On the assumption that poor people migrate to obtain better welfare benefits, the magnet hypothesis predicts that a state's poverty rate increases when its welfare benefit rises faster than benefits in surrounding states. The benefit competition hypothesis proposes that states lower welfare benefits to avoid attracting the poor from neighboring states. Previous investigations, which yield support for these propositions, suffer from weaknesses in model specification and methodology. We correct these deficiencies in a simultaneous equation model including a state's poverty rate and its benefit level for AFDC (Aid to Families with Dependent Children) as endogenous variables. We estimate the model using pooled annual data for the American states from 1960 to 1990 and find that a state's poverty rate does not jump significantly when its welfare payments outpace benefits in neighboring states. Furthermore, there is no evidence of vigorous benefit competition among states: states respond to decreases in neighboring states’ welfare benefits with only small adjustments in their own.