I use Abadie et al. (2002)’s estimation procedure. They proposed an estimation method for moments involving ( Y, D, X ) for compliers by using weighted moments. See Section 3 of Abadie et al. (2002) for details about the estimation procedure and asymptotic distribution of the estimator. Following their estimation strategy, I estimate the equation (17). 18 The estimation results for the equation (17) are documented in Table C.3 in Appendix C. Smoking is estimated to have significantly negative effects on all quantiles of birth weight. The estimated causal effect of smoking on the q -quantile of infant birth weight is − 195 grams at q = 0 . 15, − 214 grams at q = 0 . 25, and − 234 grams at q = 0 . 50. The effect significantly differs by women’s race, education, age, and the quality of prenatal care. This heterogeneity also varies across quantile levels of birth weight. For the low quantiles q = 0 . 15 and 0 . 25, the adverse effect of smoking is estimated to be the largest for births whose mothers are black and get inadequate prenatal care. In education, the adverse smoking effect is much less severe for college graduates compared to women with other education background. At q = 0 . 15, as women’s age increases up to 35 years, the adverse effect of smoking becomes less severe, but it increases with women’s age for births to women who are older than 35 years old. Controlling for the smoking status, compared to white women, black women bear lighter babies for all quantiles and Hispanic women bear similar weight babies at low quantiles q = 0 . 15 , 0 . 25 but lighter babies at higher q > 0 . 5 . Also, at low quantiles q = 0 . 15 and 0 . 25, as mothers’ education level increases, the birth weight noticeably increases except for post graduate women. Married women are more likely to give births to heavier babies for low quantiles q = 0 . 15 , 0 . 25 , 0 . 50 , but lighter babies at high quantiles q = 0 . 75 , 0 . 85. One should be cautious about interpreting the results at high quantiles. At high quantiles, heavier babies do not necessarily mean healthier babies because high birth weight could be also problematic. 19 The prenatal care seems to be associated with birth weight very differently at both ends of quantiles (at q = 0 . 15 and at q = 0 . 85). At q = 0 . 15, women with better prenatal care tend to have lighter babies, while at q = 0 . 85 women with better prenatal care are more likely to bear heavier infants. This suggests that women with higher medical risk factors are more likely to have more intense prenatal care. To estimate marginal distributions of Y$_{0}$ and Y$_{1}$$_{,}$ I first estimate the model (17) for a fine grid of q with 999 points from 0 . 001 to 0 . 999 and obtain quantile curves of Y$_{0}$ and Y$_{1}$ on the fine grid. Note that fitted quantile curves are non-monotonic as shown in Figure 16(a). I sort the estimated values of the quantile curves in an increasing order as proposed by Chernozhukov et al. (2009). They showed that this procedure improves the estimates of quantile functions and distribution functions in finite samples. Figure 16(b) shows $^{18}$I follow the same computation method as in Abadie et al. (2002). They used Barrodale-Roberts (1973) linear programming algorithm for quantile regression and a biweight kernel for the estimation of standard errors. $^{19}$High birth weight is defined as a birth weight of > 4000 grams or greater than 90 percentiles for gestational age. The causes of HBW are gestational diabetes, maternal obesity, grand multiparity, etc. The rates of birth injuries and infant mortality rates are higher among HBW infants than normal birth weight infants. 40