distribution with d degrees of freedom. For the t -test, we consider Bonferroni corrected CVs based on the standard normal distribution. Note that the Bonferroni correction is necessary to address the multiple testing problem. We consider sample sizes n equal to 100, 200, 400, 600, 800 and 1 , 000. For each design, we consider 1 , 000 Monte Carlo experiments. The { V$_{i}$ } n i = used in the bootstrap implementations are independently generated as V with P ( V = 1 − κ ) = $_{κ/}$√$_{5 and}$ P ( V = κ ) = 1 − $_{κ/}$√$_{5,}$ where κ = ( $^{√$_{5 + 1}$}$) / 2, as proposed by Mammen (1993). The bootstrapped critical values are approximated using B = 999 bootstrap replications. To compute Shaikh et al. (2009)’s test, we use the standard normal kernel Following Shaikh et al. (2009), the bandwidth sequence h$_{n}$ is chosen to be equal to cn − 1 / 8 for c equal to 0.01, 0.05, 0.10 and 0.15. We choose different c ’s to assess how sensitive Shaikh et al. (2009)’s test may be with respect to the bandwidth h$_{n}$ . K ( u ) = 1 √$_{2}$$_{π}$ exp ( − u 2 2 ) . We first consider the following data generating processes (DGPs): 4.1 Simulation 1 For each of these five DGPs, D = 1 { D ∗ > 0 } ,ε ⊥ ( X$_{1}$,X$_{2}$ ), where X$_{1}$ = Z$_{1}$ , X$_{2}$ = ( Z$_{1}$ + Z$_{2}$ ) $_{/}$√$_{2,}$ and Z$_{1}$ , Z$_{2}$, and ε are independent standard normal random variables. All the DGPs considered have the propensity score bounded away from zero and one. Finally, for each of these DGPs we consider the potential outcomes 19 Y (1) = 2 m$_{1}$ ( X ) + u (1) and Y (0) = m$_{1}$ ( X ) + u (0) , DGP 1 . D ∗ = ( X$_{1}$ + X$_{2}$ ) 3 − ε ; DGP 2 . D ∗ = − 1 + ( X$_{1}$ + X$_{2}$ + X$_{1}$X$_{2}$ ) 3 − ε ; DGP 3 . D ∗ = − 0 . 2 + ( X 2 1 − X 2 ) 2 − ε ; DGP 4 . D ∗ = (0 . 1 + X$_{1}$/ 3) exp (( X$_{1}$ + X$_{2}$ )/ 3) − ε ; DGP 5 . D ∗ = ( − 0 . 8 + ( X$_{1}$ + X$_{2}$ + X$_{1}$X$_{2}$ ) / 3) exp (0 . 2 + ( X$_{1}$ + X$_{2}$ )/ 3) − ε.