# _Additional income, human development, and interaction variables_

In each of the six regressions reported in Table 6, an additional variable is added to the model from the first column of Table 3, using the larger sample of observations and the _ex post_ income measure. The added regressor in each test is indicated in bold in the respective column headings, with the coefficient and t-statistic for the added regressor shown in bold in a row towards the bottom of Table 6.

The added variable in the first column is (the log of) PPP-adjusted per-capita income. If PPP-adjusted income is a better measure of living standards than income based on exchange rates, it may provide additional explanatory power in our graduation tests. Results show it is in fact positively and significantly related to the probability of being a graduate. Moreover, with its inclusion the coefficient on GNI per capita (based on exchange rates) falls and is no longer significant.

The second and third columns add human development outcome indicators, as proxies for the broad concept of “economic and social institutions.”<sup>23</sup> Column (ii) adds a measure of educational attainment – average years of completed education for the population age 25 and over– from Barro and Lee (2010).<sup>24</sup> Column (iii) adds instead a health outcome indicator, infant mortality, that has reasonably good data coverage.<sup>25</sup> Neither of these human development outcome proxies for economic and social institutions turns out to be significantly related to the probability of graduation. Column (iv) adds instead a gender equality indicator, the female labor force participation rate. This variable is also not significant.

Column (v) adds income inequality, as measured by the Gini coefficient.<sup>26</sup> For a given level of average income, a higher Gini will tend to be associated with higher poverty rates. Higher poverty in turn may be associated with a greater need for continued access to IBRD loans. However, the regression coefficient for the Gini measure, while positive, is insignificant in Table 6.<sup>27</sup> 23 The graduation policy does not define institutional development explicitly, but an unpublished 1982 memorandum to the Executive Directors describes as an example of institutional weakness “countries that have recently experienced rapid increases in real income because of improved terms of trade or new mineral discoveries” but with “social indicators such as health and education levels [that] are often much lower than in other countries at the same income level.” The same memorandum implies that a failure to address development disparities between groups or regions within a country reflects institutional weaknesses.

24 Data retrieved from the World Bank EdStats database. Barro and Lee provide estimates only for every fifth year between 1970 and 2010, so we linearly interpolate for the years in between. Results are very similar to those reported here if we treat the in-between years as missing data.

25 Data are from the World Bank’s World Development Indicators (WDI).

26 Data are from the World Bank’s World Development Indicators (WDI). Other measures of income equality (e.g. income share going to the middle quintile) or inequality (e.g. share going to the top decile or quintile) produced similar results.

27 Inequality changes slowly over time in most countries, so results in Table 4 are based on the country average values for Gini, from all available data over the 1982-2008 period. If we instead use the annual values and drop all years with missing data, the available sample is far smaller, and Gini is again not significant. Similarly, poverty headcount measures are available only for a very small number of annual observations, and we do not take period averages for poverty headcount because it often exhibits strong variability over time within countries.

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