Park and Kang (2008), has found a positive association between smoking behavior and other unhealthy lifestyles, and between higher education and a healthier lifestyle. Given this association, my MTE and LATE estimates suggest that births to women with an unhealthier lifestyle on average are more vulnerable to smoking. In this subsection, I estimate the effect of smoking on quantiles of infant birth weight through the quantile treatment effect (QTE) parameter. q -QTE measures the difference in the q -quantile of Y$_{1}$ and Y$_{0}$ , which is written as Q$_{q}$ ( Y$_{1}$ ) − Q$_{q}$ ( Y$_{0}$ ) where Q$_{q}$ ( Y$_{d}$ ) denotes the q -quantile of Y$_{d}$ for d ∈ { 0 , 1 } . Lemma 4 forms a basis for causal inferences for compliers under Assumption 2. Lemma 4 (Abadie et al. (2002)) Given Assumption 2(i), Lemma 4 allows QTE to provide causal interpretations for compliers. Let Q$_{q}$ ( Y | X, D, D$_{1}$ > D$_{0}$ ) denote the q -quantile of Y given X and D for compliers. Then by Lemma 4, represents the causal effect of smoking cessation on the q -quantile infant birth weight for compliers. Now I estimate the quantile regression model based on the following specification for the q -quantile of Y given X and D for compliers : for q ∈ (0 , 1) , where β$_{q}$ ( X ) = β$_{1}$$_{q}$ + X $^{′}$β$_{2}$$_{q}$ , β$_{q}$ =    β$_{1}$$_{q}$ β$_{2}$$_{q}$   $_{}$, ( α$_{q}$, β$_{1}$$_{q}$ ) ∈$_{R}$ ×$_{R}$ , β$_{2}$$_{q}$ ∈$_{R}$ k and γ$_{q}$ ∈$_{R}$ $^{k}$. 39 Q$_{q}$ ( Y | X, D, D$_{1}$ > D$_{0}$ ) = α$_{q}$ + β$_{q}$ ( X ) D + X $^{′}$γ$_{q}$ , (17) Q$_{q}$ ( Y | X, D = 1 , D$_{1}$ > D$_{0}$ ) − Q$_{q}$ ( Y | X, D = 0 , D$_{1}$ > D$_{0}$ ) ( Y$_{1}$, Y$_{0}$ ) ⊥ D | X, D$_{1}$ > D$_{0}$ 5.4.2 Quantile Treatment Effects for Compliers Table 4: Local Average Treatment Effects (grams) Dep. var.: birth weight (grams) LATE The entire sample 209 White 133 Age26-35 183 Some college and college graduates (SCCG) 112