Standard economic theory predicts that if property rights to pollute are clearly established, equilibrium outcomes in an efficient emissions permit market will be independent of how the emissions permits are initially distributed. This so-called independence property has important implications for policy design and implementation. Past studies document a strong positive correlation between the initial permit allocation and firm-level emissions, raising concerns that the independence property is failing to hold in real-world settings. We exploit the random assignment of firms to different permit allocation cycles in Southern California's RECLAIM program in order to test the independence of permit allocation and emissions. Our results lend empirical support to the independence hypothesis.