Table 2: Monte Carlo results under designs DGP 6- DGP 10 25 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). “ 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). 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 1.10 1.60 7.80 9.40 1.10 1.70 -0.29 3.71 89.40 6 200 5.70 6.10 4.00 2.50 1.00 0.40 0.90 0.30 5.70 6.50 2.30 3.90 -0.08 2.10 91.00 6 400 5.60 6.00 5.10 2.40 0.90 0.30 2.80 0.70 5.80 6.30 3.30 4.50 -0.02 1.41 91.90 6 600 5.00 5.20 4.90 1.70 0.60 0.20 3.40 1.60 3.70 5.00 3.80 3.70 -0.02 1.11 90.00 6 800 5.40 5.20 5.10 2.70 1.40 0.70 5.10 3.40 4.60 5.00 2.60 4.20 -0.01 0.97 93.30 6 1000 4.90 6.00 4.50 2.80 1.10 0.50 4.90 5.20 5.70 5.80 3.70 5.40 -0.01 0.84 92.30 7 100 9.50 10.60 4.10 1.60 0.70 0.00 0.60 5.30 6.80 8.40 2.50 3.80 0.22 6.97 96.60 7 200 15.40 14.90 5.10 3.30 2.00 1.10 0.70 1.20 13.60 13.90 2.70 6.00 0.59 4.43 99.10 7 400 26.40 24.20 5.40 6.60 6.80 5.20 0.60 0.30 23.00 19.90 4.60 7.90 0.61 2.66 99.10 7 600 37.20 33.00 9.10 10.70 11.10 8.70 0.10 0.00 33.70 30.10 8.30 9.30 0.56 1.97 96.60 7 800 49.50 46.50 9.90 16.70 17.00 13.90 0.10 0.00 46.40 37.70 13.80 13.70 0.59 1.69 89.30 7 1000 57.20 52.90 11.90 22.90 24.30 21.60 0.20 0.20 55.60 47.50 17.70 16.20 0.60 1.51 78.10 8 100 9.50 10.60 5.70 1.30 0.80 0.20 2.00 14.30 8.20 9.90 2.20 3.70 0.61 10.68 96.20 8 200 18.30 18.70 4.40 4.20 3.60 2.80 1.00 4.40 14.80 15.50 3.40 5.30 1.12 6.58 99.40 8 400 46.50 41.80 8.10 16.00 15.80 11.60 0.50 0.90 41.70 37.10 9.10 9.10 1.36 4.44 98.50 8 600 66.30 62.10 15.80 27.50 28.10 24.20 0.20 0.50 60.60 54.20 20.80 16.10 1.33 3.42 88.30 8 800 79.90 74.40 23.30 42.70 45.60 40.00 0.50 0.60 74.90 68.30 30.90 22.30 1.34 2.91 66.00 8 1000 87.00 82.10 31.30 52.70 55.00 51.20 2.10 0.30 82.40 77.70 42.20 25.40 1.30 2.51 44.00 9 100 10.00 12.00 3.50 2.40 0.40 0.20 1.70 6.80 10.10 12.40 1.20 2.50 0.06 7.76 88.30 9 200 15.10 15.10 4.70 3.70 1.80 0.80 1.60 4.10 12.40 12.00 4.00 7.10 0.60 5.02 94.60 9 400 30.40 26.80 4.50 3.10 2.80 2.90 0.80 2.70 21.30 17.00 8.50 12.00 0.97 3.70 97.30 9 600 44.10 36.10 5.70 6.10 6.70 6.00 0.50 3.30 32.50 25.30 17.10 20.10 1.00 3.01 89.20 9 800 57.60 50.20 6.60 8.80 11.00 10.40 0.70 3.00 46.80 35.60 25.40 29.30 1.03 2.63 78.60 9 1000 70.50 57.50 5.30 11.30 15.70 16.60 0.80 2.40 59.30 45.60 35.60 39.80 1.07 2.45 67.90 10 100 7.50 8.30 4.10 1.30 0.60 0.30 0.00 0.00 6.80 8.70 4.00 3.90 -0.09 2.37 97.30 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 1.26 96.50 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 -0.10 0.81 93.60 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 91.40 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