Research Article
Nonparametric Estimation of ATE and QTE: An Application of Fractile Graphical Analysis
Table 2
QTE Monte Carlo simulations.
| | MSE | MAE | Estimator | 100 | 200 | 500 | 1000 | 2000 | 100 | 200 | 500 | 1000 | 2000 |
| | |
| FGA QTE(a) | 0.964 | 0.585 | 0.328 | 0.247 | 0.155 | 0.791 | 0.611 | 0.461 | 0.404 | 0.317 | FGA QTE ()(a) | 0.825 | 0.433 | 0.224 | 0.178 | 0.117 | 0.713 | 0.525 | 0.379 | 0.339 | 0.279 | FGA QTE(b) | 0.863 | 0.491 | 0.243 | 0.146 | 0.090 | 0.802 | 0.593 | 0.409 | 0.312 | 0.241 | FGA QTE ()(b) | 1.334 | 0.849 | 0.391 | 0.241 | 0.146 | 1.074 | 0.847 | 0.561 | 0.433 | 0.339 | Firpo [18] | 0.879 | 0.633 | 0.438 | 0.332 | 0.332 | 0.733 | 0.639 | 0.525 | 0.467 | 0.453 | Bitler et al. [7] | 0.835 | 0.628 | 0.432 | 0.332 | 0.332 | 0.733 | 0.638 | 0.524 | 0.467 | 0.453 | PS Matching | | | | | | | | | | | Nearest neighbor (1) | 0.775 | 0.649 | 0.455 | 0.341 | 0.383 | 0.697 | 0.636 | 0.532 | 0.486 | 0.478 | Nearest neighbor (2) | 0.551 | 0.442 | 0.315 | 0.269 | 0.236 | 0.603 | 0.555 | 0.484 | 0.462 | 0.444 | Nearest neighbor (4) | 0.562 | 0.429 | 0.309 | 0.285 | 0.259 | 0.591 | 0.557 | 0.492 | 0.494 | 0.484 | Kernel | 0.748 | 0.566 | 0.467 | 0.401 | 0.361 | 0.691 | 0.617 | 0.580 | 0.587 | 0.581 | Spline | 0.626 | 0.519 | 0.400 | 0.389 | 0.367 | 0.646 | 0.622 | 0.575 | 0.593 | 0.591 |
| | |
| FGA QTE(a) | 0.523 | 0.333 | 0.184 | 0.133 | 0.083 | 0.585 | 0.459 | 0.336 | 0.292 | 0.230 | FGA QTE ()(a) | 0.409 | 0.246 | 0.131 | 0.088 | 0.058 | 0.507 | 0.397 | 0.291 | 0.236 | 0.194 | FGA QTE(b) | 0.866 | 0.519 | 0.270 | 0.169 | 0.116 | 0.823 | 0.631 | 0.450 | 0.352 | 0.290 | FGA QTE ()(b) | 1.400 | 0.867 | 0.462 | 0.292 | 0.195 | 1.126 | 0.874 | 0.634 | 0.503 | 0.410 | Firpo [18] | 0.721 | 0.527 | 0.360 | 0.268 | 0.226 | 0.641 | 0.543 | 0.436 | 0.377 | 0.338 | Bitler et al. [7] | 0.687 | 0.527 | 0.360 | 0.268 | 0.226 | 0.635 | 0.543 | 0.436 | 0.377 | 0.338 | PS Matching | | | | | | | | | | | Nearest neighbor (1) | 0.952 | 0.757 | 0.471 | 0.309 | 0.209 | 0.731 | 0.621 | 0.517 | 0.420 | 0.364 | Nearest neighbor (2) | 0.563 | 0.381 | 0.287 | 0.195 | 0.147 | 0.579 | 0.472 | 0.403 | 0.339 | 0.306 | Nearest neighbor (4) | 0.312 | 0.204 | 0.153 | 0.110 | 0.089 | 0.438 | 0.352 | 0.296 | 0.255 | 0.231 | Kernel | 0.519 | 0.390 | 0.299 | 0.175 | 0.101 | 0.553 | 0.469 | 0.400 | 0.313 | 0.246 | Spline | 0.491 | 0.274 | 0.154 | 0.104 | 0.095 | 0.533 | 0.406 | 0.312 | 0.276 | 0.278 |
| | |
| FGA QTE(a) | 0.305 | 0.191 | 0.105 | 0.072 | 0.046 | 0.441 | 0.344 | 0.259 | 0.211 | 0.168 | FGA QTE ()(a) | 0.252 | 0.143 | 0.070 | 0.049 | 0.029 | 0.394 | 0.301 | 0.212 | 0.175 | 0.138 | FGA QTE(b) | 0.941 | 0.616 | 0.349 | 0.242 | 0.169 | 0.871 | 0.703 | 0.529 | 0.435 | 0.367 | FGA QTE ()(b) | 1.541 | 0.977 | 0.567 | 0.370 | 0.270 | 1.187 | 0.940 | 0.716 | 0.576 | 0.496 | Firpo [18] | 0.658 | 0.540 | 0.358 | 0.249 | 0.206 | 0.606 | 0.521 | 0.401 | 0.332 | 0.285 | Bitler et al. [7] | 0.629 | 0.540 | 0.358 | 0.249 | 0.206 | 0.603 | 0.521 | 0.401 | 0.332 | 0.285 | PS Matching | | | | | | | | | | | Nearest neighbor (1) | 1.288 | 0.748 | 0.443 | 0.271 | 0.184 | 0.921 | 0.697 | 0.534 | 0.423 | 0.350 | Nearest neighbor (2) | 0.993 | 0.608 | 0.359 | 0.229 | 0.152 | 0.809 | 0.624 | 0.489 | 0.390 | 0.317 | Nearest neighbor (4) | 0.656 | 0.465 | 0.292 | 0.194 | 0.137 | 0.654 | 0.547 | 0.442 | 0.360 | 0.298 | Kernel | 0.367 | 0.250 | 0.130 | 0.084 | 0.060 | 0.476 | 0.396 | 0.292 | 0.234 | 0.200 | Spline | 0.648 | 0.349 | 0.181 | 0.121 | 0.093 | 0.642 | 0.476 | 0.343 | 0.285 | 0.235 |
| | |
| FGA QTE(a) | 0.391 | 0.256 | 0.138 | 0.092 | 0.069 | 0.497 | 0.411 | 0.295 | 0.242 | 0.205 | FGA QTE ()(a) | 0.352 | 0.218 | 0.112 | 0.071 | 0.051 | 0.466 | 0.376 | 0.267 | 0.215 | 0.180 | FGA QTE(b) | 1.043 | 0.721 | 0.452 | 0.320 | 0.250 | 0.919 | 0.768 | 0.610 | 0.515 | 0.461 | FGA QTE ()(b) | 1.635 | 1.094 | 0.675 | 0.486 | 0.368 | 1.229 | 1.001 | 0.787 | 0.670 | 0.585 | Firpo [18] | 0.652 | 0.561 | 0.356 | 0.346 | 0.250 | 0.615 | 0.548 | 0.420 | 0.390 | 0.322 | Bitler et al. [7] | 0.652 | 0.561 | 0.356 | 0.346 | 0.250 | 0.615 | 0.548 | 0.420 | 0.390 | 0.322 | PS Matching | | | | | | | | | | | Nearest neighbor (1) | 1.439 | 1.138 | 0.710 | 0.492 | 0.317 | 0.888 | 0.801 | 0.624 | 0.532 | 0.440 | Nearest neighbor (2) | 0.768 | 0.647 | 0.509 | 0.396 | 0.257 | 0.668 | 0.599 | 0.527 | 0.464 | 0.387 | Nearest neighbor (4) | 0.429 | 0.374 | 0.326 | 0.293 | 0.230 | 0.507 | 0.466 | 0.416 | 0.389 | 0.349 | Kernel | 0.486 | 0.576 | 0.407 | 0.328 | 0.255 | 0.534 | 0.556 | 0.484 | 0.445 | 0.400 | Spline | 0.713 | 0.596 | 0.342 | 0.284 | 0.258 | 0.631 | 0.578 | 0.438 | 0.412 | 0.408 |
| | |
| FGA QTE(a) | 0.711 | 0.398 | 0.229 | 0.167 | 0.125 | 0.666 | 0.505 | 0.385 | 0.328 | 0.287 | FGA QTE ()(a) | 0.707 | 0.333 | 0.185 | 0.142 | 0.100 | 0.671 | 0.457 | 0.345 | 0.304 | 0.257 | FGA QTE(b) | 1.218 | 0.837 | 0.560 | 0.417 | 0.345 | 0.979 | 0.824 | 0.678 | 0.588 | 0.544 | FGA QTE ()(b) | 1.771 | 1.176 | 0.809 | 0.589 | 0.473 | 1.269 | 1.029 | 0.860 | 0.736 | 0.664 | Firpo [18] | 0.754 | 0.717 | 0.444 | 0.462 | 0.340 | 0.651 | 0.625 | 0.479 | 0.461 | 0.401 | Bitler et al. [7] | 0.754 | 0.717 | 0.444 | 0.462 | 0.340 | 0.651 | 0.625 | 0.479 | 0.461 | 0.401 | PS Matching | | | | | | | | | | | Nearest neighbor (1) | 0.898 | 0.930 | 0.674 | 0.789 | 0.631 | 0.699 | 0.690 | 0.566 | 0.562 | 0.510 | Nearest neighbor (2) | 0.424 | 0.370 | 0.231 | 0.287 | 0.241 | 0.506 | 0.449 | 0.352 | 0.338 | 0.310 | Nearest neighbor (4) | 0.337 | 0.204 | 0.112 | 0.122 | 0.113 | 0.456 | 0.356 | 0.249 | 0.228 | 0.217 | Kernel | 0.697 | 0.708 | 0.581 | 0.394 | 0.131 | 0.613 | 0.591 | 0.504 | 0.395 | 0.267 | Spline | 0.432 | 0.287 | 0.105 | 0.078 | 0.058 | 0.501 | 0.411 | 0.256 | 0.228 | 0.209 |
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(a) , (b) . MSE: mean squared error. MAE: mean absolute error. Monte Carlo simulations based on 1000 replications of the baseline model.
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