Title: Hierarchical Parametric Models for Social Dilemma Games
1Hierarchical Parametric Models for Social Dilemma
Games
- Klaus Moeltner
- James J. Murphy, U. Massachusetts
- John Stranlund, U. Massachusetts
- Maria Alejandra Velez, Columbia University
2Overview
- Experiments and Econometrics
- Social Dilemma Games
- Hierarchical Ordered Probit (HOP)
- Hierarchical Doubly-Truncated Poisson (HDTP)
- Model Selection and Prediction
- Empirical Application / Data
- Estimation Results
- Predicted Outcomes
- Conclusions
3Empirical Data
4Processing Experimental Data The Staple
5Parametric Motivations
- Recognition of different types of noise in data
- Largely unobserved heterogeneity
- Parametric model needed to control for it
- Example Quantal Response Equilibria
- Multiple treatments, heterogeneous subjects
- Isolation of marginal effects
- Summarize all effects in a concise way
- Hypothesis testing
6Parametric Simplifications
Parametric Regressions as an Afterthought
7Parametric Considerations
- Focus on theory testing
- Identify structural parameters, test for
significance(warm-glow effects, altruism
effects, etc) - Limited attention given to
- Specification tests
- Limitations of dependent variable
- Consistency, Efficiency
- Predictive Performance, Fit with Data
8Social Dilemma Games
- Two varieties
- Public Goods Games
- Common Pool Resource (CPR) Games
- Interactive, Multiple Players
- Lots of room for unobserved heterogeneity
- Played with Integer Tokens
- Limited Dependent Variable!
- Often set in the field
- Potential to inform real-world policy decisions
- Predictive quality of econometric model becomes
important
9Past Parametric Approaches
- Treat as binary data (e.g.contribute or not)
- Loss of information, efficiency
- Basic OLS
- Biased due to truncation
- Tobit
- Inconsistent due to measurement error(Stapleton
Young, 1984) - Ordered Probit (Palfrey Prisbrey, 1996)
- Reasonable, but needs built-in control for
heterogeneity
10Hierarchical Truncated Count Data Model
- Captures Integer Nature of Data
- No lower truncation required if support starts at
0 - Hierarchical layer(s) control for unobserved
heterogeneity - Allows for cardinal comparison of predictions
- Compare performance to Hierarchical Ordered Probit
11Bayesian Estimation
- Circumvents Classical Estimation Hurdles
- Evaluation of multi-fold integrals
- Sensitivity to starting values
- Notorious problems in hierarchical count data
models - Maximum flexibility in model comparison
- Via marginal likelihoods and Bayes Factors
- No nesting required
- Option to model-average results
12Hierarchical Ordered Probit (HOP)
13OP bins thresholds
Thresholds must be estimated -gt efficiency
losscompared to count data approach
14HOP Likelihood Function
15Re-parameterization
Nandram Chen, 1996 Li Tobias, 2007
16Priors and Structure of Gibbs Sampler
17Hierarchical Doubly-Truncated Poisson (HDTP)
18HDTP Likelihood Function
19Priors and Structure of Gibbs Sampler
Useful reference Chib et al., 1998
20Posterior Density and Marginal Likelihood
21Model Probabilities and Bayes Factors
22Posterior Predictive Distribution, HOP
For the probability of falling into a given tier
of extraction levels
23Posterior Predictive Distribution, HDTP
For a given extraction level
For expected extraction
24Application
- 3 Fishing villages in Columbia
- 2004 Common Pool Resource Experiment
- 12 groups _at_5 players / village
- 20 rounds
- 10 under Open Access, all groups
- 10 under 1 of 3 treatments
- Quota with low penalty
- Quota with medium penalty
- Open communication prior to each round
- Choose 1-9 extraction level each round
25Payoff Function
- Chosen by researcher based on
- Convenience for derivation of structural models
of behavior - Large gap between social optimum and Nash
Equilibrium - Payoffs are of reasonable magnitude(large enough
to provide incentives, small enough to fit in
budget...)
26Payoff Table
27Implementation
28Aggregate Sample Results
29Individual-Level Results
30Sub-Model Selection, HOP
31Sub-Model Selection, HDTP
32Features of Winning Model
- Unobserved heterogeneity varies systematically
over treatments - Warrants separate random effects for each
treatment - Period effects matter(first 5 rounds vs second 5
rounds of each game) - Period indicator should be included in model
- Period effects vary systematically over
treatments - Warrants interaction terms with each treatment
33Estimation Results RE Means
34Estimation Results RE VCOV
35Predictions (HDTP)
36PPD of Expected Effort
37PPD of Expected Effort
38Summary Econometrics
- Best Sub-model captures
- treatment time effects
- heterogeneity over treatments
- interactions between treatments time effects
- HOP estimates noisier than HDTP
- But captures essential patterns and trends
- HOP predictions imprecise
- But replicates general sample patterns
39Summary Policy
- Pronounced heterogeneity in
- How different individuals react to treatments
- How different communities react to treatments
- Experience with policy matters
- T2, T3 work well for Pacific only
- T4 has strongest effect for Magdalena, strong
effect for Caribbean - In absence of policy experience people use own
heuristics (pos. COVs for CAR only) - Learning / trust building matters
- CAR T4 effects take longer to kick in
40Conclusions Look Ahead
- HOP gets the basic job done, but HDTP is
superior in all aspects - re-run HOP with 3 tiers prob. more efficient
- HOP invariant to scaling
- Could be advantage for data combination
- Closer look warranted
41Policy relevance of Results?
- Community heterogeneity, effect of historical
institutions prob. generalizable - To say more about policy effect on resource use
- Must link payoff table to real HH production
- Must combine experiment with broader survey
- Use experiment as a fancy focus group
- Get a good Econometrician!!