Estimating the casual effect of smoking on birth outcomes is difficult since omitted (unobserved) variables are likely to be correlated with a mother's decision to smoke. While some previous work has dealt with this endogeneity problem by using instrumental variables, this paper instead attempts to estimate the smoking effect from panel data (i.e., data on mothers with multiple births). Panel data sets are constructed with matching algorithms applied to federal natality data. The fixed effects regressions, which control for individual heterogeneity, yield significantly different results from ordinary least squares and previous instrumental variable approaches. The potential inconsistency caused by false matches and other violations of the fixed effects strict exogeneity assumption are considered.