Table 6: The proportion of potential low birth weight infants Table 7: The proportion of potential low birth weight infants (%) F$_{0}$ (2 , 500) F$_{1}$ (2 , 500) Entire Sample 6.5 4 White 7 3 SCCG 3.5 2.9 Age 26-35 5.7 3.2 (%) F$_{0}$ (2 , 500) F$_{1}$ (2 , 500) Entire Sample 6.5 4 White 7 3 SCCG 3.5 2.9 Age 26-35 5.7 3.2 while 4% babies to nonsmokers would have low birth weight. Similar results are obtained for white women and women aged 26-35. A surprising result is obtained for SCCG women. Only 3.5% of babies to SCCG women who smoke would have low birth weight. This implies that SCCG women who smoke are less likely to have low birth weight infants than women with less education who smoke. One possible explanation for this is that women with higher education are more likely to have healthier lifestyles and this substantially lowers the risk of having low infant birth weight for smoking. Recall the sharp lower bound under MTR: for δ ≥ 0 , where 0 ≤ a$_{k}$$_{+1}$ − a$_{k}$ ≤ δ for each integer k . To compute the new sharp lower bound from the estimated marginal distribution functions, I plug in the estimates of marginal distribution functions ̂ F$_{0}$ and ̂ F$_{1}$ proposed in the previous subsection. I follow the same computation procedure as in the numerical example of Section 4. I discuss the procedure in Appendix B in detail. I propose the following plug-in estimators of my new lower bound and Makarov bounds based on the estimators of marginal distributions ̂ F$_{0}$ and ̂ F$_{1}$ proposed in the previous subsection. 20 Note that the infinite sum in the lower bound under MTR in Corollary 1 reduces to the finite sum for the bounded support. For any fixed δ > 0 , the consistency of my estimators is immediate. In Figure 17, I plot my new lower bound and Makarov bounds for the entire sample. One can see $^{20}$Fan and Park (2010a, 2010b) proposed the same type plug-in estimators for Makarov bounds and studied their asymptotic properties. They used empirical distributions to estimate marginal distributions point-identified in randomized experiments. 42 5.4.3 Bounds on the Distribution and Quantiles of Treatment Effects for Compliers F L Δ ( δ ) = sup { a$_{k}$ } ∞ k = −∞ ∞ ∑ k = −∞ max { F$_{1}$ ( a$_{k}$$_{+1}$ ) − F$_{0}$ ( a$_{k}$ ) , 0 } , (18)