Students / Subjects

# A Crowding out Experiment in Rural Colombia

Cardenas, Stranlund, and Willis conducted an experiment based on harvesting from a common-pool resource, conducted in three villages in Colombia. Most participants in all groups had under six years of schooling. About half were between 30 and 50 years old, and all were 16 or older. Subjects were asked to decide how much time they would spend collecting firewood from a surrounding forest, knowing that this collection of wood has an adverse impact on local water quality, due to soil erosion, and on fish populations in the case of coastal villages, where mangroves were harvested for firewood. They were provided with a table of payoffs which made it clear that collecting more firewood was a public bad.

A subset of subjects were confronted with a government-imposed quota on the amount of time that can be spent collecting firewood; a quota known by all to be only moderately enforced (fairly typical in developing nations). The other groups did not face this external restriction, but instead were allowed to communicate with others in the group between rounds.

### The Payoff Structure

Individuals have an endowment of time e, which they can use to collect firewood, or work in another, unspecified labor market. With xi denoting the amount of time spent collecting firewood and w as the wage rate, outside labor has a payoff of w(e - xi). Time spent collecting firewood yields a private benefit, which has the following quadratic form:
g(xi) = xi - (xi2)/2
where , > 0, chosen so g(xi) > 0 for xi [1, e].

Water quality is represented by q(xj) = q0 - {(xj)2}/2, where q0 represents water quality in the absence of firewood collection. Once again, the parameters are chosen so as to ensure q(xj) > 0 for all feasible (xj). Individuals value water quality as f(xj) = , where is a positive constant.

An individual's utility function is then:
U(xi, xi) = (/)[f(xj) + g(xi) + w(e - xi)]

Each individual was allotted e = 8 units of time, and there were 8 subjects in each group, with a total of 14 groups. Subjects were given payoff tables, wherein the following parameter values had been used: w = 30; = 97.2; = 3.2; q0 = 1372.8; = 1; = 1; = 2; = 16,810 and = 2.

Since extracting firewood is a private good and a public bad, standard theory predicts that self-interested individuals will spend more time harvesting firewood than is socially optimal. The difference between an individual’s Nash best-response to the choices of the other players in the group and his or her actual choice was considered an indicator of how that individual balanced self-interests and those of the entire group, and used as the benchmark.

### Experiment Setup

Nine out of 14 groups were allowed to communicate after 8 to 11 rounds. The others would be subjected to the imperfectly enforced time quota of xi = 1. The subjects were asked to sit at desks placed in a circle, which faced outward except in the communication treatments. Subjects were given the payoff table, which they knew to be identical for all, and they were asked to choose the amount of time they would spend collecting firewood, with xi [0, 8].

For the communication treatments, they were not told in advance of the rule change, but only when it came into effect. They were prohibited from making threats or agreeing on cash transfers, but other than that, communication between rounds was unrestricted.

For the quota treatment, an audit on an individual occurs with probability . An individual found to have spent excess time collecting firewood faces a penalty p on every unit of time spent in excess of the quota s. The expected value of the penalty is then: p(xi - s). The value of s was chosen to be 1, the efficient value, = 1/16, and p = 100. The low value of reflects the lax monitoring present in most developing countries.

### Results

Before communication or regulation, for both groups:

Neither the Nash equilibrium (x=6 for each subject) nor the efficient solution (x=1) were reached. The average over the eight rounds for the nine groups who would later communicate was 4.39, and for the other groups, 4.32 -- no statistical difference, as one would expect. Average choices were relatively stable throughout the first stage for both sets of groups.

Time quota:

In the first round after the rule was introduced, average time spent collecting firewood plunged to below 2 -- it was 2.6, on average, for the first 3 rounds after the regulation was enforced. But as the game proceeded, subjects became comfortable with the weak consequences of exceeding the quota. As they understood that others were also violating the regulation, average choices rose over the rounds to exceed four units of time collecting firewood. For the final three rounds, the time spent was 4.13, a statistical and sizable difference.

Communication treatment:

The communication groups were clearly able to make more efficient choices. The average choice of these subjects shows a statistically significant decline in months of effort to extract firewood from 4.39 for all rounds in the first stage (in which they could not communicate) to 3.53 after communication was allowed. Crucially, unlike the groups with the quota, that social improvement was relatively stable from the early second stage rounds to the last. Also, their average earnings were significantly higher than for those in the quota group.

### Implications

It is clear from the results that other-regarding, social behavior was crowded out by the presence of the quota. Since that quota was imperfectly enforced, it led to a worse outcome than if it had not been there at all, given it is costly to enforce. This has strong policy implications, particularly in developing countries where one can expect external regulation to be poorly enforced.