# _Alternative per-capita income measures_

Columns (iii) and (iv) of Table 3 repeat the analyses from (respectively) columns (i) and (ii), but with one change. In the first two columns, income is measured _ex post_ , meaning that the income estimates for each year reflect the best available information as of 2009. In many cases these _ex post_ estimates represent a substantial revision from contemporaneous estimates. If graduation decisions at the time were consciously based on the degree to which income was estimated to exceed the threshold, contemporaneous income data – the numbers available to policy makers and Bank officials at the time – may better explain statistically which countries graduate and when. On the other hand, ex post estimates, which incorporate revisions based on information available only later, are presumably more accurate and thus better reflect whether or not a country was really ready to graduate at any given time. Bank and government officials may have been operating on that reality as well as on the then-available official numbers. Therefore, it is unclear which set of figures – contemporaneous or _ex post_ – might better predict actual graduation decisions.

Contemporaneous and ex post estimates are correlated at .96, but for some countries the gap is quite large. Slovakia’s _ex post_ estimates for 1993-2006 are much higher, with a gap of $730 in 1993 growing to $2780 by 2006. For the years 2000-2003, Slovakia’s income was under the IBRD threshold (by about $1200 on average) based on contemporaneous data, but over the threshold (by about $700 on average) based on _ex post_ estimates.

In the last two columns of Table 3, the sample of countries over the threshold is determined using contemporaneous income estimates. The samples are slightly smaller than in the tests using _ex post_ estimates: revisions are in most cases upward rather than downward, so more countries were (believed to be) under the threshold based on contemporaneous data. The results are nearly indistinguishable from those obtained using _ex post_ estimates. Income coefficients and their associated test statistics, and measures of goodness-of-fit (including percentage of correctlypredicted cases) are very similar. These results are consistent with an interpretation that both sets of estimates matter—the ones available to Bank and government officials at the time they were making decisions, and the ones that better reflect the country’s true income levels and thus readiness to graduate, other things equal.

# _Logit results_

Column i in Table 4 reports the logit estimation counterpart to the probit results of column (i) in Table 3. Results are very similar, for the model overall and for the significance of each variable. One advantage to logit over probit is that coefficients can be readily expressed as odds ratios, and these are reported in the table. A 1-unit increase in Political Freedoms is associated with a 27% increase in the odds of being an IBRD graduate, compared to 35% for a 1-unit increase in Institutional Capacity, or a 5% increase for Credit Rating. Odds ratios below one indicate a decrease in the odds, so the time trend odds ratio indicates that other things equal the odds of being a graduate drop by 22% per year.

A second advantage of logit is that we can control for time-invariant influences using country fixed effects, for the limited number of countries in our data set with a change in their 13