March 2017 - Quantum Global Group€¦ · windfalls, make it an imperative to harness these resource revenues in order to accelerate development. By harnessing, we mean leveraging

March 2017

1

Oil Shocks, Public Investment and Macroeconomic

and Fiscal Sustainability in Nigeria: Simulations

using a DSGE Model

Mthuli Ncube1 and Lacina Balma2

14 February 2017

Abstract

Volatility in the oil prices and subsequent revenues, is a strong rationale for oil-

producing countries to accumulate buffer-savings during oil-boom times in order to use

them during bust times, as commodity prices fall and/or the natural resource depletes.

In so doing, this allows government spending to be smoothed out and to ensure

macroeconomic stability. The paper develops and uses a Dynamic Stochastic General

Equilibrium Model(DSGE) to analyse a typical oil-producing country like Nigeria. The

paper combines various assumptions related to oil shocks—both prices and volumes

shocks—on government oil revenue and reserves, public debt and different degrees of

investment scale-ups. We find that there is need to strike the right balance between

investing with the oil windfall in order to meet development goals and saving in

stabilization fund in order to ensure macroeconomic stability. Managing both price

volatility and disruption of resource production should be the priority to overcome risks

of adverse shocks. Second, ambitious investment scale-ups through either debt-

financing or from resource windfall, creates short-run supply side bottlenecks and risks

to Dutch disease effects. This fact highlights the needs for policies that seek to address

absorptive capacity constraints and inefficiencies in public investment decisions.

Keywords: Oil Wealth; Public Investment; Fiscal Sustainability; Nigeria

JEL code classification: Q32; E22; E62

1 Managing Director and Head, Quantum Global Research Lab, Zug, Switzerland. Email: [email protected] (corresponding author). 2 Economist, Quantum Global Research Lab, Zug, Switzerland. Email: [email protected] (corresponding author).

2

I. Introduction

The Nigerian economy, which is the largest in Africa has been impacted negatively by the fall

in the oil price, the main export driver and revenue earner for the country. The Nigerian

economy is in recession and is expected to contract by -1.8% in 2016, according to the IMF.

The Nigerian currency, the NAIRA, has depreciated substantially due to falling oil revenues,

and contributing to rising inflation, and declining foreign reserves.

In order to stimulate the economy the government of Nigeria has proposed, in October

2016, a US$29.9 billion External Borrowing (Rolling) Plan, for foreign borrowing for

investment in infrastructure, health, education, water resources and other sectors. Over a period

of three years, $11.274 billion would be spent on certain proposed projects and programmes,

$10.686 billion on special national infrastructure projects, and Eurobonds of $4.5 billion, with

the remaining $3.5 billion for federal government budget support. The Nigerian government

has issued 15-year $1 billion Eurobond out the planned $4.5 billion, at a yield of about 8% on

February 2017. This Eurobond issuance is part of the government’s commitment to raise funds

externally in order to support capital expenditure. Basically, 61.2 per cent of the foreign loans

have been earmarked for bankable infrastructure projects, while social programmes in health

and education, the federal government's budget support facility, agriculture and the Eurobond

issue account for the balance. The infrastructure projects include Mambila hydro-electric power

plant - $4.8 billion; railway modernisation coastal project (Calabar-Port Harcourt-Onne Deep

Seaport segment) - $3.5 billion; Abuja mass rail transit project (Phase 2) - $1.6 billion; Lagos-

Kano railway modernisation project (Lagos-Ibadan segment double track) - $1.3 billion; Lagos-

Kano railway modernisation project (Kano-Kaduna segment double track) - $1.1 billion; and

others - $6 billion.

The impact of this is that total debt stock of the country will increase by 50 per cent to

$91.45 billion, and debt to GDP ratio would increase the ratio from 12.77 per cent to 19 per

cent. Comparing to other emerging economies, the debt-to-GDP of Russia is 17.7 per cent,

China's at 22.4 per cent, India at 66.7 per cent, Brazil 66.23 per cent, and South Africa at 50.1

per cent. Among the second-tier emerging countries, the debt-to-GDP ratios are Mexico's 43.2

per cent, Indonesia's 27.0 per cent and Turkey's 32.9 per cent, all of which are higher than

Nigeria's ratio including the proposed loan.

In this paper we analyse how Nigeria could optimize on its policy choices, as an oil-

producer, in order to grow the economy.We present a dynamic stochastic general equilibrium

(DSGE) model of a small open oil producing economy, similar to Melinda et el (2014), where

development considerations—public investment needs and volatility in natural resource

windfalls, make it an imperative to harness these resource revenues in order to accelerate

development. By harnessing, we mean leveraging the oil wealth so as to guard the economy

against volatility stemming from oil prices and production in order to ensure sustainable

economic development and diversification. Thus, in order to accommodate such precautionary

management of the oil windfall, the model includes a fiscal buffer in the form of accumulated

foreign exchange reserves or a stabilization fund. Besides natural resource management, the

model can be used to assess debt sustainability in a resource-rich developing country that

combines resource revenues and borrowing to scale up public investment. The main feature of

the model is that it assumes an exogenous path of public investment, concessional borrowing,

aid, resource production, prices, and therefore resource revenues. Under these assumptions,

resource fund can be drawn down for stimulus purposes during bust years such as commodity

3

price fall and/or when resource production depletes. But during commodity boom periods, the

resource fund can accumulate.

The DSGE model also captures Dutch disease through a learning-by-doing (LBD)

externality in the non-resource traded sector: boosting domestic spending may cause the

economy to bump into short- to medium-term constraints. The increase in domestic demand

(consumption and domestic investment) may run into supply bottlenecks that push up the price

of non-traded goods. This, in turn, could create real exchange rate appreciation and possibly

also adversely impact the non-resource tradable sector. However, in the opposite productive

public investment can also raise productivity in the non-resource traded sector, counteracting

and even eventually reversing the effects of Dutch disease.

In an early contribution van Wijnbergen (1984) relates productivity growth to learning by

doing in tradables, and investigates the impact of a resource boom in a two-period model. The

demand-driven real exchange rate appreciation in period 1 is followed by real depreciation in

the second period due to productivity effects. Torvik (2001) finds similar results in a more

general setting. Using a dynamic stochastic model of small open economy, this study goes

beyond two periods and is able to distinguish between the short-term and the long-term effects

of the LBD externalities on Dutch disease.

Additional features of the model include public investment inefficiencies and absorptive

capacity constraints that increase the economic cost of building up public capital. In particular,

the model innovates by including a threshold of expenditure beyond which public investment

binds and investment costs rise due to absorptive capacity constraints similar to Berg et al

(2013) and Balma and Ncube (2015).

Another important feature concerns strong financial frictions in the international capital

markets for borrowing by the private sector of the economy and the government as well. For

long time, many African countries have found it hard to borrow in international markets.

However, low yields in many troubled advanced economies over the last decade have shifted

the investors’ appetite for emerging market countries as well as many African countries with

high yields. Yet, the borrowing costs are high, reflecting Africa’s high risk premium. This is

captured by the introduction of a country risk-premium on top of the risk-free interest rate with

the premium depending on the country’s external debt, as in Schmitt-Grohe and Uribe (2003).

Finally, the model features two types of households. Optimizing households have access to

capital and financial markets subject to the risk-premium and rule of thumb households that are

liquidity-constrained and consume all of their disposable income in each period. The model is

calibrated for Nigeria and used to study the macroeconomic implications of leveraging oil

wealth for sustainable development and economic diversification. The Nigerian application is

appealing given the country’s high dependence on oil production as manifested by a large share

of oil in exports and budget revenues. While oil revenue provides opportunities, it is also a

source of challenges, which arise at all stages of resource management.

The central message conveyed in this study is threefold. First, it seems to be judicious to

strike the right balance between investing with the oil windfall in order to fulfill development

goals and saving in order to ensure macroeconomic stability. For a highly oil-dependent country

including Nigeria, managing both price volatility and disruption of resource production should

be the priority to overcome risks of adverse shocks. Second, Nigeria should not follow

ambitious investment scaling ups neither through debt-financing nor from resource windfall in

order to shield the economy from running into short-run supply side bottlenecks and Dutch

disease effects. Third, implementing structural reforms in order to address absorptive capacity

constraints can help mitigate adverse macroeconomic effects by improving the efficiency

constraint.

4

The remainder of the chapter is organized as follows. In section 2 we present an overview

of the related literature on natural resource management. In section 3 we describe the Nigerian

economy and the role of the oil sector. In section 4 we present the model structure and discuss

the calibration procedure in section 5. Finally, in section 6 we discuss the policy scenarios and

conclude in section 7.

II. Glance at the Nigerian Economy and the Oil Sector

A rebasing exercise undertaken in 2014 of the country’s GDP from 1990 to 2010 resulted

in an 89 percent increase in the estimated size of the economy, which has made Nigeria the

largest economy in sub-Saharan Africa. The estimated nominal GDP of USD 510 billion,

surpasses South Africa’s USD 352 billion over the same period. The exercise also reveals a

more diversified economy than previously thought.3

Prior to 2015, the Nigeria has maintained its impressive growth over the past decade with a

record estimated 7.4 percent growth of real GDP in 2013, up from 6.5 percent in 2012. This

growth rate is higher than the West African subregional level and far higher than the sub-

Saharan Africa level. The performance of the economy continues to be underpinned by

favorable improvements in the non-oil sector with real growth of 5.4 percent, 8.3 percent and

7.8 percent in 2011, 2012 and 2013, respectively. Agriculture – particularly crop production –

trade and services continue to be the main drivers of non-oil sector growth. The oil sector

growth performance was not as impressive with 3.4 percent, -2.3 percent and 5.3 percent

estimated growth rates in 2011, 2012 and 2013, correspondingly (AEO, 2014). Growth of the

oil sector was hampered throughout 2013 by supply disruptions arising from oil theft and

pipeline vandalism, and by weak investment in upstream activities with no new oil finds. In

2016, the Nigerian economy has entered a recession phase, with an expected contraction of -

1.8 percent, due to the fall in oil prices.

The oil sector in Nigeria remains an indispensable pillar of fiscal revenue, accounting for

more than half of anticipated government revenue, 90 percent of total exports and about one-

third of nominal GDP in 2013 (IMF, 2014). But, even with the re-basing of the country’s GDP

in 2014, which made Nigeria the largest economy in sub-Saharan Africa, on a per-capita basis

the country performs not better on several fronts including human development, power

generation and economic transformation. The many years with oil money have not brought the

population an end to poverty nor, at least until recently, have they enabled the economy to break

out of what seems like perennial fall of per capita income below the average Sub-Saharan Africa

(Figure 2).4 This record reflects the failure of successive governments to translate sizeable

natural resource revenues into tangible socio-economic benefits and seems to be the

unavoidable consequence of the so-called resource curse. Part of the challenges hinges on oil

revenue uncertainty due to adverse commodity price and volume shocks (due to oil theft and

pipeline sabotage).

The recent introduction of the Nigeria SWF and the transition from the traditional Excess

Crude Account (ECA) in mid-July 2012 represented an important strengthening in the

management of oil revenues.5 The Nigeria SWF made its first investment in 2013, providing

more

3 For example, the share of agriculture in employment has fallen from 70 percent to about 30 percent. 4 With the recent rebasing of the GDP, this trend could have been reversed. 5 Excess oil reserves were previously allocated to the Excess Crude Account (ECA), which was set up in 2004 as

a stabilization fund to meet the country's yearly budget deficits and to contribute to the development of local

5

Figure 1: Per capita GDP in constant 2005 USD

Source: World Development Indicator, 2014

than US$200 million to international banks to manage a fixed-income portfolio. However,

translating the framework into effective fiscal anchor and ensuring adequate fiscal buffers in a

bid to avoid procyclical spending is yet to be accomplished (IMF, 2014). For example: (i) the

budget oil price is not formally instituted; (ii) the full transition from the ECA to the Nigeria

SWF has not occurred—excess crude revenues are still being deposited in the ECA, which is

managed by political agreement among federal, state, and local governments and is subject to

discretionary withdrawals.

As shown in figure 3 and 4, the evolution of oil prices is the main driver of oil revenue

changes followed by the oil revenue yield—the ratio of revenue received by the Federation

Account to the gross value of oil production—and volume.6 Moreover, on account of the oil

theft and production losses, fiscal buffers have been depleted—the balance in the ECA and

SWF declined from US$11 billion at end-2012 to US$3 billion at end-2013.

Figure 2: Changes in Oil Revenue (Billion U.S. dollars)

Source: U.S. Energy Information Administration.

infrastructure. The constitutionality of the ECA has been brought into question which triggered the migration from

ECA to SWF through the establishment of the Nigeria Sovereign Investment Authority Act. 6 The decline in oil revenue yield in 2013 (0.47) compared to the average yield in 2000-2009 (0.70) is due to the

lack of an effective oil-revenue monitoring system which make difficult for the authorities to take appropriate

corrective measures.

450

550

650

750

850

950

1050

1150

NigeriaSSA average

0

20

40

60

80

-40

-20

0

20

Due to price

Due to oil revenue yield

Due to volume

Oil revenue yield (oil revenue to gross value of volume, RHS)

6

Figure 3: Buffer Saving and Oil Price for Nigeria

Sources: U.S. Energy Information Administration.

Nigeria has made important strides in improving much of its infrastructure in recent years.

Compared to a number of Sub-Saharan countries, Nigeria has relatively advanced power, road,

rail and information and communications technology (ICT) networks that cover extensive areas

of the country. However, the lack of maintenance has deteriorated the quality of the road

network and national connectivity is impaired. An ailing power sector with frequent shortages

in the major towns is leaving the population with no choice but to resort to private diesel and

petrol generators to meet their power needs. All available statistics paint a dismal picture of the

electric power sector in Nigeria (see for instance the World Bank indicators on business climate

in Nigeria). The African Development Bank’s Infrastructure development strategy through the

Programme for Infrastructure Development in Africa (PIDA) shows that Nigeria needs to invest

300 billion dollars in infrastructure over the next 30 years in order to close its infrastructure

deficit.

A number of important reforms in infrastructure have been launched in recent years. A

strong domestic air transport sector has emerged with a handful of private carriers that have

attained regional significance. The ports sector is exploring pragmatic reforms in the transition

into landlord models and terminal concessions to attract private investment into the sector. The

power sector is undergoing a major restructuring that is paving the way for performance

improvements, including a move towards electricity tariffs that recover a larger share of

operating costs in the sector.

This progress notwithstanding, the inadequate physical infrastructure of the country is one

of the major constraints to sustained and broad-based economic growth. Addressing these

challenges will require a substantially larger annual level of investment in infrastructure, a

significant increase in annual allocations for routine and periodic maintenance to ensure reliable

infrastructure services, and increased attention to the institutional arrangements that support the

infrastructure network of the country and the related services. Nigeria’s Vision 2020 focus on

building a modern, efficient and effective infrastructure network to support sustained economic

growth. Therefore, if well managed, oil revenue could play a vital role in unwinding the

constraints to obtaining financial resources.

The current oil slump and the ensuing big blow to oil dependent countries’ budget and

reserves will inevitably create drastic adjustments. The Nigerian economy is facing major

challenges due to the collapse of the Oil price, resulting in declining reserves, and currency

0

5

10

15

20

25

0

20

40

60

80

100

120

2005 2006 2007 2008 2009 2010 2011 2012 2013

Nigeria oil price (U.S. dollar per barrel)

ECA/SWF balance (Billions U.S. dollars, RHS)

7

depreciation and volatility. The shortage of foreign currency has resulted in import restriction

and the government imposing a fixed exchange rate. This in turn has fueled the parallel market

rate, and inflation. The government has recently re-introduced a flexible exchange rate.

Basically, the fall in oil price can undermine recent progress in achieving macroeconomic

sustainability and increase the country’s dependence on external financing. So far, the current

external debt position of Nigeria is manageable. The external debt-to-GDP ratio in the last 10

years averaged 2.4 percent and is projected to decline from 2.8 percent in 2013 to 2.0 percent

in 2018 (IMF, 2014). The government of Nigeria, in a bid to cushion the impact of an oil price

drop, recently announced its plan to raise external loans worth 5.7 billion dollars from its

development partners to finance infrastructure projects contained in the 2015 budget.7

II. The Model

The model is a three-sector model of a small open economy with three types of public sector

debt—external concessional, external commercial and domestic debt—and various fiscal

instruments along with a resource fund. Public capital enters the production of traded and

nontraded goods and the cost of building up public capital increases with public investment

inefficiencies and absorptive capacity constraints. The natural resource production and prices

are assumed to be exogenous.

1. The Households

The economy features two types of households. A fraction 𝜔, optimizing households and

denoted by the superscript OPT have access to capital and financial markets while the remaining

fraction 1 − 𝜔, rule of thumb households and denoted by the superscript ROT are liquidity

constrained and consume all of their disposable income in each period. The presence of rule of

thumb households captures a relatively less developed financial market. Optimizing households

can acquire domestic government bonds and international bonds with portfolio adjustment

costs, which restrict the degree of capital account openness. On its foreign debt the private

sector pays a constant premium over the interest rate that the government pays on its external

debt.

Both types of households consume a consumption basket 𝑐𝑡𝑖, which is described a constant-

elasticity-of-substitution (CES) aggregate of traded goods 𝑐𝑇,𝑡𝑖 and nontraded goods 𝑐𝑁,𝑡

𝑖 . Thus,

the consumption basket is

𝑐𝑡𝑖 = [𝜑

1

𝜒(𝑐𝑁,𝑡𝑖 )

𝜒−1

𝜒 + (1 − 𝜑)1

𝜒(𝑐𝑇,𝑡𝑖 )

𝜒−1

𝜒 ]

𝜒

𝜒−1

, for i=OPT, ROT, (1)

where 𝜑 indicates the nontraded good bias and 𝜒 > 0 is the intra-temporal elasticity of

substitution.

The consumption basket is the numeraire of the economy, and 𝑝𝑁,𝑡 represents the relative

price of nontraded goods, and 𝑠𝑡 corresponds to the relative price of traded goods to the

consumption basket. Assuming that the law of one price holds for traded goods implies that 𝑠𝑡

also corresponds to the real exchange, defined as the price of one unit of foreign consumption

basket in units of domestic basket.

7The development partners, from whom the loan will be sourced are the World Bank, African Development Bank,

Islamic Development Bank and China Export-Import Bank.

8

Minimizing total consumption expenditures subject to the consumption basket yields the

following demand functions for each good:

𝑐𝑁,𝑡𝑖 = 𝜑𝑝𝑁,𝑡

−𝜒𝑐𝑡

𝑖, for i=OPT, ROT, (2)

and

𝑐𝑇,𝑡𝑖 = (1 − 𝜑)𝑠𝑡

−𝜒𝑐𝑡

𝑖, for i=OPT, ROT, (3)

The numeraire of the economy which is the unit price of the consumption basket is

1 = [𝜑𝑝𝑁,𝑡1−𝜒

+ (1 − 𝜑)𝑠𝑡1−𝜒

]1

1−𝜒. (4)

Both types of households provide labor service (𝐿𝑇,𝑡𝑖 and 𝐿𝑁,𝑡

𝑖 , i=OPT, ROT) to the

traded and nontraded good sectors, denoted by subscripts T and N, respectively. Total labor 𝐿𝑡𝑖

has the following CES specification to capture imperfect substitutability between the labor

amounts supplied to the two sectors:

𝐿𝑡𝑖 = [𝛿

−1

𝜌(𝐿𝑁,𝑡𝑖 )

1+𝜌

𝜌 + (1 − 𝛿)−

1

𝜌(𝐿𝑇,𝑡𝑖 )

1+𝜌

𝜌 ]

𝜌

1+𝜌

, for i=OPT, ROT, (5)

where 𝛿 is the steady-state share of labor in the nontraded good sector, and 𝜌 > 1 is the intra-

temporal elasticity of substitution. Let 𝑤𝑇,𝑡 and 𝑤𝑁,𝑡 be the real wage rates paid in each sector,

and 𝑤𝑡 be the real wage index. Maximizing the household’s total labor income

𝑤𝑡𝐿𝑡𝑖 = 𝑤𝑁,𝑡𝐿𝑁,𝑡

𝑖 + 𝑤𝑇,𝑡𝐿𝑇,𝑡𝑖 subject to aggregate labor (5) yields the following labor supply

schedules for each sector:

𝐿𝑁,𝑡𝑖 = 𝛿 (

𝑤𝑁,𝑡

𝑤𝑡)

𝜌

𝐿𝑡𝑖 , for i=OPT, ROT (6)

𝐿𝑇,𝑡𝑖 = (1 − 𝛿) (

𝑤𝑇,𝑡

𝑤𝑡)

𝜌

𝐿𝑡𝑖 , for i=OPT, ROT (7)

The real wage index is

𝑤𝑡 = [𝛿(𝑤𝑁,𝑡)1+𝜌

+ (1 − 𝛿)(𝑤𝑇,𝑡)1+𝜌

]

1

1+𝜌 (8)

A. Intertemporal optimizing households

A representative intertemporal optimizing household maximizes its utility

𝐸0 ∑ 𝛽𝑡∞𝑡=0 𝑈(𝑐𝑡

𝑂𝑃𝑇 , 𝐿𝑡𝑂𝑃𝑇 ) = 𝐸0 {∑ 𝛽𝑡∞

𝑡=0 [1

1−𝜎(𝑐𝑡

𝑂𝑃𝑇)1−𝜎 −𝜅𝑂𝑃𝑇

1+𝜓(𝐿𝑡

𝑂𝑃𝑇)1+𝜓]}, (9)

Subject to the following budget constraint:

(1 + 𝜏𝑡𝐶)𝑐𝑡

𝑂𝑃𝑇 + 𝑏𝑡𝑂𝑃𝑇 − 𝑠𝑡𝑏𝑡

𝑂𝑃𝑇∗ = (1 − 𝜏𝑡𝐿)𝑤𝑡𝐿𝑡 + 𝑅𝑡−1𝑏𝑡−1

𝑂𝑃𝑇 − 𝑅𝑡−1∗ 𝑠𝑡𝑏𝑡−1

𝑂𝑃𝑇∗

+Ω𝑁,𝑡 + Ω𝑇,𝑡 + 𝜗𝐾𝜏𝑡𝐾(𝑟𝑁,𝑡

𝐾 𝑘𝑁,𝑡−1 + 𝑟𝑇,𝑡𝐾 𝑘𝑇,𝑡−1) + 𝑠𝑡𝑟𝑒𝑚𝑡

∗ + 𝑧𝑡 − 𝜇𝑘𝐺,𝑡−1 − Θ𝑡𝑂𝑃𝑇∗ (10)

𝐸0 is the expectation operator at time 0; 𝛽 ≡ [(1 + 𝜚)]−1 is the subjective discount factor; and

𝜚 is the pure rate of time preference. 𝜎 is the inverse of inter-temporal elasticity of substitution

of labor supply. 𝜅𝑂𝑃𝑇is the disutility weight of labor and 𝜏𝑡𝐶 and 𝜏𝑡

𝐿are the tax rates on

consumption and labor income, respectively. The intertemporal optimizing households have

access to government bonds 𝑏𝑡𝑂𝑃𝑇 that pay a gross real interest rate 𝑅𝑡. They can also borrow

from abroad 𝑏𝑡𝑂𝑃𝑇∗, by paying an interest rate 𝑅𝑡

∗. They also receive profits Ω𝑁,𝑡, Ω𝑇,𝑡 from firms

that are in the traded in the nontraded good sector. The term 𝜗𝐾𝜏𝑡𝐾(𝑟𝑁,𝑡

𝐾 𝑘𝑁,𝑡−1 + 𝑟𝑇,𝑡𝐾 𝑘𝑇,𝑡−1) is

a tax rebate that the optimizing households receive on the tax levied on the firms’ return on

9

capital.8 𝑟𝑒𝑚𝑡∗ denotes remittances from abroad and 𝑧𝑡 corresponds to government transfers. 𝜇

is the user fees charged for public capital 𝑘𝐺,𝑡 services, and Θ𝑡𝑂𝑃𝑇∗ =

𝜂

2(𝑏𝑡

𝑂𝑃𝑇∗ − 𝑏𝑂𝑃𝑇∗)2 are

portfolio adjustment costs associated to foreign liabilities,9 where 𝜂 controls the degree of

capital account openness and 𝑏𝑂𝑃𝑇∗is the steady-state value of such variable.

Let 𝜆𝑡be the Lagrange multiplier to the budget constraint (10). The first-order conditions

with respect to 𝑐𝑡𝑂𝑃𝑇, 𝐿𝑡

𝑂𝑃𝑇, 𝑏𝑡𝑂𝑃𝑇, and 𝑏𝑡

𝑂𝑃𝑇∗are

𝜆𝑡(1 + 𝜏𝑡𝐶) = (𝑐𝑡

𝑂𝑃𝑇)−𝜎, (11)

𝜅𝑂𝑃𝑇(𝐿𝑡𝑂𝑃𝑇)𝜓 = 𝜆𝑡(1 − 𝜏𝑡

𝐿)𝑤𝑡, (12)

𝜆𝑡 = 𝛽𝐸𝑡(𝜆𝑡+1𝑅𝑡), (13)

and

𝜆𝑡 = 𝛽𝐸𝑡 (𝜆𝑡+1𝑠𝑡+1𝑅𝑡

∗

𝑠𝑡−𝜂(𝑏𝑡𝑂𝑃𝑇∗−𝑏𝑂𝑃𝑇∗)

). (14)

Combining (13) and (14) gives the private demand for foreign debt which can be explicitly

defined as: 𝑅𝑡

𝑅𝑡∗ =

𝑠𝑡+1

𝑠𝑡−𝜂(𝑏𝑡𝑂𝑃𝑇∗−𝑏𝑂𝑃𝑇∗)

. This equation is also known as the uncovered interest rate

parity equation.

B. Rule-of-thumb Households

Rule-of-thumb households have the same utility function as that of intertemporal optimizing

households, so

𝑈(𝑐𝑡𝑅𝑂𝑇 , 𝐿𝑡

𝑅𝑂𝑇 ) =1

1−𝜎(𝑐𝑡

𝑅𝑂𝑇)1−𝜎 −𝜅𝑅𝑂𝑇

1+𝜓(𝐿𝑡

𝑅𝑂𝑇)1+𝜓 (15)

Their consumption is determined by the budget constraint

(1 + 𝜏𝑡𝐶)𝑐𝑡

𝑅𝑂𝑇 = (1 − 𝜏𝑡𝐿)𝑤𝑡𝐿𝑡

𝑅𝑂𝑇 + 𝑠𝑡𝑟𝑒𝑚𝑡∗ + 𝑧𝑡 − 𝜇𝑘𝐺,𝑡−1 (16)

while static maximization of the utility function gives the following labor supply function:

𝐿𝑡𝑅𝑂𝑇 = [

1

𝜅𝑅𝑂𝑇

1−𝜏𝑡𝐿

1+𝜏𝑡𝐶 (𝑐𝑡

𝑅𝑂𝑇)−𝜎𝑤𝑡]

1

𝜓 (17)

C. Aggregation

Consumption, labor, privately-owned government bonds, and net foreign liabilities are

aggregated over the two type of households as follows.

𝑐𝑡 = 𝜔𝑐𝑡𝑂𝑃𝑇 + (1 − 𝜔)𝑐𝑡

𝑅𝑂𝑇, (18)

𝐿𝑡 = 𝜔𝐿𝑡𝑂𝑃𝑇 + (1 − 𝜔)𝐿𝑡

𝑅𝑂𝑇, (19)

8 This tax rebate reflects the fact that there is a wedge between the tax burden imposed and tax revenues

that accrue to the government in developing countries. Therefore, the fraction 𝜗𝐾 of the tax revenue

related to capital income does not enter the government budget constraint. 9 These adjustment costs also ensure stationarity in small open economy model, as discussed in Schmitt-

Grohe and Uribe (2003)

10

and

𝑏𝑡 = 𝜔𝑏𝑡𝑂𝑃𝑇; 𝑏𝑡

∗ = 𝜔𝑏𝑡𝑂𝑃𝑇∗ (20)

2. Firms

The model has three production sectors: oil production, a nontraded good sector, and non-

oil traded good sector. Since the oil sector employs a small and stable fraction of the labor force

and a large part of investment in the oil sector is financed by foreign investment, the oil

production is assumed to be an exogenous process described by the following equation:

�̃�𝑂,𝑡

�̃�𝑂= (

�̃�𝑂,𝑡−1

�̃�𝑂)

𝜌𝑦𝑜

exp (휀𝑡𝑦𝑜

) (21)

where 𝜌𝑦𝑜 ∈ (0, 1) is an auto-regressive coefficient and 휀𝑡𝑦𝑜

~𝑖. 𝑖. 𝑑 𝑁(0, 𝜎𝑦𝑜2 ) is the resource

production shock. It is assumed that resource production is small relative to world production;

hence, the international commodity price (relative to the foreign consumption basket), 𝑃𝑂,𝑡∗ , is

taken as given and evolves as follows.

𝑃𝑂,𝑡

∗

𝑃𝑂∗ = (

𝑃𝑂,𝑡−1∗

𝑃𝑂∗ )

𝜌𝑝𝑜

exp (휀𝑡𝑝𝑜) (22)

where 𝜌𝑝𝑜 ∈ (0, 1] is an auto-regressive coefficient and 휀𝑡𝑝𝑜~𝑖. 𝑖. 𝑑 𝑁(0, 𝜎𝑝𝑜

2 ) is the oil price

shock. Resource GDP in units of the domestic consumption basket corresponds to

𝑦𝑂,𝑡 = 𝑠𝑡𝑃𝑂,𝑡∗ �̃�𝑂,𝑡 (23)

Firms in both nontraded and non-oil traded sectors produce according to a Cobb-Douglas

production function using labor, private capital and public capital. A representative firm in the

nontraded sector produces according to:

𝑦𝑁,𝑡 = 𝑧𝑁(𝑘𝑁,𝑡−1)1−𝛼𝑁

(𝐿𝑁,𝑡)𝛼𝑁

(𝑘𝐺,𝑡−1)𝛼𝐺

(24)

where 𝑧𝑁 is total factor productivity, 𝑘𝑁,𝑡 is end-of-period private capital, 𝑘𝐺,𝑡 is the end-of-

period public capital, 𝛼𝑁 is the labor share of sectoral income, and 𝛼𝐺 is the output elasticity

respect to public capital.

Analogously to the nontraded good sector, firms in the traded good sector produce traded

output with the following technology

𝑦𝑇,𝑡 = 𝑧𝑇,𝑡(𝑘𝑇,𝑡−1)1−𝛼𝑇

(𝐿𝑇,𝑡)𝛼𝑇

(𝑘𝐺,𝑡−1)𝛼𝐺

(25)

Therefore, total real GDP can be defined as

𝑦𝑡 = 𝑝𝑁,𝑡𝑦𝑁,𝑡 + 𝑝𝑇,𝑡𝑦𝑇,𝑡 + 𝑦𝑂,𝑡 (26)

To capture the common Dutch disease effects associated with spending resource revenues, the

total factor productivity in the tradable sector, 𝑧𝑇,𝑡, is subject to learning-by-doing externalities

similar to Berg et al, (2013):

𝑧𝑇,𝑡

𝑧𝑇= (

𝑧𝑇,𝑡−1

𝑧𝑇)

𝜌𝑧𝑇

(𝑦𝑇,𝑡−1

𝑦𝑇)

𝜌𝑦𝑇

, (27)

where 𝜌𝑧𝑇, 𝜌𝑦𝑇 ∈ [0, 1] control the severity of Dutch disease.

11

3. The government

The fiscal block of the model includes the budget and the oil fund. Government expenditure

(consumption and investment) is an aggregate of traded and nontraded goods. To finance its

expenditures government uses revenues from taxes on the oil and non-oil sectors, interest

income from accumulated oil savings, as well as domestic and foreign borrowing. The latter is

subject to a risk premium depending on the deviation of total external public debt to GDP ratio

from a steady state level. Every period the budget surplus (excess oil revenues) is saved in the

oil fund. If there is a deficit, it is absorbed by a withdrawal from the oil fund, unless the balance

of the oil fund falls below a pre-specified level. When the oil fund lower bound constraint binds,

fiscal policy has to react to cover the gap either through external borrowing, tax adjustments or

adjustments in government expenditures.

The government flow budget constraint is given by

𝜏𝑡𝑐𝑐𝑡 + 𝜏𝑡

𝐿𝑤𝑡𝐿𝑡 + (1 − 𝜗𝑘)𝜏𝑘(𝑟𝑇,𝑡𝑘 𝑘𝑇,𝑡−1 + 𝑟𝑁,𝑡

𝑘 𝑘𝑁,𝑡−1)

+𝑠𝑡𝑔𝑟𝑡∗ + 𝜇𝑘𝐺,𝑡−1 + 𝑏𝑡 + 𝑠𝑡𝑑𝑡 + 𝑠𝑡𝑑𝑐,𝑡 + 𝑡𝑂,𝑡 + 𝑠𝑡𝑅𝑅𝐹𝑓𝑡−1

∗

= 𝑃𝑡𝐺(𝑔𝑡

𝑐 + 𝑔𝑡𝐼) + 𝑧𝑡 + 𝑅𝑡−1𝑏𝑡−1 + 𝑠𝑡𝑅𝑑𝑑𝑡−1 + 𝑠𝑡𝑅𝑑𝑐,𝑡−1𝑑𝑐,𝑡−1 + 𝑠𝑡𝑓𝑡−1

∗ (28)

where besides the tax revenues from consumption, 𝜏𝑡𝑐𝑐𝑡, labor income, 𝜏𝑡

𝐿𝑤𝑡𝐿𝑡 and capital

income, (1 − 𝜗𝑘)𝜏𝑘(𝑟𝑇,𝑡𝑘 𝑘𝑇,𝑡−1 + 𝑟𝑁,𝑡

𝑘 𝑘𝑁,𝑡−1), the government also receives international

grants, 𝑔𝑟𝑡∗, user fees, 𝜇𝑘𝐺,𝑡−1, oil-related royalties, 𝑡𝑂,𝑡, and gross interests income on resource

fund, 𝑠𝑡𝑅𝑅𝐹𝑓𝑡−1∗ . The user fee charged on public capital recoups a fraction f of recurrent costs as

in Buffie et al. (2012): 𝜇 = 𝑓𝑃𝑡𝐺𝛿𝐺 . International grants follows an exogenous process as

follows:

𝑔𝑟𝑡∗

𝑔𝑟∗ = (𝑔𝑟𝑡−1

∗

𝑔𝑟∗ )𝜌𝑔𝑟

exp (휀𝑡𝑔𝑟

) (29)

where 𝜌𝑜 ∈ (0, 1] is an auto-regressive coefficient and 휀𝑡𝑖𝑜~𝑖. 𝑖. 𝑑 𝑁(0, 𝜎𝑜

2) is the shock.

The resource revenues collected each period, on the other hand, correspond to

𝑡𝑂,𝑡 = 𝑠𝑡(𝜏𝑂𝑃𝑂,𝑡∗ �̃�𝑂,𝑡 + 𝑑𝑖𝑣 ∗ Ω𝑡

∗), (30)

where Ω𝑡∗ = (1 − 𝑣𝑎𝑟𝑐𝑜 − 𝜏𝑂)𝑃𝑂,𝑡

∗ �̃�𝑂,𝑡 − 𝑓𝑐𝑜 ∗ 𝑦, is the profit in the oil sector, and 𝑑𝑖𝑣 is the

fraction of that profit that accrues to the government; 𝑣𝑎𝑟𝑐𝑜 is a cost coefficient in the oil sector

as a percent of the resource output; 𝑓𝑐𝑜 is a fixed cost on the production of oil in percent of

GDP and 𝜏𝑂 is a constant royalty rate.

The government has three debt instruments: external concessional debt, 𝑑𝑡, external

commercial debt, 𝑑𝑐,𝑡, and domestic debt, 𝑏𝑡. Concessional loans extended by official creditors

are taken as exogenous in the model and charge a constant (gross) real interest rate 𝑅𝑑.

A. Government expenditure

Government spending comprises government consumption (𝑔𝑡𝑐) and public investment (𝑔𝑡

𝐼).

Like private consumption, government expenditure, 𝑔𝑡 = 𝑔𝑡𝑐 + 𝑔𝑡

𝐼, is also a CES aggregate of

domestic traded goods, 𝑔𝑇,𝑡 and domestic nontraded goods, 𝑔𝑁,𝑡. Thus,

𝑔𝑡 = [𝜈

1

𝜒 (𝑔𝑁,𝑡)𝜒−1

𝜒 + (1 − 𝜈 )1

𝜒(𝑔𝑇,𝑡)𝜒−1

𝜒 ]

𝜒

𝜒−1

(31)

where 𝜈 is the weight given to nontraded goods in government purchases. It is assumed that

the government purchases have the same intra-temporal elasticity of substitution 𝜒 > 0 as that

of private consumption.

12

Minimizing total government expenditures, 𝑃𝑡𝐺𝑔𝑡 = 𝑃𝑁,𝑡𝑔𝑁,𝑡 + 𝑃𝑇,𝑡𝑔𝑇,𝑡, subject to the

government consumption basket, yields the following public demand functions for each good:

𝑔𝑁,𝑡 = 𝜈 (𝑃𝑁,𝑡

𝑃𝑡𝐺 )

−𝜒𝑔𝑡 (32)

𝑔𝑇,𝑡 = (1 − 𝜈 ) (𝑃𝑇,𝑡

𝑃𝑡𝐺 )

−𝜒𝑔𝑡 (33)

where 𝑃𝑡𝐺 is the government consumption price index in terms of units of the consumption

basket, defined as

𝑃𝑡𝐺 = [𝜈 (𝑃𝑁,𝑡)

𝜒−1+ (1 − 𝜈 )(𝑠𝑡)𝜒−1]

1

𝜒−1 (34)

𝜈𝑡 is time-varying. Since we focus on the effects of additional government spending in the form

of government investment, the weight given to nontraded goods for the additional government

spending, 𝜈𝑔, can differ from its steady state value,𝜈, i.e.,

𝜈𝑡 = 𝜈 +(𝑃𝑡

𝐺𝑔𝑡−𝑃𝐺𝑔)

𝑃𝑡𝐺𝑔𝑡

(𝜈𝑔 − 𝜈), (35)

To capture the common structural problems of public investment in developing countries, the

model features absorptive capacity constraints and investment inefficiency in the public sector.

To reflect this, it is assumed that effective investment �̃�𝑡𝐼(�̅�𝑡

𝐼) is a function of investment growth

rate (�̅�𝑡𝐼) relative to its steady state value and �̅�𝑡

𝐼 =𝑔𝑡

𝐼

𝑔𝐼 − 1. Specifically:

�̃�𝑡𝐼 = {

𝜖�̅�𝑡𝐼 , if �̅�𝑡

𝐺𝐼 ≤ �̅�𝐺𝐼

𝜖(̅1 + �̅�𝐺𝐼)𝑔𝐼 + 𝜖(�̅�𝑡𝐺𝐼)[1 + �̅�𝑡

𝐺𝐼 − �̅�𝐺𝐼]𝑔𝐼, if �̅�𝑡𝐺𝐼 > �̅�𝐺𝐼}, (36)

Where 𝜖̅ ∈ [0,1] represents the steady state efficiency and 𝜖(�̅�𝑡𝐺𝐼) governs the efficiency of the

portion of public investment exceeding a threshold �̅�𝐺𝐼 , in percent deviation from the initial

steady state. It is assumed that 𝜖(�̅�𝑡𝐺𝐼) takes the following specification:

𝜖(�̅�𝑡𝐺𝐼) = exp [−𝜍𝜖(�̅�𝑡

𝐺𝐼 − �̅�𝐺𝐼)] 𝜖 ̅ (37)

In other words, if the growth rate of government investment expenditure from the initial steady

state exceeds �̅�𝐺𝐼, then the efficiency of the additional investment decreases, reflecting the

presence of absorptive capacity constraints. The severity of these constraints is governed by the

parameter 𝜍𝜖 ∈ [0, ∞).

The law of motion of public capital is described as

𝑘𝐺,𝑡 = (1 − 𝛿𝐺)𝑘𝐺,𝑡−1 + �̃�𝑡𝐼 (38)

where 𝛿𝐺 is the constant depreciation rate of public capital

B. The Resource Fund (Nigerian Sovereign Wealth Fund)

A resource windfall is defined as resource revenues that are above their initial steady-state

level, i.e., 𝑡𝑂,𝑡 − 𝑡𝑂. Let 𝑓𝑡−1∗ be the foreign financial asset value in a resource fund. Each period,

the resource fund earns interest income 𝑠𝑡(𝑅𝑅𝐹 − 1)𝑓𝑡−1∗ , with a constant gross real interest rate

𝑅𝑅𝐹. The resource fund evolves by the process

𝑓𝑡∗ − 𝑓∗ = 𝑀𝑎𝑥 {𝑓floor − 𝑓∗, (𝑓𝑡−1

∗ − 𝑓∗) +

𝑓𝑖𝑛,𝑡

𝑠𝑡−

𝑓𝑜𝑢𝑡,𝑡

𝑠𝑡} (39)

where 𝑓𝑖n,𝑡 represents the total fiscal inflow, 𝑓𝑜𝑢𝑡,𝑡 represents the total fiscal outflow,

𝑓floor = 0.024 is a lower bound for the fund that the government chooses to maintain. Every

13

period, if the fiscal inflow exceeds the fiscal outflow, the value of the resource fund increases.10

Instead, if the resource fund is above 𝑓floor, any fiscal inflow that falls short of the fiscal outflow

is absorbed by drawing down the fund to support government spending . Thus, if the fund does

not have sufficient asset to be drawn down to cover the difference between the fiscal inflow and

outflow (i.e., when (𝑓𝑡−1∗ − 𝑓∗) +

𝑓𝑖𝑛,𝑡

𝑠𝑡−

𝑓𝑜𝑢𝑡,𝑡

𝑠𝑡< 0), the fiscal gap is covered via borrowing

and/or increases in taxes (on consumption and factor incomes) or cuts in government non-

capital expenditures (government consumption and transfers). Later we explicitly define 𝑓𝑖n,t

and 𝑓out,t and explain in detail the mechanism to close a fiscal gap.

One of the purposes of the model is to analyze the effects of investing a resource windfall.

A scaling-up path of public investment is specified as a second-order delay function, 𝑔𝑡

𝐼

𝑔𝐼= 1 + [1 + exp(−𝑘1𝑡) − 2 exp(−𝑘2𝑡)]𝑔𝑛𝑠𝑠

𝐼 (40)

where 𝑔𝑛𝑠𝑠𝐼 is the scaling-up investment target expressed as percentage deviation from the initial

steady state, 𝑘1> 0 represents the speed of adjustment of public investment to the new level,

and 𝑘1 ≥ 𝑘2 represents the degree of investment frontloading. In particular, if 𝑘1 = 𝑘2 = 0,

public investment stays at its original steady-state level, i.e., 𝑔𝑡𝐼 = 𝑔𝐼 , ∀ 𝑡 . If instead 𝑘1 → ∞,

public investment jumps to the new steady-state level immediately. Lastly, if 𝑘2 = 𝑘1, public

investment increases gradually and is not frontloaded. The mechanics of this functional form

are illustrated in figure 5 and 6 below.

Figure 3: Mechanics of Eq. 40: Different speeds of investment scaling-ups

Figure 4: Mechanics of Eq. 40: Different degrees of frontloading in investment scaling-ups

10 To avoid an explosive process for the resource fund in the long run, an autoregressive coeffcient 𝜌𝑓 ∈ (0,1) is

attached to (𝑓𝑡−1∗ − 𝑓∗). The model is typically solved at a yearly frequency for a 1000-period horizon. The

coefficient 𝜌𝑓 is activated after the first 100 years of simulations.

0 5 10 15 20 25 30 35 400

5

10

15

20

25

30Public Investment (%Dev. from SS)

k1=k2=0.16

k1=k2=0.20

k1=k2=0.25

k1=k2=0.30

14

C. The Fiscal Gap

The fiscal gap is obtained after a proper algebraic rearrangement of the flow budget

constraint of the government. Given the exogenous paths of public investment, grants and

external concessional borrowing, the budget constraints can be rewritten as follows:

𝑔𝑎𝑝𝑡

= 𝑓𝑜𝑢𝑡,𝑡

− 𝑓𝑖𝑛,𝑡

+ 𝑠𝑡(𝑓𝑡∗ − 𝑓

𝑡−1∗ ) (41)

where

𝑔𝑎𝑝𝑡 = ∆𝑏𝑡 + 𝑠𝑡∆𝑑𝑐,𝑡 + (𝜏𝑡𝐶 − 𝜏𝐶)𝑐𝑡 + (𝜏𝑡

𝐿 − 𝜏𝐿)𝑤𝑡𝐿𝑡 − 𝑃𝑡𝐺(𝑔𝑡

𝐶 − 𝑔𝐶) − (𝑧𝑡 − 𝑧) (42)

𝑓𝑖𝑛,𝑡 = 𝜏𝑡𝑐𝑐𝑡 + 𝜏𝑡

𝐿𝑤𝑡𝐿𝑡 + (1 − 𝜗𝑘)𝜏𝑘(𝑟𝑇,𝑡𝑘 𝑘𝑇,𝑡−1 + 𝑟𝑁,𝑡

𝑘 𝑘𝑁,𝑡−1)

+𝑠𝑡𝑔𝑟𝑡∗ + 𝑠𝑡𝑎𝑖𝑑𝑡

∗ + 𝜇𝑘𝐺,𝑡−1 + 𝑠𝑡∆𝑑𝑡 + 𝑡𝑂,𝑡 + 𝑠𝑡(𝑅𝑅𝐹 − 1)𝑓𝑡−1∗ (43)

and

𝑓𝑜𝑢𝑡,𝑡 = 𝑃𝑡𝐺𝑔𝑡

𝐼 + 𝑃𝑡𝐺𝑔𝐼 + 𝑧 + (𝑠𝑡𝑅𝑑 − 1)𝑑𝑡−1 + (𝑅𝑑𝑐,𝑡−1 − 1)𝑠𝑡𝑑𝑐,𝑡−1 + (𝑅𝑡−1 − 1)𝑏𝑡−1 (44)

Relation (41) simply says that covering the fiscal gap requires two debt instruments—domestic

and external commercial borrowing—and adjustment of fiscal instruments both on the revenue

(taxes) and spending (public consumption and transfers) sides. We can see that if 𝑓∗ > 𝑓floor,

then 𝑓𝑡∗ − 𝑓∗ = (𝑓𝑡−1

∗ − 𝑓∗) +

𝑓𝑖𝑛,𝑡

𝑠𝑡−

𝑓𝑜𝑢𝑡,𝑡

𝑠𝑡, which implies that 𝑔𝑎𝑝𝑡 = 0, i.e. the oil fund absorbs

the fiscal gap and no fiscal adjustments are required. When 𝑓∗ = 𝑓floor, the fiscal gap satisfies

𝑔𝑎𝑝𝑡 > 0 and it needs to be covered by fiscal adjustments.

D. Covering the Fiscal Gap

The simple rule below is specified in order to split the borrowing schemes between cases

where part of the fiscal gap can be filled with either external commercial loans or domestic

loans, but not with both at the same time.

𝜄∆𝑏𝑡 = (1 − 𝜄)𝑠𝑡∆𝑑𝑐,𝑡 (45)

where 𝜄 ∈ [0,1]. Given concessional borrowing and grants, this rule accommodates the limiting

cases of (i) supplementing this concessional borrowing with borrowing exclusively in domestic

markets (𝜄 = 0) and (ii) supplementing concessional borrowing with accumulating more external

commercial debt (𝜄 = 1).

Debt sustainability, however, requires that eventually revenues have to increase and/or

expenditures have to be cut in order to cover the entire gap. To calculate the debt stabilizing

0 5 10 15 20 25 30 35 400

10

20

30

40

50Public Investment (%Dev. from SS)

k1=0.08, k2=0.16

k1=0.08, k2=0.24

k1=0.08, k2=0.34

k1=0.08, k2=0.50

15

(target) values of (i) the consumption tax rate, (ii) the labor income tax rate, (iii) government

consumption, and (iv) transfers, the following equations are used:

𝜏target,𝑡𝐶 = 𝜏𝐶 + 𝜆1

𝑔𝑎𝑝𝑡

𝑐𝑡 (46)

𝜏target,𝑡𝐿 = 𝜏𝐿 + 𝜆2

𝑔𝑎𝑝𝑡

𝑤𝑡𝐿𝑡 (47)

𝑔target,𝑡𝐶 = 𝑔 + 𝜆3

𝑔𝑎𝑝𝑡

𝑃𝑡𝐺 (48)

𝑧target,𝑡 = 𝑧 + 𝜆4𝑔𝑎𝑝𝑡 (49)

where 𝜆𝑖, i=1,…,3 divide the fiscal burden across the different fiscal instruments, satisfying

∑ 𝜆𝑖4𝑖=1 = 1. Tax rates and expenditure items are then determined according to the policy

reaction functions.

𝜏𝑡𝐶 = min{𝜏rule,𝑡

𝐶 , 𝜏ceiling𝐶 } (50)

𝜏𝑡𝐿 = min{𝜏rule,𝑡

𝐿 , 𝜏ceiling𝐿 } (51)

𝑔𝑡𝐶

𝑔𝐶 = max {𝑔𝑟ule,𝑡

𝐶

𝑔𝐶 , 𝑔floor𝐶 } (52)

𝑧𝑡 = max {𝑧rule,𝑡

𝑧, 𝑧floor} (53)

where 𝜏ceiling𝐶 and 𝜏ceiling

𝐿 are the maximum levels of the tax rates that can be implemented, and

𝑔floor𝐶 and 𝑧floor are minimum deviations of government consumption and transfer from their

initial steady-state values. All these ceilings and floors are determined exogenously and reflect

policy adjustment constraints that governments may face. In turn, 𝜏rule,𝑡𝐶 , 𝜏rule,𝑡

𝐿 , 𝑔𝑟ule,𝑡𝐶 and 𝑧rule,𝑡

are determined by the following fiscal rules :

𝜏rule,𝑡𝐶 = 𝜏𝑡−1

𝐶 + 𝜍1(𝜏target,𝑡𝐶 − 𝜏𝑡−1

𝐶 ) + 𝜍2(𝑥𝑡−1 − 𝑥), 𝜍1, 𝜍1 > 0 (54)

𝜏rule,𝑡𝐿 = 𝜏𝑡−1

𝐿 + 𝜍3(𝜏target,𝑡𝐿 − 𝜏𝑡−1

𝐿 ) + 𝜍4(𝑥𝑡−1 − 𝑥), 𝜍3,𝜍4 > 0 (55)

𝑔𝑟ule,𝑡𝐶

𝑔𝐶 =𝑔𝑡−1

𝐶

𝑔𝐶 − 𝜍5 (𝑔𝑡arget,𝑡

𝐶

𝑔𝐶 −𝑔𝑡−1

𝐶

𝑔𝐶 ) + 𝜍6(𝑥𝑡−1 − 𝑥), 𝜍5,𝜍6 > 0 (56)

𝑧rule,𝑡

𝑧=

𝑧𝑡−1

𝑧− 𝜍7 (

𝑧target,𝑡

𝑧−

𝑧𝑡−1

𝑧) + 𝜍8(𝑥𝑡−1 − 𝑥), 𝜍7,𝜍8 > 0 (57)

where 𝑥𝑡 =𝑏𝑡+𝑑𝑐,𝑡

𝑦𝑡 is the sum of domestic and external commercial debt as share of GDP; 𝜍1, 𝜍3,

𝜍5, 𝜍7 are fiscal reaction parameters in fiscal instruments terms; and 𝜍2, 𝜍4, 𝜍6, 𝜍8 are fiscal

reaction parameters in debt instruments terms.

4. Accounting Identities and Market Clearing Conditions

To close the model, the goods market clearing condition and the balance of payment

conditions are imposed. The market clearing condition for nontraded goods is

𝑦𝑁,𝑡 = 𝜑𝑃𝑁,𝑡−𝜒

(𝑐𝑡 + 𝑖𝑁,𝑡 + 𝑖𝑇,𝑡) + 𝜈𝑡 (𝑃𝑁,𝑡

𝑃𝑡𝐺 )

−𝜒𝑔𝑡, (58)

The balance of payment condition corresponds to

𝑐𝑎𝑡

𝑑

𝑠𝑡= 𝑔𝑟𝑡

∗ − Δ𝑓𝑡∗+ Δ𝑑𝑡 + Δ𝑑𝑐,𝑡 + Δ𝑏𝑡

∗, (59)

Where 𝑐𝑎𝑡𝑑is the current account deficit.

16

𝑐𝑎𝑡𝑑 = 𝑐𝑡 + 𝑖𝑁,𝑡 + 𝑖𝑇,𝑡 + 𝑃𝑡

𝐺𝑔𝑡 +𝜍

2(𝑏𝑡

𝑂𝑃𝑇∗ − 𝑏𝑂𝑃𝑇∗)2 − 𝑦𝑡 − 𝑠𝑡𝑟𝑒𝑚𝑡∗ + (𝑅𝑑 − 1)𝑠𝑡𝑑𝑡−1

+(𝑅𝑑𝑐,𝑡 − 1)𝑠𝑡𝑑𝑐,𝑡−1 + (𝑅𝑡 − 1)𝑠𝑡𝑏𝑡−1∗ − (𝑅𝑅𝐹 − 1)𝑠𝑡𝑓𝑡−1

∗ , (60)

Finally, it is assumed that the private sector pays a constant premium u over the interest

rate that the government pays on external commercial debt 𝑅𝑑𝑐,𝑡 such that

𝑅𝑡∗ = 𝑅𝑑𝑐,𝑡 + 𝑢. (63)

I. Calibration to Nigeria

The model’s parameters are calibrated using data specific to Nigeria where available and

values common in the literature for comparable studies where not. To calibrate the model’s

initial steady state, in most cases we use medium term averages of the relevant variables

including cost shares, sector share in GDP, consumption shares, trade shares, and debt and asset

stocks. Other parameters include tax rates, depreciation rates and the return on infrastructure.

Once values are set for these parameters, all other parameters and variables are pinned down

through budget constraints, the first-order conditions associated with the solution to the private

agents’ optimization problems, and various adding-up constraints. Appendix 1 summarizes the

calibration, while the rationale for the parameters’ choice is discussed next.

The calibration starts with national accounting. In order, to match as much as possible, the

Nigerian averages in WEO, WDI, IFS and national sources for the last decade are used. The

share of imports in GDP is 31 percent of GDP and a share of exports of 43 percent of GDP,

which implies a trade balance of 12 percent of GDP in 2013. The share of total government

expenditure is 26 percent of which 17 percent represents government consumption and 9

percent represents public investment. Consistent with the trade surplus, the share of traded

goods is set at 50 percent in private consumption and 40 percent in government purchases.

Nigeria is at an advanced stage of oil resource exploitation; the country is reported to have

proven reserves of about 37.2 billion barrels at end 2013 (see BP Statistical Review of World

Energy, June 2014). The share of the oil sector in GDP represents 40 percent at the initial steady

state.

On the foreign asset side, Nigeria’s SWF commenced operations in 2012 and was set up by

the Nigeria Sovereign Investment Authority Act, which was signed in 2011. It is intended to

invest the savings gained on the difference between the budgeted and actual market prices for

oil to earn returns that would benefit future generations of Nigerians. The ECA/SWF represents

5.6 percent of GDP in 2012 and 2.4 percent of GDP in 2013 (IMF, 2014). Therefore, in the

initial steady state, we set the government saving from oil resource to 2.4 percent

(𝑅𝐹share =0.024). On the liabilities side, government domestic debt, concessional debt,

external commercial debt at end-2013, and grants in percent of GDP are 16.2 percent, 2.5

percent, 0.3 percent and 0 percent, according to the Nigerian Debt Management Office

(DMO)’s estimates.

Interest rates. The subjective discount rate 𝜚 is pinned down by setting the real annual interest

rate on domestic debt (𝑅 − 1) at 10 percent. Consistent with stylized facts, domestic debt is

assumed to be more expensive than external commercial debt. We fix the real annual risk-free

interest rate (𝑅𝑓 − 1) at 4 percent in line with average historical return on US T-bill rates.

The premium parameter 𝜐𝑑𝑐 is chosen such that the real interest rate on external commercial

debt (𝑅𝑑𝑐−1) is 6 percent, and the real interest rate paid on concessional loans (𝑅𝑑 − 1) is 0 as

in joint IMF-World Bank debt sustainability analysis. It is assumed a debt-elastic interest rate

similar to Schmitt-Grohe and Uribe, (2003) for the purpose of generating stationary model

17

dynamics, implying that 𝜂𝑑𝑐 = 0 in (61).11 The risk premium paid by the private sector over

the interest rate that the government pays on external commercial debt,𝑢, is chosen to be 4

percent in order to have 𝑅 = 𝑅∗ at the steady state, which is required by (13) and (14). Finally,

Based on the average real return of the Norwegian Government Pension Fund from 1997 to

2011 (Gros and Mayer (2012)), the annual real return on international financial assets in the

resource fund (𝑅𝑅𝐹 − 1) is set at 2.7 percent.

Private production. The parameters for the labor income shares in value added in the traded

and non-traded sectors correspond to 𝛼𝑁 = 0.52 and 𝛼𝑇 = 0.58 based on the social accounting

matrix for the Nigerian economy constructed by Nwafor et al. (2011). In both sectors private

capital depreciates at an annual rate of 10 percent (𝛿𝑁 = 𝛿𝑇 = 0.10). Following Berg et al.

(2013), we assume a minor degree of learning-by-doing externality in the traded good sector

(𝜌𝑦𝑇 = 𝜌𝑧𝑇 = 0.10).12 Also as in Berg et al. (2010), investment adjustment costs are set to 𝜅𝑁 =

𝜅𝑇 =25.

Households preference. The coefficient of risk aversion 𝜎 = 2.94 implies an inter-temporal

elasticity of substitution of 0.34, which is the average LICs estimate according to Ogaki et al.

(1996). We assume a low Frisch labor elasticity of 0.10 (𝜌 = 10), similar to the estimate of

wage elasticity of working in rural Malawi (Goldberg, 2011). The labor mobility parameter 𝜍

is set to 1 (Horvarth, 2000), and the elasticity of substitution between traded and nontraded

goods is 𝜒 = 0.44, following Stockman and Tesar (1995). To capture limited access to

international capital markets, we set 𝜂 = 1 as in Buffie et al. (2012). Also, the low degree of

financial development implies that a large proportion of households in Nigeria do not have

access to formal financial institutions. Therefore, we pick 𝜔 = 0.4, implying that 60 percent of

households in Nigeria are rule-of-thumb.

Mining. Resource production shocks are assumed to be rather persistent, so we set 𝜌𝑦𝑜 = 0.90.

This parameter is not relevant when a defined exogenous path for resource production is

assumed as we do in the simulations below. Given that Hamilton (2009) finds that oil prices

follow a random walk with drift, we set 𝜌𝑝𝑜 = 1. Finally the royalty tax rate, 𝜏𝑜, is set such that

the ratio of natural resource revenue to total revenue at the initial steady state represents 60

percent of total revenues as suggested by the data (IMF, 2014). To hit this ratio, we set 𝜏𝑜 =0.95 accordingly.

Tax rates. The steady-state taxes on consumption, and capital are 𝜏𝐶 = 0.18, and 𝜏𝐾 = 0.35,

respectively. To capture the fact that labor income taxes is not common in LICs, we set the

labor income tax rate ate 𝜏𝐿 = 0.05. This combination of tax rates and the implied inefficiency

in revenue mobilization imply a non-resource revenue of slightly above 20 percent of GDP at

the initial steady state, which is broadly consistent with the Nigerian data.

Fiscal rules. We impose a non-negativity constraint for the stabilization fund by setting

𝑓floor = 0. In the baseline calibration, fiscal instruments do not have floors or ceilings. This

translates in setting, for instance, 𝑔floor𝐶 = 𝑧floor = −∞, and 𝜏ceiling

𝐶 = 𝜏ceiling𝐿 = ∞. The

baseline calibration also implies that the whole fiscal adjustment takes place through changes

in external commercial borrowing and consumption taxes. This is achieved by setting 𝜄 = 𝜆1 =1, 𝜆2 = 𝜆3 = 𝜆4 = 0, 𝜍3 = 𝜍5 = 𝜍7 = 1, and 𝜍4 = 𝜍6 = 𝜍8 = 0 in the fiscal rules. To smooth tax

changes, we choose an intermediate adjustment of the consumption tax rate relative to its target

11 In Schmitt-Grohe and Uribe, (2003) this parameter value is set at 0.0007. 12 Since there is no empirical justification of the value of these parameters, we conduct some sensitivity analysis

to a range of values.

18

(𝜍1= 0.1) and a low responsiveness of the consumption tax rate to the debt-to-GDP ratio (𝜍2=

0.001).

Public investment. Pritchett’s (2000) estimates of public investment efficiency for SSA

countries point to a public investment efficiency of 50 percent. Nigeria scores very low (1.14

out of 4) in the PIMI of Dabla-Norris et al. (2011).13Therefore, public investment efficiency

parameter is set to 50 percent (𝜖̅ = 0.5), which is the average LIC estimates. The annual

depreciation rate for public capital is 7 percent (𝛿𝐺 = 0.07), somewhat lower than the

depreciation rate of private capital (𝛿𝑁 = 𝛿𝑇 = 0.10) as in Berg et al. (2013) to capture that fact

the latter is characterized by goods with stronger economic obsolescence. The home bias for

government purchases is set at 60 percent (𝜈 = 0.6), which is relatively higher to capture the

fact, at the steady state, the wage bill of public employees represents a bigger proportion of

government spending.14 However, we choose a smaller degree of home bias for government

investment spending to reflect that most of the investment goods in LICs have a higher import

content. Therefore, 𝜈𝑔 = 0.4. The output elasticity to public capital 𝛼𝐺 is set at 0.20, implying

a marginal net return of public capital of 25 percent at the initial steady state. We assume that

absorptive capacity constraints starts binding when public investment positively deviates

beyond 60 percent from its initial steady state (�̅�𝐺𝐼 = 0.6), close to the estimates of Pritchett

(2000) for sub-Saharan Africa and make of absorptive capacity constraints severe (𝜍𝜖 = 25 ) to

an extent that average investment efficiency approximately halves to around 27 percent if public

investment were to spike to around 200 percent from its initial steady state.

II. Results

1. Oil Production and Oil Price Scenarios

The oil production path for the model is obtained using the International Energy Agency

(IEA)’s World Energy Outlook 2014 (IEA, 2014)’s estimates and projected future production

until 2044; the frequency of the study is annual, 2014 being the initial period. However, these

underlying estimates and projections are subject to a range of uncertainties. For Nigeria, beside

market conditions, the oil sector outlook is immensely affected by regulatory uncertainties,

militant activities, pipeline sabotages and oil theft in the Niger Delta,15 coupled with investment

uncertainties, all of which hindering exploration activities, despite new production coming

online (EIA, 2014).16 Aging infrastructure and poor maintenance have also resulted in oil spills.

Consequently, Nigeria's proven crude oil reserve estimates have been stagnant. Crude oil

production in Nigeria reached its peak of 2.44 million barrels per day in 2005, but began to

decline significantly. Oil production recovered somewhat after 2009-2010—with the

implementation of the amnesty program that put an end to attacks on oil facilities—but still

13The index captures the institutional environment underpinning public investment management across four

different stages: project appraisal, selection, implementation, and evaluation. Covering 71 countries, including 40

low-income countries, the index allows for benchmarking across regions and country groups and for nuanced

policy relevant analysis and identification of specific areas where reform efforts could be prioritized. The index

scores range from 0 (low score) to 4 (high score). 14 The proportion of the wages of public employees averaged around 42 percent of total government spending in

the last five years. 15 The value of the estimated 150 thousand barrels lost to oil theft each day – amounting to more than 5 billion

USD per year – would be sufficient to fund universal access to electricity for all Nigerians by 2030 (IEA, 2014). 16 Nigeria scores low in the 2013 Resource Governance Index. A 2010 report by Revenue Watch Institute and

Transparency International rated the Nigeria state-run Oil Company the least transparent of 44 national and

international energy companies surveyed.

19

remains lower than its peak of 2005 because of ongoing supply disruptions.17 With deterring

investment and production, Nigeria is set to be overtaken by Angola as the largest producer of

crude oil in SSA at least until the early 2020s according to the same estimates. These

uncertainties are reflected in the revenue that the government may raise from natural resources.

Another source of uncertainty of natural resource revenue is the price volatility which

characterizes the commodity markets. The history shows many episodes of oil price swings.

The oil shocks of the 1970s and 1980s, and of 2008 among others are important facts of the

recent history. The current oil slump is another shot in the arm for the global economy in general

and for the Nigerian economy in particular. Oil prices have plunged recently, falling by nearly

50 percent since June 2014, 40 percent since September 2014 and more than 50 percent since

January 2015 with damaging effects on everyone: producers, exporters, governments, and

consumers.

Against this backdrop, we simulate two oil scenarios, both output and price scenarios:

baseline and adverse. For the output scenario, the baseline uses the recent IEA’s forecast of oil

production per year for Nigeria (see figure 7). In this scenario, the crude oil production is 1.04

billion barrels in 2014 and then increase and reach a level of 1.45 billion barrels in 2034. Then

it is projected to increase gradually but at a lower space and reach a level of about 1.52 billion

barrels in 2044. In the adverse scenario, we assume a 10 percent decline of the resource

production from the baseline by 2019 to capture the previously described uncertain oil sector

outlook in Nigeria.

Two oil price scenarios are also simulated (figure 7). We use the World Economic Outlook

(WEO) crude oil price forecast per barrel and the U.S Energy Information Outlook (EIO) data.

The WEO’s forecast for oil prices assumes reference path scenario, a conservative path in which

prices are lower than the reference prices and a more optimistic path above the reference. For

the baseline scenario, we use the reference oil price forecast of WEO. The adverse scenario

rests on the WEO’s reference forecast while updating it with most recent information on oil

price slump from EIO data. Specifically, we assume a decline in the reference oil price by more

than 50 percent in 2014-17, bringing it below 60 dollar per barrel to reflect the current fall in

oil prices.

17The government hopes to increase proven crude oil reserves to 40 billion barrels over the next few years, but

with exploration activity levels at their lowest in a decade, this goal will be challenging to achieve.

20

Figure 5: Oil production and price assumptions

Source: WEO (2013), U.S. Energy Information Administration and International Energy

Statistic database (baseline) and author’s assumptions (pessimistic).

Note: Production in million barrels (charts) and price in US$ per barrel (lines).

2. Public investment profile

In this section we discuss the effects of several scenarios for public investment, oil

revenues as well as structural reforms pertaining to efficiency and absorptive capacity

constraints. This simulation, captures the proposed USD 30 billion public investment and

expenditure program proposed by the Nigerian government in October 2016. We also

distinguish cases where external borrowing is combined or not with the resource revenue. In

particular, four scenarios with respect to different paths for public investment are examined:

Aggressive versus conservative investment scenarios and spend-as-you-go (SAYG) versus

delinked investment approach. In the first-two scenarios, investment paths eventually reach a

long-run investment level 50 percent higher than the level in the initial steady state (𝑔𝑛𝑠𝑠𝐼 =0.5)

and (k1=0.10) (see the specification (40)).

Aggressive investment scenario (k2=0.20): Under this scenario, public investment is

massively frontloaded and exhibits substantial overshooting. In particular, during the

peak year public capital investment is around 67 percent from the initial steady-state

before declining and steadily staying around the long run new steady-state of 50 percent

(figure 6).

This scenario almost corresponds to the proposed infrastructure and public investment

program of the Nigerian government, planned for the next 3 years.

Figure 6: Aggressive and large scaled-up public investment

0

20

40

60

80

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120

0

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1200

1400

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4

Baseline Pessimistic

0 5 10 15 20 25 30 35 400

10

20

30

40

50

60

70

Public investment (% from SS)

21

Conservative investment scenario (k2=0.08): In this scenario public investment stays

constant at zero-level until year around year 9 before increasing gradually above 50

percent and coming back to the projected path of the aggressive scenario around year

30 (figure 9).

Figure 8: Conservative scaled-up public investment

Spend-as-you-go investment approach: With this approach, the resource fund stays at

its initial level (𝑓𝑡∗ = 𝑓∗, ∀𝑡) and the government spends all of the resource windfall on

public investment each period.

𝑝𝑡𝐺𝑔𝑡

𝐼 − 𝑝𝐺𝑔𝐼 = (𝑡𝑜,𝑡

𝑠𝑡−

𝑡𝑜

𝑠)

Delinked investment approach (k1=k2=0.10): With the delinked approach, the

government combines investment spending with saving in stabilization fund for a given

path of public investment and public consumption, which allows for depositing when

there are surplus revenues and withdrawing when there is a revenue shortfall.

In terms of fiscal adjustment, we assume that the government makes use of external

commercial borrowing (𝜄 = 1) to supplement concessional borrowing in closing the fiscal gap

in the first-two ways of investment frontloading when the stabilization fund reaches its lower

bound. Also, the consumption tax rate is used as the adjustment instrument that stabilizes debt

in the long run (𝜆1 = 1). Furthermore, we assume no ceiling for the consumption tax rate,

which translates in setting 𝜏ceiling𝐶 = ∞. Also, as stressed out in the calibration, we choose an

intermediate adjustment of the consumption tax rate relative to its target (𝜍1= 0.1) and a low

responsiveness of the consumption tax rate to the debt-to-GDP ratio (𝜍2= 0.001) as a mean to

smooth tax changes.

With the SAYG and the delinked approach, there is no commercial (𝜄 = 0) or domestic

borrowing (𝜄 = 1) to finance public investment increases. We assume both approaches resort

only to the consumption tax rate to close any fiscal gap by setting 𝜆1 = 1; 𝜆2 = 𝜆3 = 𝜆4 = 0,

𝜍1 = 𝜍3 = 𝜍5 = 𝜍7 = 1, and 𝜍2 = 𝜍4 = 𝜍6 = 𝜍8 = 0.

A. The aggressive scenario versus conservative scenario: Additional external

commercial borrowing

The rational for an aggressive approach would be that the government anticipate more

future oil revenues than present and increase public investment spending massively early on by

combining current resource revenues with external commercial borrowing. In fact, note that in

both oil revenue scenarios (baseline and adverse), the outlook in terms of oil output in millions

of barrel per year and oil price per barrel is projected to be better in the medium to long run (see

figure 7).

0 5 10 15 20 25 30 35 400

10

20

30

40

50

60

Public investment (% from SS)

22

As expected, debt increase is most pronounced with the aggressive investment path under

the both oil scenarios. As figure 9 shows, under the baseline oil shock scenario, external

commercial debt as a share of GDP reaches a peak of 44 percent in year 24 compared to a peak

of 138 percent in year 18 under the adverse oil shock. In contrast, with the conservative path,

public commercial debt as a share of GDP does not increase significantly compared to the

aggressive scenario. It stands at 40 percent of GDP in the baseline oil revenue scenario (which

is 4 percentage points lower) and 118 percent of GDP in the adverse scenario (which is up to

20 percentage points lower). Also, not surprisingly, the conservative scenario delivers the best

outcome in terms of fiscal adjustment in order to service accumulated debt, and in terms of

financial asset accumulation in the SWF. In particular, the increase in consumption tax rate is

smaller than with the aggressive path. Accordingly, the fall of private consumption is less

pronounced in the conservative case than in the aggressive case. Moreover, while both

investment scenarios are able to accumulate some savings in the resource fund even under the

adverse scenario, the conservative scenario delivers the best outcome. With the adverse oil

shock, the stabilization fund is drawn down quickly in the initial years compared to the baseline

but reserves accumulate in subsequent years. However, after reaching its peak, the accumulated

reserves decline in the baseline and the adverse oil scenario; the pace of the decline is fast in

the aggressive investment scenario compared to the conservative scenario.

In reality, we assume that both types of investment frontloading are undertaken by

contracting external commercial borrowing and on the account of future oil revenue that will

allow her to service accumulated debt. Implicitly, it uses the anticipated future resource windfall

as a de facto “collateral” to borrow massively today and finance the investment plan. We also

assume that the consumption tax rate adjusts without any limit placed on it to stabilize debt in

the long run. The fiscal adjustment is shown to be painful and most pronounced in the

aggressive investment case and more so in the adverse oil scenario. Indeed, with aggressive

scenario (conservative scenario) the consumption tax rate tops to around 27 percent (26 percent)

in the baseline oil revenue shock. As regard the adverse oil revenue shock, the consumption tax

rate reaches around 47 percent (46 percent) at peak with the aggressive investment scenario

(conservative scenario). Despite such a huge long term fiscal effort, the fiscal adjustment seems

unable to stabilize debt. Therefore, the government has to complement by using accumulated

resource revenues to service debt. This together with the volatility of the revenue contribute to

negatively affect the stabilization fund, which is what the results show in both oil revenue

scenarios (baseline and adverse).

In addition, as expected, the aggressive scaling-up leads to faster and higher build-up of

public capital and potentially higher non-oil economic growth in the short to medium run.

However, as more resource revenue has to complement fiscal adjustment for debt service in the

long run, less can be saved in a stabilization fund, leaving the economy vulnerable to negative

shocks. Accordingly, the non-oil GDP is lower in the long run. Moreover, the painful fiscal

adjustment is felt in terms of a decline in private consumption in both investment and oil

scenarios, but most pronounced in the aggressive scenario and under the adverse oil scenario.

Another caveat with the aggressive approach to public investment scaling-up in a typical

low income country is related to short-run adverse effects. With massive public investment

frontloading in a shorter period, a typical resource-rich developing country may bump into a

short-run economic “overheating”. This is so because of absorptive capacity constraints, a

structural constraints and pervasive feature of developing countries. They are attributed

essentially to supply bottlenecks but also to poor planning, weak oversight, and a myriad of

23

coordination problems, all of which contributes to drive up investment costs with the pace of

investment scaling-up.18

As figure 9 shows, the absorptive capacity constraints are evidenced by the initial decline

in the investment efficiency following the scaling-up process. In particular, the investment

efficiency is below the optimal level of 50 percent in the initial years. It reaches a minimum of

48 percent in year 5 when public investment is at its peak. Consequently, the aggressive public

investment approach pushes up the price of non-traded goods in the short-run which stands as

an appreciation of the real exchange rate.19 This in turn adversely impacts the non-resource

tradable sector (Dutch disease). Indeed, the real exchange rate is in the negative territory (which

is an appreciation) over the first-five years in both oil scenarios, yet with the most pronounced

decline recorded under the baseline scenario. Accordingly, the tradable good sector falls in the

negative territory over the first-five years; in particular, the sector contracts by about 5 percent

(2.6 percent) in the baseline oil scenario (adverse oil scenario).

However, in the medium-to long-run, there is a progressive improvement in the

efficiency. This is so because strengthening the absorptive capacity takes times to be reflected

in better outcomes in the economy. This is seen in that the investment efficiency gradually

increases and reaches its optimal level by year 10 following the initial decline. Accordingly,

the real exchange rate responds by climbing to the positive territory (which means depreciation)

and so is the non-resource tradable sector.

Figure 9: Aggressive versus conservation investment frontloading with external commercial

borrowing

18 We study the implications of absorptive capacities in the next subsection. 19 Note that a downward movement in the charts implies an appreciation of the real exchange rate.

0 5 10 15 20 25 30 35 4060

80

100

120Oil price (USD per barrel)

0 5 10 15 20 25 30 35 4050

60

70

80

90Oil revenue (% of tot. revenue)

0 5 10 15 20 25 30 35 401000

1200

1400

1600Oil output (mb per year)

0 5 10 15 20 25 30 35 401000

1200

1400

1600Oil output (mb per year)

0 5 10 15 20 25 30 35 4020

40

60

80Oil revenue (% of tot. revenue)

0 5 10 15 20 25 30 35 4040

60

80

100

120Oil price (USD per barrel)

Baseline oil scenario Adverse oil scenario

24

Figure 10: Aggressive versus conservation investment frontloading with external commercial

borrowing

0 5 10 15 20 25 30 35 400

50

100

Pub. inv. (% from SS)

0 5 10 15 20 25 30 35 400

20

40

60

Public capital (% from SS)

0 5 10 15 20 25 30 35 400

50

100Stabilization fund (% of GDP)

0 5 10 15 20 25 30 35 400

10

20

30Stabilization fund (% of GDP)

0 5 10 15 20 25 30 35 400

50

100

Pub. inv. (% from SS)

0 5 10 15 20 25 30 35 400

20

40

60

Public capital (% from SS)

0 5 10 15 20 25 30 35 40-10

-5

0

5Transfers change (% from SS)

0 5 10 15 20 25 30 35 400

20

40

60External commercial debt (% of GDP)

0 5 10 15 20 25 30 35 4015

20

25

30Consumption tax rate (%)

0 5 10 15 20 25 30 35 400

20

40

60Consumption tax rate (%)

0 5 10 15 20 25 30 35 400

50

100

150External commercial debt (% of GDP)

0 5 10 15 20 25 30 35 40-30

-20

-10

0

Transfers change (% from SS)

Aggressive Conservative

0 5 10 15 20 25 30 35 40-10

0

10

20

Non-resource output (% from SS)

0 5 10 15 20 25 30 35 40-1

0

1

2Non-resource GDP growth (%)

0 5 10 15 20 25 30 35 40-2

0

2

4

Nontradable output(% from SS)

0 5 10 15 20 25 30 35 40-5

0

5

10

Nontradable output(% from SS)

0 5 10 15 20 25 30 35 40-1

0

1

2

3Non-resource GDP growth (%)

0 5 10 15 20 25 30 35 40-10

0

10

20

Non-resource output (% from SS)

0 5 10 15 20 25 30 35 40-5

0

5

Private consumption (% from SS)

0 5 10 15 20 25 30 35 400

5

10

15

Private investment (% from SS)

0 5 10 15 20 25 30 35 400

50

100Total public debt (% of GDP)

0 5 10 15 20 25 30 35 400

100

200Total public debt (% of GDP)

0 5 10 15 20 25 30 35 400

2

4

6

8

Private investment (% from SS)

0 5 10 15 20 25 30 35 40-20

-10

0

Private consumption (% from SS)

25

B. Aggressive investment scenario with structural reforms: Efficiency and absorptive

capacity constraints

In the previous section, we show how absorptive capacity binds in the presence of

different investment scenarios. In this section we explore the implications of structural reforms

that improve the efficiency of public investment and absorptive capacity constraints. This is

particularly important in developing countries that face tight absorptive capacity constraints,

such as coordination problems, supply bottlenecks and poor project execution and planning.

More broadly these constraints can refer to institutional policies, technical and managerial

capacities.

Equation (37) measures the mechanism capturing absorptive constraints in developing

countries. In this specification, the efficiency of the additional investment decreases if the

growth rate of government investment expenditure from the initial steady state exceeds a

predetermined threshold (�̅�𝐺𝐼). First, using this equation, we examine the effects of varying the

threshold of the growth rate of government expenditure beyond which the absorptive capacity

becomes binding and the investment efficiency declines. Second, by varying the parameter

governing the severity of these constraints (𝜍𝜖), we are able to study the consequences of

structural reforms on the aggressive scenario.

As shown in figure 11, increasing the threshold from 20 percent to 75 percent at a given

parameter of the severity of the absorptive capacity constraints (equal to 25), improves the

investment efficiency. This translates into sizable and sustainable increase in public capital,

which in turn has a positive spillover effect to the rest of the economy, as evidenced by higher

additional growth of the non-resource GDP. In addition, at a given threshold of public

investment growth rate of 60 percent, reducing the severity of absorptive capacity constraints

from 50 to 15 produces the same positive but mild effects on the efficiency of public investment

and hence public capital and non-oil GDP growth.

Figure 11: Aggressive scenario: Structural reforms

0 5 10 15 20 25 30 35 40-20

0

20

40

60

Tradable output (% from SS)

0 5 10 15 20 25 30 35 40-10

-5

0

5

10

Real exchange rate (% from SS)

0 5 10 15 20 25 30 35 4048

49

50Public invest. efficiency (%)

0 5 10 15 20 25 30 35 40-10

-5

0

5

Real exchange rate (% from SS)

0 5 10 15 20 25 30 35 40-10

0

10

20

30

Tradable output (% from SS)

Aggressive Conservative

0 5 10 15 20 25 30 35 4048

49

50Public invest. efficiency (%)

26

C. Spend-as-you-go (SAYG) investing approach versus delinked investing approach:

No additional commercial borrowing

Figure 13 depicts the SAYG investing approach versus the delinked approach with the

baseline oil revenue scenario only.

Comparing the two stylized approaches show that the SAYG approach results in a volatile

path for public investment, mirroring the volatility of resource revenue flows. In particular,

public investment spikes to 200 percent from its steady state. As a result, the stabilization fund

is drawn down to a lower value of 2.2 percent of GDP below the steady state. Fiscal volatility

in turn is translated into macroeconomic instability as shown by fluctuations in the macro

variables. In contrast, the delinked approach provides a lower and smoother path of scaling-up

and therefore, fiscal buffer is secured to shield the economy from volatility and maintain a

stable and sustainable spending path without major fiscal adjustments. In fact, unlike with the

SAYG approach, the economy is able to build a sizeable stabilization fund with the delinked

approach (around 160 percent of GDP at peak year).

In addition, sudden accelerations in public investment expenditures makes the economy

more prone to bumping into absorptive capacity constraints, translating into lower efficiency.

Earlier we have shown that the efficiency of public investment decreases to an extent

proportional to the size of the deviation (�̅�𝑡𝐺𝐼 − �̅�𝐺𝐼), with the parameter 𝜍𝜖 controlling the

severity of that decline. The results show that under the SAYG approach, public investment

accelerates to an extent that average investment efficiency drops from a baseline value of 50

percent down to 26 percent. In contrast, the delinked approach is more susceptible to perform

better as the economy runs into less absorptive capacity constraints and efficiency of investment

declines slightly. In particular, the efficiency of public investment is down to 49 percent only

under this scenario.

Furthermore, both scenarios induce a real exchange rate appreciation in the short-to

medium-run but the SAYG approach induces greater and more volatile real exchange rate

effects. Indeed, with the investment surge spiking to 200 percent and oil reserves declining

rapidly, the economy is more susceptible to overheating. Indeed, demand in the non-oil tradable

sector increases remarkably to 13 percent from the steady state at peak, leading to a significant

rise in the price of non-tradable relative to tradable, which is equivalent to an appreciation of

the real exchange rate (around 9 percent at t=13). The greater real exchange appreciation in

turn leads to greater negative learning-by-doing externalities and thus a decline in traded output

over 15 years, and particularly by about 3 percent in year 13. The appreciation, which is less

0 10 20 30 400

10

20

30

40

50

Public capital (% from SS)

0 10 20 30 40-1

0

1

2

3Non-resource GDP growth (%)

0 10 20 30 4035

40

45

50Public investment efficiency (%)

20%-threshold

40%-threshold

60%-threshold

75%-threshold

0 10 20 30 4047.5

48

48.5

49

49.5

50Public investment efficiency (%)

0 10 20 30 400

0.5

1

1.5

2

2.5

3Non-resource GDP growth (%)

0 10 20 30 400

10

20

30

40

50

60

Public capital (% from SS)

50-severity

25-severity

15-severity

�̅�𝐺𝐼 = 60

𝜍𝜖 = 25

27

pronounced in the delinked approach leads to smaller negative learning-by-doing effects and as

a result a small decline in the tradable good sector.

Figure 12: Spend-as-go versus delinked approach: No additional commercial borrowing

D. The leaning-by-doing (LBD) externalities and the Dutch disease effects

The Dutch disease effects discussed in the earlier sections is in fact the result of assumed

LBD externalities as a driving force of productivity growth. This specification is given in (27).

0 5 10 15 20 25 30 35 400

20

40

60

Public capital (% from SS)

0 5 10 15 20 25 30 35 4020

30

40

50Pub invest. efficiency (%)

0 5 10 15 20 25 30 35 400

100

200

300

Pub. inv. (% from SS)

0 5 10 15 20 25 30 35 400

50

100

Pub. inv. (% from SS)

0 5 10 15 20 25 30 35 4049

49.5

50Pub invest. efficiency (%)

0 5 10 15 20 25 30 35 400

50

100

Public capital (% from SS)

0 5 10 15 20 25 30 35 40-5

0

5

Tradable output (% from SS)

0 5 10 15 20 25 30 35 40-0.2

0

0.2

0.4

0.6Non-resource GDP growth rate (%)

0 5 10 15 20 25 30 35 40-4

-2

0

2

Real exchange rate (% from SS)

0 5 10 15 20 25 30 35 40-10

-5

0

5

Real exchange rate (% from SS)

0 5 10 15 20 25 30 35 40-0.5

0

0.5

1Non-resource GDP growth rate (%)

0 5 10 15 20 25 30 35 40-5

0

5

10

Tradable output (% from SS)

0 5 10 15 20 25 30 35 4010

15

20Consumption tax rate (%)

0 5 10 15 20 25 30 35 402

2.2

2.4Stabilization fund (% of GDP)

0 5 10 15 20 25 30 35 400

100

200Stabilization fund (% of GDP)

0 5 10 15 20 25 30 35 400

5

10

15

20

Nontradable output (% from SS)

0 5 10 15 20 25 30 35 4018

20

22Consumption tax rate (%)

0 5 10 15 20 25 30 35 400

5

10

15

Nontradable output (% from SS)

Spend-as-you-go approach Delinked approach

28

In reality, this links the growth rate of productivity of the traded good sector to its lag and the

deviation of lagged traded output from trend. Thus, a small decline in the traded-goods sector

amplifies negative effects on the growth rate of productivity. In contrast, an increases of traded

output relative to its trend can also generate productivity gains in this sector and, therefore,

amplify positive effects on the productivity. Earlier, we find that the decline in the traded-good

production is a short-term issue. This is the result of rising government spending that imposes

demand pressures and shifts factors away from tradable sectors to nontradables, also leading to

a real appreciation. Through the LBD externalities, the short-term decline of the traded-goods

sector imposes a “disease” through lost total-factor-productivity (TFP). In contrast, the short-

run shrinkage of the traded output can be reversed over longer horizons owing to the fact that

demand pressure can fade out and on the strength of public capital that crowds in the private

capital accumulation. Therefore, the resulting increases in the traded output does not impose a

“disease”; rather, it creates a productivity gain through the LBD externalities.

The extent of the LBD externalities is given by the parameters 𝜌𝑧𝑇 and 𝜌𝑦𝑇 in (27), which

measure the strength and persistence of traded output changes on its TFP deviations from trend.

To understand the role of these externalities, we compare the model dynamics under strong

externalities (𝜌𝑧𝑇 = 0.4 = 𝜌𝑦𝑇 = 0.4) and the baseline (𝜌𝑧𝑇 = 0.1 = 𝜌𝑦𝑇 = 0.1) as reported in

appendix 1.

Also, as examined in the previous sections, the extent of the Dutch disease, and thus of the

shrinkage of the traded sector depends on whether absorptive capacity is constrained (implying

low efficiency). Therefore, what could be a “disease” is likely to be amplified if the efficiency

of public investment is not high enough (or at least below its baseline value). Thus, we examine

the effects of the combined strong LBD externality (𝜌𝑧𝑇 = 0.4 = 𝜌𝑦𝑇 = 0.4) and low efficiency

or strong absorptive capacity constraint (�̅�𝐺𝐼 = 20%).

Figure 14 shows the comparison under the SAYG approach.20 The blue solid line

represents the baseline, while the green line represents the strong externalities scenario and the

line with dots represents the combination of strong LBD externalities with low efficiency.

Relative to the baseline, strong externalities have the expected effect of amplifying the decline

in the traded sector over the first 25 years, which leads to a fall in non-oil GDP—the Dutch

disease. Moreover, the real exchange rate appreciation is less pronounced, reflecting a reverse

Balassa-Samuelson effect due to the decline in productivity in the traded sector relative to that

of the non-traded sector. The non-traded sector, in contrast, is broadly unaffected by varying

the LBD externalities.

Looking beyond the first 25 years, however, shows a stronger economic performance under

the strong LBD externalities—a recovery from the “disease” owing to higher public capital

accumulation that induces crowding in effects on private capital accumulation (see the

discussions of these effects in the previous sub-section). This eventually helps raise traded

output above its steady state level. Once output exceeds the steady state, the externalities boost

traded sector TFP, which amplifies the positive long-term effect of public capital accumulation

on this sector and on the rest of the economy. Moreover, as predicted by the Balassa-Samuelson

effect, the increase in the traded sector TFP causes an appreciation of the real exchange rate

relative to the baseline scenario.

20 See the previous sub-section for the discussions of this investment approach as well as the macroeconomic

impacts.

29

The key determinant of whether the LBD externalities amplify or undermine the positive

effects of the SAYG investment is the efficiency of public investment. The low efficiency of

public investment accentuates the negative effects of the strong LBD externalities. In addition,

over the long term, the low efficiency of public investment hampers the positive effect of the

public capital accumulation and the crowding in effects on private capital, thus bringing the

additional growth of non-oil GDP into negative territory.

In summary, LBD externalities can amplify positive effects of oil revenue-financed public

investment surge similar to the SAYG investment approach, but they may also make oil revenue

harmful in the short to medium term. When absorptive capacity is binding and the efficiency of

public investment is low, it can accentuate the negative effects of strong LBD externalities and

even offset positive effects in the long term.

Figure 13: Sensitivity of the Dutch disease effect to the LBD externality parameters and

efficiency

III. Conclusion

We considered four different approaches towards public investment scaling-up: an

aggressive approach versus conservative approach and spending-as-you-go versus delinked

approach. In sum, an intermediate between the aggressive and the conservative approaches and

anticipating some but not all future oil revenue would be appropriate given Nigeria’s

infrastructure investment needs and the uncertainty regarding oil revenue. The aggressive

approach leads to higher accumulation of debt as external commercial borrowing increases in

anticipation of future oil revenue. It follows that debt service in the medium-to long-run requires

painful fiscal adjustments that require more resource revenue to complement fiscal adjustments.

This leads to a drawing down of the resource fund in the two resource revenue scenarios.

Aggressive investment scaling up leads to faster build-up of public capital and non-oil GDP

growth in the medium-run but ambitious scaled up public investment may bump into absorptive

capacity constraints, at least in the short-run. This in turn ultimately affect negatively the non-

oil tradable output (Dutch disease) and non-oil GDP growth. The conservative approach

outperforms the aggressive approach in terms of accumulation of resource revenue and short-

run adverse effects (Dutch disease), but it yields lower build-up of public capital and non-oil

GDP growth. Comparing the oil revenue scenarios, the adverse scenario leads to less

accumulated oil reserves. Of course, since Nigeria is facing pressing development needs and

0 5 10 15 20 25 30 35 40-10

-5

0

5

10

15

Tradable output (% from SS)

0 10 20 30 400

5

10

15

Nontradable output (% from SS)

0 5 10 15 20 25 30 35 40-1

-0.5

0

0.5

1Non-oil GDP growth (%)

0 10 20 30 40-10

-5

0

5

Real exchange rate (% from SS)

baseline: rhozt=rhoyt=0.1 strong LBD externality: rhozt=rhoyt=0.4 strong LBD externality with low efficiency of pub. inv.: rhozt=rhoyt=0.4, githreshold=20%

0 10 20 30 4035

40

45

50Public investment efficiency (%)

baseline: githreshold=60%

githreshold=20%

30

the government is gearing toward more public investments, the conservative approach is not

sufficient but the aggressive one seems too ambitious. Therefore, the line could be drawn

between both approaches when scaling up public investment.

We finally examined two investment approaches (spend-as-you-go (SAYG) approach

versus delinked approach) where no additional borrowing is allowed but public investment is

financed via resource windfall only. With the SAYG approach, the government spends all of

its resource windfall in public investment without saving in stabilization fund. With the

delinked approach, the government combines investment spending with saving in a resource

fund. Taking the SAYG approach forward could destabilize the economy and lead to the types

of boom-bust cycles that many oil-dependent economies have suffered in the past. The delinked

approach allows to achieve both development goals (by scaling up public investments) and

macroeconomic stability (via the resource fund).

We also studied the consequences of structural reforms on the aggressive scenario and find

that improving absorptive capacity and hence higher efficiency translates into sizable and

sustainable increase in public capital which has a positive spillover effect to the rest of the

economy as evidenced by higher additional growth of the non-resource GDP.

The policy implications from this study are threefold. First, it seems to be judicious to strike

the right balance between investing the oil windfall in order to fulfill development goals and

saving in order to ensure macroeconomic stability. For a highly oil-dependent country including

Nigeria, managing both price volatility and disruption of resource production should be the

priority to overcome the risks of adverse shocks. Second, Nigeria should not follow ambitious

investment scaling ups neither through debt-financing nor from resource windfall in order to

shield the economy from running into short-run supply side bottlenecks and Dutch disease

effects. Third, implementing structural reforms in order to address absorptive capacity

constraints can help mitigate adverse macroeconomic effects by improving the efficiency

constraint.

31

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33

Appendix 1: Table 1: Baseline calibration

Parameter Value definition Parameter Value definition

𝑒𝑥𝑝𝑠ℎ𝑎𝑟𝑒 0.43 Exports to GDP 𝜌𝑦𝑜 0.90 Persist. of the mining production

shock

𝑖𝑚𝑝𝑠ℎ𝑎𝑟𝑒 0.31 Imports to GDP 𝑓 0.50 User fees of public infrastructure

𝑔𝑠ℎ𝑎𝑟𝑒𝐶 0.17 Gvt. consumption to GDP 𝜏𝐿 0.05 Labor income tax

𝑔𝑠ℎ𝑎𝑟𝑒𝐼 0.09 Gvt. investment to GDP 𝜏𝐶 0.18 Consumption tax

𝑖𝑠ℎ𝑎𝑟𝑒 0.18 Private investment to GDP 𝜏𝐾 0.35 Tax rate on the return on capital

𝑦𝑠ℎ𝑎𝑟𝑒𝑂 0.40 Oil resource to GDP 𝑓𝑓𝑙𝑜𝑜𝑟 0.024 Lower bound for the stabilization

fund/GDP

𝑔𝑇,𝑠ℎ𝑎𝑟𝑒 0.40 Share of tradable in gvt. consumption 𝜄 1 Adjust. share by external comm.

debt

𝐶𝑇,𝑠ℎ𝑎𝑟𝑒 0.50 Share of tradable in private

consumption 𝜆1 1 Fiscal adjust. share by

consumption tax

𝑅𝐹𝑠ℎ𝑎𝑟𝑒 0.024 Stabilization fund to GDP 𝜆2 0 Fiscal adjust. share by labor tax

𝑏𝑠ℎ𝑎𝑟𝑒 0.162 Gvt. Domestic debt to GDP 𝜆3 0 Fiscal adjust. share by gvt.

consumption

𝑏𝑠ℎ𝑎𝑟𝑒∗ Private foreign debt to GDP 𝜆4 0 Fiscal adjust. share by transfer

𝑑𝑠ℎ𝑎𝑟𝑒 0.025 Concessional debt to GDP 𝜍1 0.5 Adjust. speed of consumpt. tax to

target

𝑑𝑐,𝑠ℎ𝑎𝑟𝑒 0.003 Gvt. Comm. Debt to GDP 𝜍2 0.001 Consumpt. tax response to

debt/GDP

𝑔𝑟𝑠ℎ𝑎𝑟𝑒 0.00 Grants to GDP 𝜍3 1 Adjust. speed of labor tax to

target

(𝑅 − 1) 0.10 Domestic net real int. rate 𝜍4 0 Labor tax response to debt/GDP

(𝑅𝑅𝐹 − 1) 0.027 Foreign net real int. rate on SWF 𝜍5 1 Adjust. speed of gvt. Consumpt.

to target

(𝑅𝑑 − 1) 0.00 Net real int. rate on concess. debt 𝜍6 0 Gvt. Consumpt. to debt/GDP

(𝑅𝑓 − 1) 0.04 Net real risk-free rate 𝜍7 1 Adjust. speed of transfer to

debt/GDP

(𝑅𝑑𝑐 − 1) 0.06 Net real int. rate external comm. debt 𝜍8 0 Transfer response to debt/GDP

𝜂𝑑𝑐 0 Elast. of sovereign risk 𝑔𝑓𝑙𝑜𝑜𝑟𝐶 −∞ Floor on real gvt. consumption

𝛼𝑁 0.55 Labor income share in nontraded

sector 𝑧𝑓𝑙𝑜𝑜𝑟 −∞ Floor on transfer

𝛼𝑇 0.48 Labor income share in traded sector 𝜏𝑐𝑒𝑖𝑙𝑖𝑛𝑔𝐶 +∞ Ceiling on consumption tax

𝛿𝑁 0.10 Depreciation rate of 𝑘𝑁,𝑡 𝜏𝑐𝑒𝑖𝑙𝑖𝑛𝑔𝐿 +∞ Ceiling on labor tax

𝛿𝑇 0.10 Depreciation rate of 𝑘𝑇,𝑡 𝜈 0.60 Home bias of gvt. Purchases

𝜌𝑦𝑇 0.10 Learning by doing in traded sector 𝜈𝑔 0.40 Home bias for additional

spending

𝜌𝑧𝑇 0.10 Persist. in TFP in traded sector 𝛼𝐺 0.20 Output elast. to public capital

𝜅𝑁 25 Investment adjust. cost, nontraded

sector 𝛿𝐺 0.07 Depreciation of public capital

𝜅𝑇 25 Investment adjust. cost, traded sector 𝜖 ̅ 0.50 Steady state efficiency of public

invest

𝜓 10 Inverse of Frisch labor elast. 𝑔𝑛𝑠𝑠𝐼 0.50 Planned long-term scaling up

𝜎 2.94 Inverse of intertemporal elast. of

substitution 𝑘1 - Speed of scaling up plan

𝜌 1 Intertemporal substitution elast. 𝑘2 - Degree of frontloading

𝛿 0.6 Steady-state share of labor in the

nontraded sector 𝜍𝜖 25 Severity of absorptive capacity

constraints

𝜔 0.40 Measure of optimizers in the

economy �̅�𝐺𝐼 0.6 Threshold of absorptive capacity

𝜒 0.44 Elast. of subst. traded/nontraded

goods 𝑣𝑎𝑟𝑐𝑜 0 Cost coefficient in the oil sector

𝜂 1 Elast. of portfolio adjust. cost 𝑓𝑐𝑜 0 Fixed cost in production of oil

𝜏𝑂 0.95 Royalty rate on natural resources 𝑑𝑖𝑣 0 Additional dividend share by gvt.

𝜌𝑝𝑜 1 Persistence of the commodity price

shock