The UN in the lab
AppendixB
Appendix B – Support Materials
Table 1’: Subject pool demographicsa and beliefs/preferencesb
Baseline / Low Burden Sharing / Moderate Burden Sharing / HighBurden Sharing / p-value / *
Female / 32.40% / 44.40% / 47.20% / 33.30% / 0.473 / f
White / 44.10% / 22.20% / 33.30% / 38.90% / 0.249 / f
Age (mean) / 20.35 / 19.83 / 20.03 / 20.28 / 0.352 / k
Married / 2.94% / 0.00% / 0.00% / 0.00% / 0.088 / f
Have children? / 0.00% / 0.00% / 2.78% / 0.00% / 1.000 / f
Live with parents? / 29.41% / 41.67% / 36.11% / 27.78% / 0.594 / f
Grad. Student / 11.76% / 5.56% / 5.56% / 8.33% / 0.737 / f
Econ student / 5.88% / 5.56% / 5.56% / 5.56% / 1.000 / f
High Family income / 23.53% / 19.44% / 27.78% / 16.67% / 0.695 / f
Full time Student / 97.06% / 100.00% / 88.89% / 100.00% / 0.028 / f
Christian / 35.44% / 27.78% / 33.33% / 41.67% / 0.636 / f
US Citizen / 82.35% / 69.44% / 83.33% / 83.33% / 0.449 / f
Republican / 38.24% / 41.67% / 27.78% / 47.22% / 0.373 / f
Baseline / Low
Burden Sharing / Moderate Burden Sharing / High
Burden Sharing / p-value / *
Politically conservative / 23.53% / 16.67% / 13.89% / 30.56% / 0.311 / k
US strong leadership role / 5.88% / 13.89% / 11.11% / 13.89% / 0.703 / f
Politically astute / 73.50% / 83.33% / 72.22% / 83.33% / 0.518 / f
Minorities experience racism / 70.50% / 88.90% / 80.60% / 72.20% / 0.207 / f
Immigrants in US decrease / 8.80% / 16.67% / 5.56% / 22.20% / 0.167 / f
US should be isolationist / 14.70% / 22.20% / 25.00% / 27.78% / 0.607 / f
Gov’t. spending should increase / 35.30% / 38.89% / 38.88% / 38.89% / 0.985 / f
Risk Taking? / 6.32 / 6.75 / 6.17 / 6.63 / 0.777 / k
(scale of 1 to 10) / (2.10) / (1.86) / (2.18) / (1.87)
Level of patience? / 5.06 / 4.31 / 4.39 / 4.08 / 0.225 / k
(scale of 1 to 10) / (1.88) / (2.027) / (2.587) / (2.01)
Focus on the self / 5.59 / 6.22 / 6.17 / 5.78 / 0.499 / k
(scale of 1 to 10) / (2.13) / (2.02) / (2.30) / (2.28)
* f for Fisher Exact test, k for Kruskal-Wallis test
aDemographics include binary variables gender, white (Y or N), Married (Y or N), children (Y or N), live with parents (Y or N), grad student (Y or N), economics student (Y or N), full time student (Y or N), Christian (Y or N), US Citizen (Y or N), republican (Y or N). Ordinal demographic variables are father’s education level and religiosity. Interval demographic variables are age, family income, and number of bathrooms in the subject’s household.
bBeliefs and Preferences include binary variables such as if the person views him/herself as politically conservative, if the subject believes the US should have a strong leadership role, believes that she/he is politically astute, believes that minorities face discrimination, believes that the amount of immigrants in the US should decrease, believes that the US should be a more isolationist country, and if the subject believes that government spending should increase. Preferences variables that include 10 point Likert scales are if the subject views her/himself as a risk takers, as impatient and satisfying immediate over longer term concerns, and if the subject focuses on taking care of him/herself rather than others.
Table 2’: First Round Data
Logit models, coefficients shown
Dependent Variable: Prevention / Model 1 / Model 2Low Burden Sharing / 0.334 / 0.871
(0.490) / (0.572)
Moderate Burden Sharing / 0.585 / 1.006*
(0.500) / (0.582)
High Burden Sharing / 1.843*** / 2.327***
(0.633) / (0.724)
Age / -0.0489
(0.0858)
Female / -0.0698
(0.459)
White / 0.984*
(0.513)
Father’s Education level / -0.0270
(0.168)
Econ student / 1.232
(1.212)
No. of bathrooms / -0.325
(0.307)
Christian / 0.130
(0.534)
Religiousness / 0.121
(0.272)
Republican / 0.271
(0.485)
US Citizen / -0.230
(0.534)
Married / 0.346
(0.629)
Racism / -0.171
(0.558)
Immigrants / -0.729
(0.622)
Isolationists / -0.302
(0.515)
Government Spending / 0.188
(0.476)
Risk Taking / -0.00478
(0.108)
Level of Patience / 0.206**
(0.104)
Focus on the Self / -0.00362
(0.104)
Constant / 0.236 / -0.0558
(0.345) / (2.211)
Log Likelihood / -81.593 / -73.613
McFadden’s R2 / 0.063 / 0.155
McFadden’s R2 (adjusted) / 0.017 / -0.098
AIC / 171.186 / 191.227
BIC / 183.009 / 256.255
Observations / 142 / 142
Standard errors in parentheses; *** p<0.01, ** p<0.05, * p<0.1
Table 3’: First Round Data
Multinomial Logit models, coefficients shown
Dependent Variable: Choice / Model 1a / Model 2b / Model 3c / Model 4d(TNA is the base outcome) / Prev / Prev / Prev / Prev
Low Burden Sharing / 1.107* / 1.300* / 1.153 / 1.314
(0.668) / (0.726) / (0.725) / (0.818)
Moderate Burden Sharing / 1.478** / 1.642** / 1.617** / 1.698**
(0.725) / (0.778) / (0.773) / (0.835)
High Burden Sharing / 2.824*** / 2.946*** / 3.126*** / 3.598***
(1.088) / (1.128) / (1.142) / (1.284)
Age / -0.130 / -0.177
(0.110) / (0.129)
Female / -0.127 / -0.814
(0.604) / (0.739)
White / 0.348 / 0.620
(0.686) / (0.783)
Father’s Education Level / 0.181 / 0.154
(0.237) / (0.266)
Econ student / 13.77 / 14.20
(1,016) / (2,131)
No. of bathrooms / -0.378 / -0.378
(0.401) / (0.451)
Christian / 1.040 / 1.708*
(0.793) / (0.941)
Religiousness / 0.112 / -0.148
(0.351) / (0.412)
Republican / 0.0579 / 0.226
(0.638) / (0.743)
US Citizen / -0.0270 / -0.127
(0.716) / (0.828)
Married / 0.238 / -0.0233
(0.823) / (0.925)
Racism / 0.702 / 1.229
(0.617) / (0.805)
Immigrants / -0.566 / -1.036
(0.870) / (0.955)
Isolationists / -0.389 / -0.690
(0.729) / (0.775)
Gov’t.Spending / -0.433 / 0.103
(0.582) / (0.690)
Risk Taking / 0.102 / 0.187
(0.138) / (0.163)
Level of Patience / 0.0829 / 0.133
(0.142) / (0.158)
Focus on the Self / -0.0971 / -0.132
(0.138) / (0.163)
Constant / 0.642 / 2.374 / -0.0227 / 2.305
(0.391) / (2.600) / (1.406) / (3.182)
Log Likelihood / -99.232
McFadden’s R2 / 0.147
McFadden’s R2 (adjusted) / -0.111
AIC / 258.464
BIC / 347.138
Observations / 142 / 142 / 142 / 142
Standard errors in parentheses, Multinomial Logit model, 1st round only; *** p<0.01, ** p<0.05, * p<0.1
aModel 1: IIA is violated, p = 0.0297, p = 0.0297, bModel 2: IIA is violated, p = 0.0579, p = 0.0012, cModel 3: IIA is not violated, p = 0.9352, p= 0.7797, dModel 4: IIA is not violated, p = 0.9217, p=0.7491
Table 4’: 21st Round Data
Logit models, coefficients shown
Dependent Variable: Prevention / Model 1 / Model 2 / Model 3 / Model 4 / Model 5 / Model 6 / Model 7 / Model 8Low Burden Sharing / -1.058 / -1.211* / -0.972 / -1.125 / -1.122 / -1.244 / -1.096 / -1.204
(0.658) / (0.734) / (0.699) / (0.805) / (0.684) / (0.862) / (0.682) / (0.861)
Moderate Burden Sharing / 0.570 / 0.614 / 0.675 / 0.731 / 0.324 / 0.426 / 0.357 / 0.457
(0.518) / (0.556) / (0.583) / (0.631) / (0.547) / (0.689) / (0.546) / (0.684)
High Burden Sharing / 1.843*** / 1.996*** / 2.400*** / 2.771*** / 1.334** / 2.283*** / 1.311** / 2.219***
(0.531) / (0.579) / (0.624) / (0.703) / (0.566) / (0.741) / (0.568) / (0.741)
Prev. history
(Round 1 – 20) / 0.103*** / 0.120***
(0.0342) / (0.0408)
Coop history
(Round 1 – 20) / 0.090*** / 0.107***
(0.0293) / (0.0359)
Age / 0.0338 / 0.0563 / 0.0630 / 0.0626
(0.0777) / (0.109) / (0.116) / (0.117)
Female / 0.0168 / -0.266 / -0.337 / -0.359
(0.432) / (0.520) / (0.555) / (0.555)
White / 0.552 / 0.468 / 0.415 / 0.372
(0.455) / (0.515) / (0.558) / (0.559)
Father’s Education level / -0.0563 / -0.0993 / -0.139 / -0.137
(0.164) / (0.180) / (0.186) / (0.187)
Econ student / 1.695* / 1.773* / 1.875* / 1.829*
(0.898) / (0.999) / (1.018) / (1.013)
No. of bathrooms / 0.196 / 0.493 / 0.624 / 0.606
(0.315) / (0.379) / (0.401) / (0.402)
Christian / 0.174 / -0.0418 / -0.183 / -0.119
(0.498) / (0.550) / (0.599) / (0.599)
Religiousness / -0.351 / -0.434 / -0.447 / -0.475
(0.266) / (0.314) / (0.333) / (0.333)
Republican / 0.512 / 0.310 / 0.243 / 0.268
(0.452) / (0.539) / (0.580) / (0.577)
US Citizen / -0.878 / -0.592 / -0.463 / -0.421
(0.540) / (0.604) / (0.642) / (0.645)
Married / 0.240 / -0.178 / -0.429 / -0.361
(0.705) / (0.791) / (0.817) / (0.816)
Racism / -0.367 / -0.354 / -0.116 / -0.130
(0.491) / (0.555) / (0.587) / (0.592)
Immigrants / -0.834 / -0.857 / -0.688 / -0.669
(0.695) / (0.732) / (0.781) / (0.782)
Isolationists / 0.430 / 0.625 / 0.654 / 0.557
(0.533) / (0.571) / (0.615) / (0.611)
Gov’t.Spending / -1.525*** / -1.569*** / -1.634*** / -1.586**
(0.480) / (0.587) / (0.625) / (0.626)
Risk Taking / -0.221** / -0.270** / -0.342*** / -0.362***
(0.105) / (0.116) / (0.127) / (0.129)
Level of Patience / 0.0311 / 0.0228 / 0.0125 / 0.0131
(0.0979) / (0.105) / (0.111) / (0.111)
Focus on the Self / -0.0539 / -0.142 / -0.181 / -0.185
(0.103) / (0.123) / (0.130) / (0.130)
Constant / -1.022*** / -1.484 / 1.176 / 1.385 / 0.103*** / 0.120*** / -2.044*** / 0.887
(0.389) / (1.948) / (1.095) / (2.780) / (0.0342) / (0.0408) / (0.561) / (2.981)
Log Likelihood / -78.422 / -73.037 / -69.383 / -64.320 / -70.316 / -56.603 / -73.109 / -59.065
McFadden’s R2 / 0.159 / 0.217 / 0.256 / 0.310 / 0.246 / 0.393 / 0.216 / 0.367
McFadden’s R2 adjusted / 0.116 / 0.056 / 0.138 / 0.075 / 0.193 / 0.147 / 0.163 / 0.120
AIC / 164.844 / 176.075 / 160.767 / 172.640 / 150.631 / 159.205 / 156.217 / 164.129
BIC / 176.668 / 220.412 / 193.281 / 237.668 / 165.411 / 227.189 / 170.997 / 232.113
Observations / 142 / 142 / 142 / 142 / 142 / 142 / 142 / 142
Standard errors in parentheses, logit model; *** p<0.01, ** p<0.05, * p<0.1
Table 5’:Profit, Round 21 Data (Rematched, 10x Stakes)
OLS, marginal effects shown
Dependent Variable:Round Profit / Model 1 / Model 2c / Model 3c / Model 4d
Low Burden Sharing / -5.098 / -9.660 / -9.716 / -10.28
(8.054) / (8.749) / (8.714) / (8.559)
Moderate Burden Sharing / 3.791 / -0.505 / 1.616 / 1.676
(8.054) / (8.639) / (8.736) / (8.577)
High Burden Sharing / 19.35** / 17.88** / 21.93** / 22.26**
(8.054) / (8.637) / (9.073) / (8.909)
Prev. history
(Round 1 – 20) / -0.592 / -2.79***
(0.422) / (1.032)
Profit historyb
(Round 1 – 20) / 0.645**
(0.277)
Demographics / N / Y / Y / Y
Preferences / N / Y / Y / Y
Constant / 61.76*** / 74.92** / 79.99*** / 16.12
(5.776) / (29.68) / (29.78) / (40.06)
R2 / 0.071 / 0.170 / 0.183 / 0.219
Adjusted R2 / 0.051 / 0.024 / 0.032 / 0.067
Observations / 142 / 142 / 142 / 142
Standard errors in parentheses, 21st round data only; *** p<0.01, ** p<0.05, * p<0.1
Wald test p-values for differences between treatment coefficients
BS51=BS42 / BS42=BS33 / BS51=BS33Model 1 / 0.2648 / 0.0025 / 0.0521
Model 2 / 0.2904 / 0.0019 / 0.0367
Model 3 / 0.1966 / 0.0007 / 0.0223
Model 4 / 0.1657 / 0.0004 / 0.0185
aRound Profit is defined as the subject’s token earnings in round 21.
bProfit history is defined as the cumulative sum of a subject’s round earnings from rounds 1 – 20.
cIn Models 2 and 3, the variable “white”, indicating if the subject identified him/herself as Caucasian, is significant at the 0.1 level.
dIn Model 4, “white” is significant at the 0.05 level.
Table 6’, Rounds 1 to 20 Data
Random Effects Logit, coefficients shown
Dependent Variable: Prevention / Model 1 / Model 2 / Model 3 / Model 4 / Model 5 / Model 6 / Model 7 / Model 8Low Burden Sharing / -0.0652 / 0.132 / 0.153 / 0.269 / -0.0709 / 0.140 / 0.173 / 0.296
(0.796) / (0.819) / (0.805) / (0.828) / (0.885) / (0.908) / (0.891) / (0.916)
Moderate Burden Sharing / 1.540* / 1.750** / 1.578** / 1.803** / 1.696* / 1.926** / 1.740** / 1.988**
(0.797) / (0.811) / (0.800) / (0.820) / (0.887) / (0.900) / (0.887) / (0.908)
High Burden Sharing / 3.595*** / 3.424*** / 3.716*** / 3.727*** / 3.968*** / 3.771*** / 4.100*** / 4.106***
(0.814) / (0.842) / (0.829) / (0.869) / (0.900) / (0.931) / (0.915) / (0.958)
Age / 0.137 / 0.177 / 0.148 / 0.193
(0.134) / (0.138) / (0.146) / (0.154)
Female / -0.405 / -0.0241 / -0.443 / -0.0246
(0.584) / (0.630) / (0.646) / (0.696)
White / 0.533 / 0.448 / 0.575 / 0.486
(0.644) / (0.652) / (0.713) / (0.719)
Father’s Education level / -0.110 / -0.0408 / -0.119 / -0.0424
(0.218) / (0.223) / (0.242) / (0.247)
Econ student / -0.260 / -0.413 / -0.293 / -0.473
(1.280) / (1.310) / (1.420) / (1.452)
No. of bathrooms / -0.605 / -0.635 / -0.673 / -0.704
(0.426) / (0.425) / (0.473) / (0.471)
Christian / 0.716 / 0.865 / 0.822 / 0.983
(0.684) / (0.698) / (0.751) / (0.764)
Religiousness / -0.413 / -0.332 / -0.463 / -0.376
(0.355) / (0.367) / (0.394) / (0.407)
Republican / 0.248 / 0.0462 / 0.259 / 0.0375
(0.630) / (0.676) / (0.698) / (0.748)
US Citizen / -0.414 / -0.309 / -0.475 / -0.359
(0.733) / (0.744) / (0.814) / (0.824)
Married / 0.0225 / -0.489 / 0.0189 / -0.553
(0.883) / (0.900) / (0.979) / (0.996)
Racism / -1.026 / -0.892 / -1.123 / -0.975
(0.690) / (0.750) / (0.761) / (0.827)
Immigrants / -1.105 / -1.300 / -1.226 / -1.440
(0.853) / (0.874) / (0.942) / (0.965)
Isolationists / 0.923 / 0.796 / 1.033 / 0.887
(0.694) / (0.711) / (0.766) / (0.785)
Gov’t.Spending / -0.691 / -0.727 / -0.769 / -0.810
(0.574) / (0.663) / (0.634) / (0.733)
Risk Taking / 0.0925 / 0.172 / 0.106 / 0.195
(0.138) / (0.147) / (0.153) / (0.163)
Level of Patience / 0.115 / 0.111 / 0.130 / 0.125
(0.133) / (0.138) / (0.147) / (0.153)
Time trend / 0.0183 / 0.0183 / 0.0182 / 0.0184
(0.0114) / (0.0114) / (0.0114) / (0.0114)
Period dummies / No / No / No / No / Yes / Yes / Yes / Yes
Constant / 0.510 / -1.040 / -0.294 / -3.143 / 1.023 / -0.598 / 0.117 / -2.973
(0.584) / (3.131) / (1.494) / (3.446) / (0.704) / (3.441) / (1.676) / (3.834)
Log Likelihood
-922.92 / -919.30 / -918.91 / -915.49 / -863.06 / -859.42 / -859.01 / -855.55
AIC
BIC / 1857.848 / 1872.62 / 1863.831 / 1878.992 / 1774.133 / 1788.843 / 1780.02 / 1795.101
1893.557 / 1973.796 / 1941.201 / 2021.829 / 1916.971 / 1997.147 / 1964.518 / 2045.066
Observations
Number of subjects / 2,840 / 2,840 / 2,840 / 2,840 / 2,840 / 2,840 / 2,840 / 2,840
142 / 142 / 142 / 142 / 142 / 142 / 142 / 142
Standard errors in parentheses; *** p<0.01, ** p<0.05, * p<0.1
Table 7’, Rounds 1 to 20 Data – Incorporating previous play
Dependent variable is Prevention
Panel Logit, coefficients shown
Model 1 / Model 2 / Model 3 / Model 4 / Model 5 / Model 6 / Model 7 / Model 8 / Model 9Low Burden Sharing / -0.0780 / 0.568 / 0.745 / -0.0773 / 0.912 / 1.179 / -0.0778 / 0.948* / 1.105**
(0.669) / (0.724) / (0.753) / (0.675) / (0.770) / (0.799) / (0.280) / (0.518) / (0.525)
Moderate Burden Sharing / 1.232* / 1.383* / 1.502** / 1.200* / 2.173*** / 2.356*** / 0.409 / 1.318** / 1.335**
(0.682) / (0.749) / (0.763) / (0.687) / (0.790) / (0.805) / (0.292) / (0.560) / (0.569)
High Burden Sharing / 2.72*** / 2.31*** / 2.47*** / 2.63*** / 3.14*** / 3.43*** / 0.92*** / 1.74** / 2.17***
(0.726) / (0.890) / (0.931) / (0.729) / (0.945) / (0.989) / (0.346) / (0.718) / (0.750)
Prev. lag (lagPrev) / 2.73*** / 3.14*** / 3.14*** / 3.21*** / 3.64*** / 3.70***
(0.203) / (0.378) / (0.380) / (0.220) / (0.392) / (0.394)
LowBS*lagPrev / -1.167** / -1.163** / -0.966* / -0.990**
(0.492) / (0.492) / (0.493) / (0.496)
ModBS*lagPrev / -0.284 / -0.271 / -0.449 / -0.441
(0.504) / (0.506) / (0.505) / (0.507)
HighBS*lagPrev / 0.370 / 0.275 / -0.187 / -0.328
(0.670) / (0.669) / (0.650) / (0.654)
Counterpart Prev. lag (lagCP) / 3.184*** / 4.397*** / 4.411*** / 3.290*** / 4.028*** / 4.094***
(0.225) / (0.502) / (0.510) / (0.194) / (0.406) / (0.413)
LowBS*lagCP / -1.706*** / -1.688*** / -0.897* / -0.858
(0.615) / (0.622) / (0.525) / (0.533)
ModBS*lagCP / -1.611*** / -1.644*** / -1.085** / -1.151**
(0.610) / (0.617) / (0.538) / (0.549)
HighBS*lagCP / -0.958 / -1.102 / -1.122* / -1.416**
(0.783) / (0.782) / (0.677) / (0.678)
Age / 0.170 / 0.184 / 0.115**
(0.117) / (0.118) / (0.0571)
Female / 0.00588 / 0.0861 / 0.143
(0.539) / (0.545) / (0.239)
White / 0.343 / 0.197 / 0.0830
(0.559) / (0.565) / (0.253)
Father’s Ed. level / -0.0478 / -0.0399 / -0.0413
(0.192) / (0.194) / (0.0862)
Econ student / -0.280 / -0.703 / -0.587
(1.115) / (1.125) / (0.473)
No. of bathrooms / -0.412 / -0.427 / -0.0745
(0.368) / (0.371) / (0.169)
Christian / 0.213 / 0.344 / 0.0658
(0.605) / (0.613) / (0.269)
Religiousness / -0.193 / -0.187 / -0.0567
(0.316) / (0.320) / (0.142)
Republican / 0.0605 / -0.0102 / -0.131
(0.588) / (0.597) / (0.265)
US Citizen / -0.152 / -0.0765 / 0.106
(0.644) / (0.651) / (0.287)
Married / -0.389 / -0.416 / -0.0681
(0.763) / (0.770) / (0.332)
Racism / -0.707 / -0.986 / -0.517*
(0.647) / (0.657) / (0.303)
Immigrants / -0.938 / -1.206 / -0.610*
(0.744) / (0.749) / (0.341)
Isolationists / 0.979 / 0.630 / 0.208
(0.627) / (0.632) / (0.288)
Gov’t.Spending / -0.592 / -0.483 / -0.212
(0.573) / (0.579) / (0.258)
Risk Taking / 0.115 / 0.0935 / 0.0590
(0.124) / (0.125) / (0.0542)
Level of Patience / 0.0509 / 0.0600 / -0.00962
(0.118) / (0.120) / (0.0526)
Period dummies / Yes / Yes / Yes / Yes / Yes / Yes / Yes / Yes / Yes
Constant / -1.74*** / -1.94*** / -5.35* / -1.94*** / -2.64*** / -5.97** / -3.94*** / -4.59*** / -6.75***
(0.578) / (0.609) / (2.954) / (0.592) / (0.657) / (2.992) / (0.367) / (0.479) / (1.456)
Log Likelihood / -674.446 / -670.104 / -663.588 / -658.22 / -653.21 / -646.74 / -560.23 / -555.55 / -548.5
AIC / 1396.88 / 1394.20 / 1417.17 / 1364.44 / 1360.43 / 1383.49 / 1170.46 / 1173.11 / 1195.14
BIC / 1538.48 / 1553.51 / 1682.69 / 1506.04 / 1519.74 / 1649.00 / 1317.97 / 1356.02 / 1484.30
Observations / 2,698 / 2,698 / 2,698 / 2,698 / 2,698 / 2,698 / 2,698 / 2,698 / 2,698
Number of subjects / 142 / 142 / 142 / 142 / 142 / 142 / 142 / 142 / 142
Standard errors in parentheses; *** p<0.01, ** p<0.05, * p<0.1
Table 8’: Profit in Rounds 1 to 20
OLS model
Dependent Variable:Total Profit at Round 20 / Model 1 / Model 2
Low Burden sharing / 0.248 / 0.553
(6.453) / (7.036)
Moderate Burden sharing / 11.47* / 12.14*
(6.453) / (6.948)
High Burden sharing / 24.42*** / 22.85***
(6.453) / (6.946)
Demographics and Preferences / N / Y
R2 / 0.124 / 0.212
Adjusted R2 / 0.105 / 0.074
Constant / 147.5*** / 128.2***
(4.628) / (23.87)
Observations / 142 / 142
Standard errors in parentheses; *** p<0.01, ** p<0.05, * p<0.1
Wald test p-values for differences between treatment coefficients
BS51=BS42 / BS42=BS33 / BS51=BS33Model 1 / 0.0799 / 0.0002 / 0.0438
Model 2 / 0.0974 / 0.0017 / 0.1283
Table 9’: Round 1 and Round 21 data
Mutual Cooperation in Round 1Mutual Coop / None
No Burden Sharing / 6 / 11
Low Burden Sharing / 7 / 11
Moderate Burden Sharing / 8 / 10
High Burden Sharing / 14 / 4
Round 1, p-values from Fisher exact test (Mutual Cooperation)
No Burden Sharing / Low Burden Sharing / Moderate Burden Sharing
No Burden Sharing / - / - / -
Low Burden Sharing / 1.0000 / - / -
Moderate Burden Sharing / 0.7330 / 1.0000 / -
High Burden Sharing / 0.0180 / 0.0410 / 0.0860
Mutual Cooperation in Round 21
Mutual Coop / None
No Burden Sharing / 0 / 17
Low Burden Sharing / 0 / 18
Moderate Burden Sharing / 2 / 16
High Burden Sharing / 8 / 10
Rd 21, p-values from Fisher exact test (Mutual Cooperation)
No Burden Sharing / Low Burden Sharing / Moderate Burden Sharing
No Burden Sharing / - / - / -
Low Burden Sharing / n/a / - / -
Moderate Burden Sharing / 0.4860 / 0.4860 / -
High Burden Sharing / 0.0030 / 0.0030 / 0.0600
Figure 1: Autocorrelation and Partial Autocorrelation functions for the Prevention decision
Notes on the above figure, “Baseline” refers to the Baseline data, “Low” refers to the Low Burden Sharing treatment, “Moderate” refers to the Moderate Burden Sharing treatment, and “High” refers to the High Burden Sharing treatment. The “Lag” is the Prevention lag for the ACFs and for the PACFs, it’s the Prevention lag where the linear dependence between the lag and the current time is removed. The dashed line denotes the 95% confidence interval for the ACFs that the lags are correlated and for the PACFs, they indicate the 95% confidence interval for the autoregressive order.
Figure 2: Autocorrelation and Partial Autocorrelation functions for the Mutual Prevention instances
Notes on the above figure, “Baseline” refers to the Baseline data, “Low” refers to the Low Burden Sharing treatment, “Moderate” refers to the Moderate Burden Sharing treatment, and “High” refers to the High Burden Sharing treatment. The “Lag” is the Mutual Prevention lag for the ACFs and for the PACFs, it’s the Mutual Prevention lag where the linear dependence between the lag and the current time is removed. The dashed line denotes the 95% confidence interval for the ACFs that the lags are correlated and for the PACFs, they indicate the 95% confidence interval for the autoregressive order.
Figure 3: Histograms for the decisions and final earnings
3.a Distribution of prevention decisions across subjects
3.b Distribution of final earnings across subjects
Description of figure 3
Per-subject distributions are in Figure 3. The histograms contain both the number of instances subjects choose Prevention in rounds 1 to 20 (figures 3.a), and the distribution of subjects’ earnings at the end of round 20 (figures 3.b). From Figure 3.a we see that Prevention decisions in the baseline are concentrated around the two extremes. Subjects either choose Prevention in almost every round of the game or never do so. As participants’ share the cost of Prevention, we see that subject choices move away from Defense to a point where in the High Burden Sharing treatment, almost 80% of subjects never select Defense in Rounds 1 through 20. (3)
Figure 3b confirms that treatment effects have a prominent welfare impact, as suggested by Table 7. As the burden sharing mechanism is strengthened, total earnings at round 20 cluster around 180 tokens (the earnings amount if both subjects in a group routinely select Prevention) and total earnings less than 180 tokens are less frequent, and become rare when burden sharing reaches its maximum level.
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