Figure 15: Marginal smoking effects I estimate the equation (16) using a series approximation. This method is especially convenient to estimate MTE ∂µ $_{∂p}$. The estimation results for the regressions (15) and (16) are reported in Table C.1 and Table C.2, respectively, in Appendix C. Figure 15 shows estimated marginal treatment effects for each propensity to not smoke. It is observed that the positive effect of smoking cessation on infant birth weight increases as the tendency to smoke increases. That is, the benefit of quitting smoking on child health is larger for women who will still smoke despite facing higher tax rates. In turn, the adverse effect of smoking on infant birth weight is more severe for women with the higher tendency to smoke during pregnancy. Next, I estimate LATE from the MTE. The LATE is interpreted as the benefit of smoking cessation for compliers, women who change their smoking status from smoker to nonsmoker in response to the tax increase. It is obtained from marginal treatment effects as follows: for p ( x ) = Pr ( D = 1 | Z = 1 ,X = x ) and p = Pr ( D = 1 | Z = 0 ,X = x ) , Table 4 presents estimated LATE for the entire sample and three subgroups of white women, women aged 26- 35, and women with some college or college graduates (SCCG). The estimated benefit of smoking cessation is noticeably small for SCCG women, compared to the entire sample and women whose age is between 26 and 35. These MTE and LATE estimates show that births to less educated women or women with a higher tendency to smoke are on average more vulnerable to smoking. The literature, such as Deaton (2003) and E [ Y$_{1}$ − Y$_{0}$ | X = x,D$_{1}$ > D$_{0}$ ] = 1 p ( x ) − p ( x ) ∫ p ( x ) p ( x ) MTE ( x,p ) dp. 38