Most theoretical models predict that institutions allowing for direct legislation should lead, on average, to policies more closely reflecting the wishes of the voters. While some agreement exists at the theoretical level about the expected policy consequences of direct legislation, empirical evidence has been scant so far. In this paper I discuss the reasons for this scantiness of empirical evidence, namely the intricacies of the adequate empirical model to test the theoretical proposition, and suggest possible solutions to this problem. Re-analyzing a dataset with which some authors have found no evidence in support of the theoretical claim, I show that with a better adapted empirical model we find results in synch with our theoretical expectations. Thus, policies in states that allow for direct legislation reflect on average more closely the voters' wishes. Using Monte-Carlo simulations I also demonstrate the properties of the proposed estimator and suggest that it could be used in other contexts, like when assessing the responsiveness of legislators.