Analysis of Public Goods Experiments Using Dynamic Panel Regression Models*

Laboratory experiments on the provision of public goods follow each subject over time as he interacts with a small group of others, deciding in each period how much of an initial allocation to contribute to a group good that yields a return to all group members. These experiments produce data sets that are rich in dynamics, as subjects respond not only to the parameters of the experiment, but also to previous allocation decisions made by themselves and the other individuals in their group. In most early studies, the data analysis consisted of an informal inspection of the time plots of data for each treatment, averaged over all participants. Subsequent studies conducted simple statistical tests of average behavior. There has been very little analysis of the individual data. Data sets from these experiments thus provide an unexploited opportunity to understand how an individual’s behavior evolves over time in response to feedback about the behavior of others. A better understanding of the dynamics of behavior in these games has the potential to lead to the design of institutions that improve the efficiency of the private provision of public goods. Proper analysis of these data presents several challenges. In addition to modeling the (possibly complex) interactions among agents, the data are almost always substantially censored from both above and below. We analyze the results of two classic public goods experiments (Isaac and Walker (1988) and Andreoni (1995)) explicitly as double-censored panel data in which both lagged dependent variables and lagged allocations from the remainder of the group play important roles as explanatory variables. We find that modeling the dynamic interactions and double censoring extract a richer set of results than previously seen. In particular, failure to take into account the censoring of the data may substantially underestimate the magnitude of treatment effects. More importantly, there are economically and statistically significant, and asymmetric, cross-subject dynamics in these data. Subjects respond much more dramatically when their contributions are above average than when they are below average. Thus heterogeneity in initial contribution levels inherently leads to the deterioration of average contributions over time. JEL Codes: C920, C230, C240, C700