There is a new paper by Sebastian Galiani, Stephen Knack, Lixin Colin Xu, and Ben Zou, and the results are intriguing:
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. This threshold is predetermined and arbitrary, so it is plausibly exogenous to recipient countries in a model that conditions on initial income levels, country and period fixed effects. 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 by about 60% 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 0.6 percentage points. We also demonstrate that an important reason for underestimating aid effects is the attenuation bias associated with measurement errors in aid that the literature has ignored so far. Finally, there is some evidence that our results may apply to the other low-income countries that are still below the threshold.