Column (ii) reports results from a random-effects tobit model.<sup>33</sup> In general, results are very similar to column (i). A notable exception is that the positive time trend is no longer significant when using random effects.

Column (iii) follows the method and specification for column (i), but for Sample 2 instead of Sample 1. Results based on this smaller sample of borrowers are nearly identical to those for the larger sample.

Columns (iv) and (v) of Table 8 present results on lending per capita for expanded samples. (Summary statistics for these expanded samples are presented in Table 9.) Sample 3 expands on Sample 1 by adding all country-year observations with per-capita incomes exceeding the IDA operational cutoff. Some of these observations are technically eligible for concessional IDA loans, despite having incomes over the IDA cutoff, for example because of the exception for small island economies. As shown in column (iv), income and creditworthiness remain significant in this sample, although with diminished coefficients relative to results for Samples 1 and 2. In this expanded sample, we can add a dummy for observations over the IBRD threshold (in samples 1 and 2 all observations were over it). The coefficient for this dummy is negative and significant, indicating (unsurprisingly) that countries over the notional threshold borrow less. We can also control for the volume of IDA borrowing per capita in this test. Lending from these two sources appears to be substitutes: more IDA borrowing is negatively associated with IBRD borrowing.

Sample 4 expands on Sample 3 by adding in observations below the IDA income cutoff. Results on income per capita, IDA borrowing, and the over-IBRD-threshold dummy in this sample (with results reported in column (v) of Table 8) are all similar to results in column (iv). There are several notable differences in results using Samples 3 and 4. First, institutional capacity is significant in column (v). Second, creditworthiness is insignificant. Third, the transition dummy is positive and significant. Fourth, we add a dummy for observations over the IDA income cutoff.<sup>34</sup> Per-capita IBRD borrowing is higher for these observations than for those below the IDA cutoff, even when controlling for the volume of IDA borrowing.

Overall, the similarities in results for borrowing and graduation outweigh the differences, and the same variables that predict a greater probability of graduation also tend to predict reduced likelihood of borrowing from IBRD and reduced amounts borrowed. Because the most likely graduates—high-income countries with strong institutions and credit ratings—are also attractive low-risk borrowers from the standpoint of the Bank’s balance sheet, it is unlikely that the reduction in borrowing is driven by unwillingness of the Bank to lend to these countries. Therefore, these results are consistent with a graduation model that is evolutionary rather than abrupt: the same factors that gradually reduce a country’s demand for IBRD loans also eventually lead it to graduate.

> 33 Fixed-effects tobit models (similarly to probit) cannot be estimated using conditional maximum likelihood, and unconditional fixed-effects tobit estimates are biased.

> 34 Data on the IDA operational cutoff threshold begin only in 1987, so the period covered is 1987-2008.

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