Borrowing for Growth: Big Pushes and Debt Sustainability in Low-Income Countries

Crowding Out in the Simplified Model

		Benchmark Model
		τ*			\|$\bar{\tau }$\|
		R = 0.10	R = 0.20	R = 0.30	R = 0.10	R = 0.20	R = 0.30
ρ = 0.06	α = 0.40	2.66	2.66	2.66	0.12	0.46	0.75
	α = 0.50	2.14	2.14	2.14	0.15	0.50	0.77
ρ = 0.10	α = 0.40	2.65	2.65	2.65	–	0.25	0.51
	α = 0.50	2.13	2.13	2.13	–	0.29	0.54
		CIC_SR when τ = 0.25			CIC_SR when τ = 0.50
		R = 0.10	R = 0.20	R = 0.30	R = 0.10	R = 0.20	R = 0.30
ρ = 0.06	α = 0.40	−0.80	−1.33	−1.87	−0.57	−0.95	−1.34
	α = 0.50	−0.85	−1.42	−1.98	−0.60	−1.00	−1.40
ρ = 0.10	α = 0.40	−0.60	−1.00	−1.41	−0.43	−0.72	−1.01
	α = 0.50	−0.64	−1.06	−1.49	−0.45	−0.76	−1.06
		Open Private Capital Account
		ξ*
		τ = 0.25	τ = 0.50		τ = 0.75	τ = 1
ρ = 0.06	α = 0.40	61.0	47.1		36.9	29.0
	α = 0.50	61.2	46.5		35.3	26.4
ρ = 0.10	α = 0.40	33.6	26.2		20.6	16.2
	α = 0.50	33.6	25.8		19.7	14.7
		CIC_SR when τ = 0.25 and α = 0.40			CIC_SR when τ = 0.50 and α = 0.40
		R = 0.10	R = 0.20	R = 0.30	R = 0.10	R = 0.20	R = 0.30
ρ = 0.06	α = 0.40	−0.78	−1.29	−1.81	−0.55	−0.92	−1.29
	α = 0.50	−0.68	−1.14	−1.59	−0.48	−0.79	−1.11
ρ = 0.10	α = 0.40	−0.57	−0.95	−1.33	−0.40	−0.67	−0.94
	α = 0.50	−0.45	−0.75	−1.05	−0.31	−0.51	−0.72

		Benchmark Model
		τ*			\|$\bar{\tau }$\|
		R = 0.10	R = 0.20	R = 0.30	R = 0.10	R = 0.20	R = 0.30
ρ = 0.06	α = 0.40	2.66	2.66	2.66	0.12	0.46	0.75
	α = 0.50	2.14	2.14	2.14	0.15	0.50	0.77
ρ = 0.10	α = 0.40	2.65	2.65	2.65	–	0.25	0.51
	α = 0.50	2.13	2.13	2.13	–	0.29	0.54
		CIC_SR when τ = 0.25			CIC_SR when τ = 0.50
		R = 0.10	R = 0.20	R = 0.30	R = 0.10	R = 0.20	R = 0.30
ρ = 0.06	α = 0.40	−0.80	−1.33	−1.87	−0.57	−0.95	−1.34
	α = 0.50	−0.85	−1.42	−1.98	−0.60	−1.00	−1.40
ρ = 0.10	α = 0.40	−0.60	−1.00	−1.41	−0.43	−0.72	−1.01
	α = 0.50	−0.64	−1.06	−1.49	−0.45	−0.76	−1.06
		Open Private Capital Account
		ξ*
		τ = 0.25	τ = 0.50		τ = 0.75	τ = 1
ρ = 0.06	α = 0.40	61.0	47.1		36.9	29.0
	α = 0.50	61.2	46.5		35.3	26.4
ρ = 0.10	α = 0.40	33.6	26.2		20.6	16.2
	α = 0.50	33.6	25.8		19.7	14.7
		CIC_SR when τ = 0.25 and α = 0.40			CIC_SR when τ = 0.50 and α = 0.40
		R = 0.10	R = 0.20	R = 0.30	R = 0.10	R = 0.20	R = 0.30
ρ = 0.06	α = 0.40	−0.78	−1.29	−1.81	−0.55	−0.92	−1.29
	α = 0.50	−0.68	−1.14	−1.59	−0.48	−0.79	−1.11
ρ = 0.10	α = 0.40	−0.57	−0.95	−1.33	−0.40	−0.67	−0.94
	α = 0.50	−0.45	−0.75	−1.05	−0.31	−0.51	−0.72

Source: Authors’ calculations based on solutions from Mathematica programs.

Note: The depreciation rate and the ratio of infrastructure investment to GDP equal 5 percent in all runs. ρ is the pure time preference rate; α is the income share of private capital; R is the return on infrastructure (net of depreciation); τ* (⁠|${\rm {\bar{\tau }}}$| d) is the value of the intertemporal elasticity of substitution below which private (total) investment decreases at t = 0 CIC_SR is the crowding-in coefficient for private investment in the short run (t = 0); and ξ* is the value of elasticity of capital flows (measured as a percentage of GDP, with respect to the interest rate differential) below which private investment decreases. (ξ* is independent of the return on infrastructure.)

Table 1.

Crowding Out in the Simplified Model

		Benchmark Model
		τ*			\|$\bar{\tau }$\|
		R = 0.10	R = 0.20	R = 0.30	R = 0.10	R = 0.20	R = 0.30
ρ = 0.06	α = 0.40	2.66	2.66	2.66	0.12	0.46	0.75
	α = 0.50	2.14	2.14	2.14	0.15	0.50	0.77
ρ = 0.10	α = 0.40	2.65	2.65	2.65	–	0.25	0.51
	α = 0.50	2.13	2.13	2.13	–	0.29	0.54
		CIC_SR when τ = 0.25			CIC_SR when τ = 0.50
		R = 0.10	R = 0.20	R = 0.30	R = 0.10	R = 0.20	R = 0.30
ρ = 0.06	α = 0.40	−0.80	−1.33	−1.87	−0.57	−0.95	−1.34
	α = 0.50	−0.85	−1.42	−1.98	−0.60	−1.00	−1.40
ρ = 0.10	α = 0.40	−0.60	−1.00	−1.41	−0.43	−0.72	−1.01
	α = 0.50	−0.64	−1.06	−1.49	−0.45	−0.76	−1.06
		Open Private Capital Account
		ξ*
		τ = 0.25	τ = 0.50		τ = 0.75	τ = 1
ρ = 0.06	α = 0.40	61.0	47.1		36.9	29.0
	α = 0.50	61.2	46.5		35.3	26.4
ρ = 0.10	α = 0.40	33.6	26.2		20.6	16.2
	α = 0.50	33.6	25.8		19.7	14.7
		CIC_SR when τ = 0.25 and α = 0.40			CIC_SR when τ = 0.50 and α = 0.40
		R = 0.10	R = 0.20	R = 0.30	R = 0.10	R = 0.20	R = 0.30
ρ = 0.06	α = 0.40	−0.78	−1.29	−1.81	−0.55	−0.92	−1.29
	α = 0.50	−0.68	−1.14	−1.59	−0.48	−0.79	−1.11
ρ = 0.10	α = 0.40	−0.57	−0.95	−1.33	−0.40	−0.67	−0.94
	α = 0.50	−0.45	−0.75	−1.05	−0.31	−0.51	−0.72

		Benchmark Model
		τ*			\|$\bar{\tau }$\|
		R = 0.10	R = 0.20	R = 0.30	R = 0.10	R = 0.20	R = 0.30
ρ = 0.06	α = 0.40	2.66	2.66	2.66	0.12	0.46	0.75
	α = 0.50	2.14	2.14	2.14	0.15	0.50	0.77
ρ = 0.10	α = 0.40	2.65	2.65	2.65	–	0.25	0.51
	α = 0.50	2.13	2.13	2.13	–	0.29	0.54
		CIC_SR when τ = 0.25			CIC_SR when τ = 0.50
		R = 0.10	R = 0.20	R = 0.30	R = 0.10	R = 0.20	R = 0.30
ρ = 0.06	α = 0.40	−0.80	−1.33	−1.87	−0.57	−0.95	−1.34
	α = 0.50	−0.85	−1.42	−1.98	−0.60	−1.00	−1.40
ρ = 0.10	α = 0.40	−0.60	−1.00	−1.41	−0.43	−0.72	−1.01
	α = 0.50	−0.64	−1.06	−1.49	−0.45	−0.76	−1.06
		Open Private Capital Account
		ξ*
		τ = 0.25	τ = 0.50		τ = 0.75	τ = 1
ρ = 0.06	α = 0.40	61.0	47.1		36.9	29.0
	α = 0.50	61.2	46.5		35.3	26.4
ρ = 0.10	α = 0.40	33.6	26.2		20.6	16.2
	α = 0.50	33.6	25.8		19.7	14.7
		CIC_SR when τ = 0.25 and α = 0.40			CIC_SR when τ = 0.50 and α = 0.40
		R = 0.10	R = 0.20	R = 0.30	R = 0.10	R = 0.20	R = 0.30
ρ = 0.06	α = 0.40	−0.78	−1.29	−1.81	−0.55	−0.92	−1.29
	α = 0.50	−0.68	−1.14	−1.59	−0.48	−0.79	−1.11
ρ = 0.10	α = 0.40	−0.57	−0.95	−1.33	−0.40	−0.67	−0.94
	α = 0.50	−0.45	−0.75	−1.05	−0.31	−0.51	−0.72

Source: Authors’ calculations based on solutions from Mathematica programs.

Note: The depreciation rate and the ratio of infrastructure investment to GDP equal 5 percent in all runs. ρ is the pure time preference rate; α is the income share of private capital; R is the return on infrastructure (net of depreciation); τ* (⁠|${\rm {\bar{\tau }}}$| d) is the value of the intertemporal elasticity of substitution below which private (total) investment decreases at t = 0 CIC_SR is the crowding-in coefficient for private investment in the short run (t = 0); and ξ* is the value of elasticity of capital flows (measured as a percentage of GDP, with respect to the interest rate differential) below which private investment decreases. (ξ* is independent of the return on infrastructure.)

Opening the Private Capital Account

When the capital account is open, the private agent takes out foreign loans b_f. It is assumed that the loan rate r_f is exogenous and that deviations of foreign loans from their steady-state level (⁠|$\bar{b}_{f}$|⁠) incur portfolio adjustment costs |$\eta (b_{f}-\bar{b}_{f})^{2}/2$|⁠. The national budget constraint in (7) changes to

$$\begin{equation} \dot{k}=q+\dot{b}_{f}-i_{z}-c-r_{f}b_{f}-\delta k-\eta (b_{f}-\bar{b} _{f})^{2}/2. \end{equation}$$

(14)

and

$$\begin{equation} \eta (b_{f}-\bar{b}_{f})=q_{k}-\delta -r_{f} \end{equation}$$

(15)

joins the set of first-order conditions. Equation (15) and q_k = αq/k tie the path of b_f to the paths of k and z:

$$\begin{equation} \dot{b}_{f}=\xi q_{k}\left[ q_{k}\frac{\alpha -1}{\alpha }\dot{k}+(R+\delta ) \dot{z}\right] , \end{equation}$$

(16)

where ξ ≡ [|$(b_{f}-\bar{b}_{f})/q]/(q_{k}-\delta -r_{f})=1/\eta q$| is the elasticity of capital flows (measured as a percentage of GDP) with respect to the interest rate differential (q_k − δ equals the domestic interest rate).

The Euler equation for consumption and the law of motion for the stock of infrastructure are unchanged. To get (14) in the right form, substitute for |$\dot{b}_{f}$| and solve for |$\dot{k}$|⁠. Straightforward algebra delivers

$$\begin{equation} \dot{k}=\frac{\alpha }{\alpha +(1-\alpha )\xi q_{k}^{2}}[q(k,z)+q_{k}(R+ \delta )(i_{z}-\delta z)-c-i_{z}-r_{f}b_{f}-\delta k-(b_{f}-\bar{b} _{f})^{2}/2\xi q]\text{.} \end{equation}$$

(17)

The linearized version is

$$\begin{eqnarray} \dot{k} &=&\frac{\alpha }{\alpha +(1-\alpha )\xi (\rho +\delta )^{2}}\lbrace \rho [1+\xi (1-\alpha )(\rho +\delta )^{2}/\alpha ](k-k^{\ast })\phantom{000000000000000000000} \nonumber \\ &&+\,(R+\delta )[1-\xi (\rho +\delta )^{2}](z-z^{\ast })-(c-c^{\ast })\rbrace . \end{eqnarray}$$

(17′)

ξ = 0 gives back the solution for the closed economy. At the opposite extreme, perfect capital mobility (ξ → ∞) implies

$$\begin{eqnarray} \dot{k} &=&\frac{R+\delta }{\rho +\delta }\frac{\alpha }{1-\alpha } (i_{z}^{\ast }-\delta z)\gt 0,\forall t, \end{eqnarray}$$

(18)

$$\begin{eqnarray} c &=&c^{\ast },\forall t. \end{eqnarray}$$

(19)

Consumption jumps immediately to its new steady-state level, and the capital stock rises in synch with the stock of infrastructure. There is no transitory decrease in private investment because access to a perfect, frictionless world capital market allows the private agent to completely smooth the path of consumption.

In the general case, crowding out gives way to crowding in at some threshold level of capital mobility ξ*. It is evident from inspection of (17′), however, that ξ* is out of reach for LDCs. All of the terms involving ξ are multiplied by (ρ + δ)², a number on the order of 0.01 to 0.02. Consequently, even elastic capital flows do not help very much: near-perfect capital mobility is required to eliminate temporary crowding out, and for believable values of ξ the results are quantitatively similar to those in the closed economy. The lower half of table 1 elaborates. Since |$\xi ^{\ast }=15$|–|$61$| for |$\tau =0.25$|–|$1$|⁠, the conclusion that private investment decreases in the short run seems safe. Nor is there much of a reduction in the magnitude or the duration of crowding out. Even when ξ equals five—way too large for an LIC—the numbers for CIC_SR and the length of the crowding out phase are only 5–15 percent lower than in the benchmark model.

Concessional Borrowing

Suppose concessional loans are available from International Financial Institutions (IFIs) at a zero real interest rate to finance a fraction χ of the investment program. During the borrowing period,

$$\begin{equation} \dot{k}=q(k,z)+\chi (i_{z}^{\ast }-i_{z,o})-i_{z}^{\ast }-c-\delta k,\quad 0\le t\le t_{1}. \end{equation}$$

(20a)

The loans are repaid in equal installments in the next t₁ years

$$\begin{equation} \dot{k}=q(k,z)-\chi (i_{z}^{\ast }-i_{z,o})-i_{z}^{\ast }-c-\delta k,\quad t_{1}\le t\le 2t_{1,} \end{equation}$$

(20b)

after which

$$\begin{equation} \dot{k}=q(k,z)-i_{z}^{\ast }-c-\delta k,\quad t\ge 2t_{1}. \end{equation}$$

(20c)

Equations (4), (5), and (20a) to (20c) define the core dynamic system. The economy follows distinct noncovergent paths in phases (0, t₁) and (t₁, 2t₁). From time 2t₁ onward, it rides the saddle path to the steady state (c*, k*, z*).

Once again, it proves hard to escape temporary crowding out. In Buffie et al. (2016) appendix B, it is demonstrated that

$$\begin{equation} \frac{i(0)-i_{o}}{i_{z}^{\ast }-i_{z,o}}\gtrless 0\quad \text{as} \mathop{\underbrace{\frac{\lambda _{2}+\delta }{J}+\alpha }}\limits_{\text{Determines }\tau ^{\ast }\text{ in table 1}} + \,\,\,\,\frac{\rho +\delta }{R+\delta }\mathop{ \underbrace{\left( 2-e^{-\lambda _{3}t_{1}}\right) e^{-\lambda _{3}t_{1}}}}\limits_{\lt 1} (1-\alpha )\chi \gtrless 0, \end{equation}$$

(21)

where

$$\begin{equation*} \lambda _{3}=\frac{\rho +\sqrt{\rho ^{2}+4\tau (1-\alpha )(\rho +\delta )c/k} }{2}. \end{equation*}$$

The problem, visible to the naked eye, is that the coefficient multiplying χ is the product of three fractions all smaller than one when R > ρ. This suggests that for normal/high rates of return on infrastructure χ = 1 will not push τ* below 0.75 (that is, the empirically relevant range). Results presented in Buffie et al. (2016) confirm the conjecture: 100 percent concessional financing is insufficient; excess borrowing—borrowing to pay for the investment program plus temporary tax cuts—is required to prevent temporary crowding out. Intuitively, the consumption-smoothing motive is weaker but still potent. Consider a country that secures 100 percent financing for its big-push program. Given the long amortization period characteristic of concessional loans, steady increases in disposable income will continue past the borrowing period into the repayment phase as long as infrastructure investment pays a decent return (>10 percent). Although disposable income does not temporarily decrease as in the no-borrowing case, there is still a strong incentive to consume some future income gains today by reducing investment; ergo τ* is smaller than in table 1, but still large in absolute terms.⁷

The Welfare Metric

The study measures social welfare as

$$\begin{equation} SW=\int \nolimits _{0}^{\infty }\frac{c^{1-1/\tau }}{1-1/\tau }e^{-\bar{\rho } t}dt,\quad \bar{\rho }\le \rho . \end{equation}$$

(22)

SW allows the benevolent social planner to set |$\bar{\rho }$| below the private time preference rate ρ. Should (s)he?

The position of policy makers is clear. In both developed and less developed countries, the social time preference rate used to calculate the cost-benefit ratio for public sector projects is usually much lower (1–2 percent) than the private rate. The authorative guide to project evaluation in LDCs, Little and Mirrlees (1974), puts the upper limit on |$\bar{\rho }$| at 3 percent.

Theory cannot determine whether 3 percent is a sensible number for |$\bar{\rho }$|⁠, the view of Little and Mirrlees notwithstanding. It does, however, provide cogent arguments for |$\bar{\rho }\lt \rho$|⁠. In Sen’s (1967) isolation paradox, private saving is suboptimal because individuals would be willing to enter into a social contract that required everyone to save more. Feldstein (1964) and Baumol (1965) reach the same conclusion more quickly by appealing to the notion that economic development is partly a public good; if the premise is granted, then the social time preference rate “must be adminstratively determined as a matter of public policy [because] the market cannot express the ‘collective’ demand for investment to benefit the future” (Feldstein 1964, 362, 365).

For |$\bar{\rho }\lt \rho$|⁠, the steady-state capital stock k* is below its constrained socially optimal level. An increase in k* is not sufficient, however, for capital accumulation to add to SW. If the crowding-out phase lasts too long and is too deep, the overall welfare gain decreases even though k eventually rises far above k_o.

To demonstrate this formally, return to the benchmark model in which the private capital account is closed and transfers adjust immediately to pay for the increase in i_z. Taking a first-order Taylor series approximation of (21) and substituting for c − c_o leads to (Buffie et al. 2016)

$$\begin{equation} \frac{SW-SW_{o}}{c^{-1/\tau }(z^{\ast }-z_{o})}=\frac{\delta (R-\bar{\rho })}{ \bar{\rho }(\bar{\rho }+\delta )}+\frac{(R+\delta )(\rho -\bar{\rho })\delta }{ (\rho +\delta )(\bar{\rho }+\delta )(1-\alpha )\bar{\rho }}\left( \alpha + \frac{\lambda _{2}+\delta }{J}\frac{\bar{\rho }}{\bar{\rho }-\lambda _{2}} \right) . \end{equation}$$

(23)

The solution has the expected form and agrees with intuition. When |$\bar{\rho }=\rho$|⁠, the impact on private capital accumulation is irrelevant. The welfare gain is simply the capitalized value of the consumption stream generated by the investment program.⁸ The transition path—but not k*—is also irrelevant in the limiting case where |$\bar{\rho } \rightarrow 0$| and welfare depends only on steady-state consumption. In between these polar cases, the path of the capital stock matters. Recall that temporary crowding out occurs when α + (λ₂ + δ)/J < 0. Since (λ₂ + δ)/J < 0 is marked down by |$\bar{\rho }/( \bar{\rho }-\lambda _{2})\lt 1$|⁠, the solution in (23) says that the path traversed by the capital stock contributes positively to welfare provided temporary crowding out is not too severe.^9,10 More generally, programs with less crowding out generate larger welfare gains.¹¹

The Long-Run Fiscal Impact

Across steady states, equations (1) and (4)–(7) can be solved for q, k, z, c and T as a function of h, i_z, and f ≡ μ/δ (the of user fees to recurrent costs). More investment in infrastructure increases net national product and revenue from the consumption VAT and user fees. The revenue gain pays for the additional investment and leaves something left over to finance higher transfer payments when (Buffie et al. 2016)

$$\begin{equation} R\gt \frac{\delta (1+h-f)(1-\alpha )}{h\left[ 1-\alpha \delta /(\rho +\delta ) \right] }-\delta . \end{equation}$$

(24)

The crucial implication of (24) is that R does not have to be unusually high for the increase in infrastructure investment to be self-financing. For the base case in the full model (h = 0.15, δ = 0.05, ρ = 0.10, f = 0.5, and α = 0.475) the borderline value of R is a modest 8.5 percent. The base case assumes that user fees cover half of recurrent costs. Even with f = 0, however, (24) holds for R > 18.8%. This is high but well within the range of empirical estimates.

3. The Full Model

The framework for DSA is the standard two-sector model of a small open economy embellished with fiscal reaction functions, multiple types of public sector debt, and multiple tax and spending variables. The country produces a composite traded good and a nontraded good. All quantity variables except labor are detrended by (1 + g)^t, where g is the exogenous long-run growth rate of real GDP. The traded good is the numeraire and x and n subscripts refer to the tradables and nontradables sectors.

The full model incorporates addtional factors that influence private investment and growth (nonsaving households, imported capital goods, asymmetric sectoral factor intensities, and absorptive capacity constraints). More importantly, it allows policy makers to determine whether a detailed program of borrowing, investment, and fiscal adjustment is compatible with debt sustainability.

The study lays out the model in stages, starting with the specification of technology.

Technology

Cobb-Douglas production functions convert inputs into output, with infrastructure entering as a public good that enhances productivity in both sectors:

$$\begin{eqnarray} q_{x,t} =a_{x}z_{t-1}^{\psi _{x}}k_{x,t-1}^{\alpha _{x}}L_{x,t}^{1-\alpha _{x}}, \end{eqnarray}$$

(25)

$$\begin{eqnarray} q_{n,t} =a_{n}z_{t-1}^{\psi _{n}}k_{n,t-1}^{\alpha _{n}}L_{n,t}^{1-\alpha _{n}}. \end{eqnarray}$$

(26)

Factories and infrastructure are built by combining one imported machine with a_j (j = k, z) units of a nontraded input (e.g., construction). The supply prices of private capital and infrastructure are thus

$$\begin{eqnarray} P_{k,t} &=&1+a_{k}P_{n,t}, \end{eqnarray}$$

(27)

$$\begin{eqnarray} P_{z,t} &=&1+a_{z}P_{n,t}, \end{eqnarray}$$

(28)

where P_n is the relative price of the nontraded good.

Factor Demands

Competitive profit-maximizing firms equate the marginal value product of each input to its factor price. This yields

$$\begin{eqnarray} P_{n,t}(1-\alpha _{n})q_{n,t}/L_{n,t} &=&w_{t}, \end{eqnarray}$$

(29)

$$\begin{eqnarray} (1-\alpha _{x})q_{x,t}/L_{x,t} &=&w_{t}, \end{eqnarray}$$

(30)

$$\begin{eqnarray} P_{n,t}\alpha _{n}q_{n,t}/k_{n,t-1} &=&r_{n,t}, \end{eqnarray}$$

(31)

$$\begin{eqnarray} \alpha _{x}q_{x,t}/k_{x,t-1} &=&r_{x,t}, \end{eqnarray}$$

(32)

where w is the wage and r_j is the rental earned by capital in sector j. Labor is intersectorally mobile, so the same wage appears in (29) and (30). Capital is sector-specific, but r_x differs from r_n only on the transition path. After adjustment is complete and k_x and k_n have settled at their equilibrium levels, the rentals are equal.

Private Sector Optimization Problems

There are two types of private agents, savers and nonsavers (with the latter distinguished by a 1 subscript). Labor supply of savers is fixed at L while that of nonsavers is L₁ = aL. Preferences of the two agents qua consumers are described by a linearly homogeneous constant elasticity of substitution (CES) utility function. The optimal choices for consumption of the traded and nontraded goods are subsumed in the composite consumer goods c and c₁. The exact consumer price index is |$P=[\kappa +(1-\kappa )P_{n}^{1-\epsilon }]^{1/(1-\epsilon )}$|⁠, where κ and |${\epsilon}$| are CES distribution and substitution parameters.

Nonsavers live hand to mouth, consuming all of their income from wages and transfers each period. Transfers are proportional to the agent’s share in aggregate employment so the nonsaver’s budget constraint reads

$$\begin{equation} (1+h_{t})P_{t}c_{1,t}=w_{t}L_{1}+\frac{a}{1+a}T_{t}\text{.} \end{equation}$$

(33)

Savers’ behavior is more complicated. They solve the problem

$$\begin{equation} Max\sum _{t=0}^{\infty }\beta ^{t}\frac{(c_{t})^{1-1/\tau }}{1-1/\tau }, \end{equation}$$

(34)

subject to

$$\begin{eqnarray} P_{t}b_{t}-b_{f,t} &=&r_{x,t}k_{x,t-1}+r_{n,t-1}k_{n,t-1}+w_{t}L_{t}+\frac{ T_{t}}{1+a}-\frac{1+r_{f}}{1+g}b_{f,t-1}+\frac{1+r_{t-1}}{1+g}P_{t}b_{t-1} \nonumber \\ &&-\,P_{k,t}\left[ i_{x,t}+i_{n,t}+\frac{v}{2 }\left( \frac{i_{x,t}}{k_{x,t-1}}-\delta -g\right) ^{2}k_{x,t-1}+\frac{v}{2}\left( \frac{i_{n,t}}{k_{n,t-1}}-\delta -g\right) ^{2}k_{n,t-1}\right] \nonumber \\ && -\,\frac{\eta }{2}(b_{f,t}-\bar{b} _{f})^{2}-P_{t}c_{t}(1+h_{t})-\mu _{t}z_{t-1}, \end{eqnarray}$$

(35)

$$\begin{eqnarray} (1+g)k_{x,t} &=&i_{x,t}+(1-\delta )k_{x,t-1}, \end{eqnarray}$$

(36)

$$\begin{eqnarray} (1+g)k_{n,t} &=&i_{n,t}+(1-\delta )k_{n,t-1}, \end{eqnarray}$$

(37)

where β = 1/[(1 + ρ)(1 + g)^(1−τ)/τ] is the discount factor; i_j is gross investment in sector j; and v is a positive constant. In the budget constraint (35), v(·)²k_{j, t−1}/2 captures adjustment costs incurred in changing the capital stock and P_t multiplies b_t and b_t−1 because domestic bonds are indexed to the price level.

The choice variables in the optimization problem are c_t, b_t, b_{f, t}, i_{j, t}, and k_{j, t}. See the long paper for statements of the first-order conditions and the Euler equations that govern the paths of consumption, investment, and private capital flows.

Public Investment Efficiency and Accumulation of Infrastructure

Casual observation and indirect empirical evidence support the conjecture in Hulten (1996) and Pritchett (2000) that often a good deal of public investment spending fails to increase the stock of productive capital. The model allows for this slip betwixt cup and lip. Public investment i_z increases the stock of physical infrastructure |$\tilde{z}$| :

$$\begin{equation} (1+g)\tilde{z}_{t}=i_{z,t}+(1-\delta )\tilde{z}_{t-1}. \end{equation}$$

(38)

Some of the newly built infrastructure, however, may not be economically valuable, productive infrastructure:

$$\begin{equation} z_{t}=z_{o}+s(\tilde{z}_{t}-\tilde{z}_{o}),\quad s\le 1. \end{equation}$$

(39)

Fiscal Adjustment and the Public Sector Budget Constraint

When revenues fall short of expenditures, the resulting deficit is financed through external borrowing, viz.:¹²

$$\begin{eqnarray} dc_{t}-dc_{t-1}+d_{t}-d_{t-1} &=&P_{z,t}\left[ \left( 1+\frac{i_{z,t}}{ \tilde{z}_{t-1}}-\delta -g\right) ^{\phi }(i_{z,t}-i_{z,o})+i_{z,o}\right] \nonumber \\ &&+\,\frac{r_{d}-g}{1+g}d_{t-1}+\frac{r_{dc}-g}{1+g}dc_{t-1}+\frac{r_{t-1}-g}{ 1+g}P_{t}b_{t-1} \nonumber \\ &&+\,T_{t}-h_{t}P_{t}(c_{t}+c_{1,t})-\mu _{t}z_{t-1}, \end{eqnarray}$$

(40)

where r_d and r_dc are the interest rates (in dollars) on concessional debt d and commercial debt dc.

The term P_{z, t}[·] needs some explanation. Because skilled administrators are in scarce supply in LICs, ambitious public investment programs are often plagued by poor planning, weak oversight, and myriad coordination problems, all of which contribute to large cost overruns during the implementation phase.¹³ To capture this, the study multiplies new investment (i_z,t − i_{z, o}) by |$(1+i_{z,t}/\tilde{z}_{t-1}-\delta -g)^{\phi }\approx [1+(\tilde{z}_{t}-\tilde{z}_{t-1})/\tilde{z}_{t-1}]^{\phi }$|⁠, where ϕ ≥ 0 determines the severity of the the absorptive capacity constraint in the public sector. Cost overruns depend on both ϕ and the speed of scaling up, as measured by the growth rate of the infrastructure stock. The absorptive capacity constraint affects only implementation costs for new projects as |$i_{z}/\tilde{z}-\delta -g=0$| in a steady state.

Policy makers happily accept all concessional loans proffered by official creditors. The borrowing + amortization schedule for these loans is fixed exogenously. Thus, in any given year, the ex ante financing gap (GAP) is

$$\begin{eqnarray} \text{GAP}_{t} &=&P_{z,t}\left[ \left( 1+\frac{i_{z,t}}{\tilde{z}_{t-1}} -\delta -g\right) ^{\phi }(i_{z,t}-i_{z,o})+i_{z,o}\right] +T_{o}+\frac{ 1+r_{d}}{1+g}d_{t-1}-d_{t} \nonumber \\ &&+\frac{r_{dc}-g}{1+g}dc_{t-1}+\frac{r_{t-1}-g}{1+g} P_{t}b_{t-1}-h_{o}P_{t}(c_{t}+c_{1,t})-\mu _{t}z_{t-1}, \end{eqnarray}$$

(41)

while the stock of commercial debt grows at the rate

$$\begin{eqnarray} dc_{t}-dc_{t-1} &=&P_{z,t}\left[ \left( 1+\frac{i_{z,t}}{\tilde{z}_{t-1}} -\delta -g\right) ^{\phi }(i_{z,t}-i_{z,o})+i_{z,o}\right] +\frac{1+r_{d}}{ 1+g}d_{t-1}-d_{t} \nonumber \\ &&+\,\frac{r_{dc}-g}{1+g}dc_{t-1}+\frac{r_{t-1}-g}{1+g} P_{t}b_{o}+T_{t}-h_{t}P_{t}(c_{t}+c_{t-1})-\mu z_{t-1}, \end{eqnarray}$$

(42)

GAP is revenue collected at the initial tax rate (h_o) and current user fee less the sum of infrastructure investment, net concessional borrowing, interest payments on the debt, and initial transfers (T_o). In the short/medium run, part of this gap can be financed by commercial borrowing. Debt sustainability requires, however, that the VAT and transfers eventually adjust to cover the entire gap. We let policy makers divide the burden of adjustment (net windfall when GAP < 0) between spending cuts and tax increases. The debt-stabilizing values for transfers and the VAT—their long-run target values—are

$$\begin{eqnarray} T_{\text{target,t}} &=&T_{o}-\lambda \text{GAP}_{\text{t}},\quad 0\le \lambda \le 1, \end{eqnarray}$$

(43)

$$\begin{eqnarray} h_{\text{target,t}} &=&h_{o}+(1-\lambda )\frac{\text{GAP}_{\text{t}}}{ P_{t}(c_{t}+c_{1,t})},\quad 0\le \lambda \le 1, \end{eqnarray}$$

(44)

where policy makers’ preferences fix λ.

Equations (43) and (44) are paired with targets for the long-run levels of domestic and external commercial debt. The reaction functions that govern the paths of h and T incorporate these targets as well as sociopolitical constraints on how much and how fast fiscal policy can change:

$$\begin{eqnarray} h_{t} &=&Min\left\lbrace h_{t-1}+\lambda _{1}(h_{\text{target,t} }-h_{t-1})+\lambda _{2}\frac{dc_{t-1}-dc_{\text{target}}}{ P_{n,t}q_{n,t}+q_{x,t}},\,\,\bar{h}\right\rbrace ,\quad \end{eqnarray}$$

(45)

$$\begin{eqnarray} T_{t} &=&Max\left\lbrace T_{t-1}+\lambda _{3}(T_{\text{target,t} }-T_{t-1})-\lambda _{4}(\text{ }dc_{t-1}-dc_{\text{target}}),\,\,\bar{T} \right\rbrace . \end{eqnarray}$$

(46)

|$\bar{h}$| is the upper bound on the VAT, and |$\bar{T}$| is the lower bound on transfers.¹⁴ Inside the bounds, the parameters λ₁–λ₄ determine whether policy adjustment is fast or slow. Under “slow” adjustment, dc may rise above its target level in the time it takes h and T to reach h_target and T_target. When this happens, the transition path includes a phase in which T < T_target and h > h_target to generate the fiscal surpluses needed to pay down the debt.

Market-Clearing Conditions

Flexible wages and prices ensure that demand continuously equals supply in the labor market

$$\begin{equation} L_{x}+L_{n}=L+L_{1} \end{equation}$$

(47)

and in the nontradables market

$$\begin{eqnarray} q_{n,t} &=&(1-\kappa )\left( \frac{P_{n,t}}{P_{t}}\right) ^{-\epsilon }(c_{t}+c_{1,t})+a_{k}\left[ i_{x,t}+i_{n,t}+\frac{v}{2}\big(\frac{i_{x,t}}{ k_{x,t-1}}-\delta -g\big)^{2}k_{x,t-1}\right. \nonumber \\ &&\left. +\,\frac{v}{2}\big(\frac{i_{n,t}}{k_{n,t-1}}-\delta -g\big)^{2}k_{n,t-1} \right] +a_{z}\left[ \left( 1+\frac{i_{z,t}}{\tilde{z}_{t-1}}-\delta -g\right) ^{\phi }(i_{z,t}-i_{z,o})+i_{z,o}\right] . \end{eqnarray}$$

(48)

The first term to the right of the equal sign in (48) is demand for nontraded consumer goods (retrieved from private agents’ indirect utility functions via Roy’s identity), while the second and third terms link public and private investment to orders for new capital goods. On the right side in (47), both components of labor supply are fixed.

External Debt Accumulation and the Current Account

Finally, adding the public and private sector budget constraints produces the accounting identity that growth in the country’s net foreign debt equals the difference between national spending and national income:

$$\begin{eqnarray} d_{t}-d_{t-1}+dc_{t}-dc_{t-1}+b_{t}^{\ast }-b_{t-1}^{\ast } &=&P_{t}(c_{t}+c_{1,t})+P_{z,t}\left[ \left( 1+\frac{i_{z,t}}{\tilde{z}_{t-1} }-\delta -g\right) ^{\phi }(i_{z,t}-i_{z,o})+i_{z,o}\right] \nonumber \\ &&+\,P_{k,t}[i_{x,t}+i_{n,t}+\frac{v}{2}(i_{x,t}/k_{x,t-1}-\delta -g)^{2}k_{x,t-1} \nonumber \\ &&+\,\frac{v}{2}(i_{n,t}/k_{n,t-1}-\delta -g)^{2}k_{n,t-1}]+\frac{r_{d}-g}{1+g} d_{t-1}+\frac{r_{dc}-g}{1+g}dc_{t-1} \nonumber \\ &&+\,\frac{r_{f}-g}{1+g}b_{f,t-1}+\frac{\eta }{2}(b_{f,t}-\bar{b} _{f})^{2}-P_{n,t}q_{n,t}-q_{x,t}. \end{eqnarray}$$

(49)

Equations (25)–(49) comprise the benchmark model. Results for alternative variants of the model will be presented in section 6.

4. Calibration of the Model and Solution Technique

To prepare the model for calibration, it is necessay to (i) link the adjustment cost parameters for changes in the capital stock to an observable elasticity and to (ii) pin down the relationship between the return on infrastructure, the parameter ψ, and private sector output. This is readily done. Starting with the first item, note that in each sector the first-order condition for investment reads [1 + v(i_t/k_t−1 − δ − g)]Λ_1,tP_k,t = Λ_2,t, where Λ₁ and Λ₂ are the multipliers associated with the budget constraint and the law of motion for the capital stock. Since Λ₂/Λ₁ is the shadow price of K measured in dollars, Λ₂/Λ₁P_k is effectively Tobin’s q, the ratio of the demand price to the supply price of capital. Let |$\Omega \equiv \hat{I}/\hat{q}$| denote the q-elasticity of investment spending. Evaluated at a stationary equilibrium, v(δ + g)Ω = 1. Hence v = 1/(δ + g)Ω.

The only inputs needed to calculate the return on infrastructure are the purchase price P_z and the shadow rental r_z. The latter is simply the marginal value product of infrastructure at constant prices. From (26) and (27),

$$\begin{equation*} r_{z}=\frac{\psi _{x}q_{x}+P_{n}\psi _{n}q_{n}}{z}. \end{equation*}$$

The return, net of depreciation, is

$$\begin{equation} R=\frac{r_{z}}{P_{z}}-\delta =\frac{\psi _{x}q_{x}+\psi _{n}P_{n}q_{n}}{ P_{z}z}-\delta , \end{equation}$$

(50)

δ is set directly, while q_n, q_x, z, and P_z are derived from the values of other variables. (P_n = 1 by choice of units.) This leaves R, ψ_x, and ψ_n as unknowns in equation (50). The study assigns values to R and ψ_n/ψ_x and solves (50) for ψ_x.¹⁵

Base Case Calibration

The values in table 2 are based on a mixture of data, guess estimates, and judgment. The long version of the paper contains a detailed discussion of the rationale for the value assigned to each parameter. Below, the study comments on the numbers for the most important parameters:

Real interest rates on concessional and nonconcessional loans(r_d, r_dc). Ghana paid 8.7 percent on the |${\$}$|750 mn. Eurobond it floated in 2007. This is slightly above Gueye and Sy’s (2010) estimate of the average interest rate Sub-Saharan Africa (SSA) pays (8.55 percent) on debt raised in external capital markets.¹⁶ The IMF’s DSAs show an average interest rate of 2.3 percent on nonconcessional loans taken out by LICs in 2009–2010. Assuming 2.5 percent inflation in world prices of traded goods, the corresponding real rates in dollars are 6 percent and 0.
Ratio of user fees to recurrent costs per unit of infrastructure (f ). The user fee for infrastructure services is a fixed multiple/fraction f of recurrent costs (μ = fδP_zo). Fuel taxes (earmarked for road maintenance and construction), electricity tariffs, and user charges for water and sanitation are low but not trivial in LICs. On average, user fees recoup 50 percent of recurrent costs in SSA (Briceno-Garmendia, Smits, and Foster 2008). Again, however, there is considerable variation—Zambia’s average electricity tariff was three cents per kWH in 2008. The authors decided therefore to let f vary from 0.2 to unity, with f = 0.5 in the base case.
Consumption VAT (h). The consumption VAT in the model proxies for the average indirect tax rate. The rate of 15 percent is about the same as the average indirect tax rate on consumption in Ghana.¹⁷ Combined revenue from the VAT and user fees ranges from 12.6 percent to 16.1 percent of GDP depending on the value assigned to the user fee. This is comparable to the range of total domestic revenue to GDP in SSA [12.2–15.5 percent for different LIC groups in Briceno-Garmendia, Smits, and Foster (2008)].
Efficiency of public investment (s) and the absorptive capacity constraint (ϕ). The base case assumes that public investment is efficient and that scaling up does not strain absorptive capacity (ϕ = 0). Motivated by the findings in Hulten (1996), Pritchett (2000), and Foster and Briceno-Garmendia (2010), the authors also investigate scenarios with extreme inefficiency (s = 0.7) and a tight absorptive capacity constraint (ϕ = 5).¹⁸
Return on infrastructure (R) and the elasticity parameters (ψ_i). Estimates of the return on infrastructure are all over the map, but the weight of the evidence in both micro and macro studies points to a high average return. The median rate of return on World Bank projects circa 2001 was 20 percent in SSA and 15–29 percent for various subcategories of infrastructure investment. In the Bank’s recently-completed, comprehensive study of infrastructure in Africa, estimated returns for electricity, irrigation, and roads range from 17 percent to 24 percent (Foster and Briceno-Garmendia 2010, chapter 2);¹⁹ in developing Asia, the average returns for roads, electricity transmission and distribution, and power generation are 23 percent, 20 percent, and 33 percent, respectively (Asian Development Bank 2017). Similarly, the macro-based estimates in Dalgaard and Hansen (2005) cluster between 15 percent and 30 percent for a wide array of different estimators. Hulten, Bennathan, and Srinivasan (2006) and Escribano, Guasch, and Pena (2008), supply additional evidence of high returns. Some growth regressions suggest low or insignificant returns, but these are dominated by studies that use cumulative public investment instead of physical indicators to measure the stock of instructure.
All of this adds up to a presumption that high returns are the norm. These low-, average-, and high-return scenarios assume therefore initial returns of 10 percent, 20 percent, and 30 percent, respectively. The associated values for ψ, the elasticity of GDP with respect to infrastructure (when ψ_n = ψ_x) are 0.138, 0.231, and 0.323. The values in the average- and high-return scenarios are close to the average estimate for LDCs (0.22) and the estimate for Africa (0.32) in Ivanchovichina et al. (2013), the estimate for Chile (0.219) in Albala-Bertrand and Mamazatkis (2001), and the range of estimates for South Asia (0.21–0.34) in Sahoo and Dash (2012), while the value in the low-return scenario is slightly lower than the range of estimates (0.15–0.18) in Calderon and Serven (2003) and slightly higher than the range (0.07–0.10) in Calderon, Moral-Benito, and Serven (2015).
The pure time preference rate (ρ), the real interest rate (r) on domestic bonds, and the real return on private capital. Across steady states, the real interest rate on domestic debt and the real return on private capital equal (1 + ρ)(1 + g)^τ − 1. The study chooses ρ jointly with τ and g so that the domestic real interest rate is 10 percent at the initial equilibrium. This is consistent with the data for SSA in Fedelino and Kudina (2003), with the estimated return on private capital in Isham and Kaufmann (1999), Dalgaard and Hansen (2005), and Marshall (2012), with the stylized fact that domestic debt in low- and middle-income countries is usually much more expensive than external commercial debt, and with the range of real loan rates in LDCs (generally 7–15 percent) reported in World Development Indicators. There is tremendous variation in real interest rates across countries and time periods, however. To test the robustness of the results, the study also carries out runs for r = 0.07.
The long-run target for commercial debt (dc_target) and the division of fiscal adjustment between expenditure cuts and tax increases (λ). Across steady states, noninvestment expenditure and taxes share the burden of fiscal adjustment equally (λ = 0.5) and commercial loans are repaid in full (dc_target = 0).

Table 2.

Calibration of the Model

Parameter/variable	Value in base case
Consumption share of the nontraded good (γ_n)	0.5
Intertemporal elasticity of substitution (τ)	0.34
Elasticity of substitution between traded and nontraded consumer goods (⁠\|${\epsilon}$\|⁠)	0.5
Capital’s share in value added (α_n, α_x)	α_n = 0.55, α_x = 0.40
q-elasticity of investment spending (Ω )	2
Long-run target for external commercial debt (dc_target)	0
Real interest rate on concessional loans (r_d)	0
Real interest rate on nonconcessional loans (r_dc)	0.06
Trend growth rate (g)	0.015
Real interest rate on domestic bonds (r)	0.10
Ratio of user fees to recurrent costs (f)	0.5
Consumption VAT (h)	0.15
Real interest rate on foreign loans held by the private sector (r*)	0.10
Ratio of private foreign loans and public external debt (d, b*, dc) to initial GDP	d = 0.5, dc = 0, b* = 0
Ratio of infrastructure investment to GDP (i_{z, o}/GDP_o)	0.06
Ratio of labor supply of nonsavers to labor supply of savers (a)	0.60
Efficiency of public investment (s)	1
Absorptive capacity constraint (ϕ)	0
Cost share of nontraded inputs in the production of capital goods	α_k = α_z = 0.5
Interest elasticity of private capital flows (ξ)	1
Return on infrastructure (R)	0.20
Depreciation rate (δ)	0.05
Ratio of elasticities of sectoral output with respect to the stock of infrastructure (ψ_x/ψ_n)	1
Division of fiscal adjustment between expenditure cuts and tax increases (λ)	0.5

Parameter/variable	Value in base case
Consumption share of the nontraded good (γ_n)	0.5
Intertemporal elasticity of substitution (τ)	0.34
Elasticity of substitution between traded and nontraded consumer goods (⁠\|${\epsilon}$\|⁠)	0.5
Capital’s share in value added (α_n, α_x)	α_n = 0.55, α_x = 0.40
q-elasticity of investment spending (Ω )	2
Long-run target for external commercial debt (dc_target)	0
Real interest rate on concessional loans (r_d)	0
Real interest rate on nonconcessional loans (r_dc)	0.06
Trend growth rate (g)	0.015
Real interest rate on domestic bonds (r)	0.10
Ratio of user fees to recurrent costs (f)	0.5
Consumption VAT (h)	0.15
Real interest rate on foreign loans held by the private sector (r*)	0.10
Ratio of private foreign loans and public external debt (d, b*, dc) to initial GDP	d = 0.5, dc = 0, b* = 0
Ratio of infrastructure investment to GDP (i_{z, o}/GDP_o)	0.06
Ratio of labor supply of nonsavers to labor supply of savers (a)	0.60
Efficiency of public investment (s)	1
Absorptive capacity constraint (ϕ)	0
Cost share of nontraded inputs in the production of capital goods	α_k = α_z = 0.5
Interest elasticity of private capital flows (ξ)	1
Return on infrastructure (R)	0.20
Depreciation rate (δ)	0.05
Ratio of elasticities of sectoral output with respect to the stock of infrastructure (ψ_x/ψ_n)	1
Division of fiscal adjustment between expenditure cuts and tax increases (λ)	0.5

Source: Values chosen by the authors for the base case.

Table 2.

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Calibration of the Model

Parameter/variable	Value in base case
Consumption share of the nontraded good (γ_n)	0.5
Intertemporal elasticity of substitution (τ)	0.34
Elasticity of substitution between traded and nontraded consumer goods (⁠\|${\epsilon}$\|⁠)	0.5
Capital’s share in value added (α_n, α_x)	α_n = 0.55, α_x = 0.40
q-elasticity of investment spending (Ω )	2
Long-run target for external commercial debt (dc_target)	0
Real interest rate on concessional loans (r_d)	0
Real interest rate on nonconcessional loans (r_dc)	0.06
Trend growth rate (g)	0.015
Real interest rate on domestic bonds (r)	0.10
Ratio of user fees to recurrent costs (f)	0.5
Consumption VAT (h)	0.15
Real interest rate on foreign loans held by the private sector (r*)	0.10
Ratio of private foreign loans and public external debt (d, b*, dc) to initial GDP	d = 0.5, dc = 0, b* = 0
Ratio of infrastructure investment to GDP (i_{z, o}/GDP_o)	0.06
Ratio of labor supply of nonsavers to labor supply of savers (a)	0.60
Efficiency of public investment (s)	1
Absorptive capacity constraint (ϕ)	0
Cost share of nontraded inputs in the production of capital goods	α_k = α_z = 0.5
Interest elasticity of private capital flows (ξ)	1
Return on infrastructure (R)	0.20
Depreciation rate (δ)	0.05
Ratio of elasticities of sectoral output with respect to the stock of infrastructure (ψ_x/ψ_n)	1
Division of fiscal adjustment between expenditure cuts and tax increases (λ)	0.5

Parameter/variable	Value in base case
Consumption share of the nontraded good (γ_n)	0.5
Intertemporal elasticity of substitution (τ)	0.34
Elasticity of substitution between traded and nontraded consumer goods (⁠\|${\epsilon}$\|⁠)	0.5
Capital’s share in value added (α_n, α_x)	α_n = 0.55, α_x = 0.40
q-elasticity of investment spending (Ω )	2
Long-run target for external commercial debt (dc_target)	0
Real interest rate on concessional loans (r_d)	0
Real interest rate on nonconcessional loans (r_dc)	0.06
Trend growth rate (g)	0.015
Real interest rate on domestic bonds (r)	0.10
Ratio of user fees to recurrent costs (f)	0.5
Consumption VAT (h)	0.15
Real interest rate on foreign loans held by the private sector (r*)	0.10
Ratio of private foreign loans and public external debt (d, b*, dc) to initial GDP	d = 0.5, dc = 0, b* = 0
Ratio of infrastructure investment to GDP (i_{z, o}/GDP_o)	0.06
Ratio of labor supply of nonsavers to labor supply of savers (a)	0.60
Efficiency of public investment (s)	1
Absorptive capacity constraint (ϕ)	0
Cost share of nontraded inputs in the production of capital goods	α_k = α_z = 0.5
Interest elasticity of private capital flows (ξ)	1
Return on infrastructure (R)	0.20
Depreciation rate (δ)	0.05
Ratio of elasticities of sectoral output with respect to the stock of infrastructure (ψ_x/ψ_n)	1
Division of fiscal adjustment between expenditure cuts and tax increases (λ)	0.5

Source: Values chosen by the authors for the base case.

The numerical simulations are free of approximation error—in all scenarios, they simulations track the global nonlinear saddle path. The solutions were generated by set of programs written in Matlab 7.10 and Dynare 4.1.1.

5. Nonconcessional External Borrowing

Increasingly LICs have access to external debt markets. In recent years, Uganda, Tanzania, Senegal, Ghana, Angola, Democratic Republic of Congo, Mali, Mauritania, and Rwanda have all entered into nonconcessional loan agreements or issued sovereign bonds in international capital markets.

The Investment Program and the Comparison Run

Infrastructure investment is initially 6 percent of GDP. The government then aims for a transformative big push. Unless otherwise noted, the time lines for infrastructure investment and concessional borrowing are

$$\begin{eqnarray} \begin{array}{c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c}& & & & & & & & & \text{Year} & & & & & & & & \\ & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & . & . & . & 27 & 28 & . & \infty \\ & & & & & & & & & & & & & & & & & \\ \displaystyle\frac{P_{zo}(i_{z}-i_{zo})}{GDP_{o}}\,\, & 6 & 7 & 8 & 8 & 8 & 7.5 & 6.5 & 5.5 & 4 & 4 & . & . & . & . & . & . & 4 \\ & & & & & & & & & & & & & & & & & \\ \displaystyle\frac{d_{t}-d_{t-1}}{GDP_{o}} & 4 & 4 & 4 & 4 & 4 & 3 & 1.75 & 0.5 & -1.329 & -1.329 & . & . & . & -1.329 & 0 & . & 0 \end{array} \end{eqnarray}$$

Infrastructure investment jumps 6 percent of GDP in year 1, rises to 8 percent in years 3–5, and then decreases to its steady-state level. Concessional borrowing equals 4 percent of initial GDP for five years, after which net inflows decrease in step with investment. Repayment occurs in equal payments over 18 years after an 8-year grace period.²⁰ Cumulative borrowing in years 1–8 equals 45 percent of cumulative investment.²¹

A comparison run is needed to evaluate the pros and cons of schemes that supplement nonconcessional borrowing with commercial borrowing. This is provided by a run in which the government refrains from nonconcessional borrowing. The NNB (no nonconcessional borrowing) run assumes therefore that taxes and transfers adjust continuously to close the ex ante financing gap.²²

The Base Case

Figure 1 shows two runs for the base case. In the NNB run, the VAT rises to 17.8 percent at year three, while transfers decrease by 2.1 percent of initial GDP. Conditions improve thereafter, but very slowly; after two decades, the VAT is still 17 percent.

Figure 1.

The Transition Path in the Base Case When the Government Takes Out only Concessional Loans vs. Concessional Loans Supplemented by Commercial Borrowing

Source: Numerical solutions generated by the authors’ Dynare programs.

Note: The fiscal deficit and debt are expressed as a percentages of current GDP while the plot for transfers (T) shows the change in transfers as a percentage of initial GDP. All other plots, except those for taxes (h) and the interest rate (r), show the percentage deviation of the variable from its initial steady-state value on the y axis, with time on the x axis.

The government’s protracted fiscal problems stem from the disappointing medium-run (i.e. 10–20 year) impact on private capital accumulation and growth. Unfortunately, disappointment is not specific to the base case but rather a highly robust feature of the transition path—see the results in the simplified model. Higher taxes and lower transfer payments reduce private sector disposable income by 2.3–4.4 percent in the short run. Because future returns rise, it might be optimal to maintain or increase investment at the same time that the budget constraint shifts inward. But this is improbable: realizing that future income will be much higher, private agents with believable values of τ (τ < 2) will prefer to smooth the path of consumption by temporarily dissaving. In the case at hand, consumption decreases 1 percent and aggregate investment (i_x + i_n) falls 3.5 percent in the first year. Private investment stays depressed for another six years and then rises a feeble 0.5 percent per annum until debt service ends at year 27. Due to the lengthy period of lower/stagnant investment, growth of the private capital stock and real income lag far behind growth in the stock of infrastructure. At the 20-year horizon, z has increased 58 percent (87 percent of the 67 increase across steady states), but k and y are only 5.2 percent and 13.6 percent higher (vs. 25 percent higher across steady states). And because income and the tax base grow slowly the revenue demands of debt service keep the VAT high and transfers low until the last concessional loan is paid off. Eventually policy makers are rewarded for their perseverance with a tiny revenue windfall and a large increase in the private capital stock, but this occurs in a distant future too far away to matter.

The alternative to the NNB run is to smooth the path of fiscal adjustment by borrowing against future revenue gains in the commercial debt market. This strategy fares poorly in the base case because the revenue gains are too small for too long. There are benefits on the real side: crowding in of private investment is immediate, and real wages and real GDP are slightly higher at the 10–20 year benchmarks. The fiscal bind persists, however. External commercial borrowing merely delays the day of fiscal reckoning; two decades out, the VAT and expenditure cuts exceed their peak/trough values in NNB.

Problematic as they are, the results in the base case may be overly optimistic. The most significant worries concern whether expenditure will really help share the burden of fiscal adjustment. This is perhaps the shakiest assumption in the base case. After investment, interest payments, and untouchable antipoverty programs are put to one side, there is not much left to cut except the wage bill. But if public sector unions demand raises in line with those granted in the private sector, it will be difficult to prevent expenditure from increasing, let alone enforce cuts on the order of 2 percent of initial GDP.

In future sections we aim for greater realism. Most of the analysis will concentrate on two scenarios with downwardly inflexible expenditure. In the first, transfers are constant until growth generates a fiscal windfall:

$$\begin{equation} T_{t}=Max\lbrace T_{t}^{1},T_{o}\rbrace , \end{equation}$$

(51)

where T¹ is the value of T in (46). The second, more pessimistic scenario assumes the government is unable to cut other expenditures to offset increases in public sector wages. This implies

$$\begin{equation} T_{t}=Max\lbrace T_{t}^{1},T_{o}+0.05\, GDP_{o}\, (w_{t}-w_{o})/w_{o}\rbrace \end{equation}$$

(52)

when the initial wage bill is 5 percent of GDP and raises in the public sector match raises in the private sector.

Relatively Optimistic Scenarios

Governments vary in their willingness and capacity to quickly increase tax rates. The criterion for operational success, based on interactions with policy makers in numerous applications of the model and on the difficulties LDCs—especially LICs—have experienced in raising the ratio of nonresource tax revenue to GDP (Keen and Mansour 2010; IMF 2011; Bahl 2013), is that debt sustainability proves compatible with increases in the VAT of two percentage points or less when either (51) or (52) determines the path of transfers. Predictably, the base case fails this criterion: the debt-sustainable VAT rises to 19–20.3 percent and stays there for 40+ years (Buffie et al. 2016). If success is possible, it requires higher user fees and/or higher returns on infrastructure. Faster revenue growth may then reconcile rapid scaling up with politically acceptable increases in the VAT.

Figure 2 shows the outcome when user fees pay for all recurrent costs, the initial return on infrastructure is 20–30 percent, and cuts in transfer payments are infeasible (⁠|$\bar{T}=T_{o}$|⁠). These paths are considerably better than the paths in the base case. In the runs with R = 0.30, another six percentage points are added to the gains in real output and the real wage at the 20-year horizon. More important, the increase in the VAT is limited to 1.4–2.2 points.

Figure 2.

Paths of the VAT Rate, Transfers, and Debt When User Fees Finance All Recurrent Costs, the Return on Infrastructure is 20–30 Percent, and Cuts in Transfers are not Feasible

Source: Numerical solutions generated by the authors’ Dynare programs.

Note: The ceiling on the VAT rate is 17.2 percent in panel A and 16.4 percent in panel B. Time is on the x axis. Debt is expressed as a percentage of current GDP and the change in transfers as a percentage of initial GDP.

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Regrettably, the case for BOAF (borrowing on all fronts) is much weaker in countries where (52) applies. When growth in the public wage bill fuels continuous growth in noninvestment expenditure, the ceiling on the VAT has to increase another full percentage point (to 17.5–18.2 percent) to preserve debt sustainability (Buffie et al. 2016). This pushes the boundary of feasible adjustment; it is suspected that policy makers in most LICs would tell their economic team to go away and work on a new plan.

Despite the likelihood that public sector wage growth will keep pace with private wage growth, the case for optimism is not dead. Optimism makes a strong comeback in the next scenario the paper examines—a scenario especially relevant to SSA.

Average user fees equal or slightly exceed average costs for operation and maintenance of physical infrastructure in SSA. Because of low collection rates, however, revenues cover only half of recurrent costs (Briceno-Garmendia, Smits, and Foster 2008; Eberhard et al. 2008).

The low collection rate represents both a problem and an opportunity. Raising the collection rate from 50 to 100 percent would capture more revenue not only from the expansion of infrastructure services but also from services supplied by the existing network. Of course the prevalence of low collection rates suggests that the problem is not easy to solve (Foster and Bricendo-Garmendia 2010, chapter 3). But the transition from partial to full collection does not have to occur overnight to greatly reduce the demands made on other fiscal instruments. In fig. 3 it takes a decade to complete the task. The VAT does not increase at all in panel B and rises only half a percentage point in panel A. The only blemish in the runs is that the commercial debt stays at a high level for a long time when public wages increase apace with private wages.

Figure 3.

Paths of the VAT Rate, Transfers, and Debt When Revenue from User Fees Increases from 50 Percent to 100 Percent of Recurrent Costs over a Period of 10 Years

Source: Numerical solutions generated by the authors’ Dynare programs.

Note: The return on infrastructure is 20–30 percent, the ceiling on the VAT rate is 15–15.5 percent, and public sector wage increases match private wage increases. Time is on the x axis. Debt is expressed as a percentage of current GDP and the change in transfers as a percentage of initial GDP.

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These results look too good to be true, and maybe they are. Undoubtedly some governments will succeed in raising the collection rate in upcoming decades. That said, it is not clear in the experiments whether the collection rate would be expected to rise or fall over time. The complicating factor is that scaling up public investment adds to the collection task by increasing the share of the population with access to infrastructure services. If collection capacity does not increase as fast as the supply of services, the collection rate might fall. The runs in fig. 3 are relevant and important, but also highly speculative.²³

Debt Blowups

It is easy to unintentionally abuse the flexibility afforded by borrowing in the commercial debt market. Policy makers might overestimate their capacity for fiscal adjustment, finance low-return projects, misplace the blueprints for reforms to improve governance and the efficiency of public investment, or repeatedly succumb to the temptation to put off necessary but unpopular tax increases and expenditure cuts. In which event the debt blows up. The study summarizes here the results from impulse responses presented in the long paper. All of the runs assume optimistically (as in fig. 2) that user fees cover all recurrent costs (f = 1) and that the return to infrastructure is high (⁠|$R=0.20$|–|$0.30$|⁠). In Scenario 1 politicians improve the original plan by ordering increases in the VAT to be delayed for five years. Because of the delay, policy makers lose the race against time, and the debt blows up. In Scenario 2 the government borrows heavily in the commercial market as it pays off its concessional debt, counting on growth in future tax revenues to ensure debt sustainability. But since public investment is inefficient (s = 0.7), future revenue gains are too small to stabilize the debt, even though policy makers subsequently increase the VAT from 16.5 percent to 18.5 percent.²⁴ A similar problem arises in Scenario 3. The actual return, although quite respectable (20 percent), is 10 points below the expected return (30 percent). When the lower-than-expected return maps into lower-than-expected revenue growth, the external debt keeps rising after the path in the comparison run turns south; just three years after concessional loans are repaid, the ratio of the commercial debt to GDP hits 61 percent. Finally, in Scenario 4 borrowing to cover temporary cost overruns proves a bad gamble; again, a belated attempt to regain fiscal control by further increasing the VAT comes too late to save the day.

An Interim Assessment

There is a wide variety of scenarios and results in figs. 1 and 2. Taking stock, what do they reveal about the risks and rewards of nonconcessional borrowing? Is BOAF a sensible strategy for LICs?

Given the magnitude of the ex ante financing gap (4–5.3 percent of initial GDP), it is difficult to rapidly scale up public investment when concessional loans are the only source of external funds. This is transparent from the counterfactual runs. Few, if any, policy makers will rush to embrace a program that increases the VAT 4–6 points for 10–20 years. Access to the commercial debt market can therefore be the difference between success and failure. Early on, domestic opposition to the program will be less if nonconcessional borrowing allows tax increases and expenditure cuts to be phased in more slowly. Later, when the limits of fiscal adjustment have been reached, new borrowing can avert default or a collapse in public investment.

The catch is that the path to success is narrow and slippery. If the return on infrastructure is high, if public investment is efficient, if user fees cover all recurrent costs, and if new projects can be implemented quickly on a large scale without cost overruns (i.e., absorptive capacity is sufficient), then an increase in the VAT of 1.5–2 points for five years suffices to make scaling up work. But this is too many ifs. In all other scenarios, either the debt blows up or the VAT rises to levels that threaten social and political stability. Borrowing-on-all-fronts (BOAF) is a high-risk, high-return strategy. It may greatly enhance the prospects for debt sustainability or lead to spectacular failure.

6. Sensitivity Analysis

There is a good deal of information in section 5 about how the return on infrastructure, the efficiency of public investment, revenue from user fees, and constraints on expenditure cuts affect the path of debt accumulation. Below the paper reports the findings from other runs undertaken in the long paper to test the robustness of the results:

Small differences in fiscal effort have big effects on debt accumulation and small differences in borrowing rates for concessional and commercial loans have big effects on the amount of fiscal adjustment required for debt sustainability. In many of the runs the magnitude and the duration of the increase in the public commercial debt is discomfiting. Consider, for example, panel B in fig. 2. Certainly strong nerves will be needed to stick with the program as the commercial debt rises toward 50 percent of GDP. If the government feels uncomfortable carrying this much debt, then it should raise the ceiling on the VAT from 15 percent to 15.5 percent. The debt then crests much earlier at a much lower level (32 percent); moreover, descent from the peak is rapid, with the debt falling to just 18 percent of GDP at t = 40.
The debt dynamics are equally sensitive to small variations in borrowing rates. The real interest rate on public commercial loans is 6 percent in the base case. Lowering the rate to 4 percent reduces the minimum increase in the VAT required for debt sustainability by 1.4 percentage points (Buffie et al. 2016). For the same VAT, the peak ratio of the debt to GDP decreases 18 to 20 percentage points. Changes in the real rate charged on concessional loans have similarly large effects.
The results are insensitive to variations in deep parameters that describe preferences, technology, and the general structure of the economy. The study has carried out runs for a wide range of alternative values of the intertemporal elasticity of substitution, the interest-elasticity of private capital flows, the consumption share of traded goods, the q-elasticity of investment spending, the elasticity of substitution between traded and nontraded goods, the percentage of hand-to-mouth consumers, the time preference rate, and factor cost shares. None of these parameters significantly affect the peak level of debt accumulation or the minimum increase in the VAT consistent with debt sustainability.
The fiscal effort required for debt sustainability increases substantially when the risk premium is sensitive to the ratio of debt to GDP. In the runs with an endogenous risk premium,
$$\begin{equation} r_{dc,t}=\bar{r}+0.03e^{\chi (D_{t}/GDP_{t}-D_{o}/GDP_{o})},\quad \chi \ge 0, \end{equation}$$
(53)
where |$\bar{r}=0.03$| is the risk-free rate and D ≡ d + dc + b_f is the sum of public and private external debt.²⁵ The parameter χ sets the slope of the inverse loan supply curve. Some estimates in the literature support the choice for the base case (χ ≈ 0); others find |$\chi =0.25$|–|$2.$|²⁶ In the run where χ = 1, a 10 percentage point increase in the debt-GDP ratio raises the borrowing rate from 6 percent to 6.31 percent. For χ = 2, the rate increases to 6.66 percent.
Moving up the loan supply curve is costly in big-push programs. The reason is simply that the debt rises to and stays at a high level for a long time. This increases the borrowing rate 1–1.4 percentage points for 56 years in the run χ = 1 and 2–3.4 percentage points for 49 years in the run χ = 2. As a result, the minimum VAT compatible with debt sustainability jumps from 19 percent to 19.9–21.5 percent.

Alternative Investment Programs

Investment programs come in a variety of shapes, sizes, and colors. At the outset, the government has to decide whether to go big or small, whether to scale up quickly or slowly, and whether to invest solely in new projects or in a mix of new projects and capital maintenance. While there is no case for scaling up slowly and only a weak case for going small, the return to getting the right mix of new investment and maintenance is potentially very high:

Fast scaling up is superior to gradual scaling up. If the investment program is sound, the government should scale up as fast as absorptive capacity constraints permit. In the base case, gradual scaling up sacrifices 3.8 percent of GDP at year twenty without decreasing the amount of fiscal adjustment required for debt sustainability (Buffie et al. 2016).²⁷
If empirical estimates are correct, programs that rectify underfunding of maintenance pay a very high return. More spending on maintenance increases the supply of infrastructure by extending the service life of the existing stock and newly created infrastructure. In the language of the model, the depreciation rate is a decreasing function of the ratio of real maintenance expenditure m to the stock of infrastructure:²⁸
$$\begin{equation} (1+g)z_{t}=i_{z,t}+[1-\delta _{o}e^{-\Lambda m_{t}/z_{t-1}}]z_{t-1,}\quad \Lambda \gt 0. \end{equation}$$
(54)
Maintenance is underfunded relative to new investment when Λ > e^Λm/z/δ_o. Development economists universally agree that this condition holds with margin to spare. According to empirical estimates and countless case studies, the return to m is 2–5 times higher than the return to i_z.²⁹
The study sets Λ equal to two or three and increased maintenance spending from zero to 2 percent of GDP by reducing new investment.³⁰ Unsurprisingly, the more efficient investment program yields impressive gains: real output rises another 2–7 percentage points at year 20 and |$\bar{h}$| decreases from 17.8–19 percent to 16.1–18.1 percent (Buffie et al. 2016).

7. Welfare Rankings

Solving for the optimal debt-sustainable borrowing + investment program is beyond the scope of the current paper. It is possible, however, to rank competing programs along certain key dimensions. Do the welfare gains from smoother paths for consumption and private investment exceed the cost of commercial borrowing? Are big investment programs preferable to small programs, and is fast scaling up superior to gradual scaling up when absorptive capacity constraints penalize size and speed?

Table 3 provides answers for the base case. The first panel shows that commercial borrowing to smooth consumption and forestall temporary crowding out of private investment delivers large additional welfare gains, especially for poor, nonsaving households. When the social discount rate (⁠|$\bar{\beta }$|⁠) equals the private rate, the equivalent variation welfare gain rises from 4.5 percent to 5.3 percent of consumption for savers and from 2.3 percent to 4 percent for nonsavers. In the runs where the social rate is 2–4 points higher than the private rate, the gains increase to 6.1–7.4 percent for savers and to 5.1–6.9 percent for nonsavers.³¹

Table 3.

Equivalent Variation Measure of the Welfare Gain in Alternative Investment Programs

	\|$\bar{\beta } =\beta$\|	\|$\bar{\beta } =1.02\beta$\|		\|$\bar{\beta } =1.04\beta$\|
Concessional borrowing only
– Savers	4.48	5.62		7.42
– Nonsavers	2.32	3.77		6.05
Commercial borrowing also
– Savers	5.27	6.14		7.57
– Nonsavers	3.99	5.12		6.91
	No ACC		ACC with ϕ = 5
Big-push program
– Savers	6.14		5.48
– Nonsavers	5.12		3.91
Program 50% Smaller
– Savers	3.50		3.33
– Nonsavers	2.94		2.64
	No ACC		ACC with ϕ = 5
Fast scaling up
– Savers	6.14		5.48
– Nonsavers	5.12		3.91
Gradual scaling up
– Savers	4.36		4.10
– Nonsavers	3.39		3.01

	\|$\bar{\beta } =\beta$\|	\|$\bar{\beta } =1.02\beta$\|		\|$\bar{\beta } =1.04\beta$\|
Concessional borrowing only
– Savers	4.48	5.62		7.42
– Nonsavers	2.32	3.77		6.05
Commercial borrowing also
– Savers	5.27	6.14		7.57
– Nonsavers	3.99	5.12		6.91
	No ACC		ACC with ϕ = 5
Big-push program
– Savers	6.14		5.48
– Nonsavers	5.12		3.91
Program 50% Smaller
– Savers	3.50		3.33
– Nonsavers	2.94		2.64
	No ACC		ACC with ϕ = 5
Fast scaling up
– Savers	6.14		5.48
– Nonsavers	5.12		3.91
Gradual scaling up
– Savers	4.36		4.10
– Nonsavers	3.39		3.01

Source: Solutions from the authors’ Dynare programs.

Note: The equivalent variation measure of welfare is the permanent increase in consumption that produces the same welfare gain as the borrowing + investment program. ACC stands for absorptive capacity constraint. In the second and third panels, |$\bar{\beta } = 1.02\beta$| and commercial borrowing supplements concessional loans. In the gradual scaling-up scenario, infrastructure investment increases by 2 percent of initial GDP in year one and then takes another six years to rise to its steady-state level. Results in all runs are for the base case calibration in table 2.

Table 3.

Equivalent Variation Measure of the Welfare Gain in Alternative Investment Programs

	\|$\bar{\beta } =\beta$\|	\|$\bar{\beta } =1.02\beta$\|		\|$\bar{\beta } =1.04\beta$\|
Concessional borrowing only
– Savers	4.48	5.62		7.42
– Nonsavers	2.32	3.77		6.05
Commercial borrowing also
– Savers	5.27	6.14		7.57
– Nonsavers	3.99	5.12		6.91
	No ACC		ACC with ϕ = 5
Big-push program
– Savers	6.14		5.48
– Nonsavers	5.12		3.91
Program 50% Smaller
– Savers	3.50		3.33
– Nonsavers	2.94		2.64
	No ACC		ACC with ϕ = 5
Fast scaling up
– Savers	6.14		5.48
– Nonsavers	5.12		3.91
Gradual scaling up
– Savers	4.36		4.10
– Nonsavers	3.39		3.01

	\|$\bar{\beta } =\beta$\|	\|$\bar{\beta } =1.02\beta$\|		\|$\bar{\beta } =1.04\beta$\|
Concessional borrowing only
– Savers	4.48	5.62		7.42
– Nonsavers	2.32	3.77		6.05
Commercial borrowing also
– Savers	5.27	6.14		7.57
– Nonsavers	3.99	5.12		6.91
	No ACC		ACC with ϕ = 5
Big-push program
– Savers	6.14		5.48
– Nonsavers	5.12		3.91
Program 50% Smaller
– Savers	3.50		3.33
– Nonsavers	2.94		2.64
	No ACC		ACC with ϕ = 5
Fast scaling up
– Savers	6.14		5.48
– Nonsavers	5.12		3.91
Gradual scaling up
– Savers	4.36		4.10
– Nonsavers	3.39		3.01

Source: Solutions from the authors’ Dynare programs.

Note: The equivalent variation measure of welfare is the permanent increase in consumption that produces the same welfare gain as the borrowing + investment program. ACC stands for absorptive capacity constraint. In the second and third panels, |$\bar{\beta } = 1.02\beta$| and commercial borrowing supplements concessional loans. In the gradual scaling-up scenario, infrastructure investment increases by 2 percent of initial GDP in year one and then takes another six years to rise to its steady-state level. Results in all runs are for the base case calibration in table 2.

The second and third panels compare programs that differ in size and speed. The parameter ϕ determines how fast costs escalate when the investment program bumps up against the absorptive capacity constraint. The study assumes a tight constraint: ϕ = 5 implies that choosing rapid over gradual scaling up increases unit investment costs 63–308 percent for the first seven years of the program.

Consistent with the results in the simplified model, big investment programs beat small programs and fast scaling up beats gradual scaling up by 1.8–2.6 percentage points when absorptive capacity is not an issue. More interestingly, although the margin of victory decreases, big and fast scaling-up programs still win comfortably in the scenario with a tight absorptive capacity constraint. Arguably, LDCs are right to take an aggressive line in attacking their infrastructure deficits. If the deficit is large, as measured by the gap between the return on infrastructure and the social time preference rate, borrowing on commercial terms to finance big, rapid increases in public investment is justified, potential absorptive capacity problems notwithstanding.

8. Concluding Remarks

This paper has developed a new model-based framework for DSA (MBDSA). The MBDSA is grounded in a fully-articulated, dynamic macroeconomic model. It allows for financing schemes that mix concessional and external commercial debt, while taking into account the impact of public investment on growth and constraints on the speed and magnitude of fiscal adjustment. The borrowing + investment program is judged sustainable if it satisfies the natural and theoretically correct criterion that the ratio of debt to GDP eventually converge to a stationary level.

The MBDSA has its share of shortcomings. The authors’ decision to focus on traditional procurement (i.e., own investment by the public sector) precludes analysis of public-private partnerships. Treating public capital as a shift factor in Cobb-Douglas production functions is defensible for many types of infrastructure, but in the case of energy the empirical evidence favors a more flexible specification of technology that allows substitution between infrastructure and primary factors to differ from substitution between primary factors. The absence of uncertainty limits the reach of the results. While the MBDSA can determine if the proposed borrowing + investment program is fiscally sound—if, ceteris paribus, it reduces the likelihood of a future debt blowup—answering the bigger question of whether the country remains vulnerable to debt distress, given its history of internal and external shocks, requires the aid of a fully stochastic model. Finally, the assumption of perfect wage flexibility is overly restrictive and increasingly unappealing. Open unemployment and underemployment are enduring facts of life in many LDCs. Building models that acknowledge this reality deserves the highest priority. Social returns are much greater in general equilibrium when public and private investment reduces unemployment/underemployment. And since higher returns generate more revenue, the prospects for debt sustainability should also improve.³²

Policy-oriented DSA is challenging. Some big-push programs enlist private partners, others do not. Some programs invest heavily in transportation, others concentrate on energy. The structure of the labor market and the frequency and severity of various internal and external shocks are very different in South Africa, Bangladesh, and Jamaica. As usual, one size does not fit all. Future research needs to supply policy makers with choice from a suite of models.

Author Biographical

Luis-Felipe Zanna is Senior Economist, Institute for Capacity Development, at the International Monetary Fund; his email address is [email protected]. Edward F. Buffie (corresponding author) is a professor of economics at Indiana University; his email adress is [email protected]. Rafael Portillo is Deputy Division Chief of the Economic Modeling Division at the International Monetary Fund; his email address is [email protected]. Andrew Berg is Deputy Director of the Institute for Capacity Development at the International Monetary Fund; his email address is [email protected]. Catherine Pattillo is Assistant Director and Division Chief, Fiscal and Surveillance Division of the Fiscal Affairs Department, at the International Monetary Fund; her email address is [email protected]. The authors are indebted to two anonymous referees for helpful comments and constructive criticisms of earlier drafts of the paper. The current paper is a short version of a longer paper, Buffie et al. 2016, available at http://pages.iu.edu/∼ebuffie. A supplementary online appendix to this article is available at The World Bank Economic Review website

Footnotes

1

The estimate for the long-run multiplier is statistically insignificant in 20 of 22 OECD countries.

2

Mendoza and Oviedo (2004) and Ghosh et al. (2011) allow the external risk premium to vary with the level of debt.

3

Additional effects come into play when infrastructure investment is financed by some distortionary tax instead of a lump-sum tax. After increasing sharply at t = 0, the tax decreases monotonically as the tax base expands and revenues from user fees rises. This may exacerbate or lessen short-run crowding out of private investment depending on the tax in question. A time-varying consumption VAT weakens the incentive to cut investment by increasing the price of current vs. future consumption. A time-varying income or profits tax, however, lowers the after-tax return today relative to the future and has the opposite effect. When both taxes adjust, the overall impact is ambiguous in sign and probably small in magnitude.

4

The authors are indebted to Luis Serven for spotting this result.

5

Allowing for adjustment costs to changes in the capital stock strenghtens the incentive to smooth the path of investment and reduces the value of τ* in table 1. This does not, however, alter the conclusion that private investment is virtually certain to decrease in the short run. The most reliable empirical estimates suggest the q-elasticity of investment spending lies between two and five in both developed and less developed countries (see Buffie et al. 2016 for references). With standard quadratic adjustment costs and values for the q-elasticity in this range, τ* in table 1 varies from 1.19 to 1.55. Even for implausibly low values of the q-elasticity between 0.1 and 1, |$\tau ^{\ast }=0.77\,$|–|$\, 1.07$|⁠.

6

Typically 80–90 percent of infrastructure investment in big-push programs is devoted to roads and power in roughly equal proportions. In the case of power, it may be more appropriate to work with a production function of the form F[H(k, z), L], where H(k, z) is a constant elasticity of substitution (CES) aggregate of k and z. For this specification, τ* = 0.23–|$\, 0.82$| in table 1 when the elasticity of substitution between power and private capital ranges from 0.3 to 0.6 and the elasticity of substitution between H and L equals unity; in the case of a non-nested CES production function, τ* = 1.37–2.81 when the substitution elasticity equals 0.5–0.75. This suggests that temporary crowding out of private investment in big-push programs comes mainly from the nonpower component of infrastructure investment (assuming that private capital is less substitutable with power than with other types of infrastructure).

7

In contrast to private capital inflows, concessional loans significantly decrease the severity of crowding out. Increasing the share of concessional finance from zero to 50–100 percent in the case where ρ = 0.10, τ = 0.50, and R = 0.20 reduces the crowding-out coefficient at t = 0 from 1.0 to 0.41–0.56 and shortens the crowding-out phase by 5.8–8.4 years. All of the gains disappear, however, during the repayment period. After year nineteen, the path for the capital stock is virtually identical to the path without borrowing.

8

When the private capital stock is fixed, |$c-c_{o}=(R+\delta )(z-z_{o})-(i_{z}^{\ast }-i_{z,o})=[(R+\delta )(1-e^{-\delta t})-\delta ](z^{\ast }-z_{o})$|⁠. Computing |$\int \nolimits _{0}^{\infty }(c-c_{o})e^{-\rho t}dt$| then gives the first term in (23) (with |$\bar{\rho }=\rho$|⁠).

9

Despite the second-best setting, the welfare gain is always positive and larger for |$\bar{\rho }\lt \rho$| than for |$\bar{\rho }=\rho$|⁠. The second term in (23) is negative and largest (in absolute value) when τ is small. But even in the limiting case τ → 0,

$$\begin{equation*} \left. \frac{SW-SW_{o}}{c^{-1/\tau }(z^{\ast }-z_{o})}\right|_{\bar{\rho }\lt \rho }=\frac{\delta (R-\rho )}{(\rho +\delta )\bar{\rho }}\gt \left. \frac{SW-SW_{o}}{c^{-1/\tau }(z^{\ast }-z_{o})}\right|_{\bar{\rho }=\rho }= \frac{\delta (R-\rho )}{(\rho +\delta )\rho }. \end{equation*}$$

10

The second term in (23) is negative only for low values of τ. For α = 0.3–0.5 and |$\bar{\rho }=0.25\rho$|–0.75ρ, the threshold value of τ ranges from 0.095 to 0.35.

11

When profits are taxed at the rate θ, ρ/(1 − θ) replaces ρ in equation (23). Programs with less crowding out of private investment then produce larger welfare gains even when |$\bar{\rho } =\rho$|⁠. In the fully-loaded model that allows for poor nonsaving households, distributional concerns also boost the welfare gains on paths that minimize temporary crowding out.

12

In the interests of saving space, the authors decided not to analyze domestic borrowing and investment programs. Results for this scenario are available, however, in Buffie et al. (2012).

13

Development agencies report that cost overruns of 35 percent and more are common for new projects in Africa. The most important factor by far is inadequate competitive bidding for tendered contracts (Foster and Bricendo-Garmendia 2010).

14

|$\bar{T}$| may be rising over time, as in the case where other cuts in noninvestment expenditure do not offset growth in public sector wages.

15

The value of ψ in the base case (where R = 0.20) is 0.2308. Ivanchovichina et al. (2013) cite 11 estimates of ψ in LDCs. The average value is 0.22 (0.226 when the highest and lowest estimates are excluded).

16

8.55 percent is the average excluding the Seychelles (where the distress rate was estimated at 32.2 percent) and South Africa.

17

For 2003–2006, consumption, indirect taxes, and trade taxes averaged 81 percent, 9.6 percent, and 4.6 percent of GDP, respectively. If duties on consumer imports accounted for half of trade taxes, then the average consumption tax was 14.7 percent. (Data from IMF 2007).

18

In runs analzyed in section 7, a value of 5 for ϕ implies that choosing rapid over gradual scaling up increases unit investment costs 63–308% for the first seven years of the program.

19

The estimated return for road maintenance is 139 percent.

20

These correspond to the average maturity and grace period for new concessional loans to LICs in 2009–2010, based on available IMF and World Bank DSAs. The study applies an equal principal payment formula to generate the repayment profile.

21

The big push is on the scale of ambitious programs recently initiated by several LICs in SSA (Mozambique, Rwanda, Tanzania, and Uganda). The financing share of concessional loans and the time path of public investment is based on data from applications of the MBDSA to diverse countries by IMF staff.

22

Setting λ₁ = λ₃ = 1 and λ₂ = λ₄ = 0 in (45) and (46) yields

$$\begin{eqnarray} \left. T_{t}\right|_{\text{counterfactual}} &=&T_{\text{target,t} }=T_{o}-\lambda \text{GAP}_{\text{t}}, \\ \left. h_{t}\right|_{\text{counterfactual}} &=&h_{\text{target,t} }=h_{o}+(1-\lambda )\frac{\text{GAP}_{\text{t}}}{P_{t}(c_{t}+c_{1,t})}. \end{eqnarray}$$

23

The argument against the ambivalent position of this paper is that collection rates vary widely across countries at similar levels of development. (See Briceno-Garmendia, Smits, and Foster [2008]. The collection rate for electricity, for example, is only 53–55 percent in Kenya and Ghana, but 100 percent in Tanzania, Rwanda and Cameroon.) This suggests that raising the collection rate is largely a matter of political will. (Why cannot Kenya achieve the same collection rate as Tanzania or Cameroon?)

24

It is important to note that the run here assumes new investment is less efficient than past investment, not less efficient than in other countries. At the initial equilibrium, |$z_{o}=s_{o}\tilde{z}_{o}$|⁠. The current calibration of the model assumes s_o = 1. Hence s < 1 means investment efficiency is lower than in the past. As demonstrated in Berg et al. (2018), there is no presumption that the return on investment is lower in an historically inefficient economy (where s_o = s = 1) than in a structurally-identical efficient economy (where s_o = s = 1).

25

The risk-free rate equals the average real interest rate on 10-year U.S. treasury bonds for 1993–2007. Endogenous variations in the risk premium affect borrowing rates for both the public and private sector.

26

See the long paper (Buffie et al. 2016) for a discussion of the results in different studies.

27

In the gradual program, infrastructure investment increases by 2 percent of initial GDP at year one and then takes another six years to rise to its steady-state level.

28

The supply price of maintenance is assumed to be the same as the supply price of infrastructure. See Adam and Bevan (2014) for a more in-depth analysis of maintenance investment in a variant of the current model.

29

Heggie and Vickers (1998) estimate the return on road maintenance in World Bank projects at 38.6 percent. Foster and Briceno-Garmendia (2010, chapter 2) estimate the return in Sub-Saharan Africa to be 139 percent. Gramlich (1994) cites Congressional Budget Office (CBO) estimates that the return to highway maintenance in the United States was 35 percent in the 1980s.

30

The increase in maintenance expenditure occurs in a single step in year one.

31

The authors apply the same discount rate when calculating the welfare gains of savers and nonsavers. Arguably, however, the discount rate for nonsavers exceeds the real interest rate. The issue of the right discount rate for nonsavers—hopefully informed by some empirical evidence—deserves consideration in future research.

32

The study does not expect the results for temporary crowding out of private investment to change significantly when there is open unemployment. Since higher employment increases both future income and the equilibrium private capital stock, both the investment-depressing consumption-smoothing effect and the pro-investment pull of the long-run fundamentals are stronger. The outcome in the case of underemployment (i.e., full employment but a large gap between the marginal value product of labor in the formal vs. informal sector) is less clear: larger future income gains make the consumption-smoothing effect stronger, but the equilibrium private capital stock may increase more or less than in the current model depending on sectoral factor intensity rankings.

References

Abiad

A.

,

Ostry

J.

.

2005

. “

Primary Surpluses and Sustainable Debt Levels in Emerging Market Countries

.”

IMF Policy Discussion Paper No. 05/6

,

International Monetary Fund

,

Washington, DC

.

Adam

C.

,

Bevan

D.

.

2014

. “

Public Investment, Public Finance, and Growth: The Impact of Distortionary Taxation, Recurrent Costs, and Incomplete Appropriability

.”

IMF Working Paper No. 14/73

,

International Monetary Fund

,

Washington, DC

.

Albala-Bertrand

J.

,

Mamatzakis

E.

.

2001

. “

Is Public Infrastructure Productive? Evidence from Chile

.”

Applied Economics Letters

8

(

3

):

195

–

98

.

Asian Development Bank

.

2017

. “

Meeting Asia’s Infrastructure Needs

.”

Special Report, Manila, the Philippines

.

Bahl

R.

2013

. “

A Retrospective on Taxation in Developing Countries: Will the Weakest Link Be Strengthened?

”

Working Paper 13-18

,

International Center for Public Policy, Georgia State University

,

Atlanta, Georgia

.

Baumol

W.

1965

.

Welfare Economics and the Theory of the State

.

London

:

G. Bell and Sons

.

Berg

A.

,

Buffie

E.

,

Pattillo

C.

,

Portillo

R.

,

Presbitero

A.

,

Zanna

L.

.

2018

. “

Some Misconceptions About Public Investment Efficiency and Growth

.”

Economica

,

forthcoming

.

Bohn

H.

,

1998

. “

The Behavior of U.S. Public Debt and Deficits

.”

Quarterly Journal of Economics

113

(

3

):

949

–

63

.

Bohn

H.

2008

. “

The Sustainability of Fiscal Policy in the United States

.” In

Sustainability of Public Debt

, edited by

Neck

R.

,

Sturm

J.

,

15

–

49

.

Cambridge, MA

:

MIT Press

.

Briceno-Garmendia

C.

,

Smits

K.

,

Foster

V.

.

2008

. “

Financing Public Infrastructure in Sub-Saharan Africa: Patterns and Emerging Issues

.”

AICD Background Paper 15

,

World Bank

,

Washington, DC

.

Buffie

E.

,

Berg

A.

,

Pattillo

C.

,

Portillo

R.

,

Zanna

L.

.

2012

. “

Public Investment, Growth, and Debt Sustainability: Putting Together the Pieces

.”

IMF Working Paper, No. 12/144

,

International Monetary Fund

,

Washington, DC

.

Buffie

E.

,

Zanna

L.

,

Portillo

L.

,

Berg

A.

,

Pattillo

C.

.

2016

. “

Borrowing for Growth: Big Pushes and Debt Sustainability in Low-Income Countries

.”

Mimeo

.

Calderon

C.

,

Moral-Benito

E.

,

Serven

L.

.

2015

. “

Is Infrastructure Capital Productive? A Dynamic Heterogeneous Approach

.”

Journal of Applied Econometrics

30

(

2

):

177

–

98

.

Calderon

C.

,

Serven

L.

.

2003

. “

The Output Cost of Latin America’s Infrastructure Gap

.” In

The Limits of Stabilization: Infrastructure, Public Deficits, and Growth in Latin America

, edited by

Easterly

W.

,

Serven

L.

,

95

–

118

.

Palo Alto, CA

:

Stanford University Press

.

Carranza

L.

,

Daude

C.

,

Melguizo

A.

.

2014

. “

Public Infrastructure Investment and Fiscal Sustainability in Latin America: Incompatible Goals?

”

Journal of Economic Studies

41

(

1

):

29

–

50

.

Celasun

O.

,

Debrun

X.

,

Ostry

J.

.

2007

. “

Primary Surplus Behavior and Risks to Fiscal Sustainability in Emerging Market Countries: A Fan-Chart Approach

.”

IMF Staff Papers

53

(

3

):

401

–

25

.

Dalgaard

C.

,

Hansen

H.

.

2005

. “

The Return to Foreign Aid

.”

Discussion Paper No. 05-04

,

Institute of Economics, University of Copenhagen

,

Copenhagen, Denmark

.

Eberhard

A.

,

Foster

V.

,

Bricendo-Garmendia

C.

,

Ouedraogo

F.

,

Camos

D.

,

Shkaratan

M.

.

2008

. “

Underpowered: The State of the Power Sector in Sub-Saharan Africa

.”

AICD Background Paper 6, World Bank

.

Escribano

A.

,

Guasch

J.

,

Pena

J.

.

2008

. “

Impact of Infrastructure Constraints on Firm Productivity in Africa

.”

AICD Working Paper No. 9

,

World Bank

,

Washington, DC

.

Fedelino

A.

,

Kudina

A.

.

2003

. “

Fiscal Sustainability in African HIPC Countries: A Policy Dilemma?

”

IMF Working Paper No. 03/187

,

International Monetary Fund

,

Washington, DC

.

Feldstein

M.

,

1964

. “

The Social Time Preference Discount Rate in Cost Benefit Analysis

.”

Economic Journal

74

(294):

360

–

79

.

Foster

V.

,

Briceno-Garmendia

C.

.

2010

.

Africa’s Infrastructure: A Time for Transformation

.

Washington, DC

:

World Bank

.

Garcia

M.

,

Rigobon

R.

.

2005

“

A Risk Management Approach to Emerging Market’s Sovereign Debt Sustainability with an Application to Brazilian Data

.” In

Inflation Targeting, Debt, and the Brazilian Experience: 1999 to 2003

, edited by

Giavazzi

F.

,

Goldfajn

I.

,

Herrera

S.

,

251

–

305

.

Cambridge, MA

:

MIT Press

.

Ghosh

A.

,

Kim

J.

,

Mendoza

E.

,

Ostry

J.

,

Qureshi

M.

.

2011

. “

Fiscal Fatigue, Fiscal Space and Debt Sustainability in Advanced Economies

.”

NBER Working Paper No. 16782

,

National Bureau of Economic Research

,

Cambridge, MA

.

Gramlich

E.

1994

. “

Infrastructure Investment: A Review Essay

.”

Journal of Economic Literature

32

(

3

):

1176

–

96

.

Gueye

C.

,

Sy

A.

.

2010

. “

Beyond Aid: How Much Should African Countries Pay to Borrow?

”

IMF Working Paper No. 10/140

,

International Monetary Fund

,

Washington, DC

.

Heggie

I.

,

Vickers

P.

.

1998

. “

Commercial Management and Financing of Roads

.”

World Bank Technical Paper No. 409

,

World Bank

,

Washington, DC

.

Hevia

C.

2012

. “

Using Pooled Information and Bootstrap Methods to Assess Debt Sustainability in Low-Income Countries

.”

World Bank Policy Research Working Paper No. 5978

,

World Bank

,

Washington, DC

.

Hulten

C.

1996

. “

Infrastructure Capital and Economic Growth: How Well You Use It May Be More Important Than How Much You Have

.”

NBER Working Paper No. 5847

,

National Bureau of Economic Research

,

Cambridge, MA

.

Hulten

C.

,

Bennathan

E.

,

Srinivasan

S.

.

2006

. “

Infrastructure, Externalities, and Economic Development: A Study of Indian Manufacturing

.”

World Bank Economic Review

20

(

2

):

291

–

308

.

International Monetary Fund (IMF)

.

2007

. “

Ghana: Staff Report for the 2007 Article IV Consultation

.”

International Monetary Fund

,

Washington, DC

.

International Monetary Fund (IMF)

.

2011

. “

Revenue Mobilization in Developing Countries

.”

Fiscal Affairs Department

,

International Monetary Fund

,

Washington, DC

.

Isham

J.

,

Kaufmann

D.

.

1999

. “

The Forgotten Rationale for Policy Reform: The Productivity of Investment Projects

.”

Quarterly Journal of Economics

114

(

1

):

149

–

84

.

Ivanchovichina

E.

,

Estache

A.

,

Foucart

R.

,

Garsous

G.

,

Yepes

T.

.

2013

. “

Job Creation Through Infrastructure Investment in the Middle East and North Africa

.”

World Development

45

(May):

209

–

22

.

Kamps

C.

2004

. “

The Dynamic Effects of Public Capital: VAR Evidence for 22 OECD Countries

.”

Kiel Working Paper No. 1224

,

Kiel Institute for the World Economy

,

Kiel, Germany

.

Keen

M.

,

Mansour

M.

,

2010

. “

Revenue Mobilisation in Sub-Saharan Africa: Challenges from Globalisation I—Trade Reform

.”

Development Policy Review

28

(

5

):

553

–

71

.

Kraay

A.

,

Nehru

V.

.

2006

. “

When Is External Debt Sustainable?

”

World Bank Economic Review

20

(

3

):

341

–

65

.

Little

I.

,

Mirrlees

J.

.

1974

.

Project Appraisal and Planning for Developing Countries

.

New York

:

Basic Books

.

Marshall

K.

2012

. “

Factor Payment Shares in a Large Cross-Section of Countries

.”

California Polytechnic State University

,

San Luis Obispo, CA

,

Mimeo, Department of Economics

.

Mead

R.

2017

. “

The Prophet of Dystopia

.”

Mimeo, Department of Economics, New York, April 17, 2017

.

Mendoza

E.

,

Ostry

J.

.

2008

. “

International Evidence on Fiscal Solvency: Is Fiscal Policy ‘Responsible’?

”

Journal of Monetary Economics

55

(

6

):

1081

–

93

.

Mendoza

E.

,

Oviedo

M.

.

2004

. “

Public Debt, Fiscal Solvency and Macroeconomic Uncertainty in Latin America: The Cases of Brazil, Colombia, Costa Rica and Mexico

.”

NBER Working Paper No. 10637

,

National Bureau of Economic Research

,

Cambridge, MA

.

Pegoraro

R.

2007

. “

Apple's iPhone Is Sleek, Smart and Simple

.”

Mimeo, Department of Economics, Washington Post, July 5, 2007

.

Pereira

A.

,

Andraz

J.

.

2010

. “

On the Economic and Fiscal Effects of Investments in Road Infrastructures in Portugal

.”

Working Paper No. 33

,

Department of Economics, College of William and Mary

,

Williamsburg, VA

.

Pereira

A.

,

Pinho

M.

.

2006

. “

Public Investment, Economic Performance and Budgetary Consolidation: VAR Evidence for 12 Euro Countries

.”

Working Paper No. 40

,

Department of Economics, College of William and Mary

,

Williamsburg, VA

.

Perotti

R.

2004

. “

Public Investment: Another (different) Look

.”

Working Papers 277

,

IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University

,

Milan, Italy

.

Pritchett

L.

2000

. “

The Tyranny of Concepts: CUDIE (Cumulated, Depreciated, Investment Effort) Is Not Capital

.”

Journal of Economic Growth

5

:

361

–

84

.

Prizzon

A.

,

Mustapha

S.

.

2014

. “

Debt Sustainability in HIPCs in a New Age of Choice

.”

Working Paper No. 397

,

Overseas Development Institute

,

London, UK

.

Sahoo

P.

,

Dash

R.

.

2012

. “

Economic Growth in South Asia: Role of Infrastructure

.”

Journal of International Trade and Economic Development

21

(

2

):

217

–

52

.

Sen

A.

1967

. “

Isolation, Assurance and the Social Rate of Discount

.”

Quarterly Journal of Economics

81

(

1

):

112

–

24

.

Serven

L.

2007

. “

Fiscal Rules, Public Investment, and Growth

.”

World Bank Policy Research Working Paper No. 4382

,

World Bank

,

Washington, DC

.

Sulaiman

T.

2014

. “

Analysis: Decade After Debt Relief, Africa’s Rush to Borrow Stirs Concern

.”

Reuters, London, March 18. https://www.reuters.com/article/us-africa-debt-sustainability-analysis-idUSBREA2H08B20140318.