S TRICT RATIONALITY

CCEI and FOSD measures the two separate parts of strict rationality and a measure of strict rationality should include both these measures. A criterion for strict rationality can be that both CCEI and FOSD should be above 0.95, which would be met by 51 of the subjects in the high-stake treatment and 35 of the subjects in the low-stake treatment. The linear probability model in table 8-9, show that it is 13 % more likely that a subject has both FOSD and CCEI scores above 0.95 if the subject is in the high-stake treatment. This result indicates that even though the difference between the FOSD scores and the CCEI scores are not statistically significant separately, a larger number of subjects in the high-stake treatment are both

consistent and taking non-dominated choices. However, the results are not robust to a test where strict rationality is measured continuously with equal weights on CCEI and FOSD.

Table 8-9 – Regression with dummy for strictly rational on high-stake

(1) (2)

Note: The table reports a regression of strictly rational on treatment status, where regression 2 includes covariates. Strictly rational is a dummy for having both CCEI and FOSD score above 0.95 and high-stake is a dummy for being allocated to high-stake treatment. Covariates include sex, age, education background of parents (whether they attended secondary school and university) and big-five personality traits. Standard errors in parentheses; *p<0.1, **p<0.05 ***p<0.01

A second control for strict rationality is the CCEI-combined, which is the CCEI score for the combined data set, with the 50 real observations and the 50 mirrored decisions. By mirroring all the decisions a measure of dominance is included in the CCEI score, as a decision that was previously dominated will in combination with the mirrored decision give a violation of GARP as explained in section 3.2.

The treatment effect of high-stake on the CCEI-combined is close to significant, with a p-value of 0.12 in the regression with covariates. Furthermore the coefficient is positive indicating that high-stake subjects take more strictly rational decisions than low-stake subjects. From the adjusted R-squared ²⁵ it can be noted that adding the covariates does not increase the explanatory power of the model, meaning that there may be other covariates which could improve the model and reduce the standard errors.

25 In linear regressions the R² is the sample correlation coefficient between the outcomes and their predicted values or in other words how much the variables included in the regression model explain the dependent variable. The adjusted R² adjust for the fact that adding covariates will always increase R², and the adjusted R² will only increase if the new term improves the model more than would be expected by chance. (Woolridge 2009)

Table 8-10 – Regression of treatment on CCEI score for combined dataset

Note: The table reports regressions of CCEI for the combined dataset on treatment status, controlling for covariates. CCEI is a measure of the extent to which the budget constraints must be relaxed in order to remove all violations of GARP in the decision set, bound between 0 and 1. High-stake is a dummy for being assigned to receive high-stake treatment. Covariates include sex, age, education background of parents (whether they attended secondary school and university) and big-five personality traits. Standard errors in parentheses^* p <

0.1, ^** p < 0.05, ^*** p < 0.01

8.5 Effort

There is some evidence that the high-stake subjects are more strictly rational than the low-stake subjects. A further control is whether the high-low-stake subjects have higher effort than the low-stake subjects, which would increase performance unless there are psychological mechanisms that may lead to performance decrements. In analysing effort, time spent on each decision can be used as a proxy. The causal effect of time cannot be identified with the data available, which means that it cannot be controlled whether taking more time on each decision causes more rational decision. A regression of time on CCEI would give a significant and positive coefficient; however, this can be a result of selection bias and does not necessarily mean that using more time causes the decisions to be more consistent.

However, it can be identified causally whether subjects exposed to higher stakes spend more time on the decisions. High-stake subjects are taking 2.36 more seconds on each decision than low-stake individuals, significant at a 10 % level. On average, low-stake subjects take 19.7 seconds, and high-stake subjects take 22.0 seconds per decision, reported in table 8-11.

This provides suggestive evidence that high-stakes induces more effort, even though this does not translate into more rational decisions.

There are three possible explanations for why higher effort does not translate into statistically significant more rational decisions. A first possible explanation is that effort is not the only thing affecting the measures of rationality on the margin, which is the case if decision making is subject to psychological mechanisms like stress which can reduce performance. A second possible explanation is that increased effort only marginally affects

(1) (2)

the rationality of the decision. This would be the case if decision making is a task that is either hard to improve on or easy to do. For example an irrational subject, may not have the abilities necessary to make rational decisions, which would mean that he could only slightly increase his rationality for any level of incentives. On the other hand, a subject that is rational may consider the task at hand reasonably simple, requiring minimum effort, which would make him rational at any level of incentives. However, this second explanation is not necessarily consistent with the high-stake subjects spending more time on making the decisions, and this theory will be studied further under heterogeneity. A third possible explanation is that the incentives influence the subjects heterogeneously.

Table 8-11 Time

Note: The table reports regressions of time on treatment status, where (2) controls for covariates. Time is measured by the average time spent on each decision and high-stake is a dummy variable for belonging to the high-stakes treatment. Covariates include age, sex, education level of parents (whether they attended secondary school and university), IQ and big-five personality traits. Standard errors in parentheses ^* p < 0.1,

** p < 0.05, ^*** p < 0.01