disbursements in a given country-year associated with past loan approvals will be uncorrelated with contemporaneous shocks and will thus be a valid instrument for aid.<sup>3</sup> We therefore estimate the local projection regressions in Equation (1) by two-stage least squares, using predicted disbursements on loans from official creditors, expressed as a share of GDP, as an instrument for aid. Since the set of right-hand-side variables in the local projection regressions is the same for all projection horizons, there is just one first-stage regression of aid on the instrument, lags of the real exchange rate, and of course country and year fixed effects. As we will document in the following sections, predicted disbursements on loans from official creditors has very strong predictive power for actual aid, implying a strong first-stage relationship.

The main aid variable of interest is the standard measure of net official development assitance (ODA) reported by the OECD's Development Assistance Committee. Net ODA consists of disbursements on concessional loans and disbursements on grants, and nets out repayments on past concessional loans. By design, the instrument described above will only have predictive power for the first component of aid, disbursements on concessional loans.<sup>4</sup> However, as we shall see below, despite this limitation the instrument has very strong predictive power for overall aid. Finally, our benchmark measure of the real exchange rate is the IMF's trade-weighted multilateral real exchange rate. This is oriented such that an increase (decrease) corresponds to an appreciation (depreciation). We rebase these so that the real exchange rate index is equal to 100 in 2005 for each country. This implies that only within-country over-time fluctuations in the real exchange rate are economically meaningful, and accordingly in all our empirical specifications that follow we include a full set of country fixed effects.

3 The predicted disbursements instrument is constructed as follows. We start with a set of approximately 60,000 loans from official creditors to developing country governments, as recorded in the Debtor Reporting System database of the World Bank. For each loan we have the year of the original commitment, and the schedule of subsequent annual actual disbursements. For each loan we construct a 10-yeardisbursement profile, i.e. the fraction of the original commitment that is disbursed in year 0, 1,2,...,10, with year zero corresponding to the approval year of the loan. We next sort loans into creditor-decade-region-specific bins and average disbursement profiles across loans within bins. We then apply these typical disbursement profiles to individual loans within each bin, and construct predicted disbursements for each loan, i.e. the disbursements that would have occured had the loan disbursed at the typical rate for all loans in the same bin. The rationale for this step is that it removes any country-specific source of variation in actual disbursements on previously approved loans, which might respond endogenously to contemporaneous macroeconomic shocks. Finally, we aggregate the predicted disbursements across all loans for each country-year observation, but excluding loans approved in the same year. By construction, the only country-specific variation in this predicted disbursements measure reflects loan approval decisions from previous years, which we assume to be uncorrelated with contemporaneous macroeconomic shocks. For details, see Sections 2 and 3 of Kraay (2012b).

4 A companion paper, Kraay (2013) extends the methodology in Kraay (2012a,b) to develop an analogous instrument for grant-financed aid.

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