Table B.1: Monte Carlo results under designs DGP 1- DGP 5 with trimming DGP n CvM$_{n}$ KS$_{n}$ T$_{n}$ (0 . 01) T$_{n}$ (0 . 05) T$_{n}$ (0 . 10) T$_{n}$ (0 . 15) Max- t Wald CvM unp n KS unp n CvM trad n KS trad n Bias CI length Coverage 1 100 5.00 5.60 4.90 2.30 0.80 0.20 0.10 0.30 5.40 5.00 5.40 6.10 0.02 1.26 93.70 1 200 4.40 4.60 4.90 2.30 0.60 0.20 2.40 2.10 4.00 4.50 4.40 3.90 0.01 0.91 94.00 1 400 5.10 5.80 4.10 2.40 1.10 0.40 4.20 4.50 4.70 5.30 4.70 4.80 0.01 0.67 93.90 1 600 5.20 5.70 4.30 1.80 0.70 0.40 4.80 5.00 5.00 5.30 4.60 5.50 0.00 0.56 93.30 1 800 5.30 4.30 4.50 1.50 0.50 0.40 5.00 6.10 4.90 4.50 6.20 4.70 0.00 0.49 93.70 1 1000 5.00 5.90 4.50 2.90 1.20 0.80 6.00 6.80 5.10 4.90 5.70 5.00 0.00 0.44 93.80 2 100 28.90 26.40 6.70 7.60 7.70 6.20 14.20 21.40 17.90 18.70 16.10 16.80 0.64 3.30 76.10 2 200 61.50 55.30 7.30 17.30 20.80 18.70 12.50 19.70 41.60 42.60 35.50 30.50 0.68 2.62 75.40 2 400 90.60 84.30 18.50 44.60 50.40 50.40 13.80 20.00 79.80 74.80 71.50 60.60 0.68 1.94 70.00 2 600 98.90 96.30 33.60 66.60 74.00 75.80 19.60 26.10 94.90 93.40 89.80 82.80 0.68 1.63 59.70 2 800 99.70 99.10 50.40 83.50 89.20 89.70 22.60 28.60 99.10 98.00 97.70 93.80 0.67 1.43 51.60 2 1000 100.00 100.00 67.40 93.90 96.10 96.80 28.50 31.70 99.90 99.90 99.40 98.40 0.68 1.29 45.20 3 100 32.80 26.10 6.20 5.30 1.50 0.40 0.10 0.00 33.60 25.00 15.90 18.10 0.01 0.87 95.90 3 200 59.10 49.90 18.70 16.50 6.40 1.10 0.00 0.00 59.00 49.60 40.80 38.80 -0.01 0.57 94.70 3 400 69.20 64.10 38.40 28.60 9.20 2.40 0.00 0.00 69.70 63.70 83.00 80.30 0.00 0.39 94.70 3 600 79.70 74.60 56.60 40.90 14.70 3.80 0.00 0.00 80.10 75.30 98.70 97.10 0.00 0.32 95.70 3 800 81.00 77.70 63.40 42.30 15.20 4.10 0.00 0.00 81.30 77.80 99.70 99.70 0.00 0.27 96.20 3 1000 83.30 81.30 71.00 48.90 17.70 3.90 0.10 0.00 82.90 81.00 100.00 100.00 0.00 0.24 95.80 4 100 15.20 12.20 4.40 1.50 1.10 0.50 0.10 0.00 15.60 12.00 20.00 11.40 0.16 0.90 90.80 4 200 35.00 27.00 5.10 7.30 6.50 3.50 0.50 0.30 37.50 26.80 42.00 25.10 0.16 0.60 81.20 4 400 64.70 53.80 8.10 17.20 21.10 17.00 3.60 1.60 70.30 51.20 74.60 46.30 0.16 0.42 69.30 4 600 85.30 75.40 13.40 33.00 39.00 35.70 7.80 4.80 88.30 72.50 90.50 69.90 0.16 0.34 56.10 4 800 92.50 86.70 19.00 50.00 60.40 59.40 9.40 7.40 94.80 85.00 96.70 83.70 0.16 0.29 42.00 4 1000 96.50 93.80 29.80 63.20 74.00 75.40 12.60 10.00 97.60 92.00 99.20 90.40 0.16 0.26 32.50 5 100 11.00 7.80 5.00 2.20 1.30 0.60 4.20 4.10 9.20 6.90 9.20 5.70 0.37 1.68 72.70 5 200 16.40 13.70 4.90 2.70 2.30 1.60 9.50 10.90 13.80 9.70 13.00 7.80 0.44 1.29 62.10 5 400 26.70 23.00 5.90 5.70 4.70 3.90 18.80 18.90 23.50 15.80 22.70 11.10 0.47 0.99 48.60 5 600 35.80 32.80 5.30 8.70 9.90 8.40 23.70 26.20 35.20 21.70 32.40 15.50 0.46 0.84 42.60 5 800 45.00 39.30 5.70 11.80 14.30 12.90 28.80 31.60 44.00 28.60 38.80 19.10 0.46 0.74 32.40 5 1000 56.00 49.20 7.80 17.00 20.70 19.30 35.30 35.70 57.20 38.30 52.40 27.00 0.46 0.66 23.90 42 Note: Simulations based on 1,000 Monte Carlo experiments. “ CvM$_{n}$ ” and “ KS$_{n}$ ” stand for our proposed Cram´er-von Mises and Kolmogorov-Smirnov tests. “ T$_{n}$ ( c )” stands for Shaikh et al. (2009)’s test, with bandwidth h$_{n}$ = cn $_{−}$1 / $^{8}$. “Max- t ” and “ Wald ” stand for, respectively, the Bonferroni-corrected Max- t -test, and Wald balancing tests based on ̂ ATE$_{n}$ ( X $^{j}$) defined in (4.2) but with observations with estimated propensity score outside [0 . 05 , 0 . 95] trimmed. “ CvM unp n ” and “ KS unp n ” are the Cram´er-von Mises and Kolmogorov- Smirnov tests based on the unprojected empirical process ˆ R$_{n}$ ( u ) defined in (2.10), whereas “ CvM trad n ” and “ KS trad n ” are defined analogously, but based on ˆ R trad n ( x ) as defined in (4.1). Finally, “Bias”, “CI length’, and “Coverage” stand for the average simulated bias, estimated 95% confidence interval length, and 95% coverage probability for the ATE estima- tor ̂ ATE$_{n}$ as defined in (4.3), but with observations with estimated propensity score outside [0 . 05 , 0 . 95] trimmed. All entries are proportions of rejections at 5% level, in percentage points, except “Bias” ,“CI length”, and “Coverage” (measure in percentage points), which are as described above. See the main text for further details.