retained.<sup>31</sup> Here, again, only the results of the low-income groups are reported. For the results of the other two country groups, see Appendix A.6. The data on public expenditure is obtained from the IMF's Government Finance Statistics. Since these are too detailed for our analysis, the different expenditure categories are summarized to match the following model parameters: public investment in infrastructure, α 1<sup>_v_</sup> 1 , education, α 1<sup>_v_</sup> 2 , and health, α 1<sup>_v_</sup> 3 , public transfers, α 2 , public consumption, α 3 and debt services, α 4 = (1 −α 1 −α 2 −α 3) .<sup>32</sup> Note that the values reflect the averages for all countries of one category.

By plugging the obtained numerical values ( α 1 = 0.4035 , α 2 = 0.0623 , α 3 = 0.4342 ) into the model, setting ρ = 0.03 , δ _k_ = 0.075 , δ _h_ = 0.075 , δ _g_ = 0.05 , α = β = γ = 0.33,<sup>_u_</sup> 1 = 0.85 , ε 1 = ε 2 = 0.2 , ε 3 = 0.25 , _r_ = 0.08 , η = 0.1 , and using the values for _A_ and<sup>_i_</sup> _pf_<sup>that were found in</sup> the previous section ( _A_ = 1, _n_ = 0.0195<sup>_i_</sup> _pf_ = 3.361), one can simulate the effect of changes in the composition of public expenditure on the stationary states by letting<sup>_v_</sup> 1<sup>,</sup><sup>_v_</sup> 2<sup>and</sup><sup>_v_</sup> 3<sup>vary.33</sup> In the following this is done for the low-income country group.<sup>34</sup> Although all graphs are presented in the 3-dimensional space such that the interaction of all three investment expenditure parameters can be observed at the same time, the stationary states for shifts from public investment in health, α 1<sup>_v_</sup> 2 , to public investment in education, α 1<sup>_v_</sup> 3 , are of particular interest.<sup>35</sup> Generally, the results suggest that, in order to maximize the growth of per capita income, more than half of public investment expenditure should be on infrastructure while the residual should be roughly equally allocated to investments that support production of human capital. Figures 4 to 12, all of which are hump-shaped, depict the effects of changes in the investment expenditure composition on the various model parameters. Figures 4 to 9 show all possible investment expenditure compositions for income, _y_ , capital, _k_ , public capital, _g_ , public debt, _b_ , consumption, _c_ and total public resource absorption,<sup>_e_</sup> _p_<sup>, are qualitatively the same.</sup> _b_ Only the graphs for human capital, _h_ , utility, _U_ , and debt/income ratio, , differ in their _y_ behavior. In Figure 12 one can see that human capital can be increased beyond its welfare- and growth-maximizing level by setting<sup>_v_</sup> 2 = 0.30 and<sup>_v_</sup> 3 = 0.20 (and<sup>_v_</sup> 1 = 0.5 ). At this point the maximal _h_ is reached, however, the benefits of its increase do not offset the costs of higher depreciation. Figure 10 depicts the changes in utility over the range of<sup>_v_</sup> 1<sup>,</sup><sup>_v_</sup> 2<sup>and</sup><sup>_v_</sup> 3<sup>. Whilst the</sup> curvature of _U_ is less pronounced than in the previous graphs, it is hump-shaped and possesses an interior maximum which lies at general maximum, i.e.<sup>_v_</sup> 1 = 0.65 ,<sup>_v_</sup> 2 = 0.15 and<sup>_v_</sup> 3 = 0.20 . The _b_ shape of the debt to income ratio, , differs completely from the other variables as it does not _y b_ possess an interior maximum. As one can see in graph 11, the curvature of is strictly concave _y_ and attains its maximum value at the origin, i.e. _v_ 2 = _v_ 3 = 0 (and<sup>_v_</sup> 1 = 1 ). The fact that is, however, more interesting is that the ratio is approximately stable through most of the range of<sup>_v_</sup> 2<sup>and</sup><sup>_v_</sup> 3<sup>.</sup>

> 31 See appendix A.4 for the complete list of countries.

> 32 See appendix A.3 for details.

> 33 Note that described the numerical values for ρ , δ _k_ , δ _h_ , δ _g_ , α , β , γ , _u_ 1, ε 1, ε 2, ε 3, α 1 , α 2 , α 3 and η remain

> the same for the remainder of this section. 34 Similar results hold for the other two groups. Complete sets of graphs for the other groups are listed in Appendix A.6. 35 Note that _v_ 1 + _v_ 2 + _v_ 3 = 1 always has to hold which restricts the plane to a triangular space. By fixing<sup>_v_</sup> 2<sup>or</sup><sup>_v_</sup> 3<sup>the</sup>

> effects of changes in<sup>_v_</sup> 1<sup>are also always observable.</sup>

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