

Surprisingly, the economic literature on sequential contributions is rather scarce, while an overwhelming bulk of knowledge has been accumulated on simultaneous contributions environments. Other things being equal, should one expect a higher level of public good provision when contributions are sequential? Getting back to the telethon example, does the publicly released information about contributions affect donations during the campaign?

The recent experimental literature about leading-by-example, based on the linear public good games, provides mixed evidence about the effect of sequentiality on the level of group contributions. The relevant papers are based on a procedure where the contribution of a first mover (leader) is publicly announced, and later movers contribute simultaneously. While this form of sequential moves tends to increase group contributions compared to simultaneous moves contribution games, the effect is not always significant. Taking the simultaneous contribution game as a benchmark, Guth et al. (2007) found a strong positive effect of this type of leadership, while Moxnes and van der Heijden (2003) found only a negligible (but significant) effect. Others found no significant difference in group contributions between sequential and simultaneous moves games (Potters, Sefton, and Vesterlund 2007; Rivas and Sutter 2009). (1,2) It is therefore fair to say that the available experimental evidence is mixed, and that more data are needed to understand and disentangle the various effects that contributing sequentially might induce. Some of these effects are already clearly established: there is robust evidence that first movers tend to make larger contributions than later movers, and that later movers' contributions are strongly correlated to the first mover's contributions, suggesting that sequentiality stimulates reciprocal behavior (Arbak and Villeval 2007; Gachter et al. 2009b; Guth et al. 2007; Levati, Sutter, and van der Heijden 2007; Pogrebna et al. 2009; Potters, Sefton, and Vesterlund 2007; Rivas and Sutter 2008). Similar observations were made in the sequential prisoners' dilemma game by Clark and Sefton (2001) who report that second movers tend to "cooperate" if the first mover chose to cooperate, and in field experiments (Martin and Randal 2005; Shang and Croson 2005).

Why do first movers contribute more than second movers and why--on average--are group contributions larger when individual contributions are ordered sequentially? Take the point of view of the first mover: he can have an incentive to make a large contribution either because he is aware that second movers observe his contribution decision (leading-by-example), or simply because he is assigned to the first mover's role (pure ordering effect). The experimental literature on common pool resource games documented significant order effects even if later decision makers cannot observe previous moves (see Budescu, Suleiman, and Rapoport 1995; Rapoport 1997; Rapoport, Budescu, and Suleiman 1993; Suleiman, Rapoport, and Budescu 1996). Whether or not such pure order effects also arise in voluntary contribution games remains an open question (however, see Guth, Huck, and Rapoport 1998).

Consider now the point of view of second movers: they may contribute less than first movers, either because of imperfect reciprocity, or because of an "end-of-sequence" effect. Endof-game effects have been observed in repeated simultaneous contribution games (see e.g., Keser and Van Winden 2000; Gonzalez, Gueth, and Levati 2005). However, such effects may also occur within rounds in sequential moves games. Therefore, it is important to try to control for such effects. According to the imperfect reciprocity hypothesis second movers tend to condition their contribution on the first mover's contribution, but with a slight "selfish-bias" (Fischbacher and Gachter 2010; Neugebauer et al. 2009).

The available experimental literature on sequential contributions is restricted to two-stage games: one player decides first, and one (or more) player(s) decide (simultaneously) after having observed the decision of the first mover. But experimental data, collected with two-stage games, does not allow to disentangle selfish biased reciprocity from end-of-sequence effects. In Stage 2, after having observed the leader's contribution, the remaining group members choose their contribution simultaneously. (3) It remains an open question what happens with longer sequences, that is, for large populations of sequentially ordered contributors. Does the leading-by-example effect carry over to later contributors in the sequence who know that their contribution will be observed by later potential contributors? How does the leading-by-example motive interact with the reciprocity motive?

In the present paper, we seek to contribute to the understanding of contribution decisions in a sequential context, by trying to provide answers to the above questions. We summarize these questions as follows: (1) How do sequentiality and information about previous contributions in a sequence affect the contributions of subjects who have to decide later in the sequence?; (2) To what extent does the "length" of the sequence (i.e., the size of the population of ordered players) affect contributions in various positions?; (3) What reasons, if any, lead to larger group contributions under sequential moves compared to simultaneous moves?

We address the first question by comparing our reference treatment that consists of a simultaneous public good game (no sequential move and no information) with two sequential treatments: a sequential treatment with information and a sequential treatment without information. In the sequential treatment without information, subjects know the ordering of their contribution decision, but are unaware about previous contributions at the time they have to decide on their own contribution. In the sequential treatment with information, each subject observes all the individual contributions of subjects who were called to decide before him in the sequence. Each treatment has the same number of rounds. In treatments where contributions are made sequentially, in each round subjects are randomly assigned to a rank.

We address the second question by comparing the average contribution of groups of four players to the average contribution of groups of eight players. In each case, the group members are randomly ranked in a sequence, and contributions of lower ranks are observed by higher-ranked subjects. In a sequential contribution environment, the decision of the leader may depend crucially on the size of the population on which he may have an influence. The larger the population the stronger the leader's potential influence. But the leader's influence may become weaker for more distant followers.

The third question, what are the determinants of individual contributions in a sequential context, is the most difficult. The experimental literature suggests at least three reasons for larger contributions under sequentiality: reciprocity, leading-by-example, and pure ordering. We describe each of them briefly as follows. The reciprocity motive rests on the idea that some decisions are motivated by moral sentiments. A gift or a favor as a response to a gift or a favor enters into this category (Kolm 2006). In a public good context, a contributor reacts to the observed contributions of lower-ranked players to maintain a balance or to avoid moral indebtedness, even if he believes that he has no influence on subsequent contributors, and on the level of public good he will enjoy. Second, according to the "leading-by-example" hypothesis, early contributors may feel responsible for setting a good example for later contributors. By making a large contribution, they expect later contributors to react positively, for instance in accordance with the reciprocity motive, lt is likely that the strength of such feeling declines with the rank, because there are fewer players who are likely to be influenced. Finally, as already discussed even a subject who is unable to observe previous contributions and who is aware that his contribution is not observable by subsequent movers, might still be influenced by the mere knowledge of his ranking in the sequence.

Our experimental design allows us to isolate pure order effects and to identify the effect of players' rank on their level of contribution. We also propose a way to disentangle the leadership effect from the end-of-sequence effect and the reciprocity effect.

Our main experimental findings are the following: (1) in the sequential contribution treatment with information the average contribution is larger than in the sequential contribution treatment without information and to some extent larger than in the simultaneous contribution treatment, but individual contributions decline with the order of play; (2) sequentiality without information about contributions (pure ordering) has no effect on contributions; (3) the length of the sequence (group size) has no significant impact on the average level of contributions; (4) the decline of the average contribution with the rank of the player is attributable to the combination of a vanishing leading-by-example effect and the erosion of reciprocity.

The paper is organized as follows. Section II describes the experimental design. In Section III, we present the theoretical predictions and our behavioral conjectures about the expected treatment effects. Section IV presents our results and Section V concludes.

II. EXPERIMENTAL DESIGN

The experiment consisted of 16 sessions of 15 periods each. Experimental sessions were conducted both at the University of Rennes and at the University of Montpellier in France. (4) As many as 252 subjects were recruited from undergraduate classes in business and economics at both sites. None of the subjects had previously participated in a public good experiment and none of them participated in more than one session. The experiment was computerized using the Ztree program (Fischbacher 2007). On average, a session lasted about 1 hour and 20 minutes (5) including the time required for reading the instructions and answering questions, and the time needed to pay subjects at the end of the session. Subjects earned 14.01 [euro] on average including a show-up fee. (6) We set up an experimental design that allows us to investigate the effect of information accumulation on individual contributions in a sequential contribution environment. The reference treatment is a simultaneous voluntary contribution game. At the beginning of each period, each member of a group of n subjects was endowed with 10 tokens that he had to allocate between a private account and a group account. Following previous notations, player i's payoff is given by:

u 9[x.sub.i], [x.sub.-i]) = 10-[x.sub.i] + 0.5 x [n.summation over (h=1)[x.sub.h].

Subjects were instructed to indicate only their contribution to the group account, the remainder of their endowment being automatically invested in their private account. Any token invested in the group account generated the same payoff for each member of the group.

Besides the "simultaneous contributions" treatment which was our benchmark, we had two test treatments for which subjects had to take their decisions sequentially, either with or without information about prior contributions: in the remainder of the paper we call them sequential treatment with information and sequential treatment without information. In the latter treatment previous contributions are not observable while in the former they are. Sequentiality is obtained by assigning in the beginning of each round each subject a rank in the decision sequence. Each subject is informed about his rank for the current round, and about the individual contributions of all lower-ranked subjects in the sequential treatment with information. Therefore, the least informed subject is the subject who is ranked first in the sequence, whereas the most informed subject is the one who is ranked last in the sequence.

While the information condition is our main treatment variable, we also study the impact of group size on the level of contribution in the sequential contribution environment, by comparing the average contributions of groups of four subjects (small groups) to average contributions of groups of eight subjects (large groups).

We relied on the same presentation for all treatments. (7) The ranking of the subjects in the sequential treatments was randomly determined by the computer program, both within and across rounds. Therefore, subjects' rank in the sequence varied from round to round. At the end of each round, the computer screen displayed each subject's investment decision, the total group contribution, and the earnings of the group account as well as the total earnings. Cumulated earnings since the beginning of the game, as well as the number of the round were also on display. After each round, subjects could see their detailed records since the beginning of the experiment. Contributions were anonymous. Table 1 provides a summary of the experimental design. A partner matching protocol was in effect for all sessions (i.e., all the groups remained unchanged during the entire session).

III. THEORETICAL PREDICTIONS

In this section, we contrast two types of theoretical predictions. First, we rely on standard behavioral assumptions to derive the Nash equilibrium for the simultaneous contribution game, and a Stackelberg equilibrium for the sequential contribution game with information. Second, we consider alternative predictions based on other behavioral assumptions.

A. Standard Predictions

In the reference treatment, players choose their contributions simultaneously (simultaneous treatment thereafter). Under standard behavioral assumptions, there exists a unique dominant strategy equilibrium for the one-shot game where each player i = 1, ..., n contributes [x.sub.i] = 0. Furthermore, there exists a unique subgame perfect equilibrium for the finitely repeated game where each player i contributes [x.sub.i] = 0 in every period. In the experiment, the constituent game was repeated exactly 15 periods. The same prediction applies to the sequential treatment without information, as players move sequentially, but without observing previous decisions.

In the sequential game with information, agents play a Stackelberg game. By backward induction, we can easily see that there is a unique Subgame Perfect Stackelberg Equilibrium: the last-ranked player contributes zero whatever the observed contributions of others, therefore the player before the last also contributes zero, and so on up to the player who is ranked first in the sequence, and who also contributes zero as a consequence.

Standard predictions are therefore identical for the three treatments, irrespective of group size: each player contributes zero in each round. On the other hand, the group optimum is achieved whenever each player contributes all his endowment to the public good.

B. Behavioral Conjectures

The above predictions are based on the standard assumption that individuals are exclusively pursuing their own material self-interest, irrespective of others. However, empirical evidence suggests that this assumption does not hold for all individuals. Many individuals condition their decisions on the observation of others' decisions in finitely repeated simultaneous public good games (see e.g., Fischbacher and Gachter 2006; Herrmann and Thoni 2007; Keser and Van Winden 2002). (8) Similarly, in sequential games later movers' contributions are generally positively correlated to the first mover's contribution (see the references introduced earlier in this paper). (9) Therefore, we take as a more empirically relevant behavioral assumption the idea that individuals' contributions are partly influenced by the observations of others' contributions (conditional cooperation or reciprocity). First movers who expect such behavior, choose their contribution in order to try to influence positively later contributors in the sequence (leading-by-example). We state this as conjecture C1.

C1: The combined effects of leadership and reciprocity influence positively the level of contributions in the sequential treatment with information compared to the sequential treatment without information.

According to C1, the contrast between the two sequential treatments--with and without information--provides a measure of the combined effects of leadership and reciprocity resulting from the information asymmetry between players.

According to the pure order effect, individuals' contributions might also be affected by the knowledge of their rank in the contribution sequence even if they are unable to observe others' contributions. Pure order effects have been documented in experiments on requests from a common pool (Budescu et al. 1995; Rapoport, Budescu, and Suleiman 1993; Rapoport 1997; Suleiman, Rapoport, and Budescu 1996) in ultimatum bargaining games and "weak link" coordination games (Weber et al. 2004). We state conjecture C2 as follows:

C2: Pure order effects positively influence voluntary contributions in a sequential game without information compared to the simultaneous treatment.

The comparison of average contributions in the benchmark and in the sequential treatment without information allows us to isolate a possible pure ordering effect. Finally, the comparison between the sequential treatment with information and the benchmark treatment will capture both the effect of sequentiality and of information asymmetry.

Our third conjecture is directly related to the dynamics of the sequential game with information. Previous studies have highlighted the fact that first movers in the sequence tend to contribute more than later movers. Presumably this finding is because of the combination of the three effects: imperfect reciprocity, vanishing leading-by-example, and end-of-sequence.

Imperfect reciprocity supposes that followers condition their contribution on the first mover's decision, but with a slight "selfish-bias" (Fischbacher and Gachter 2010; Neugebauer et al. 2009). End-of-sequence effects rely on the idea that the type of end-game effects observed in terminal rounds of repeated games (see e.g., Gonzalez et al. 2005; Keser and Van Winden 2000) also occur within sequences when contributions are made sequentially. Finally, a decline in contribution levels within a sequence may also be attributed to a vanishing leading-by-example effect. Our hypothesis is that the strength of this effect declines with the rank, because there are fewer players that are likely to be influenced. For instance, in the last position of the game, leading-by-example disappears as there are no more players to be influenced. We summarize this as conjecture C3.

C3: The combined effects of imperfect reciprocity, vanishing leading-by-example and endof-sequence lead contribution levels to decline with the positions in the sequential treatment with information.

Our data analysis will allow us to identify which of these three effects drives the decline in contributions according to the rank of the player in the sequential treatment with information. Furthermore, to some extent we are able to isolate ex post these motives by comparing subjects' contributions in extreme positions (first and last) with subjects' contributions in intermediary positions. Indeed, the first player's contribution within a sequence cannot be motivated by "reciprocity" as no information about others' contributions is available to him. However, he might be motivated by leading-by-example. At the other extreme, the last player cannot lead by example within a sequence, and therefore his contribution can only be motivated by reciprocity or by the end of the sequence. Only players that have an intermediary position can be influenced both by "reciprocity" and "leadership." If an end-of-sequence effect exists in our data, we should observe a higher decline in the last position compared to the other positions.

Finally, our final conjecture concerns the effect of increasing the size of the group, that is, the length of the sequence in the sequential contribution games. According to the standard prediction for linear public good game described in Subsection A of Section III, the size of the group has no effect at all on contributions in all treatments. However, as Ledyard (1995) noted,. "whether contributions increase or decrease with group size, other than whether contributions will occur at all, remains one of the longest running debates among theorists." (10) For instance one may argue that subjects may be influenced by efficiency considerations and therefore contributions will be higher in larger groups as social benefits are larger when group size increases]l Introducing sequentiality and observability may also interact with group size and influence contributions. An increase of the size of the group of contributors can have two opposite effects on the average level of contributions in the sequential treatment with information. A positive one strengthens the leadership effect, as for any rank there are more subsequent players who are likely to be influenced. However, if the size of the group becomes larger, there might also be a greater temptation to free ride on lower-ranked subjects as the accumulated contribution becomes larger. Our idea is that the temptation to free ride might be stronger in larger groups for two reasons: (1) each individual has a lesser impact (in relative terms) on the size of the pie as group size increases; (2) individuals may feel less concerned by the public good in large groups than in small groups, in the sense that they might think that others will provide "enough" public good according to their tastes. This is summarized in C4 as follows:

C4: An increase in group size has an ambiguous effect on contributions.

IV. RESULTS

This section is organized as follows. Subsection A reports the observed patterns of average contributions for our three treatments. We analyze the treatments in relation to each other and to the benchmark treatment in Tables 2 and 3. In Subsection B we analyze the determinants of the contribution behavior separately for each treatment. The dynamics of contribution in the sequence is investigated in Subsection C. A. Average Individual Contribution

Figures 1 and 2 illustrate the time path of average individual contributions by period for small and large groups, respectively. The period number is shown on the horizontal axis and the average individual contribution on the vertical axis, where the maximum possible individual contribution is 10. These figures show the same pattern for all treatments: there is initially a positive level of contribution to the group account which declines with repetition (except for the sequential treatment with information in large groups, in which the average contribution level does not change appreciably as the game is repeated). This result is in line with several other experiments that have documented that the average contribution tends to decline with repetition (Andreoni 1988; Isaac and Walker 1988; Isaac, Walker, and Thomas 1984; Weimann 1994).

Result 1 summarizes our findings both about the effects of sequential contributions with and without information.

Result 1: Average levels of contribution are significantly higher in the sequential treatment with information than in the sequential treatment without information. Sequentiality without observability has no significant impact on the level of average contribution.

Support for Result 1: Table 2 shows the average contribution for each treatment. The first three columns of Table 2 indicate the average individual contribution for each small group. The last three columns contain the same data for each large group. Comparison of treatments suggests that sequentiality with information positively affects average contributions. For both small and large groups, average contribution levels are higher in the sequential treatment with information than in the sequential treatment without information. A nonparametric Mann-Whitney rank-sum test (12) for small groups shows that the difference in average contributions between the sequential treatments with and without information is significant at the p < .10 level, (z =-1.68; p = .09; two-tailed). A similar test of the difference between the sequential treatments with and without information for large groups also indicates a positive and significant effect of information (z = 2.082; p = 0.03; two-tailed).

To isolate the pure effect of sequentiality, we compare the average level of contribution in the simultaneous treatment and in the sequential treatment without information. Our results indicate that for both small and large groups changing the timing of moves without changing the information condition has no significant effect on contributions (z = -0.145; p = .88 for small groups and z = 1.601; p = .11 for large groups, respectively). The comparison of the simultaneous treatment to the sequential treatment with information indicates that the combined effect of sequentiality and observability of previous contributions in the sequence increases the average contribution level in small groups (z = -1.843; p = 0.06 two-tailed), but not in large groups (z = -1.44; p =. 14; two-tailed). The insignificant difference between the baseline treatment and the sequential treatment with information for large groups suggests that the positive effect of information is partly offset by a negative effect induced by sequentiality alone, although this effect is not significant. Average contributions do not differ significantly with respect to group size, whatever the treatment. The two-tailed Mann-Whitney test does not detect any difference in average contributions between groups of four members and groups of eight members in the simultaneous treatment (z = 0.307; p = 0.75; two-tailed). Similar results are obtained for the sequential treatment without information (z = -1.486; p = 0.14; two-tailed) and for the sequential treatment with information (z = -0.480; p = .63; two tailed).

Table 3 provides econometric evidence about the influence of sequentiality and observability on contributions. The dependent variable is the amount of tokens contributed in the tth round. Table 3 consists of two panels. The left panel displays the results of five regressions that focus on treatment effects. Column 1 shows results of a generalized least squared regression. As each subject's contribution decision was observed repeatedly (15 occurrences), we appeal to panel data methods, and estimate all of the regressions with random effects. Column 2 replicates column 1 by using a random effects Tobit model to account for left censoring. (13) Columns 3, 4, and 5 present estimates that aim to isolate the pure effect of sequentiality (column 3), information (column 4), and the combined effect of sequentiality and observability (column 5). The right panel presents the results for specifications focusing on the sequential treatment with information only (see columns 6, 7, and 8).

[FIGURE 1 OMITTED]

The independent variables include several dummy variables. The dummy variable "information" controls for the influence of information on contributions. It takes value 1 if subjects are informed about previous contributions in the sequence and 0 otherwise. The binary variable "sequentiality" controls for a pure order effect. We also included two variables that account for the influence of past contributions: the lagged average contribution of the other members of the group ([[bar.x].sup.t-1.sub.-i]) and the average contribution of lower-ranked subjects in the current period [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. In the simultaneous treatment and the sequential treatment without information, the only information about past periods that is available is ([bar.x].sup.t-1.sub.-i])). In contrast, in the sequential treatment with information, subjects might be influenced both by ([bar.x].sup.t-1.sub.-i])) and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Finally, we introduced a dummy variable for the last round (period 15) to detect a possible end-game effect and a dummy that controls for group size.

The estimates summarized in Table 3 confirm most of our previous findings. The variable "sequentiality" is negative, but insignificant in column 1, confirming that sequentiality alone without observability has no significant impact on the level of average contribution. In contrast, the variable "information" captures a positive and significant effect, indicating that subjects contribute significantly more in the sequential treatment with observability. The dummy variable controlling for group size is not significant, which confirms our previous finding. The trend variable shows a negative and significant effect. The Tobit models in columns 2, 3, and 4 all deliver the same conclusion: individual contributions are sensitive to observability only. Finally, the positive and highly significant coefficient associated to the variable "sequentiality and observability" in column 5 shows that, after controlling for group size and several other variables, the combined effect of sequentiality and observability increases contribution level. (14)

[FIGURE 2 OMITTED]

B. Determinants of Contributions

We now turn to our main question: how does sequentiality and observability of others' contributions affect a subject's contribution? Our answer is stated in Results 2 and 3. Result 2 summarizes our findings about the relationship between observability of other players' contributions and the level of own contribution. In Result 3 we report our findings about the dynamics of the leadership effect and the reciprocity effect within a sequence. Remember that our conjecture is that a subject's contribution is both affected by the observed contributions of the lower-ranked subjects (reciprocity effect) and by his attempt to influence the contributions of higher-ranked subjects (leadership effect).

Result 2: Consistent with the "reciprocity" effect, a subject's contribution in period t is higher (a) the higher the average contribution of the other group members in period t-1 for all treatments, (b) the higher the contributions of the lower-ranked subjects in the period t sequence (in the sequential treatment with observability).

Support for Result 2: Table 3 shows that in all treatments the variable "others' lagged average contribution" has a positive and significant influence. High contributions on the part of the other group members are imitated or reciprocated by high individual contributions. Note that this effect is stronger for the simultaneous treatment and sequential treatment without information (column 3) than for the sequential treatment with information (column 6). For the latter treatment, the variable "contribution of lower-ranked players" has a positive and highly significant impact on own contribution. This result suggests that in the sequential treatment with information subjects rely more strongly on the observed contributions within the current sequence than on past periods' contributions, to choose their current contribution level. Our interpretation is that the information about within-sequence contributions is more relevant to subjects than the information about past periods contributions. The variable "contribution of lower-ranked subjects" has also a significant and positive impact on the last player's contribution in the sequence (see column 7). This result suggests the existence of a pure reciprocity effect, as the last player in the sequence has no influence on the lower-ranked subjects within the sequence. Taken together, the above results support the idea that individuals reciprocate previously observed contributions in the sequence. Interestingly, our data also indicate that the first-ranked player who cannot rely on any information generated within the sequence relies more strongly on the previous period average contribution observed in the group than the last-ranked player, as shown by the positive and significant coefficient associated to the interaction term "others' lagged average contribution x positionl" (see column 8).

We conclude that the higher average contribution levels observed in the sequential treatment with information is mainly driven by a strong reciprocity effect induced by the possibility to observe previous contributions by lower-ranked contributors. However, our findings also show that there are two types of reciprocity effects in our data: first, group members reciprocate to others' average contribution in the previous period; second, group members reciprocate to previous contributions within a sequence. A key question is whether these two reciprocity effects act as complements or as substitutes. According to our analyses, the within-sequence reciprocity effect is more likely to be a substitute than a complement with respect to past contributions (the robustness check shows only a weak significance of past contributions).

C. Contribution Dynamics within Sequences

In this subsection, we investigate subjects' contribution behavior within sequences under observability (sequentiality with information). Result 3 indicates the dynamics in the sequence over time.

Result 3: Consistent with a "'leadership" effect, individuals who decide first in the sequence, contribute significantly more than other group members in the sequential treatment with observability. The level of contribution declines with the position in the group. In contrast, contributions are unaffected by the position in the sequential treatment without information.

Support for Result 3: Figure 3 shows the average contribution of small groups, by position (rank) in the group, for the two sequential treatments. Figure 4 provides similar information for large groups. Both figures indicate that the average contribution in the sequential treatment with information decreases with the position in the game. In contrast, the average level of contribution in the sequential treatment without information does not vary across positions. Figures 3 and 4 also reveal that the average contribution of the early players in the sequence is higher than in the baseline, whereas the opposite is true for later players in the sequence. Indeed for small groups, the average contribution of the three first players in the sequence is larger than the average contribution in the simultaneous treatment, but the average contribution of the fourth player is lower than in the benchmark suggesting a possible "end-of-sequence effect." Figure 4 shows a similar pattern for large groups: the average contribution of the first six players in the sequence is larger than the average contribution in the simultaneous treatment, whereas the average contribution of the last two players is lower than in the benchmark treatment. These facts suggest that the combined effect of leadership and reciprocity explains why subjects who have to decide early in the sequence contribute larger amounts under observability than under nonobservability.

Further evidence about the decline of contributions with the position can be found in Tables 4 and 5 which display the average contribution levels by position, respectively, for small and large groups. In both tables, the second and the fifth columns indicate the overall average individual contribution for each group, respectively, for the sequential treatments with and without information. The third and sixth columns give the average individual contribution for the first position in the group. Finally, the fourth and seventh columns provide similar information for the final position of the group. Our data clearly indicate that contributions in the sequential treatment with information are higher in the first position than in the last position. Our finding that the average contribution declines within a sequence according to the rank of the contributor, seems to mimic the general pattern of the decline of the average contribution in a repeated game where contributions are simultaneous. No such rank-effect appears in the sequential treatment without information.

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

Table 6 provides the results of a more refined analysis of the dynamics of contributions within sequences. The reported evidence supports the hypothesis of the co-existence of an imperfect reciprocity effect and a vanishing leading-by-example effect. The dependent variable is [x.sub.it] the contribution of subject i in period t. The left panel displays the results of four regressions for small groups and the right panel reproduces similar regressions for large groups. The independent variables include dummy variables for each position in the group. The variable "position 2" is equal to 1 if subject i is in the second position and equal to 0 otherwise. The other position dummies are defined in a similar way. The results from columns 1, 2, 5, and 6 are interpreted in relation with the omitted category position 1. Columns 3, 4, 7, and 8 report similar estimates with the notable exception that the "average contribution of lower-ranked subjects" variable is included in the regressions. The "position" variables are therefore interpreted in reference to the omitted variable "position 2" in these estimates as observations from position 1 are excluded from the analysis when one controls for average contribution of lower-ranked players.

As expected from previous results, the position in the sequence has no influence on players' contribution in the sequential treatment without information (see columns 1 and 5). In contrast, the position in the sequence has a strong negative impact in the sequential treatment with information, for both group sizes (see columns 2 and 6). Notice that the absolute value of the coefficients tends to become larger for later positions, indicating that the negative impact gets stronger as the position rank increases. Similar results are found using Random Effects Tobit models (see columns 4 and 8).

The above result is compatible with a vanishing leadership effect, an imperfect reciprocity effect, or a combination of these two effects. To obtain some insight about which of the two effects fits our data best, we included the variable "average contribution of lower-ranked subjects" in estimates 3, 4, 7, and 8. The coefficient associated with this variable is positive and significant, indicating that subjects are positively influenced by the observation of previous contributions in the rank. For each token contributed by lower-ranked players, subjects contribute 0.310 tokens (0.168 tokens), in the sequential treatment with information in small (large) groups (see columns 3 and 7). We interpret the fact that the magnitude of the coefficient on "average contribution of lower-ranked subjects" is less than one as evidence of imperfect reciprocity within sequences. Furthermore, the fact that the coefficient of the variable "others' lagged average contribution" is also less than one, provides evidence about imperfect reciprocity across periods. Both results are in line with recent findings about imperfect reciprocity (Fichbacher and Gachter 2009; Neugebauer et al. 2009).

However, imperfect reciprocity is not the sole driving force of the dynamics of contributions in our data. After controlling for average contribution of lower-ranked players, most of the estimated coefficients of the "position" variables are still negative and significant, suggesting that imperfect reciprocity is not the only reason of the decline of contributions within sequences of the sequential game with information. Column 3 indicates that players in position 3 (position 4) contribute 0.998 (2.558) tokens less than players in position 2 for small groups, which is consistent with a vanishing leadership effect.

Finally, Table 6 provides a rather mixed support for the existence of an end-of-sequence effect. A t test comparing "position 4" and "position 3" shows a significant difference at the 1% level, a difference that we tentatively attribute to an "end-of-sequence" effect. However, no such effect can be found under the large group size condition (see column 7). (15)

Taken together, these findings indicate that the decline of contributions with the position in the sequence would be mainly because of the combination of a fading reciprocity effect and a vanishing leadership effect. Early contributors in the sequence may feel responsible for setting a good example for later contributors, expecting later contributors to imperfectly reciprocate their decisions.

Our findings are consistent with the experimental literature on two-stage sequential contribution games (Arbak and Villeval 2007; Gachter et al. 2009b; Gachter and Renner 2010; Guth et al. 2007; Levati, Sutter, and van der Heijden 2007; Moxnes and van der Heijden 2003; Rivas and Sutter 2009): the first mover contributes a larger amount, but the second mover reciprocates strongly. When more stages are involved, as in our experiment, the leadership effect characterizes also later movers, but tends to become consistently weaker as the number of remaining players decreases.

V. CONCLUSION

We studied an experimental game of voluntary contributions to a public good, in which players move sequentially. In our two test treatments, players contribute sequentially--with or without being able to observe the contributions of lower-ranked subjects, while in our control treatments all players have to make their contribution simultaneously. Our paper contributes to the existing literature by showing what effects sequentiality and information induce on the individual contribution levels. Our results show that sequentiality without observability does not significantly affect the average level of contribution, compared to the simultaneous contribution treatment, in accordance with Guth, Huck, and Rapoport (1998), who showed that in a game with a unique equilibrium, the positional order effect is seriously weakened.

Two major experimental results have been obtained: (1) the average level of contribution is significantly increased with respect to simultaneous contributions when subjects contribute sequentially and have the opportunity to observe previous contributions, and (2) the average contribution declines with the position in the sequential contribution game with information. We showed that Result (1) is because of the combined effect of leadership and reciprocity while Result (2) is mainly because of the combination of a vanishing leadership effect and imperfect reciprocity.

These findings are consistent with the fact that contributions are not purely intrinsically motivated, but are conditioned on observed contributions within each sequence and across sequences, which is in line with earlier findings on conditional cooperation in social dilemma games. Our results are also compatible with the so-called leadership effect, highlighted in several experiments on public goods provision. Subjects who decide earlier in the sequence expect that their contribution will affect positively the contributions of later decision makers. Accordingly, they try to encourage them by making a large contribution. As the decision sequence moves toward the last player, implying that fewer players are likely to be influenced, the leadership effect vanishes, and the average contribution declines in the higher ranks of the game.

We also found that in the sequential treatment with observability, the level of contribution is only weakly influenced by the previous period average contribution in contrast to the treatments without observability. Instead, subjects rely more strongly on the contributions observed in the current sequence. Also, we found that the size of the group does not have a significant impact on contributions.

The fact that later contributors are influenced by the observed contributions of early players in sequential games might have important policy implications. Posting information on previous contributions might be considered as a tool for increasing the level of contributions, and the design of some public policies could take into account the leading-by-example effect. For example, public announcements of previous efforts to reduce polluting emissions might increase society's overall abatement effort. However, according to our findings, such effect is weak in particular as group size increases. Nevertheless, our findings also show that it might be effective at solving social dilemmas arising within small groups of players who can potentially increase their well-being by cooperating in the form of voluntary contributions.

ABBREVIATIONS

RE GLS: Random Effects Generalized Least Squares RE Tobit: Random Effects Tobit

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(1.) Rivas and Sutter (2009) use a slightly different procedure for assigning the first mover position in a group, but which does not fundamentally differ from a random assignment.

(2.) In the case of quasi-linear self-centered preferences, Varian (1994) demonstrated that, incentives to free ride are exacerbated when contributions are sequential with respect to a simultaneous contribution environment. Two experimental papers (Andreoni, Brown, and Vesterlund 2002; Gachter et al. 2009a) addressed the issue, with mixed evidence concerning Varian's conjecture.

(3.) Experiments considered either a two-player game (Gachter et al. 2009b; Kumru and Vesterlund 2008; Potters, Sefton, and Vesterlund 2007), or larger numbers of players (Arbak and Villeval 2007; Guth et al. 2007; Levati et al. 2007; Moxnes and van der Heijden 2003; Pogrebna et al. 2009; Rivas and Sutter 2008).

(4.) CREM (Centre de Recherche en Economie et Management), LABEX (Laboratoire d'Experimentation en Sciences Sociales), LAMETA (Laboratoire de Recherche en Economie Theorique et Appliquee). No significant differences were found in data between the two locations of the experiments.

(5.) The sequential treatments took slightly more time in large groups.

(6.) Instructions are available upon request to the authors.

(7.) To control for the existence of a possible "framing effect," we also ran two sessions with a variant of the reference treatment, labeled " simultaneous treatment with framing." This control was useful because the sequential version of the contribution game required a slight alteration of the usual presentation of the instructions. For this variant the investment in the group account is presented as an explicit addition of individual contributions which matches the presentation that was used for the sequential contribution treatments. The instructions pointed out that each subject's contribution would be identified by an index, for example, subject i's contribution is noted [I.sub.i], and that the payoff of the group account would be given by 0.5 x ([I.sub.1] + [I.sub.2] + ... + [I.sub.N]).

This point was described to the subjects in the following language:

"[I.sub.1] is member 1's investment to the collective account [I.sub.2] is member 2's investment to the collective account [I.sub.3] is member 3's investment to the collective account" This presentation, by making explicit the summation of individual contributions, could have influenced the subjects' decisions in a nonpredictable way. However, the results indicate no significant difference (at any conventional level of significance) in average contribution between the simultaneous treatments with and without framing. Note that this presentation was only used for simultaneous contribution treatments. In sequential treatments index i referred to the rank of the players.

(8.) Fischbacher, Gachter, and Fehr (2001) investigated the importance of conditional cooperation in the context of a one-shot game using a variant of the strategy method. The authors found that 50% of subjects are conditional cooperators.

(9.) To some extent the effects of sequentiality with information may be comparable to the effects of some reduced form of communication. Previous research has found that communication (including nonbinding, pre-play, face-to-face communication between players) increases the level of contributions. However, there is no consensus on why this occurs (see Krishnamurthy 2001 for a survey).

(10.) As Ledyard (1995) noted, "Those arguing for a decrease as group size increases argue that, in larger groups, non-cooperative behavior is more difficult to detect and therefore self-interested subjects should contribute less. The opposite argument usually relies on the fact that any tendency toward altruism may be also reinforced as N increases." Furthermore, with other regarding preferences a la Bolton and Ockenfels (2000), it is easy to check that marginal incentives to contribute depend on the size of the group, in an ambiguous way however.

(11.) We thank an anonymous referee for this helpful remark.

(12.) In all statistical tests reported in this paper, the unit of observation is the group.

(13.) There were no right-censored observations in our data.

(14.) Separate estimates for each size condition (not reported here but available upon request) provide similar findings. These findings contrast with our previous nonparametric results presented above. The difference between our parametric and nonparametric analysis can be easily explained by the fact that estimates provide more precise results as we control for several other effects as well as for panel dimension.

(15.) Note that the interpretation in term of end-of-sequence effect also coincides with the absence of the leading-by-example effect in the last position of the game. Another interpretation is to consider that the end-of-sequence effect simply results from the absence of a leading-by-example effect in the last position of the sequence.

CHARLES FIGUIERES, DAVID MASCLET, and MARC WILLINGER *

* We thank participants at the 2009 International Meetings of the Association for Public Economic Theory (APET) at the National University of Ireland, Galway. We also thank Marie-Claire Villeval for helpful comments, and Elven Priour and Dimitri Dubois for programming and research assistance. Financial support from the Agence Nationale de la Recherche (ANR-08-JCJC-0105-01, "CONFLICT" project) is gratefully acknowledged.

Figuieres: Research Director, INRA, CNRS, Universite Montpellierl, LAMETA, INRA, 2 place Viala, 34060 Montpellier, France. Phone +33 (0)499 61 22 09, E-mail [email protected]

Masclet: Research Associate Professor, CNRS, CREM, Universite Rennes 1, 7 Place Hoche, 35065 Rennes, France; CIRANO, Montreal, Canada. Phone +33(0)223 23 33 18, E-mail [email protected]

Willinger: Professor, INRA, CNRS, Universite Montpellierl, LAMETA, Faculte d'Economie, Avenue Raymond Dugrand--Site de Richter C.S. 79606, 34960 Montpellier CEDEX 2, France. Phone +33(0)434 43 25 19, E-mail [email protected].

doi: 10.1111/j.1465-7295.2011.00415.x

TABLE 1
Number of Independent Observations Per Cell

Session Number Number of
Number Treatment of Groups Subjects

 1 Simultaneous game 5 20
 2 Simultaneous game # 4 16
 3 Simultaneous game # 4 16
 4 Simultaneous game 2 16
 5 Simultaneous game 2 16
 6 Simultaneous game 2 16
 7 Sequential game with info 3 12
 8 Sequential game with info 3 12
 9 Sequential game with info 2 16
 10 Sequential game with info 2 16
 11 Sequential game with info 2 16
 12 Sequential game without info 4 16
 13 Sequential game without info 4 16
 14 Sequential game without info 2 16
 15 Sequential game without info 2 16
 16 Sequential game without info 2 16

Session Size of
Number the Group Location

 1 4 Rennet
 2 4 Montpellier
 3 4 Rennet
 4 8 Montpellier
 5 8 Montpellier
 6 8 Rennet
 7 4 Rennet
 8 4 Montpellier
 9 8 Montpellier
 10 8 Rennet
 11 8 Montpellier
 12 4 Rennet
 13 4 Montpellier
 14 8 Rennet
 15 8 Rennet
 16 8 Montpellier

Note: # indicates simultaneous game with framing.

TABLE 2
Group Average Contribution Levels (SD in brackets)

Group N=4

 Sim Seq. without Info Seq. with Info Sim

 1 4.3 # 5.4 4.58 4.84
 (2.94) (4.57) (3.67) (3.44)
 2 4.15 # 4.7 6.23 4.95
 (2.83) (3.17) (3.11) (3.38)
 3 5.91 # 4.28 5.15 3.48
 (2.33) (4.72) (2.99) (3.44)
 4 2.78 # 5.93 5.53 5.26
 (3.26) (3.06) (3.31) (3.34)
 5 5.25 # 4.21 5.35 3.52
 (2.93) (3.12) (3.30) (3.61)
 6 6.08 # 4.1 4.68 3.18
 (2.52) (3.05) (3.11) (3.35)
 7 2.61 # 2.28
 (2.96) (2.59)
 8 2.5 # 3.05
 (2.48) (3.03)
 9 4.95
 (1.92)
 10 2.05
 (1.99)
 11 2.96
 (3.17)
 12 5.25
 (2.47)
 13 4.46
 (3.13)
 4.09 4.24 5.25 4.20
 (2.68) (3.41) (3.32) (3.42)

Group N=8

 Sim Seq. without Info Seq. with Info

 1 4.3 # 2.65 3.85
 (2.94) (3.43) (3.08)
 2 4.15 # 2.7 3.88
 (2.83) (2.5) (3.85)
 3 5.91 # 3.22 6.025
 (2.33) (2.43) (3.08)
 4 2.78 # 4.28 5.50
 (3.26) (2.91) (4.03)
 5 5.25 # 4.05 4.24
 (2.93) (3.04) (2.22)
 6 6.08 # 3.34 6.53
 (2.52) (2.72) (4.28)
 7 2.61 #
 (2.96)
 8 2.5 #
 (2.48)
 9 4.95
 (1.92)
 10 2.05
 (1.99)
 11 2.96
 (3.17)
 12 5.25
 (2.47)
 13 4.46
 (3.13)
 4.09 3.37 5.03
 (2.68) (2.83) (3.42)

Notes: # indicates that the results show no significant difference at
any level of significance in average contribution between the
simultaneous treatments with and without framing. All simultaneous
treatments with large groups were conducted with framing.

TABLE 3
Determinants of Individual Contribution

 All All Sim. and Seq.
Treatments Treatments Treatments without Info.
Models RE GLS (1) RE Tobit (2) RE Tobit (3)

Others' average 0.299 *** 0.388 *** 0.485 ***
 contribution (lagged) (0.030) (0.039) (0.047)

Others' average
 contribution (lagged)
 x position 1
Information 1.047 *** 1.252 ***
 (0.293) (0.401)
Sequentiality -0.272 -0.228 -0.177
 (0.369) (0.370) (0.387)
Seq. and info

Contribution of
 lower-ranked subjects
Size N = 4 0.232 0.325 0.311
 (0.230) (0.316) (0.386)
Round 15 -1.070 *** -1.676 *** -1.626 ***
 (0.191) (0.255) (0.299)
Constant 2.751 1.681 1.275
 (0.249) (0.338) (0.382)
Observations 3528 3528 2520
[R.sup.2] 0.08
Left cens. 839 651

 Seq. with and Sim. and Seq.
Treatments Without Info. with Info.
Models RE Tobit (4) RE Tobit (5)

Others' average 0.363 *** 0.319 ***
 contribution (lagged) (0.049) (0.046)

Others' average
 contribution (lagged)
 x position 1
Information 1.295
 (0.361)
Sequentiality

Seq. and info 1.080
 (0.405)
Contribution of
 lower-ranked subjects
Size N = 4 0.363 0.274
 (0.369) (0.405)
Round 15 -1.445 *** -1.914 ***
 (0.340) (0.046)
Constant 1.498 2.022
 (0.340) (0.389)
Observations 2128 2408
[R.sup.2]
Left cens. 493 534

 Seq. with
 Seq. with Seq. with Info. First
 Info. All Info. Final and Final
Treatments Positions Position Positions
Models RE Tobit (6) RE Tobit (7) RE Tobit (8)

Others' average 0.142 * 0.321 -0.092
 contribution (lagged) (0.075) (0.201) (0.116)
 0.739***
Others' average (0.078)
 contribution (lagged)
 x position 1
Information

Sequentiality

Seq. and info

Contribution of 0.345 *** 0.300 **
 lower-ranked subjects (0.040) (0.121)
Size N = 4 -0.126 0.487 0.026
 (0.580) (1.275) (0.705)
Round 15 -1.433 *** -2.221 -1.571*
 (0.535) (1.680) (0.873)
Constant 1.800 -1.714 ** 3.026
 (0.545) (1.407) (0.732)
Observations 840 168 336
[R.sup.2]
Left cens. 177 73 84

Note: Standard errors in parentheses.

*** Significant at the 0.01 level; ** significant at the 0.05 level;
* significant at the 0.1 level.

TABLE 4
Small Groups Average Contribution by Position in the Game (SD in
brackets)

 Sequential Treatment with Info

Group All Positions First Position Last Position

 1 4.58 6.33 2.26
 (3.67) (3.24) (3.43)
 2 6.23 7.33 4.33
 (3.11) (1.87) (3.90)
 3 5.15 6.86 3.4
 (2.99) (2.16) (3.37)
 4 5.53 6.33 3.13
 (3.31) (2.60) (3.15)
 5 5.35 6.93 2.86
 (3.30) (2.93) (2.58)
 6 4.68 4.4 4.13
 (3.11) (2.13) (3.92)
 7

 8

 5.25 6.36 3.35
 (3.32) (2.64) (3.40)

 Sequential Treatment without Info

Group All Positions First Position Last Position

 1 5.4 5.13 6.2
 (4.57) (4.77) (4.49)
 2 4.7 3.8 4
 (3.17) (3.21) (3.11)
 3 4.28 4.33 4.73
 (4.72) (4.77) (4.90)
 4 5.93 5.46 4.93
 (3.06) (2.97) (3.69)
 5 4.21 3 3.66
 (3.12) (2.92) (2.46)
 6 4.1 5.33 4.13
 (3.05) (3.08) (2.97)
 7 2.28 1.53 1.8
 (2.59) (1.84) (3.12)
 8 3.05 3 3.8
 (3.03) (3.42) (2.73)
 4.24 3.94 4.15
 (3.41) (3.37) (3.43)

TABLE 5
Large Groups Average Contribution by Position in the Game (SD
in brackets)

 Sequential Treatment with Info

Groups All Positions First Position Last Position

1 3.85 4.26 2
 (3.08) (3.41) (2.23)
2 3.88 6.33 0.93
 (3.85) (3.19) (2.63)
3 6.025 8.26 6.2
 (3.08) (1.83) (3.91)
4 5.50 7.86 2.66
 (4.03) (3.02) (4.23)
5 4.24 4.6 2.8
 (2.22) (2.55) (2.54)
6 6.53 6.6 5.53
 (4.28) (4.70) (4.71)
Average 5.03 6.31 3.35
 (3.42) (3.11) (3.37)

 Sequential Treatment without Info

Groups All Positions First Position Last Position

1 2.65 3.13 2.93
 (3.43) (3.96) (3.55)
2 2.7 2.8 2.53
 (2.5) (2.30) (2.79)
3 3.22 3.46 3.2
 (2.43) (2.41) (1.89)
4 4.28 4.2 4.06
 (2.91) (3.12) (3.08)
5 4.05 2.46 5
 (3.04) (2.19) (3.31)
6 3.34 2.4 2.86
 (2.72) (2.5) (2.26)
Average 3.37 3.07 3.43
 (2.83) (2.74) (2.81)

TABLE 6
Regression of Contribution by Position in the Game

 Group Size N = 4

 N=4 N=4 N=4
 Seq. without Seq. with Seq. with
Treatment Info Info Info
Models RE GLS (1) RE GLS (2) RE GLS (3)

Others' average 0.457 *** 0.229*** 0.160 ***
 contribution (0.068) (0.0718) (0.082)
 (lagged)

Position 1 Ref. Ref.

Position 2 0.717 -0.375 Ref.
 (0.435) (0.435)

Position 3 -0.07 -1.453*** -0.998 **
 (0.435) (0.434) (0.417)

Position 4 0.286 -3.353*** -2.558 ***
 (0.435) (0.440) (0.430)

Position 5

Position 6

Position 7

Position 8

Average contribution 0.310 ***
 lower ranks (0.062)

Round 15 -1.766 *** -2.066 *** -1.642 ***
 (0.609) (0.597) (0.680)

Constant 1.971 *** 5.462 *** 3.411 ***
 (0.471) (0.541) (0.701)

Observations 448 336 252
Lef. cens.

 Group Size
 N = 4 Group Size N = 8

 N=4 N=8 N=8
 Seq. with Seq. without Seq. with
Treatment Info Info Info
Models RE Tobit (4) RE GLS (5) RE GLS (6)

Others' average 0.197 ** 0.236 ** 0.078
 contribution (0.100) (0.093) (0.075)
 (lagged)

Position 1 Ref. Ref.

Position 2 Ref. 0.409 -0.639
 (0.406 (0.461)

Position 3 -1.258 ** -0.254 -1.143 **
 (0.503) (0.405) (0.457)

Position 4 -3.254 *** -0.203 -0.947 **
 (0.531) (0.407) (0.453)

Position 5 0.182 -1.837 ***
 (0.407) (0.469)

Position 6 -0.387 -2.274 ***
 (0.412) (0.457)

Position 7 0.342 -3.687 ***
 (0.405) (0.460)

Position 8 -0.119 -3.763 ***
 (0.395) (0.460)

Average contribution 0.365 ***
 lower ranks (0.078)

Round 15 -2.357 *** 0.139 -0.858 *
 (0.889) (0.395) (0.442)

Constant 2.823 *** 2.216 *** 6.442 ***
 (0.849) (0.250) (0.580)

Observations 252 672 672
Lef. cens. 51

 Group Size N = 8

 N=8 N=8
 Seq. with Seq. with
Treatment Info Info
Models RE GLS (7) RE Tobit (8)

Others' average 0.076 0.073
 contribution (0.079) (0.099)
 (lagged)

Position 1

Position 2 Ref. Ref.

Position 3 -0.369 -0.362
 (0.466) (0.568)

Position 4 -0.109 -0.137
 (0.456) (0.555)

Position 5 -1.001** -1.135 **
 (0.471) (0.574)

Position 6 -1.354*** -1.599 ***
 (0.464) (0.570)

Position 7 -2.684*** -3.449 ***
 (0.470) (0.586)

Position 8 -2.647*** -3.788 ***
 (0.476) (0.604)

Average contribution 0.168 *** 0.195 ***
 lower ranks (0.036) (0.046)

Round 15 -0.724 -1.208 **
 (0.470) (0.606)

Constant 4.684 *** 4.386 ***
 (0.640) (0.782)

Observations 588 588
Lef. cens. 126

Note: Standard errors in parentheses.
*** Significant at the 0.01 level; ** significant at the 0.05 level;
 * significant at the 0.1 level.