Table B.2: Monte Carlo results under designs DGP 6- DGP 10 with trimming 43 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” stands for the average simulated bias, estimated 95% confidence interval length, and 95% coverage probability for the ATE estimator ̂ 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. 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 6 100 8.50 9.40 5.80 2.50 1.00 0.20 0.30 0.30 7.80 9.40 1.10 1.70 -0.05 2.94 95.20 6 200 5.70 6.10 4.00 2.50 1.00 0.40 0.30 0.10 5.70 6.50 2.30 3.90 -0.01 1.80 95.00 6 400 5.60 6.00 5.10 2.40 0.90 0.30 0.40 0.00 5.80 6.30 3.30 4.50 -0.01 1.22 95.10 6 600 5.00 5.20 4.90 1.70 0.60 0.20 1.20 0.10 3.70 5.00 3.80 3.70 -0.01 0.98 93.60 6 800 5.40 5.20 5.10 2.70 1.40 0.70 1.20 0.40 4.60 5.00 2.60 4.20 -0.01 0.84 94.80 6 1000 4.90 6.00 4.50 2.80 1.10 0.50 1.90 0.80 5.70 5.80 3.70 5.40 0.00 0.76 93.70 7 100 9.50 10.60 4.10 1.60 0.70 0.00 0.40 2.60 6.80 8.40 2.50 3.80 0.00 5.56 95.70 7 200 15.40 14.90 5.10 3.30 2.00 1.10 0.70 1.50 13.60 13.90 2.70 6.00 0.22 3.45 97.70 7 400 26.40 24.20 5.40 6.60 6.80 5.20 0.40 0.60 23.00 19.90 4.60 7.90 0.39 2.30 98.50 7 600 37.20 33.00 9.10 10.70 11.10 8.70 0.70 0.70 33.70 30.10 8.30 9.30 0.44 1.82 97.30 7 800 49.50 46.50 9.90 16.70 17.00 13.90 0.60 0.50 46.40 37.70 13.80 13.70 0.47 1.56 90.80 7 1000 57.20 52.90 11.90 22.90 24.30 21.60 0.50 0.30 55.60 47.50 17.70 16.20 0.50 1.41 82.70 8 100 9.50 10.60 5.70 1.30 0.80 0.20 1.30 5.50 8.20 9.90 2.20 3.70 -0.12 7.46 93.00 8 200 18.30 18.70 4.40 4.20 3.60 2.80 1.40 5.00 14.80 15.50 3.40 5.30 0.21 4.69 97.30 8 400 46.50 41.80 8.10 16.00 15.80 11.60 1.10 3.00 41.70 37.10 9.10 9.10 0.49 3.26 98.80 8 600 66.30 62.10 15.80 27.50 28.10 24.20 1.70 2.00 60.60 54.20 20.80 16.10 0.59 2.65 96.30 8 800 79.90 74.40 23.30 42.70 45.60 40.00 2.10 2.80 74.90 68.30 30.90 22.30 0.67 2.27 87.60 8 1000 87.00 82.10 31.30 52.70 55.00 51.20 2.20 2.80 82.40 77.70 42.20 25.40 0.73 2.03 77.90 9 100 10.00 12.00 3.50 2.40 0.40 0.20 0.30 1.90 10.10 12.40 1.20 2.50 -0.30 4.82 89.80 9 200 15.10 15.10 4.70 3.70 1.80 0.80 0.50 2.40 12.40 12.00 4.00 7.10 -0.17 2.89 90.40 9 400 30.40 26.80 4.50 3.10 2.80 2.90 0.70 1.80 21.30 17.00 8.50 12.00 0.01 2.03 93.70 9 600 44.10 36.10 5.70 6.10 6.70 6.00 1.50 4.10 32.50 25.30 17.10 20.10 0.05 1.67 93.10 9 800 57.60 50.20 6.60 8.80 11.00 10.40 2.10 4.30 46.80 35.60 25.40 29.30 0.10 1.44 90.50 9 1000 70.50 57.50 5.30 11.30 15.70 16.60 1.60 4.70 59.30 45.60 35.60 39.80 0.13 1.31 89.50 10 100 7.50 8.30 4.10 1.30 0.60 0.30 0.10 0.10 6.80 8.70 4.00 3.90 -0.11 2.24 97.20 10 200 10.00 10.10 5.10 1.80 0.80 0.30 0.00 0.00 10.30 9.30 4.40 4.90 -0.10 1.25 96.70 10 400 19.20 16.70 5.20 3.80 2.80 1.80 0.00 0.00 20.60 14.90 6.90 8.60 -0.11 0.81 93.50 10 600 36.20 28.10 4.60 7.30 6.80 4.80 0.10 0.00 37.70 27.70 10.10 8.20 -0.11 0.65 91.30 10 800 50.20 38.90 7.70 11.30 13.20 11.10 0.10 0.00 52.80 38.80 15.20 12.60 -0.12 0.55 87.50 10 1000 64.30 51.70 8.20 18.20 22.30 18.90 0.10 0.00 67.00 51.40 21.00 13.90 -0.12 0.49 83.10