# **4  Exploring the Basic Structure of the Model**

We want to explore the effect of foreign aid,<sup>_i_</sup> _fp_<sup>, the productivity factor,</sup><sup>_A_, and the fraction of</sup> human capital used in market goods production,<sup>_u_</sup> 1<sup>, on the steady-state variables of three group of</sup> countries classified by income level. We follow the World Bank's 2006 paper to the Development Committee in classifying countries in low-income, lower-middle-income, and upper-middle-income groups. Due to the quality of the data, however, only a reduced list of countries is used for the calibration exercise.<sup>25</sup> We employ only data for the time period 1994 to 2004. First, we will _f_ calibrate the effect of foreign aid,<sup>_i_</sup> _p_<sup>.26 By looking at actual data of foreign aid per capita, we are</sup> able to determine a range in which our parameters can vary. Before we can evaluate the effect of foreign aid, productivity factor, and the fraction of human capital used in market goods production on per capita income, we need to calibrate our above-mentioned model (1) to (5) such that we can roughly reproduce the differences in per capita income across the three groups of countries. Since, as discussed above, there are many forces of growth causing the differences in per capita income, we adjust the productivity level of the three groups, the parameter _A_ , such that we roughly obtain the actual differences in per capita income, normalizing the parameter, _A_ , of the lowest per capita income group. Therefore _A_ is set to 1 for the lowest income group. We hereby take the composition of total public expenditure, α 1 , α 2 , α 3 , and α 4 , as given for each group as we find them in the data. Now we employ our _Mathematica_ program to obtain stationary state solutions for the three groups of countries.<sup>27</sup> This is equivalent to a comparative static analysis for the three country groups. Our exercise consists in keeping the parameter, _A_ , constant for each group of countries and equal to its calibrated value. Then we let foreign aid,<sup>_i_</sup> _pf_<sup>, vary during that period and</sup> _b_ see how such a change affects the steady-state values , _k_ , _h g_ , , _c_<sup>_e_</sup> _p_ , _y_ , , and _U_ . Such an _y_ exercise was conducted for the low-, lower-middle-, and upper-middle income groups. In the next step we vary the productivity parameter, _A_ , for each group of countries, employing for each country group the _A_ that we used to calibrate the model to obtain the actual differences in per capita income, and increasing it gradually. The parameter, _A_ , is set equal to 1, 1.18, and 1.45 for the low-, lower-middle-, and upper-middle income groups respectively. Finally, we vary<sup>_u_</sup> 1<sup>, the</sup> fraction of human capital used in market goods production, from 0.1 to 0.8, keeping foreign aid equal to its 10-year average, and the other parameters constant.

## **_4.1  Effects of Foreign Aid per Capita,_**

### _f_<sup>_i_</sup> _p_

_b_ The comparative static results for all income groups show that _k_ , _h_ , _g_ , _c_ ,<sup>_e_</sup> _p_<sup>,</sup><sup>_y_,</sup> , and _y_

> _U_ are linear in _f_

> <sup>_i_</sup> _p_<sup>and there is clearly a positive relationship between the level of foreign aid and</sup> _b_ all the variables, except for public resources per capita,<sup>_e_</sup> _p_<sup>, and debt per GDP,</sup> , which show a _y_

> 25 See Appendix A.4 for the complete list of countries.

> 26 _f_

> Note that in the following we presume that there is no new borrowing, so that<sup>_i_</sup> _p_ is solely foreign aid.

> 27 The _Mathematica_ code is available at www.newschool.edu/gf/cem.

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