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
100
120
0
200
400
600
800
1000
1200
1400
1600
201
5
201
6
201
7
201
8
201
9
202
0
202
1
202
2
202
3
202
4
202
5
202
6
202
7
202
8
202
9
203
0
203
1
203
2
203
3
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4
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204
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