ناهماهنگی شناختی، بدبینی و اثرات سرریز رفتاری

Abstract A two-stage experiment was designed to examine spillover effects of a type of optimism/pessimism. We first exploit cognitive dissonance to induce optimism/pessimism by random assignment of high/low piece rates for performing a task. Subjects receiving the low piece rate are significantly more pessimistic with respect to performance. In Stage 2 individuals participate in an ultimatum game. Pessimistic subjects have significantly lower minimum acceptable offers, though pessimism was randomly generated in an unrelated environment. These results reveal behaviorally and economically important spillover effects – for example, pessimism regarding one’s initial conditions (e.g., living in poverty) may have spillover effects on one’s future labor market outcomes.

3. Results A total of 86 individuals participated in the study, with each session lasting approximately 45 min. Table 1 presents the summary statistics from Stage 1 and 2 of the experiments.9 The first four columns report Stage 1 data. Here, we find no differences in performance on the grammatical reasoning task or expectations across piece rates (Kolmogorov–Smirnov p > 0.70 for each). However, we do identify differences in the distribution of optimism/pessimism, which we measured by the difference between expected and actual performance (see Fig. 1): K–S p = 0.011 between those receiving the high piece rate (mean 4.03, σ = 9.78) and those receiving the low piece rate (mean −0.18, σ = 12.15), thus rejecting the hypothesis that high and low piece-rate subjects have similar beliefs in favor of the one-tailed alternative hypothesis that high piece-rate subjects are more optimistic than low piece-rate subjects—this supports H1.2. Table 1. Summary statistics–Mean (SD). Score Task earnings expected score Enjoyment Offer MAO $1.25 piece rate (n = 44) 37.71 (17.11) $47.66 (24.05) 41.73 (18.37) 5.10 (2.25) 4.43 (1.09) 3.34 (1.35) $0.25 piece rate (n = 42) 40.27 (15.46) $11.08 (4.04) 40.09 (15.43) 5.84 (1.98) 4.45 (0.95) 2.59 (1.55) Table options Distributions of optimism/pessimism (i.e., difference between score and expected ... Fig. 1. Distributions of optimism/pessimism (i.e., difference between score and expected score) by piece rate in Stage 1. Figure options Also, we identify differences between the distributions of elicited ex-post enjoyment across piece rates (K–S p = 0.041), again in the direction predicted by the cognitive dissonance hypothesis—supporting H1.1. Thus, our Stage 1 protocol successfully exploits cognitive dissonance theory and, importantly, generates a randomly assigned set of optimistic and pessimistic subjects in the domain of their individual cognitive task performance. With respect to Stage 2 behavior in the ultimatum game, we identify no differences in the distribution of offers across piece rate groups (K–S p = 0.788) and thereby reject hypothesis H2.1. However, we do identify differences in the distribution of minimum acceptable offers (MAO) across each group: Individuals receiving the low piece rate (who consequently were more likely to be pessimistic) were willing to accept lower offers than those receiving the high piece rate (who were more likely to be optimistic). These differences are significant (K–S p = 0.037, one-tailed test) and we are able to reject the hypothesis that the distributions of MAO by piece rate are drawn from the same population. The distributions of MAO are presented in Fig. 2. Distributions of minimum acceptable Ultimatum offers by piece rate in Stage 2. Fig. 2. Distributions of minimum acceptable Ultimatum offers by piece rate in Stage 2. Figure options Moreover, we identify a direct effect of the degree of optimism/pessimism on minimum acceptable offers. Specifically, we regress MAO on the degree of optimism/pessimism and piece rates, identifying separate coefficients for each piece rate. That is we estimate equation(1) MAO=β1×OP×(1-I1.25)+β2×OP×I1.25+β3×PR×(1-I1.25)+β4×PR×I1.25+ε,MAO=β1×OP×(1-I1.25)+β2×OP×I1.25+β3×PR×(1-I1.25)+β4×PR×I1.25+ε, Turn MathJax on where OP is the degree of optimism/pessimism, PR is the piece rate a participant received, and I1.25 ϵ {0, 1} is an indicator variable taking on a value of one if the participant received a piece rate of a $1.25. This allows us to estimate separate effects of optimism/pessimism across the treatment variable. Table 2 presents the results of these OLS regressions. We find no difference across piece rates regarding the effect of optimism/pessimism on MAO (β1 ≈ β2 ≈ 0.026, F(1, 81) = 0.02 comparing these coefficients). Thus, we can also pool data across treatments (i.e., eliminate the I1.25 dummy variable), which also confirms that the degree of optimism/pessimism has a small positive effect on MAO (β = 0.073, p = 0.021). This suggests that an individual’s MAO increases by $0.73 with a 10 point difference between expected and actual performance. Relative to the typical ultimatum offer of between $3 and $4 (e.g., see discussion in Camerer (2003, chap. 2) and Holt (2007, chap. 12)), this effect implies an 18–24% difference in one’s MAO resulting from this level of induced optimism/pessimism. Table 2. Results of regressions on MAO. Indep. var. Coefficient Std. err. Full model (Eq. (1); R2 = 0.816) OP × (1 − I1.25) 0.024 0.018 OP × I1.25 0.028 0.026 PR × (1 − I1.25) 2.58*** 0.196 PR × I1.25 10.38*** 0.877 Pooled data (eliminating I1.25; R2 = 0.645) OP 0.0730*** 0.031 PR 2.935*** 0.251 *, **, *** indicate significant at the .10, .05, or .01 level, respectively, for the two-tailed test. Table options The largest effect on MAO is due to the piece rate. We find β3 = 2.58 (p < 0.01) and β4 = 10.38 (p < 0.01), and these coefficients are significantly different from one another (F(1, 81) = 75.38). Similarly, for the pooled data we find a significant positive effect of piece rate on MAO (2.935, p < 0.01). Fig. 3 presents the scatterplot of MAO against our measure of optimism/pessimism. These results suggest that the effect of the piece rate on MAO is in some sense discrete: Inducing pessimism results in substantially lower MAO among participants. This is in accord with our hypothesis H2.2. Because our design implies that subjects have some sense of whether they would earn more versus less from the cognitive task at the time they engage in the ultimatum game—they know their assigned piece rate but not their task score at the start of the stage two experiment—one might be concerned that wealth effects are responsible for the piece rate effect on MAOs that we estimate. MAO plotted against optimism/pessimism measure: $0.25 piece rate fit given by ... Fig. 3. MAO plotted against optimism/pessimism measure: $0.25 piece rate fit given by diamonds (solid line OLS fit); $1.25 piece rate given by squares (dashed line OLS fit). Figure options As an additional test of the potential for wealth effects, we conducted a further analysis of our data, regressing MAO on an indicator variable for piece rates (high piece rates = 2, low piece rate = 1), task score, and earnings. This analysis would identify any manner in which MAO are related to piece rates. However, in this analysis, we find no statistically significant coefficients (p > 0.44 on all coefficients). This suggests that neither the piece rates per se nor the actual earnings (which were unknown at the time of Stage 2 but could have been estimated by participants) had any effect on elicited MAO. This further strengthens our conjecture that wealth effects are not at play in our analysis in Eq. (1) and Fig. 3. In a related vein, Armantier (2006) examines wealth effects in ultimatum games, however, and concludes that initial round wealth effects work the opposite way. That is, higher endowment subjects have lower MAOs in an effort to equate overall experimental earnings. Given that our piece rate effect is opposite the wealth-effect result found in Armantier (2006), we feel that our discrete piece rate (indirect) effect of optimism/pessimism on MAOs does not result from unexpected wealth effects in our two-stage design. In fact, to the extent that there would be a wealth effect in our ultimatum data as in Armantier (2006), our behavioral spillover results are actually strengthened because they are significant in spite of an opposite direction wealth effect on MAOs. Of course, our results are strongest if we can safely rule out other alternative explanations in addition to ruling out the wealth-effects hypothesis. Indeed, one might hypothesize that the discrete effect of lower MAOs in the low piece rate subset of subjects results from subjects anchoring their MAO to the stage-one piece rate. However, such anchoring could not explain the direct effect of pessimism on MAOs, only the indirect effect of piece rate level on MAO. Furthermore, both high and low piece rate are significantly less than average ultimatum MAOs, which weakens anchoring as a possible explanation for the direct piece rate effect we observe on MAOs in our setting.