Experimental Methods in Social Ecological Systems. Juan-Camilo Cárdenas Universidad de los Andes Jim Murphy University of Alaska Anchorage. Agenda – Day 1. Noon –12:15 Welcome, introductions 12:15 – 1:15Play Game #1 (CPR: 1 species vs. 4 species)
Experimental Methods in Social Ecological Systems
Universidad de los Andes
University of Alaska Anchorage
1. “Speaking to Theorists”
2. “Searching for Facts”
3. “Whispering in the Ears of Princes”
Subjects choose a level of extraction 0 – 8
Low harvest levels
High harvest levels
Payoffs also depend on choices of other 4 group members
Group earnings largest if all choose 1
Strong incentives to harvest more than 1
Social optimum:All choose 1
Nash equilibrium:All choose 6
These 2 treatments have been conducted ad nauseum.
Are they necessary?
Also see:John A. List · Sally Sadoff · Mathis Wagner
“So you want to run an experiment, now what? Some simple rules of thumb for optimal experimental design”
Experimental Economics (2011). 14:439-457
A. 0 (control) / 1 (treatment), equal outcome variances
B. 0/1 treatment, unequal outcome variances
C. Treatment Intensity—no longer binary
Assume that X0is N(μ0,σ02) and X1 is N(μ1, σ12); and the minimum detectable effect μ1– μ0= δ. H0: μ0= μ1and H1: μ1– μ0= δ. We need the difference in sample means X1 –X0to satisfy:
1.Significance level (probability of Type I error) = α:
2. Power (1 – probability of Type II error) = 1-β:
A. Our usual approach stems from the standard regression model: under a true null what is the probability of observing the coefficient that we observed?
B. Power calculations are quite different, exploring if the alternative hypothesis is true, then what is the probability that the estimated coefficient lies outside the 95% CI defined under the null.
Another Rule of Thumb—if the outcome variances are not equal then:
The ratio of the optimal proportions of the total sample in control and treatment groups is equal to the ratio of the standard deviations.
Example: Communication tends to reduce the variance, so perhaps groups in this treatment.
Do we need 3 levels of enforcement?
Y = XB + e
One goal in this case is to derive the most precise estimate of B by using exogenous
variation in X.
Recall that the standard error of B is =
Intuition:The test for a quadratic effect compares the mean of the outcomes at the extremes to the mean of the outcome at the midpoint
m = number of subjects in a cluster
k = number of clusters
CE = 1 + ρ(m-1)
ρ = intracluster correlation coefficient
= s2B/(s2B + s2w)
s2B = variance between clusters
s2w = variance within clusters