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100 obs. TABLE 2 Simulation Results for Truncated Regression Estimators Design 2: Homoskedastic Chi-squared Errors Slope Intercept Mean Bias Med. Bias RMSE MAD Mean Bias Med. Bias RMSE MAD WLS -0.4032 -0.3551 1.7932 0.8954 -0.1212 -0.1635 0.3996 0.2269 AWLS -2.0899 -0.2006 34.7590 3.1147 0.0446 -0.0573 1.8738 0.4271 STLS 0.0701 0.0415 0.5857 0.4451 -0.4990 -0.4992 0.5352 0.5002 PWD 0.0846 0.0445 0.9777 0.7649 - - - - MLE -0.1215 -0.1054 0.5470 0.4398 0.4803 0.4768 0.4988 0.4803 200 obs. WLS -0.2424 -0.2234 0.6936 0.5272 -0.1246 -0.1211 0.2941 0.1641 AWLS -0.0403 -0.1456 0.9074 0.6695 0.0052 -0.0132 0.2305 0.1749 STLS 0.1170 0.1351 0.4528 0.3487 -0.4990 -0.4989 0.5135 0.4990 PWD 0.0358 0.0392 0.6091 0.4690 - - - - MLE -0.1414 -0.1391 0.3626 0.2867 0.4969 0.4935 0.5059 0.4969 400 obs. WLS -0.2245 -0.2717 0.4694 0.3809 -0.1127 -0.1204 0.1516 0.1297 AWLS -0.0732 -0.1457 0.6271 0.4622 0.0180 0.0088 0.1531 0.1224 STLS 0.0846 0.0811 0.2954 0.2386 -0.5183 -0.5179 0.5260 0.5183 PWD -0.0018 -0.0337 0.4710 0.3706 - - - - MLE -0.1492 -0.1595 0.2995 0.2453 0.4960 0.4921 0.5005 0.4960 800 obs. WLS -0.1761 -0.1950 0.3305 0.2711 -0.0950 -0.0986 0.1182 0.1024 AWLS -0.0187 -0.0826 0.5945 0.3752 0.0503 0.0425 0.1390 0.1060 STLS 0.1048 0.1041 0.2189 0.1764 -0.5204 -0.5202 0.5238 0.5204 PWD 0.0083 -0.0160 0.2974 0.2403 - - - - MLE -0.1442 -0.1524 0.2230 0.1822 0.4962 0.4970 0.4986 0.4962 45
100 obs. TABLE 3 Simulation Results for Truncated Regression Estimators Design 3: Heteroskedastic Truncated Normal Errors Slope Intercept Mean Bias Med. Bias RMSE MAD Mean Bias Med. Bias RMSE MAD WLS -0.3353 -0.3621 0.7405 0.5880 -0.0174 -0.0157 0.1596 0.1187 AWLS -0.1248 -0.2202 0.7371 0.5817 -0.0073 -0.0052 0.1695 0.1302 STLS 0.0363 0.0333 0.5515 0.4215 0.0616 0.1078 0.2444 0.2014 PWD 0.3649 0.3590 0.6053 0.4870 - - - - MLE 0.0980 0.0970 0.3757 0.3023 0.3370 0.3368 0.3460 0.3370 200 obs. WLS -0.2775 -0.2860 0.4948 0.4028 -0.0221 -0.0221 0.1008 0.0799 AWLS -0.0879 -0.1069 0.4762 0.3774 -0.0128 -0.0149 0.1144 0.0903 STLS 0.0567 0.0718 0.3643 0.2894 0.0856 0.0992 0.1699 0.1414 PWD 0.3755 0.3565 0.4989 0.4188 - - - - MLE 0.1001 0.0970 0.2629 0.2103 0.3379 0.3396 0.3419 0.3379 400 obs. WLS -0.2517 -0.2490 0.3999 0.3286 -0.0151 -0.0141 0.0674 0.0538 AWLS -0.0847 -0.1322 0.3819 0.3100 -0.0053 -0.0049 0.0746 0.0598 STLS 0.0099 0.0327 0.2512 0.2008 0.0947 0.1004 0.1400 0.1187 PWD 0.3544 0.3603 0.4259 0.3703 - - - - MLE 0.0836 0.0876 0.1908 0.1549 0.3389 0.3412 0.3414 0.3389 800 obs. WLS -0.1803 -0.1711 0.2810 0.2287 -0.0094 -0.0089 0.0511 0.0402 AWLS -0.0180 -0.0460 0.2970 0.2164 -0.0019 0.0022 0.0580 0.0457 STLS 0.0074 0.0101 0.1790 0.1392 0.0895 0.0940 0.1207 0.1013 PWD 0.3581 0.3586 0.3934 0.3607 - - - - MLE 0.0852 0.0909 0.1491 0.1223 0.3354 0.3365 0.3365 0.3354 46
Page 1 and 2: WEIGHTED AND TWO STAGE LEAST SQUARE
Page 3 and 4: and augmented data in semiparametri
Page 5 and 6: ei ≥ 0 (i.e., discarding draws wh
Page 7 and 8: is the interval [L, K], then Proof:
Page 9 and 10: Assumption A.1 defines the truncate
Page 11 and 12: such that [∂H(y, x, e)/∂y] /f
Page 13 and 14: ASSUMPTION A.3’: The underlying,
Page 15 and 16: it also depends on α0. Equation (2
Page 17 and 18: to infinity. To allow for an augmen
Page 19 and 20: and and ψµi(k) = I[0 ≤ yi ≤ k
Page 21 and 22: 4 Monte Carlo Results In this secti
Page 23 and 24: 5 Conclusions This paper proposes n
Page 25 and 26: [17] Lewbel, A. (2000), “Semipara
Page 27 and 28: and denote the estimator by ˆ f
Page 29 and 30: C7 The functions and ϕna(z) (A.12)
Page 31 and 32: Turning to the trimming procedure,
Page 33 and 34: We note that the last term is o(n
Page 35 and 36: To write this in U−statistic form
Page 37 and 38: ¯ f ∗ zi −f ∗ zi∞ = O(hp n
Page 39 and 40: WLS2 The sequences of random vector
Page 41 and 42: A.1.2 Asymptotics for the Instrumen
Page 43 and 44: function satisfies Assumption C6. D
Page 45: 100 obs. TABLE 1 Simulation Results

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