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Hierarchical Parametric Models for Social Dilemma Games

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Convenience for derivation of structural models of behavior ... CAR: T4 effects take longer to kick in. Conclusions & Look Ahead. HOP gets the basic job done, ... – PowerPoint PPT presentation

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Title: Hierarchical Parametric Models for Social Dilemma Games


1
Hierarchical Parametric Models for Social Dilemma
Games
  • Klaus Moeltner
  • James J. Murphy, U. Massachusetts
  • John Stranlund, U. Massachusetts
  • Maria Alejandra Velez, Columbia University

2
Overview
  • 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

3
Empirical Data
4
Processing Experimental Data The Staple
5
Parametric 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

6
Parametric Simplifications
Parametric Regressions as an Afterthought
7
Parametric 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

8
Social 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

9
Past 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

10
Hierarchical 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

11
Bayesian 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

12
Hierarchical Ordered Probit (HOP)
13
OP bins thresholds
Thresholds must be estimated -gt efficiency
losscompared to count data approach
14
HOP Likelihood Function
15
Re-parameterization
Nandram Chen, 1996 Li Tobias, 2007
16
Priors and Structure of Gibbs Sampler
17
Hierarchical Doubly-Truncated Poisson (HDTP)
18
HDTP Likelihood Function
19
Priors and Structure of Gibbs Sampler
Useful reference Chib et al., 1998
20
Posterior Density and Marginal Likelihood
21
Model Probabilities and Bayes Factors
22
Posterior Predictive Distribution, HOP
For the probability of falling into a given tier
of extraction levels
23
Posterior Predictive Distribution, HDTP
For a given extraction level
For expected extraction
24
Application
  • 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

25
Payoff 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...)

26
Payoff Table
27
Implementation
28
Aggregate Sample Results
29
Individual-Level Results
30
Sub-Model Selection, HOP
31
Sub-Model Selection, HDTP
32
Features 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

33
Estimation Results RE Means
34
Estimation Results RE VCOV
35
Predictions (HDTP)
36
PPD of Expected Effort
37
PPD of Expected Effort
38
Summary 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

39
Summary 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

40
Conclusions 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

41
Policy 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!!
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