Research Article
Nonparametric Estimation of ATE and QTE: An Application of Fractile Graphical Analysis
Table 4
QTE estimators of the effect of training on earnings.
| | Nontrimmed | Trim 1 | Trim 2 | | Estimator | Coef. | Average | Std. error | Coef. | Average | Std. error | Coef. | Average | Std. error |
| | |
| | FGA QTE(a) | 0.0 | 149.4 | 188.2 | 0.0 | 146.8 | 190.9 | 0.0 | 145.5 | 183.0 | | FGA QTE ()(a) | 95.7 | 382.5 | 325.2 | 78.0 | 371.3 | 311.2 | 101.9 | 392.4 | 340.2 | | FGA QTE(b) | 0.0 | 150.9 | 190.5 | 0.0 | 148.6 | 190.9 | 0.0 | 145.0 | 185.2 | | FGA QTE ()(b) | 95.7 | 369.7 | 317.7 | 78.0 | 364.6 | 312.0 | 240.1 | 385.1 | 335.9 | | Firpo [18] | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | | Bitler et al. [7] | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | | PS matching | | | | | | | | | | | Nearest neighbor (1) | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | | Nearest neighbor (2) | 0.0 | 0.7 | 15.2 | 0.0 | 0.7 | 15.2 | 0.0 | 1.1 | 21.0 | | Nearest neighbor (4) | 0.0 | 73.8 | 184.5 | 0.0 | 69.7 | 179.3 | 0.0 | 74.5 | 188.7 | | Kernel | 0.0 | 292.5 | 356.3 | 0.0 | 281.0 | 351.0 | 0.0 | 298.9 | 365.8 | | Spline | 0.0 | 295.3 | 355.7 | 0.0 | 278.5 | 349.5 | 0.0 | 291.2 | 361.0 |
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| | FGA QTE | 409.6 | 653.5 | 480.2 | 376.4 | 686.1 | 475.9 | 623.2 | 701.7 | 502.8 | | FGA QTE () | 628.8 | 853.5 | 546.4 | 487.4 | 864.3 | 540.9 | 836.9 | 880.2 | 547.8 | | FGA QTE(b) | 414.2 | 649.8 | 488.0 | 361.9 | 685.8 | 484.2 | 500.9 | 705.8 | 511.8 | | FGA QTE ()(b) | 694.5 | 843.3 | 546.3 | 363.1 | 853.3 | 554.6 | 856.6 | 872.1 | 561.9 | | Firpo [18] | 0.0 | 295.8 | 341.3 | 0.0 | 291.3 | 340.4 | 289.8 | 276.8 | 343.2 | | Bitler et al. [7] | 0.0 | 295.8 | 341.3 | 0.0 | 291.3 | 340.4 | 289.8 | 276.8 | 343.2 | | PS matching | | | | | | | | | | | Nearest neighbor (1) | 0.0 | 159.1 | 290.8 | 0.0 | 145.5 | 278.6 | 0.0 | 134.9 | 273.8 | | Nearest neighbor (2) | 1067.5 | 804.7 | 523.1 | 1254.6 | 783.1 | 527.8 | 1152.1 | 763.5 | 763.5 | | Nearest neighbor (4) | 1568.0 | 1455.8 | 738.6 | 1682.1 | 1454.2 | 733.0 | 803.4 | 1440.0 | 748.0 | | Kernel | 3068.7 | 2808.3 | 986.1 | 3180.7 | 2864.5 | 992.4 | 3074.4 | 2892.7 | 1036.1 | | Spline | 2628.7 | 2363.8 | 1019.7 | 2708.2 | 2486.6 | 1023.5 | 2715.1 | 2470.7 | 1053.1 |
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| | FGA QTE | 1131.0 | 1379.9 | 851.0 | 1321.2 | 1404.8 | 870.5 | 1026.0 | 1376.2 | 869.2 | | FGA QTE () | 914.2 | 1466.4 | 887.3 | 965.5 | 1501.7 | 866.6 | 385.5 | 1488.7 | 873.5 | | FGA QTE(b) | 1193.9 | 1403.5 | 871.6 | 1306.0 | 1432.7 | 891.8 | 1066.3 | 1384.7 | 883.4 | | FGA QTE ()(b) | 1078.8 | 1476.8 | 939.7 | 981.7 | 1509.1 | 919.9 | 262.5 | 1492.6 | 916.5 | | Firpo [18] | 1063.0 | 1178.5 | 901.6 | 1254.9 | 1260.9 | 938.1 | 763.8 | 1257.8 | 973.9 | | Bitler et al. [7] | 1063.0 | 1178.5 | 901.6 | 1254.9 | 1260.9 | 938.1 | 763.8 | 1257.8 | 973.9 | | PS matching | | | | | | | | | | | Nearest neighbor (1) | 5.2 | 910.5 | 1034.6 | 368.5 | 984.4 | 1042.5 | 77.5 | 990.4 | 1066.2 | | Nearest neighbor (2) | 388.1 | 1050.9 | 859.9 | 563.4 | 1093.0 | 877.5 | 284.4 | 1088.4 | 898.4 | | Nearest neighbor (4) | 695.5 | 1171.6 | 810.5 | 801.8 | 1210.6 | 814.5 | 616.7 | 1201.0 | 842.8 | | Kernel | 1567.1 | 1351.2 | 752.2 | 1643.1 | 1365.3 | 759.6 | 1587.8 | 1357.7 | 783.7 | | Spline | 846.6 | 1261.7 | 776.9 | 1843.3 | 1259.1 | 783.4 | 1578.1 | 1272.3 | 811.9 |
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| | FGA QTE | 2110.9 | 1948.9 | 1180.7 | 1960.5 | 1986.9 | 1190.8 | 1710.1 | 1950.1 | 1233.8 | | FGA QTE () | 1614.6 | 2162.8 | 1376.1 | 1640.0 | 2215.2 | 1369.5 | 742.6 | 2131.1 | 1424.7 | | FGA QTE(b) | 2240.9 | 1968.0 | 1191.9 | 1815.5 | 2010.4 | 1221.5 | 1706.4 | 1954.1 | 1264.7 | | FGA QTE ()(b) | 1351.3 | 2222.8 | 1447.2 | 1549.0 | 2253.0 | 1440.5 | 789.2 | 2159.8 | 1449.7 | | Firpo [18] | 2274.1 | 2060.9 | 919.6 | 2258.0 | 2071.3 | 942.1 | 2214.5 | 2034.2 | 979.1 | | Bitler et al. [7] | 2274.1 | 2060.9 | 919.6 | 2258.0 | 2071.3 | 942.1 | 2214.5 | 2034.2 | 979.1 | | PS matching | | | | | | | | | | | Nearest neighbor (1) | 1537.0 | 1663.9 | 1111.7 | 1921.1 | 1699.6 | 1081.8 | 1263.0 | 1637.5 | 1116.7 | | Nearest neighbor (2) | 585.5 | 1598.8 | 1106.4 | 877.6 | 1640.8 | 1097.4 | 393.7 | 1589.5 | 1115.2 | | Nearest neighbor (4) | 1280.1 | 1634.1 | 1046.5 | 1243.8 | 1653.2 | 1047.7 | 1239.6 | 1595.4 | 1084.2 | | Kernel | 1399.3 | 1735.3 | 972.3 | 1399.5 | 1754.3 | 971.5 | 1180.6 | 1710.6 | 984.8 | | Spline | 1381.6 | 1963.1 | 1088.7 | 1320.6 | 1954.4 | 1087.3 | 1108.5 | 1870.9 | 1101.3 |
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| | FGA QTE | 3093.8 | 3345.7 | 2315.2 | 3426.5 | 3401.9 | 2364.0 | 2789.1 | 3233.7 | 2459.3 | | FGA QTE () | 3170.8 | 3301.2 | 2157.9 | 4126.5 | 3317.0 | 2174.2 | 4161.9 | 3118.0 | 2096.5 | | FGA QTE(b) | 3093.8 | 3493.2 | 2421.2 | 3518.0 | 3512.3 | 2454.9 | 3189.5 | 3189.9 | 2442.7 | | FGA QTE ()(b) | 3142.1 | 3343.0 | 2221.1 | 4819.4 | 3351.2 | 2213.4 | 3998.6 | 3154.9 | 2133.0 | | Firpo [18] | 2713.4 | 2854.3 | 1890.4 | 2150.6 | 2797.8 | 1889.2 | 2126.2 | 2715.5 | 1895.0 | | Bitler et al. [7] | 2713.4 | 2854.3 | 1890.4 | 2150.6 | 2797.8 | 1889.2 | 2126.2 | 2715.5 | 1895.0 | | PS matching | | | | | | | | | | | Nearest neighbor (1) | 1861.2 | 2425.7 | 2150.1 | 1392.3 | 2372.7 | 2111.8 | 444.7 | 2249.4 | 2130.0 | | Nearest neighbor (2) | 1279.4 | 2388.4 | 1915.6 | 1278.0 | 2336.6 | 1900.4 | 45.4 | 2172.0 | 1892.5 | | Nearest neighbor (4) | 2047.9 | 2180.9 | 1716.8 | 2153.7 | 2181.3 | 1743.9 | 2153.7 | 2030.9 | 1758.1 | | Kernel | 175.0 | 691.5 | 1389.5 | 208.0 | 770.6 | 1431.7 | 327.6 | 566.2 | 1415.4 | | Spline | 571.5 | 881.2 | 1520.4 | 261.8 | 899.4 | 1477.9 | 327.6 | 755.2 | 1458.8 |
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(a) , (b) . Averages and standard errors are obtained using 1000 bootstrapping random samples with replacement of the original database.
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