This paper studies the impact of aid volatility in a two-period model where production may occur with either a traditional or a modern technology. Public spending is productive and "time to build" requires expenditure in both periods for the modern technology to be used. The possibility of a poverty trap induced by high aid volatility is first examined in a benchmark case where taxation is absent. The analysis is then extended to account for self insurance (taking the form of a first-period contingency fund) financed through taxation. An increase in aid volatility is shown to raise the optimal contingency fund. But if future aid also depends on the size of the contingency fund (as a result of a moral hazard effect on donors' behavior), the optimal policy may entail no self insurance.