The literature on aid and growth has not found a convincing instrumental variable to identify the causal effects of aid. In this paper we exploit an instrumental variable based on the fact that since 1987, a major criterion for IDA (International Development Association) eligibility has been whether or not a country is below a certain threshold of per capita income. We find evidence that other donors tend to reinforce rather than compensate for reductions in IDA aid following threshold crossings. Overall, the aid to GNI ratio drops about 59% on average after countries cross the threshold. Focusing on the 35 countries that have crossed the IDA income threshold from below between 1987 and 2010, we find a positive, statistically significant, and economically sizable effect of aid on growth. A one percentage point increase in the aid to GNI ratio from the sample mean raises annual real per capita GDP growth by approximately 0.35 percentage points. We show that the main channel through which aid promotes growth is by increasing physical investment.