VOL 87 NO.5 PALFREY AND PRISBREY:PUBLIC GOODS EXPERIMENTS 83 we examine the nature of the decision rule in detail,giving more consideration to the En=(ra V)-gi-a(N 1)V, errors generating dev od to the role of other factors such as ex where the right-hand side contains all the el. ements of the subject's utility function that de erience and altruism,that are likely to af- termine his or her choicex fect contribution decisions. Accordingly,we estimate a probit model C.The Probit Model The probit model provides a standard way the independent variables in the model.Giver ch don ent trea the public good value.and experience.The the difference (r).which we call structural model underlying this analysis is the diff;and of the ublic c good, that were controlled in the ariables exper,for experience,which takes on a U (xa,x-n) zero for decisions in bloo =yΣ+(8-nx+m period sequence of the same public good value: +aw-1y which takes on values from one to ten. +∑[(g-)x:+w1 D.The Representative Subject Model where V,is the public good value in period. e t in these rep riod and altruism effects a d t be the same across individuals.An observatio riod, is a contribution decision in a single period. player i's ruism term,and odel we assume that for each of subject i's decisions to the warm-glow her subject hen the tw ume that the are independent,identical Normally distrib uted random variables with mean zero and VOL 87 NO. 5 PALFREY AND PRISBREY: PUBLIC GOODS EXPERIMENTS 835 noise rather than some systematic compo￾nent of the decision rule. In the next sections, we examine the nature of the decision rule in detail, giving more consideration to the structure of errors generating deviations, to possible heterogeneity across individuals, and to the role of other factors such as ex￾perience and altruism, that are likely to af￾fect contribution decisions. C. The Probit Model The probit model provides a standard way to measure the probability of contribution as a function of the different treatment variables, such as the individually assigned token values, the public good value, and experience. The structural model underlying this analysis is the following. We assume that the utility player i gets in period t from contributing ;c,, units of the private good is: = V, X A subject contributes if and r L (N￾j*i J where V, is the public good value in period t, gi is player /'s warm-glow term, r,, is player i's token value in period t, Wi, is player I's endowment of tokens in pe￾riod /, a, is player I's altruism term, and A^ is number of players in /'s group. Finally, in order to estimate the model we assume that for each of subject fs decisions at period t there is a random component, e^,, that is added to the warm-glow term. This error term represents some random added propensity for the subject to either contribute or not contribute. We assume that the e^/s are independent, identical. Normally distrib￾uted random variables with mean zero and variance only if where the right-hand side contains all the el￾ements of the subject's utility function that de￾termine his or her choice Xi,. Accordingly, we estimate a probit model, where the probability of contributing a unit of the endowment is given by the cumulative Normal transformation of a linear function of the independent variables in the model. Given our specification of the decision rule of the subject, our independent variables are: • a constant term, which we call constant; • the difference (r, - V^), which we call diff; and • the value of the public good, V. In addition, we include three other variables that were controlled in the experiment: • exper, for experience, which takes on a value of zero for decisions in the first ten￾period sequence with a given public good value, and one for decisions in the second ten￾period sequence of the same public good value; • endow, which takes on a value of zero if the endowment is indivisible and one if it is divisible; and • period, which takes on values from one to ten. D. The Representative Subject Model We present estimates from two probit mod￾els which differ only in which independent variables are included. Note that in these rep￾resentative subject models, the warm-glow and altruism effects are implicitly assumed to be the same across individuals. An observation is a contribution decision in a single period.'" '" We pool observations across all experiments. Deci￾sions in the divisible endowment treatment {endow = 1) are coded as either 0 or 1, depending on whether subjects contributed less than half or more than half their endow￾ment of tokens in a given period, respectively. Similar conclusions obtain when the iwo endowment U'eatment samples are estimated separately. This is addressed in de￾tail in the next section, where some minor differences are also discussed