Figure 13: Marginal distributions of potential outcomes bounds. I compare my new bounds to Makarov bounds to demonstrate the informativeness and usefulness of my methodology. Birth weight has been widely used as an indicator of infant health and welfare in economic research. Researchers have investigated social costs associated with low birth weight (LBW), which is defined as birth weight less than 2500 grams, to understand the short term and long term effects of children’s endowments. For example, Almond et al. (2005) estimated the effects of birth weight on medical costs, other health outcomes, and mortality rate, and Currie and Hyson (1999) and Currie and Moretti (2007) evaluated the effects of low birth weight on educational attainment and long term labor market outcomes. Almond and Currie (2011) provide a survey of this literature. Smoking has been acknowledged as the most significant and preventable cause of LBW, and thus various efforts have been made to reduce the number of women smoking during pregnancy. As one of these efforts, increases in cigarette taxes have been widely used as a policy instrument between 1980 and 2009 in the U. S. Tax rates on cigarettes have increased by approximately $0 . 80 each year on average across all states, and more than 80 tax increases of $0 . 25 have been implemented in the past 15 years (Simon (2012) and 31 5.1 Background