A. Features of the Model

The model economy is comprised of two sectors, one for traded goods and one for non-traded goods. There is also an imported good (a traded good produced in another country), which can be consumed or used to produce capital. In each sector i (with i = n, x, where n is for the non-traded sector and x is for the traded/export sector), representative firms take private capital (k_i,t), labor (L_i,t), and effective public capital (z_t) to produce output using Cobb-Douglas technology:

The role of public capital in the production function is the core feature of the model. Public capital is not sector-specific and, all else being equal, an increased stock of public capital increases output and raises the return on private capital and labor. An increased flow of public investment therefore boosts growth because of this complementarity of public and private capital.

Firms maxize the following objective function, where the choice variables are the labor and capital used as production inputs:

The price of output in each sector is denoted by p_i,t, the wage by w_t, and the rental rate of capital by r_i,t. Note that the wage—unlike the rental rate of capital—is not sector-specific, as labor is mobile across sectors.

The economy is populated by two types of consumers: savers and non-savers. Each type i consumes a constant elasticity of substitution (CES) basket of goods given by equation (3), with a price index given by equation (4):

The parameter ϵ governs the intra-temporal elasticity of substitution. The parameters ρ_x, ρ_m, and ρ_n govern the distribution of goods in the basket and sum up to one.

Non-savers are constrained by an inability to access capital markets and must therefore consume all of their earned income in the period in which it is earned. Their hand-to-mouth behavior creates non-Ricardian outcomes that we observe in a low-income country like Liberia. Non-savers are subject to the following budget constraint:

The constraint says that consumption (c_t, and the superscript h stand for “hand-to-mouth”) after taxes (a value-added tax give by h_t) must be equal to labor income plus remittances and transfers. The parameter a governs the ratio of savers to non-savers in the economy.

Savers behave like standard utility-optimizing agents. They are able to smooth consumption over time by investing in traded or non-traded capital, or by borrowing in domestic or international debt markets. Their maximization problem is given by:

subject to a budget constraint and two capital accumulation equations:

Domestic bonds are denoted by $b_t^s$ and foreign bonds by $b_t^{s*}$; the interest rates on each are given by r_t and $r_t^{*}$, respectively. Capital adjustment costs are given by AC_i,t for each sector. Portfolio adjustment costs linked to foreign liabilities are given by $Y_t^s$, which captures the degree of financial account openness. Profits of domesic firms are represented by ${\mathrm{\Phi }}_t^s$, and finally, the rate of depreciation of capital is given by δ.

The budget constraint simply says that income (from labor, capital, remittances, transfers, bond holdings, and firm profits) must not exceed expenses (on debt accumulation, investment, investment adjustment, and portfolio adjustment).

An important feature of the model, designed specifically to match low-income economies, is the process by which public capital is accumulated. It is best understood as a two-step process. In the first step, the government allocates money to be invested in public capital, which evolves according to a standard accumulation equation:

In the second step, some of that public capital is allocated for productivity-enhancing infrastructure ($z_t^e$), which we have been calling effective public capital:

The parameter s governs the efficiency of public investment; that is, the rate at which public capital is turned into productivity-enhancing infrastructure. This parameter takes a value between zero and one, implying that one dollar spent on public investment yields less than one dollar’s worth of public infrastructure. Note that it is this $z_t^e$ which enters into the representative firm’s production function.

In low-income countries, as written in Hulten (1996) and Pritchett (2000), the productivity of infrastructure is high while the return on public spending is low. This feature of the model accounts for this fact, since the return on investment can be quite low if the efficiency of that investment is also low.

The government is also subject to a budget constraint, which allows us to specify the size of the fiscal adjustment required for a given investment buildup. The budget constraint equates government financing from domestic debt, external commercial debt (d_c,t), concessional debt (d_t), and taxes with expenditures on debt service, investment, transfer spending (T_t), and grant aid (G_t), which is exogenous:

The path for concessional debt and public investment spending is exogenous to the model.

For a given initial level of taxes and transfer spending, the budget constraint can be re-written as a gap between spending and revenues:

In the long run, for debt to be sustainable, the gap must be covered by adjustments in taxes and transfers (current transfers). In the short and medium term, though, the gap may be closed with additional borrowing. If the fiscal adjustment occurs too slowly, however, the interest payments on accrued debt will rise faster than revenue and the path of debt explodes. This is the core dilemma facing policymakers—timing the fiscal adjustment so that it is not too painful, but not so slow that debt is unsustainable.

B. Calibration to Liberia

Three parameters govern the dynamics of debt in the model. First is the return on public investment, which is the marginal product of effective public capital net of the depreciation rate. There is no estimate of this parameter for Liberia, so we set it at 25 percent, based on estimates for Sub-Saharan Africa, though there is considerable variation across countries.

The second key parameter is the efficiency of public investment, or the rate at which public investment is converted into productivity-enhancing capital. Pritchett (2000) estimates that around half of government investment spending does not actually create capital. We use this estimate to inform our baseline, which assumes that, over the projection period, 50 percent of investment spending goes towards productive public capital formation while the remaining is spent in non-productive projects. While this assumption maybe realistic in the early years of increasing public investment as the country faces important capacity constraints, it may not be fully accurate once a solid public investment framework is in place to ensure that projects selected are aligned to the government’s priorities, they are efficiently evaluated and selected based on their value for money.

By increasing the efficiency of investment over time, it is possible to lower the debt path and increase the growth dividend for a given level of investment spending, or alternatively achieve the same growth dividend with reduced reliance on new tax revenue or commercial borrowing. In one scenario below, we increase this parameter over time to demonstrate the effect of increased investment efficiency.

Third is the absorptive capacity constraint, which captures the difficulties stemming from planning, coordination, and management problems. This can manifest itself in cost overruns or low execution ratios (i.e., inability to spend all allocated money). Constraints on absorptive capacity are currently a problem for Liberia, and we assume that cost overruns are approximately 20 percent to begin with (i.e., similar to the cost overrun estimated by the government for the rehabilitation of the hydropower plant). Reducing this constraint can have a significant effect on the path of debt, and we show in a scenario below how big this impact can be. Box 1 details strategies for how this may be achieved.

Because we are using a general equilibrium model, it is important to carefully consider how our steady state is parameterized as the simulations we show are all deviations from the model’s initial equilibrium. We use the latest data and medium-term macroeconomic framework underlying the joint IMF-World Bank debt sustainability analysis (DSA) for Liberia to calibrate the level of initial debt-to-GDP ratios (commercial, domestic, and concessional), remittances, and grants. Based on the underlying data, we assume a per capita potential growth rate of 3.0 percent and an initial public investment level of 4.0 percent of GDP (steady state).

Because the model divides consumers into those who can smooth consumption across time and those who cannot, the calibrated level of savers to non-savers is very important. It controls the degree to which domestic interest rates react to fiscal policy. Because there is not a reliable estimate of this value for Liberia, we use the estimate from Buffie, et al. (2012). It is possible that the proportion of savers is higher than what we assume here due to widespread adoption of microfinance. However, it is likely that the informal nature of microfinance institutions in rural areas and the limited degree to which rural workers are able to save means that many users would still be considered non-savers.²

We parameterize the model to reflect the high import share of Liberia’s public capital. For many of the current investment projects, labor and materials are imported rather than locally hired. We expect that this will have implications for the exchange rate effects of large-scale public borrowing (this is the case, detailed in the simulations below). Specifically, we assume that 70 percent of public capital components are imported.

For the rest of the parameters, no data are available for Liberia-specific estimates. We use the values presented in Buffie, et al. (2012), which are estimates taken from the literature for Sub-Saharan African.

Table 2.

Model Calibration for Baseline Scenarios

Table 2.

Model Calibration for Baseline Scenarios

Parameter	Value	Definition
τ	0.34	Intertemporal elasticity of substitution
ϵ	0.90	Intratemporal elasticity of substitution across goods
α x	0.40	Capital’s share in value added – traded sector
α n	0.55	Capital’s share in value added – non-traded sector
α k	0.50	Cost share of non-traded inputs in the production of private capital
α z	0.41	Cost share of non-traded inputs in the production of public capital
δx, δn, δz	0.05	Capital depreciation rates
ρ x	0.32	Distribution parameter – traded goods
ρ n	0.44	Distribution parameter – non-traded goods
g	0.03	Trend per capita growth rate
r o	0.10	Initial real interest rate on domestic debt
r dc,o	0.06	Real interest rate on external commercial debt
R z,o	0.25	Initial return on public investment
b o	0.017	Initial public domestic debt to GDP ratio
d o	0.10	Initial external concessional debt to GDP ratio
G o	0.017	Initial grants to GDP ratio
R o	0.05	Remittances to GDP ratio
I z,o	0.041	Initial ratio of public investment to GDP
s	0.50	Efficiency of public investment
h o	0.07	Initial consumption VAT rate
a	1.50	Ratio of savers to non-savers

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Table 2.

Model Calibration for Baseline Scenarios

Parameter	Value	Definition
τ	0.34	Intertemporal elasticity of substitution
ϵ	0.90	Intratemporal elasticity of substitution across goods
α x	0.40	Capital’s share in value added – traded sector
α n	0.55	Capital’s share in value added – non-traded sector
α k	0.50	Cost share of non-traded inputs in the production of private capital
α z	0.41	Cost share of non-traded inputs in the production of public capital
δx, δn, δz	0.05	Capital depreciation rates
ρ x	0.32	Distribution parameter – traded goods
ρ n	0.44	Distribution parameter – non-traded goods
g	0.03	Trend per capita growth rate
r o	0.10	Initial real interest rate on domestic debt
r dc,o	0.06	Real interest rate on external commercial debt
R z,o	0.25	Initial return on public investment
b o	0.017	Initial public domestic debt to GDP ratio
d o	0.10	Initial external concessional debt to GDP ratio
G o	0.017	Initial grants to GDP ratio
R o	0.05	Remittances to GDP ratio
I z,o	0.041	Initial ratio of public investment to GDP
s	0.50	Efficiency of public investment
h o	0.07	Initial consumption VAT rate
a	1.50	Ratio of savers to non-savers

A. Baseline Investment Scenario

The baseline scenario roughly corresponds to the government’s current investment strategy. Public investment is rapidly scaled up from 4 percent of GDP to 12 percent of GDP. After six years, investment declines almost as quickly back to around 5 percent of GDP, where it stays permanently.

Grant aid rises modestly from its initial level of 1.7 percent of GDP to 2.1 percent of GDP and remains constant. There is no fiscal adjustment in the form of changes to tax policies or current spending, and all additional financing is assumed to come from concessional lending.

Under the baseline scenario, the increase in foreign financing (i.e., grants and concessional lending) leads to an 11 percent exchange rate appreciation by year two, returning to its original level by year ten. This is accompanied by a decline in traded output as the higher exchange rate causes the export goods sector to contract by nearly six percent by year two.

Private investment initially dips by about one percent before rising back above its initial level, caused by the sharp decline in traded output. Real per capita GDP growth is also stagnant at the 3 per cent in the steady state for years one and two before it rises above its long run level of three percent. On the plus side, private consumption increases immediately as a result of the inflow of foreign aid, though the increase is rather modest (it is nearly four percent higher by year 12 before it begins to return to its initial level).

Total public debt as a share of GDP rises to 58 percent at year ten before falling to 38 percent by year 30 (the new debt is composed entirely of concessional loans). Real per capita GDP growth stays above four percent per year from years three through seven, then gradually declines back to its long run level of three percent.

The peak debt-to-GDP ratio of 58 percent is not unreasonably high, but the composition of the growth dividend in this scenario is somewhat worrisome. Real per capita growth comes mostly from an increase in non-traded output, with other traditional measures of debt sustainability like debt-to-exports pointing out to higher risk of debt distress. Despite this result implies that Liberia is going against the pattern of export-led growth that has successfully brought other countries, notably those in Southeast Asia, out of poverty, further adaptation of the model to capture the uniqueness of Liberia’s economy is still warranted.

Ultimately, the investment surge is meant to boost growth so that Liberia can reach middle-income country status by 2030, but given the relative conservative level of the scaling up of investment, it is likely that the strategy will fall short of that goal. Given the path of debt in this scenario is sustainable, it is possible the government could afford to borrow higher amounts. This suggests that a more ambitious investment strategy is needed to achieve the country’s long-run growth goals. In the next section, we analyze just such a strategy as laid out by the authorities.

It is likely that the exchange rate path outlined in this scenario is more volatile than what would be experienced in Liberia given exports are driven by commodities will be less affected by the exchange rate. It is expected that the natural resource sector will continue to drive the projected increase in exports in Liberia. Additionally, the country’s investment plan focuses in large part on developing the electricity grid and improving the country’s road and transportation infrastructure which represents the two main binding constraints to growth. Currently, Liberia has the highest electricity prices in the world, and its roads coverage is among the lowest in the world.

In the model, the exchange rate appreciation is caused by increased demand for domestic goods from the influx of foreign money (in this case, concessional lending and grant aid). This domestic price pressure is likely to be mitigated in Liberia because the investment projects specifically target two industries currently contributing to high domestic prices. The model accounts only partially for this industry-specific investment, but we believe that the exchange rate story is likely to be more muted than it appears here—and so the negative impact on growth from this channel is also likely to be much smaller. This conclusion holds for the rest of the scenarios, some of which show particularly extreme exchange rate appreciations.

B. Aggressive Investment Scenario

This scenario corresponds roughly to the authorities’ aspirational plans. It follows from the belief that a more aggressive investment strategy will be needed for Liberia to achieve middle income country status. Public investment, starting from 4 percent of GDP as before, quickly rises to 20 percent of GDP by year six, then falls again and is back to 5 percent, permanently, by year twelve. Additional financing is assumed by the authorities to come from grants, which increase to three percent of GDP, and from concessional lending.

The story here is similar to that in the baseline scenario with the exchange rate appreciating. The higher grant aid and the non-concessional lending provide a massive inflow of foreign cash to the economy, and as in the baseline case, the traded goods sector is affected negatively. In this case, the exchange rate appreciates by about 37 percent from its initial level and does not fall back until year nine of the simulation.

This exchange rate appreciation by itself would likely be without precedent. Panel 4 in Figure 2 shows that the exchange rate appreciation would lead to a rapid decline in the tradable sector of about 20 percent in the short run. This presents the same challenges as the baseline case, in that it exacerbates other traditional measurements of debt risk like total debt-to-exports ratio.

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Baseline Investment Strategy

Citation: IMF Working Papers 2013, 237; 10.5089/9781475534931.001.A001

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Aggressive Investment Strategy

Citation: IMF Working Papers 2013, 237; 10.5089/9781475534931.001.A001

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On the bright side, private investment rises significantly after a short hiccup in year one of the scenario, peaking at about 12 percent above its initial level in year six before slowly declining. Consumption also rises permanently, increasing by seven percent by year ten and declining slowly as well. This suggests that debt-financed public investment can increase consumer welfare, though the costs of doing so in this case are overwhelming given the increase in consumption and investment.

Most worrisome is the rise in the total stock of debt. Panel 8 of Figure 2 shows that the debt-to-GDP ratio rises to over 150 percent of GDP in year nine of the scenario. Although the debt level appears sustainable in the strict sense that it eventually begins to decline, in no real way is it a sustainable level of debt. The working assumption is that nonconcessional loans will arise to close the fiscal gap, but nonconcessional borrowing channels are likely to close far before the nation reaches this kind of debt level. This level of debt would likely trigger a crisis by almost any conventional measure and paints this scenario as unrealistic.

C. Intermediate Investment Scenario

In this section, we outline a moderate investment scenario designed to create modest and sustained real per capita GDP growth while keeping the stock of debt at manageable levels. As before, public investment is assumed to begin at 4 percent of GDP, then it rises for four years before peaking at 13 percent of GDP. Over the next seven years it falls gradually to its new permanent level of 5 percent of GDP (depicted in Figure 3).

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Intermediate Investment Strategy

Citation: IMF Working Papers 2013, 237; 10.5089/9781475534931.001.A001

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Grant aid is assumed to increase only modesty from its initial level of 1.7 percent of GDP to 2.1 percent of GDP. There is no fiscal adjustment, so all remaining financing needs must be covered by concessional borrowing. This assumption is used to compare this scenario to the two prior scenarios.

As before, the influx of borrowed money and grants lead to an exchange rate appreciation. Traded output falls and non-traded output rises. Total output initially contracts, though on balance real per capita GDP growth increases from its steady state of 3 percent to about five percent per year. Consumption rises by about five percent by the time the investment surge is over, so this strategy is welfare-enhancing.

The stock of debt, which again begins at 11 percent of GDP, shoots up to 86 percent of GDP, considerably higher than any reasonably sustainable level. The debt profile is not explosive (i.e., continues to increase permanently) in the sense that it eventually begins to decline only because the debt is assumed to be concessional; so compounding interest payments (i.e., commercial borrowing) will not either lead to an explosive but certainly to a more unsustainable trajectory in a shorter period of time. Still, no external lender would consider providing lending to a country with high risks of debt distress, even if prospects for growth were otherwise good.

In other simulations not presented in this paper, financing with commercial lending is explored. The burden of maintaining the debt becomes overwhelming, and the debt trajectory rapidly becomes explosive. After ten years, the stock of debt is over 100 percent of GDP, and then continues to rise to nearly 200 percent of GDP after 30 years. This level of debt is not only unmanageable but will require a permanent and painful fiscal adjustment for a several years.

D. Intermediate Investment Strategy with Structural Reforms

One possibility is that the authorities can explore structural reforms aimed at increasing the efficiency of the public investment process. We consider two parallel strategies: increasing the efficiency of public investment (that is, directing a higher share of investment toward productivity-enhancing projects) and reducing the level of cost overruns. In reality, these two are very tightly related concepts that are difficult to measure separately, whereas they are separate concepts in the context of the model used here.

Recall that for every dollar directed towards infrastructure investment, some fraction s is spent on productivity-enhancing public capital that enters into the firm production function. In the baseline calibration, we assume that this fraction is 50 percent. In this scenario (depicted in Figure 4), we gradually increase investment efficiency over 10 years, so that by the end of the investment period, 90 percent of allocated money was spent on effective public capital. Additionally, in the baseline calibration, we assume that public investment projects run over cost by about 20 percent. Here, we assume that the level of cost overruns slowly declines over the 10 year investment surge to about 10 percent.

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Intermediate Investment Strategy with Structural Reforms

Citation: IMF Working Papers 2013, 237; 10.5089/9781475534931.001.A001

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As in the case of aggressive investment, we assume that grant aid increases to three percent of GDP. This matches the authorities’ assumption that donors will be able to fill some of the government’s financing needs and give more fiscal space for public infrastructure investment. Additional financing comes from concessional lending, as has been the working assumption throughout the paper. Taxes are again held constant so that the investment surge does not come at the expense of private consumption.

This scenario delivers a very productive investment surge, real per capita GDP growth rises to five and a half percent by year five, and stays above four percent per capita through the end of year ten. There is still an increase in the exchange rate that leads to a fairly sharp contraction of traded output, but private consumption and investment both increase substantially, indicating that the strategy is likely to be welfare-enhancing. Total debt-to-GDP rises, but peaks at a level of 70 percent of GDP around year nine before it begins to decline over the next two decades. This compares very favorably to the intermediate investment simulation with no reform, where debt rises to 86 percent of GDP.

The cumulative growth dividend is calculated as the cumulate difference over 10 years of annual per capita GDP growth above and beyond the steady state baseline growth rate of 3 percent, and this intermediate scenario with structural reforms boosts growth by 16 percentage points. The table below compares the scenarios:

Table 3.

Comparison of Scenarios

Table 3.

Comparison of Scenarios

Scenario	Growth Dividend	Peak Debt-to-GDP
Baseline Investment	9.0	57.2
Aggressive Investment	21.8	167.1
Intermediate Investment	12.4	85.8
Intermediate Investment with Structural Reforms	16.4	70.0

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Table 3.

Comparison of Scenarios

Scenario	Growth Dividend	Peak Debt-to-GDP
Baseline Investment	9.0	57.2
Aggressive Investment	21.8	167.1
Intermediate Investment	12.4	85.8
Intermediate Investment with Structural Reforms	16.4	70.0

This simply confirms what we learned from the simulations above: an intermediate investment strategy combined with an increase in aid and some structural reforms offer the best path forward for achieving sustained growth and manageable debt.