With this solution technique we can undertake the above described comparative static analyses and some important calibrations, see sects. 4 and 5.<sup>19</sup>

# **_3.2  Fiscal Policy to Ensure Debt Sustainability_**<sup>**_20_**</sup>

The model of section 3.1 permits government to borrow from capital markets, in particular to borrow from abroad in order to undertake public investment. In this section, we want to explore the effects and implications of government borrowing from capital markets and briefly discuss the sustainability of fiscal policy when borrowing is allowed for.<sup>2122</sup> Let us assume that the government has borrowed from abroad for undertaking public investment. The implication of this type of expenditure is that along the transition path, this will raise the growth rate of public infrastructure and lead to a higher level of public capital. This higher level brings a distortion into the model by raising the marginal product of private capital. As a consequence, the investment share is increased and the growth rate of consumption rises implying higher welfare after a sufficiently long adjustment period. Note that this also leads to higher growth of physical and human capital. However, in our growth model these growth effects only hold on the transition path. In the long-run, higher public investment leads to higher levels of output and consumption but does not affect the growth rate of endogenous variables.

Since here borrowing from abroad equals loans or issuing of bonds to foreigners, the government must pay it back plus interest payments. Debt repayment is represented by α 4<sup>_e_</sup> _p_ . More concretely, the government has to stick to the inter-temporal budget constraint which can be written as where _s_ denotes the primary surplus which, in our model, is given by α 4<sup>_e_</sup> _p_ . The first term in (15) states that per-capita government debt at time zero must equal the discounted stream of future primary surpluses. This implies that the government must run primary surpluses, if it starts with a positive stock of debt. Equivalent to this formulation is the requirement that discounted debt converges to zero asymptotically. It should be mentioned that in theoretical exogenous growth models the inter-temporal budget constraint is met, provided the interest rate exceeds the population growth rate on average, because per-capita debt converges to a finite value. Nevertheless, it is _A_ = 1 , η = 0.1, _r_ = 0.07 .

> 17 The _Mathematica_ code is available at www.newschool.edu/gf/cem.

> 18 Note that these values are dimensionless and are calibrated in such a way as to fit the data. Economic implications are derived in later sections, where the effects of comparative changes are explored. 19 Allowing for additional borrowing by adding a constant in eqns. (4) and (5) and setting this borrowing at the same

_b_ size as foreign aid,<sup>_i_</sup> _p_ = 0.05 , we obtain the following numerical values: _k_<sup>*</sup> = 88.67 , _h_<sup>*</sup> = 22.36 , _g_<sup>*</sup> = 18.43 ,

> 20 Since this section treats empirical matters, its notation is changed in order to comply with readily available data (e.g. _G_ now refers to primary expenditure and not public capital as in the rest of the paper).

21 _f_ Again, note that in case of net borrowing a constant needs to be added to eqn. ((5)) and the foreign aid parameter<sup>_i_</sup> _p_

> in eqn. ((4)) is supposed to be corrected for the availability of new investment funds for public capital.

22 In Greiner et al. (2005), ch. 6, more particular model versions are developed with government borrowing for specific government expenditures.

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