An Econometric Analysis of Voluntary Contributions

Contributions to public goods simulated in economists' laboratory experiments have two peculiarities from the perspective of statistical modelling. There is a variety of contributor behaviours (Ledyard, 1995), suggestive perhaps of separate classes of individuals, and contributions are doubly censored. We present an econometric model of contributions in sequential play, which takes into account the censoring, admits variation both within and between individuals, and allows for the existence of a distinct class of free-riders. The model synthesises the 2-limit tobit analysis of Nelson (1976), the extension of tobit to panel techniques by Kim and Maddala (1992) and the "p-tobit" hurdle model of Deaton and Irish (1984). We estimate it for panel data from a public good experiment reported in Bardsley (2000). It reveals pronounced inter- and intra- individual variation, and shows significant effects for subjects' order in a sequential game, others' contributions and the position of the choice task within the experiment. These effects are plausibly attributable to egoism, reciprocity and learning respectively. In addition, the existence of a distinct class of free-riders, who conform to a game theoretic prediction of unconditional non- contribution, is confirmed. The model is estimated for tasks in which "others' behaviour" was controlled by the experimenter (but without using deception). We compare its predictions for actual play (in which others' behaviour is not controlled) with behaviour in a real game task. The predictions are consistent with the data.