This study estimates the effect of physical punishment on the cognitive development of 1,167 low-income Colombian children (M[subscript age] = 17.8 months old) using 3 analytic strategies: lagged-dependent variables, a difference-in-differences-like approach (DD), and a novel strategy combining matching with a DD-like approach. Across approaches, physical punishment at ages 9-26 months predicted reductions in children's cognitive development of 0.08-0.21 SD at ages 27-46 months. These results, plus null results of falsification tests, strengthen the argument that physical punishment leads to slower cognitive growth and illustrate the utility of alternative statistical methods to reduce problems of selection bias in developmental research.