Table 3.

Simulation results for the second setting

	DIF		CM			GPS
	Bias	MSE	Bias	MSE	Coverage	Bias	MSE	Coverage
$\widehat{\tau }(1,2)$	0.3018	57.84	0.0018	0.1274	100	-0.01	0.6792	96
$\widehat{\tau }(1,3)$	1.3952	49.369	0.2054	0.1596	92	0.5358	0.7599	100
$\widehat{\tau }(1,4)$	1.5757	100.8098	0.2399	0.2752	95	0.5586	1.2158	98
$\widehat{\tau }(1,5)$	0.5084	67.0518	0.0395	0.1463	98	0.1034	0.715	99
$\widehat{\tau }(1,6)$	1.1749	171.6227	-0.0126	0.352	99	0.247	1.7528	100
$\widehat{\tau }(1,7)$	0.158	112.809	0.2096	0.2655	94	0.3157	1.2102	99
$\widehat{\tau }(1,8)$	-0.821	180.6354	0.1273	0.3762	99	-0.0071	1.6007	99
$\widehat{\tau }(1,9)$	2.0151	143.3044	0.2893	0.4069	95	0.6285	1.8175	99
$\widehat{\tau }(2,3)$	1.0935	90.0545	0.2036	0.2307	96	0.5457	1.2592	96
$\widehat{\tau }(2,4)$	1.2739	141.8236	0.2381	0.3722	95	0.5685	1.8167	99
$\widehat{\tau }(2,5)$	0.2066	108.4089	0.0377	0.2094	98	0.1133	1.273	99
$\widehat{\tau }(2,6)$	0.8732	213.3382	-0.0144	0.3651	97	0.2569	2.1094	99
$\widehat{\tau }(2,7)$	-0.1438	153.8053	0.2078	0.3398	95	0.3257	1.7631	98
$\widehat{\tau }(2,8)$	-1.1228	221.493	0.1255	0.4262	98	0.0029	2.0662	97
$\widehat{\tau }(2,9)$	1.7133	181.401	0.2875	0.482	92	0.6384	2.3613	98
$\widehat{\tau }(3,4)$	0.1805	132.7905	0.0345	0.2152	100	0.0228	1.2421	100
$\widehat{\tau }(3,5)$	-0.8868	98.2762	-0.1659	0.233	94	-0.4324	1.2247	100
$\widehat{\tau }(3,6)$	-0.2203	203.3266	-0.218	0.4787	96	-0.2888	2.0927	100
$\widehat{\tau }(3,7)$	-1.2373	144.9614	0.0042	0.2239	100	-0.2201	1.5009	100
$\widehat{\tau }(3,8)$	-2.2163	212.7647	-0.0782	0.3516	99	-0.5428	2.2201	99
$\widehat{\tau }(3,9)$	0.6199	174.6271	0.0839	0.3254	98	0.0927	1.8084	99
$\widehat{\tau }(4,5)$	-1.0673	150.22	-0.2004	0.3493	97	-0.4552	1.6829	99
$\widehat{\tau }(4,6)$	-0.4007	255.1281	-0.2525	0.648	95	-0.3116	2.3817	100
$\widehat{\tau }(4,7)$	-1.4177	196.272	-0.0303	0.2876	100	-0.2429	1.9039	98
$\widehat{\tau }(4,8)$	-2.3967	263.7386	-0.1126	0.4394	99	-0.5656	2.6361	100
$\widehat{\tau }(4,9)$	0.4394	228.3766	0.0494	0.3819	99	0.0699	2.1243	98
$\widehat{\tau }(5,6)$	0.6666	219.9407	-0.0521	0.4228	96	0.1436	2.1538	100
$\widehat{\tau }(5,7)$	-0.3504	162.5709	0.1701	0.3206	96	0.2124	1.7036	99
$\widehat{\tau }(5,8)$	-1.3294	232.1535	0.0877	0.4387	98	-0.1104	2.1514	99
$\widehat{\tau }(5,9)$	1.5067	193.1234	0.2498	0.4427	96	0.5251	2.271	98
$\widehat{\tau }(6,7)$	-1.017	268.8625	0.2222	0.5564	95	0.0687	2.7217	100
$\widehat{\tau }(6,8)$	-1.996	335.0898	0.1399	0.6331	99	-0.254	3.2473	100
$\widehat{\tau }(6,9)$	0.8402	294.916	0.3019	0.6769	97	0.3815	3.1403	98
$\widehat{\tau }(7,8)$	-0.979	274.7638	-0.0823	0.3908	100	-0.3228	2.6812	100
$\widehat{\tau }(7,9)$	1.8571	240.759	0.0797	0.3587	99	0.3128	2.43	99
$\widehat{\tau }(8,9)$	2.8361	306.5584	0.162	0.5289	98	0.6355	3.2702	100

DIF is the sample difference. CM is the covariates matching estimator. GPS is the generalized propensity score matching estimator