# **4. Regression framework and specifications**

The before and after statistics reported in Tables 3A and 3B can reflect a variety of factors in addition to graduation, including structural differences across countries and the effects of graduating in different years or decades. To isolate the effect of IDA graduation, we use a country and year fixed effects approach and estimate the following regression specification: where, 1�IBRD� is an indicator, which equals 1 if the country is an IBRD country; 0 if IDA or blend country. γ� represents year fixed effects, and we include these in all specifications. X�� is a vector of controls, and we estimate regressions with and without these effects. We control for four main variables – log of population, GNI per capita, Net Aid Flow (non-Bank aid only), and Polity IV score.<sup>13</sup> In separate regressions, we add Fiscal Spending in HD as another control. τ� represents country fixed effects, and we estimate regressions with and without these effects. ε�� is the idiosyncratic error term that we cluster at the country-level. The main coefficient of interest is β, which represents the average difference between IDA and IBRD countries on the outcome of interest y.

The year fixed effects capture the effect of graduating in different years. Among these, they capture the effects of prevailing interest rates (that vary from year to year) as well as any effects due to graduating in different time periods (for example, in a boom vs. a recession). The country fixed effects capture any country-specific characteristics that may affect the outcomes of interest, including national priorities for the HD sectors and/or an appetite for HD lending. They also ensure that the identifying variation comes from countries that transition from IDA to IBRD (since the fixed effects will be collinear for countries that remain in the same status throughout). Given the fact that IDA graduation policy based on the GNI per capita cut-off came into existence in 1987, for our main results, we restrict the analysis to data from 1988-2015. In our robustness checks, we report the results from the full sample of years – 1961-2015.

# **5. Regression results**

Table 4A reports the marginal effects of estimating Probit regressions of the likelihood of any project (Columns 1-4) and the likelihood of any HD project (Columns 5-8). For each outcome variable, the first column reports the results from estimating equation 1 without controls and without country fixed effects. The second column then adds the control variables. The third column then reports results including country fixed effects but no controls. The fourth column then adds the control variables. All regressions include fiscal year fixed effects. Results for other variables are reported in the same format. We primarily focus our discussion on the fourth column, which includes year and country fixed effects, as well as the control variables, but present all results for completeness.

> 13 In other versions of the results, we also included controls for other bilateral and multilateral net flows (DAC data from OECD) as well as countries’ own spending levels in the HD sectors (data from IMF). We chose not to include these covariates because the data are incomplete (resulting in a large loss of number of observations) and because these data did not have much explanatory power. Results are available upon request.

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