Policy and Complex Systems
five rounds are equal to zero , meaning that group 3 is the group that tends to behave in accordance with the theoretical prediction . Group 1 and Group 2 have median values that are lower and higher than the target pollution , respectively . This means that Group 1 is the group that tends to generate less pollution than theoretically predicted and Group 2 is the group that tends to generate more pollution than theoretically predicted . We do not see obvious skewness or scarcity of any groups and the magnitudes of the separation seem reasonable . Next , we assign agents in the ABM into behavior groups using a multinomial logit model .
Mixed-Effects Multinomial Logit Model to Assign Group Probabilities
Based on cluster analysis , agents ’ behavior could be clustered into three categories . Cluster 3 corresponds to agents that tend to agree with theoretical predictions , and clusters 1 and 2 correspond to agents that tend to under and over pollute , respectively . In this part , we use a mixed effects multinomial logit model to estimate the cluster distributions among agents conditioning on the policy , heterogeneity , and information treatments .
The multinomial logit model could be formulated as follows :
where u 1 , i , u 2 , i are the random effects on the intercept and are assumed to follow a normal distribution . J equals 1 or 0 and denotes whether the policy treatment is in place or not , respectively .
Therefore , the predicted probabilities for the three clusters could be calculated as
The results of the mixed effects multinomial logit model for both policy and no policy treatments are presented in Table 3 .
In the no policy treatments , it is always in the agents ’ best interest to produce at the maximum and not adopt the technology , therefore , the theoretical optimal strategy is the upper bound of the pollution level . As a result , only two clusters exist in the no policy treatments , as reflected by having one intercept value in Table 3 . Based on the above regressions , we calculate the cluster probabilities for each of the treatment cases to initialize the model .
Modeling Agent Production and Adoption Behavior
For production decisions , we calculate the percentage deviations from the target production decisions , taking into account the size of the farm . The metric is defined as
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