where y is the average per capita income, c and t indicate countries and years, respectively, and λt’ + εct’ is a composite error term. In other words, the dependent variable is the period average growth rate of growth in real per capita income. The natural logarithm of real per capita income of the initial year, lnyc0, is included as an explanatory variable to examine the conditional β-convergence.

Furthermore, we examined the impact of institutional quality<sup>3</sup> on development effectiveness by dividing the samples into two different groups, by (a) level and (b) change in institutional quality respectively, in order to show the differences in development effectiveness among different sets of countries: (i) countries whose initial level of institutional quality is higher than the sample mean; (ii) countries whose initial level of institutional quality is lower than the sample mean; (iii) countries whose institutional quality is improving (i.e., the change ratio of institutional quality is positive); and (iv) countries whose institutional quality is not improving (i.e., the change ratio of institutional quality is zero or negative).<sup>4</sup>

# **2.2 Leg 2: Aid and Inequality (Inequality Regressions)**

We examined the possible impact of aid on reducing inequality, employing three different equations: a) level regressions for the average income of the poorest quintile; b) growth regressions for the average income of the poorest quintile; and c) growth regressions for the Gini indices. We give most attention to b), as we consider that looking at the impact of aid to change in the poverty situation of the bottom quintile, rather than levels, is more appropriate and important for assessing development effectiveness. Our interest in a) conducting level regressions, is to identify pro-poor country fixed effects, which consist of various aspects of a country and make a country pro-poor, but are difficult to quantify. Lastly, we tested the impact of aid on changes in Gini indices, or c), for a robustness check, as Gini indices are often used in inequality analyses. However, this study pays more attention to changes in the inequality situation of the poor than that of the entire country, in order to assess development effectiveness.

# _a) Estimation by the level relationship for the average income of the poorest quintile._

We examined the level relationship between average income of the poorest quintile and that of the country, as well as other variables similar to Dollar and Kraay (2002, Eq. 1) by employing a fixed-effects regression model. We looked at the parameter of θ as an indicator of the pro-poorness of aid. Impact of aid to the poor, indicated by the parameter of θ, can be compared with that of policies and institutions,

> 3 We employed indices for the quality of institutions extracted from the International Country Risk Guide (ICRG) indicator (PRS Group, 2012).

> 4 Splitting samples based on certain criteria is a common approach in empirical growth literature. For instance, the sample can be divided by positive/negative growth of a country (Dollar and Kraay, 2001), or income groups (Mosely, 1980; Burnside & Dollar, 2004). We also tested interaction terms in order to see the joint effects and nonlinearity, i.e., whether policy/institutional quality is a key determinant of development effectiveness. Nevertheless we found in estimating coefficients of cross terms, aid and institutions were not statistically significant. This arises from the fact that estimating marginal effects (i.e., marginal elasticity parameters) of aid heavily depends on the sample selection, time duration, and sets of variables, as has been expounded in much of the literature. Kraay (2005, Figure 5) showed the interaction term of aid and policy (Burnside & Dollar, 2000) accounted for only four percent contribution to growth.

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