Table A2:
Simulations results (N=5,000) comparing to Average Treatment Effects (ATEs) - %Bias (Coeff. Var.) {Coverage Pr}
| E(Y) | Estimators | Pr(D) = 0.55 | Pr(D) = 0.70 | Pr(D) = 0.85 | Pr(D) = 0.93 | Pr(D) = 0.995 |
|---|---|---|---|---|---|---|
| 0.50~0.60 | Naïve Probit | 248 [.02] {0} | 237 [.03] {0} | 210 [.03] {0} | 187 [.03] {0} | 163 [.04] {0} |
| 2SLS | 28 [.27] {.88} | 18 [.35] {.91} | −13 [.71] {.94} | −47 [2.08] {.94} | −89 [27.76] {.96} | |
| 2SRI | −32 [.59] {.86} | −17 [.5] {.9} | 31 [.37] {.89} | 84 [.35] {.66} | 61 [.85] {.71} | |
| 2SRI - sres | 44 [.27] {.81} | 58 [.29] {.68} | 78 [.33] {.64} | 88 [.42] {.68} | 47 [.99] {.67} | |
| 2SRI - dres | −104 [−9.25] {.3} | −99 [38.24] {.39} | −52 [1.25] {.8} | 38 [.58] {.85} | 77 [.75] {.69} | |
| 2SRI - ares | −85 [2.74] {.42} | −78 [1.98] {.53} | −38 [.94] {.84} | 33 [.59] {.86} | 64 [.81] {.69} | |
| 2SRI - gres | −31 [.56] {.86} | −18 [.49] {.90} | 12 [.44] {.91} | 52 [.46] {.81} | 39 [.98] {.7} | |
| Bi.Probit | 1 [.31] {.93} | 0 [.34] {.93} | −1 [.49] {.93} | −8 [1.06] {.86} | 11 [1.83] {.5} | |
| 0.80 ~0.90 | Naïve Probit | 244 [.04] {0} | 314 [.04] {0} | 407 [.04] {0} | 488 [.04] {0} | 582 [.06] {0} |
| 2SLS | 0 [.52] {.95} | 43 [.37] {.84} | 97 [.36] {.71} | 121 [.53] {.82} | 95 [1.74] {.93} | |
| 2SRI | 0 [.47] {.95} | −7 [.54] {.95} | −40 [1.01] {.81} | −49 [1.71] {.77} | 17 [1.71] {.9} | |
| 2SRI - sres | 79 [.19] {.36} | 145 [.17] {.07} | 213 [.18] {.02} | 262 [.22] {.07} | 331 [.34] {.31} | |
| 2SRI - dres | −74 [2.27] {.74} | −93 [7.59] {.53} | −105 [−9.52] {.39} | −87 [5.58] {.59} | 40 [1.26] {.89} | |
| 2SRI - ares | −50 [1.07] {.83} | −53 [1.09] {.78} | −51 [1.15] {.75} | −32 [1.18] {.81} | 71 [1.02] {.89} | |
| 2SRI - gres | −1 [.45] {.97} | 1 [.47] {.94} | −3 [.58] {.92} | −8 [.87] {.88} | 29 [1.35] {.88} | |
| Bi.Probit | −2 [.4] {.94} | 0 [.4] {.95} | 4 [.45] {.95} | 9 [.62] {.91} | 41 [1.11] {.9} | |
| 0.9 ~ 0.95 | Naïve Probit | 226 [.05] {0} | 327 [.05] {0} | 482 [.05] {0} | 648 [.06] {0} | 883 [.08] {0} |
| 2SLS | −25 [.96] {.91} | 28 [.61] {.91} | 121 [.46] {.68} | 208 [.52] {.65} | 260 [1.15] {.85} | |
| 2SRI | 22 [.44] {.9} | 18 [.54] {.94} | −32 [1.18] {.84} | −80 [4.73] {.64} | −37 [3.52] {.86} | |
| 2SRI - sres | 81 [.19] {.3} | 154 [.19] {.05} | 260 [.2] {0} | 340 [.21] {.02} | 472 [.29] {.19} | |
| 2SRI - dres | −44 [1.35] {.93} | −70 [2.57] {.81} | −93 [10.3] {.59} | −93 [12.3] {.57} | −13 [2.09] {.85} | |
| 2SRI - ares | −23 [.86] {.93} | −29 [.96] {.91} | −25 [.98] {.87} | −14 [1.08] {.86} | 71 [1.13] {.93} | |
| 2SRI - gres | 18 [.43] {.92} | 18 [.51] {.94} | 17 [.63] {.91} | 3 [.9] {.9} | 27 [1.47] {.9} | |
| Bi.Probit | −4 [.54] {.95} | 2 [.51] {.94} | 10 [.57] {.93} | 16 [.71] {.91} | 52 [1.09] {.93} | |
| 0.95~0.98 | Naïve Probit | 202 [.07] {0} | 326 [.07] {0} | 546 [.08] {0} | 815 [.09] {0} | 1277 [.12] {0} |
| 2SLS | −50 [2] {.89} | −3 [1.1] {.94} | 110 [.66] {.86} | 265 [.58] {.7} | 491 [.9] {.79} | |
| 2SRI | 32 [.47] {.96} | 35 [.53] {.99} | −16 [1.22] {.95} | −103 [−37.55] {.71} | −50 [6.21] {.79} | |
| 2SRI - sres | 72 [.29] {.79} | 146 [.21] {.17} | 295 [.24] {.03} | 417 [.26] {.03} | 612 [.34] {.24} | |
| 2SRI - dres | −20 [1.15] {.96} | −52 [2.02] {.98} | −83 [5.92] {.8} | −94 [15.37] {.71} | −25 [2.92] {.83} | |
| 2SRI - ares | −5 [.82] {.96} | −14 [.91] {1} | −4 [.96] {.96} | 10 [.98] {.93} | 109 [1.27] {.93} | |
| 2SRI - gres | 27 [.47] {.95} | 26 [.52] {.99} | 32 [.7] {.98} | 21 [.89] {.94} | 55 [1.64] {.91} | |
| Bi.Probit | −36 [2.05] {.94} | −6 [.78] {.97} | 7 [.73] {.94} | 18 [.74] {.93} | 78 [1.25] {.93} | |
2SRI – sres: 2SRI with standardized residuals; 2SRI – dres: 2SRI with deviance residuals; 2SRI – ares: 2SRI with Anscombe residuals; 2SRI-gres: 2SRI with generalized residuals