WPS7910
Policy Research Working Paper 7910
Optimal Allocation of Natural Resource Surpluses
in a Dynamic Macroeconomic Framework
A DSGE Analysis with Evidence from Uganda
Albert Zeufack
Alexandre Kopoin
Jean-Pascal Nganou
Fulbert Tchana Tchana
Laurent Kemoe
Africa Region
Office of the Chief Economist
&
Macroeconomics and Fiscal Management Global Practice Group
December 2016
Policy Research Working Paper 7910
Abstract
In low-income, capital-scarce economies that face financial a sustainable-investing approach that proposes a constant
and fiscal constraints, managing revenues from newly found share of resource revenues to finance public investment
natural resources can be a daunting challenge. The policy and the rest to be saved. The analysis finds that a gradual
debate is how to scale up public investment to meet huge scaling-up of public investment yields the best outcome, as
needs in infrastructure without generating a higher public it minimizes macroeconomic volatility. The analysis then
deficit, and avoid the Dutch disease. This paper uses an open investigates the optimal oil share to use for public invest-
economy dynamic stochastic general equilibrium model that ment; the criterion minimizes a loss function that accounts
is compatible with low-income economies and calibrated on for households’ welfare and macroeconomic stability in an
Ugandan’s data to tackle this problem. The paper explores environment featuring oil price volatility. The findings show
macroeconomic dynamics under three stylized fiscal policy that, depending on the policy maker’s preference for sta-
approaches for managing resource windfalls: investing all bility, 55 to 85 percent of oil windfalls should be invested.
in public capital, saving all in a sovereign wealth fund, and
This paper is a product of the the Office of the Chief Economist, Africa Region and the Macroeconomics and Fiscal
Management Global Practice Group. It is part of a larger effort by the World Bank to provide open access to its research
and make a contribution to development policy discussions around the world. Policy Research Working Papers are also
posted on the Web at http://econ.worldbank.org. The authors may be contacted at azeufack@worldbank.org, alexandre.
kopoin@oecd.org, jnganou@worldbank.org, ftchanatchana@worldbank.org, and laurent.kemoe@umontreal.ca
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development
issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the
names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those
of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and
its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.
Produced by the Research Support Team
Optimal Allocation of Natural Resource Surpluses in
a Dynamic Macroeconomic Framework:
A DSGE Analysis with Evidence from Uganda
Albert Zeufack∗ Alexandre Kopoin† Jean-Pascal Nganou‡
Fulbert Tchana Tchana§ Laurent Kemoe¶
December 8, 2016
JEL Classiﬁcation : E22, F43, O41, Q32
Keywords: Fiscal policy; public investment; resource-rich developing countries; macroeconomic
volatility; optimal resource allocation.
∗
Chief Economist, Africa Region, The World Bank, email: azeufack@worldbank.org.
†
Economics Department, OECD and Laval University, email: alexandre.kopoin@oecd.org.
‡
Senior Country Economist, The World Bank, email: jnganou@worldbank.org.
§
Senior Economist, The World Bank, email: ftchanatchana@worldbank.org.
¶
Department of Economics and CIREQ, University of Montreal, email: laurent.kemoe@umontreal.ca.
We are grateful to Kevin Moran, Jean-Pierre Par´ e, Gilles Belanger, Fall Falilou, Juste Some, seminar
participants at CSAE Conference 2015: Economic Development in Africa and anonymous referees for
helpful comments.
1 Introduction
In low-income, capital-scarce economies that face ﬁnancial and ﬁscal constraints, managing rev-
enues from newly found natural resources such as oil can be a daunting challenge. The policy
debate is how to scale up public investment to meet huge needs in public infrastructure with-
out generating a higher public sector deﬁcit, and avoid the Dutch disease, all in an uncertain
world characterized by high occurrence of shocks and price volatility. This less documented
cutting-edge issue − viewed as the optimal scaling-up of public investment in an uncertain pro-
duction environment − remains one of the key elements to accelerate structural transformation
and achieve developmental goals while maintaining the country’s macroeconomic stability and
global competitiveness.
There is a huge literature that looks into the impact of oil windfalls on macroeconomic ag-
gregates and conventional wisdom suggests that natural resource revenues should be either saved
externally in a sovereign wealth fund (SWF) or invested in productive public infrastructures.
However, the ﬁrst option has a weak ability to avoid poor living conditions and limits sustain-
able investment, in particular in a credit-constrained environment. The second approach which
was promoted to signiﬁcantly reduce the public infrastructure gap in resource-rich low-income
countries has also become obsolete due to lack of sustainable public policies. (Davis et al. (2001),
Barnett and Ossowski (2003), Berms and Irineu (2011)). Then, the policy trade-oﬀs emanating
from saving ﬁscal revenue from oil resources to smooth consumption versus spending it upfront
to boost growth is considered as one of the most frequently-cited challenges to resource-rich
low-income countries.
Given this unsolved natural resources management issue, one of the major tasks faced by
economic policymakers is how to reduce the eﬀects of volatile resource prices on the domestic
economy. For instance, if all of the windfall gains are passed through into the economy, this will
generally result in a high inﬂation and an overvalued real exchange rate. In addition, exports
of other products are unable to gain a foothold in the economy, leaving the economy vulner-
able when the resource wealth runs out and causing a Dutch disease. Thus, addressing these
challenges requires state-of-art macroeconomic models and reﬁned strategies for strengthening
institutional capacities for more eﬀective governance, especially in the area of strategic planning,
2
budgeting and public ﬁnance management.
This paper contributes to the ongoing debate by developing an open-economy dynamic
stochastic general equilibrium model with a natural resource sector to study macroeconomic
impacts and ﬁscal policy responses to natural resource inﬂows. In low-income countries, given
tremendous infrastructure needs in public infrastructures and international borrowing con-
straints, resource revenues are valuable to ﬁnance public investment and can also serve as a
collateral for accessing international ﬁnancial markets, making it possible to build up a sovereign
capital. In this spirit, the investing-saving pattern becomes not obvious and requires an assess-
ment of several scenarios based on the country’s speciﬁc macroeconomic strengths and weak-
nesses. The focus of the analysis is to explore macroeconomic dynamics under three stylized
ﬁscal policy approaches for managing a resource windfall: (i) investing all in public capital (the
All-Investing Approach); (ii) saving all in a sovereign wealth fund (the All-Saving Approach);
and (iii) using a constant share of the oil revenues to ﬁnance public investment and saving the
remaining share in a sovereign wealth fund (the Sustainable-Investing Approach). The paper
also contributes to this literature by providing the optimal share of oil revenue to use in the the
Sustainable-Investing Approach.
In the state-of-the-art macroeconomic modelling and ﬁscal policy assessments, this paper
contributes to two strands of literature. First, we provide a contribution to the literature
that looks the pattern of natural resources and macroeconomic stability in a developing country.
Sachs and Warner (1999) is considered as a reference paper in this strand of literature by showing
that investing resource windfalls does not necessarily promote sustained economic growth in
developing countries. Second, our paper complements the existing literature that analyzes the
optimal ﬁscal policy rule in managing of natural resources income by analyzing three innovative
ﬁscal policy approaches. The model includes key features of a small open economy model with
optimizing agents and nominal rigidities and several important features that are common in New
Keynesian models and developing countries, including Dutch disease, investment ineﬃciencies
and weak tax systems. In addition, we propose and test diverse approaches to analyze ﬁscal
policy responses in low-income countries.
However, recent theoretical and empirical studies have looked at the impact of natural re-
3
source revenues on ﬁscal responses and among others, Devarajan et al. (2015) sheds light on this
issue by simulating the impact of resources windfalls on long-term economic growth and welfare
enor (2014) provides a characterization of the optimal ﬁscal
under resource price uncertainty. Ag´
response in the presence of oil price shocks using a small open low-income country DSGE model.
While these papers focus on oil price shocks, we analyze the optimal ﬁscal response from a dif-
ferent perspective by focusing on oil production shocks only, because our paper’s objective is to
provide policy advice to countries that, like Uganda, have not yet started producing. Tilak et al.
(2015) uses the IMF DSGE model to assess some ﬁscal policy options: i) Household transfers, ii)
Front-load public investment and iii) Gradual public investment. Their ﬁscal policies are similar
to Berg et al. (2013) as well as Giovanni et al. (2014); but slightly diﬀerent from ours, because
we do not consider the front-loading option.
Although we focus our impulse response analysis on oil production shocks as we aim to assess
how a sudden increase in public revenues due to oil production aﬀects macroeconomic dynamics,
in our investigations regarding the optimal share of oil windfalls to use for public investment,
we reckon that most of the volatility in oil revenue for a new oil producer comes from oil price
volatility instead of production volatility. For this reason, in these investigations, we use oil
price volatilities as the main source of uncertainty.
We calibrate this model to reproduce key features of the Uganda economy, a Sub-Saharan
Africa low-income country that recently discovered signiﬁcant oil resources, with an estimated
2.5 billion barrels of reserves. This is a signiﬁcant development milestone, as it represents
great opportunities for the ﬁnancing of Uganda’s National Development Plan. According to
the World Bank’s economic projections, oil revenues in Uganda are expected to be relatively
important at an estimate around of 3 percent of the national Gross Domestic Product (GDP)
over the next ﬁve years. These estimates, associated with large movements in commodity prices
in the world natural resources market over the past decade, have sparked renewed interest in a
better understanding of the impact of this natural windfall on the Ugandan economy.
Our results show that a better ﬁscal management is to save the resource income in a sovereign
wealth fund for future generation when public capital is almost unproductive. We also ﬁnd that
the gradual scaling-up of public investment (The Sustainable-Investing Approach ) yields the
4
best outcomes as it minimizes macroeconomic volatility. For example, the real exchange rate
appreciation is 30 percent lower than in the all-investing approach, which might be viewed as an
attractive ﬁscal policy to accelerate economic development in public capital-scarce economies.
The trade balance improves substantially and impulse response functions suggest that output,
non-tradable and tradable goods production, employment and wages rebound faster. We then
investigate the optimal oil share to use for public investment; our optimization criterion is based
on a loss function that accounts for households’ welfare and macroeconomic/ﬁscal stability in an
environment featuring oil price volatility. Households’ welfare is captured by the volatilities of
consumption and employment along the simulated path of the model; the ﬁscal stability measure
is captured by the volatility of the non-oil ﬁscal balance whereas the macroeconomic stability
measure is captured by an equally weighted average of the volatility of the non-oil ﬁscal balance
and that of the real exchange rate. We ﬁnd that depending on the degree of the policy maker’s
preference for stability, 55 to 85 percent of oil windfalls should be used for public investment,
suggesting that 15 to 45 percent of the resource income should be saved in a sovereign wealth
fund. Our optimal share to invest domestically mainly depends on the persistence of oil shocks
and on the interest rate paid on savings. In comparison with the recent literature, the optimal
enor (2014), which ranges
share to invest is slightly higher than the values estimated in Ag´
from 30 percent to 60 percent. Our ﬁgures are higher because we abstract from oil production
volatility in our simulations as we are dealing with a country that newly discovered oil; this
reduces the economic volatility and therefore the need for savings in a sovereign wealth fund.
Overall, the key recommendation of this paper is that unlike the all-investing approach which
seems to exacerbate Dutch disease eﬀects, the sustainable approach appears to dominate in
terms of wealth and resources stability with the optimal oil share to be saved in a sovereign fund
varying with the persistence of oil shocks.
The rest of the paper is organized as follows. Section 2 describes the model, whereas section
3 presents a parametrization to mimic the key features of a small open economy such as Uganda.
Section 4 presents our main ﬁndings and Section 5 oﬀers a conclusion.
5
2 Model setup
The framework is a small open New Keynesian model adapted from Obstfeld and Rogoﬀ (2000)
and Christiano et al. (2005), in which we include three production sectors: non-traded goods,
traded goods, and a natural resource. The model includes the standard friction of investment
adjustment costs, which is standard in DSGE literature. We also include the friction `
a la Calvo
in the prices and wages setting as in Christiano et al. (2005) and Kopoin et al. (2013). The
model is calibrated from the Uganda data and includes various exogenous shocks as well as
various ﬁscal policy regimes.
2.1 Households
The economy is composed of a continuum of inﬁnitely-lived households of mass 1. Households
obtain utility from consumption ct , which is produced by domestic ﬁrms, and receive disutility
from labor supply lt . Accordingly, the preferences of the representative household are given by
the following lifetime utility function, which is separable with respect to consumption and hours
worked.
∞
E0 β t (log (ct − γct−1 ) + ψ log (1 − lt )) (2.1)
t=0
where β denotes the household’s discount factor and ψ is the inverse of Frisch elasticity of labor
supply, whereas γ ∈ (0, 1) is the parameter that controls the extent of habit. Finally, E0 denotes
the conditional expectation operator evaluated at time 0.
Households are assumed to be able to borrow or lend freely in national ﬁnancial markets
by buying or issuing risk-free bonds denominated in units of consumptions goods, and those
in the non-tradable goods sector set nominal wage using Calvo’s partial indexation mechanism.
Finally, the representative household maximizes the aforementioned utility function subject to
budget constraint in units of domestic composite consumption:
Rt−1 bt−1
(1 + τtc )ct + iN T
t + it + bt = + (1 − τtl )wt lt + ΩN T
t + Ωt
πt (2.2)
N N T T
+ rt kt−1 + rt kt−1 + zt ,
6
where τtc and τtl denote the tax rates on consumption and income from labor supply. Total
private investment − deﬁned as the sum of private investment in the tradable sector and that
in non-tradable sector − is given by: it = iT N
t + it . bt is the domestic government debt paying
b ), π is the domestic inﬂation and w is the real wage index
a gross nominal rate of Rt = (1 + rt t t
expressed in units of consumptions goods. zt denotes total government transfers to households,
whereas ΩN T N N T T
t and Ωt are proﬁts from the non-traded and traded goods sectors. rt kt−1 + rt kt−1
is capital income. Throughout the analysis, we assume that households do not have access to
foreign loans.1 This assumption is consistent with the fact that in a typical low-income country,
households are generally hand-to-mouth households. So, they do not have access to assets and
capital markets and consume all their disposable income from labor supply (see Jihad et al.
(2012) and Cherif and Fuad (2012)). However, domestic bonds play an important role in our
setup, allowing households to smooth idiosyncratic shocks. Since these bonds are in zero net
supply, households are subject to the following no-Ponzi game constraint:
Et [bt+j ]
lim j
≤ 0. (2.3)
t→∞ Rt+j
Finally, the consumption basket is a composite of traded goods and non-traded goods, aggregated
using a constant-elasticity-of-substitution (CES) technology.
χ
1 χ−1 1 χ−1 χ−1
ct = φ χ cN
t
χ
+ (1 − φ) χ cT
t
χ
, (2.4)
with χ and φ denoting the intratemporal elasticity of substitution and the degree of home con-
sumption bias. Thus, if φ > 1/2, the representative household has a home bias in consumption.
In this framework, we assume that the composite consumption is the numeraire of the economy
and the law of one price holds for traded goods. Accordingly, the real exchange rate st is also
the relative price of traded goods to composite consumption. As consequence, the price of one
1
Most of low-income countries are not able to borrow on international ﬁnancial markets. This situation
has been worsened by the last ﬁnancial crisis, which led to credit-rating agencies to downgrade most low-
income countries’ obligation bonds.
7
unit of composite consumption is:
1−χ
1 = φ pN
t + (1 − φ) (st )1−χ . (2.5)
In equation [2.5], pN
t denotes the relative price of non-traded goods to composite consumption.
Recall that, non-traded and traded consumption are a composite goods.
χ χ
1 1 χ−1 1 1 χ−1
1− χ 1− χ
cN
t = cN
t (i) di , and cT
t = cT
t (i) di . (2.6)
0 0
N and
Finally, households supply diﬀerentiated labor lt to both traded and non-traded sectors (lt
T ), and we assume that there is imperfect labor mobility captured by the following constant
lt
elasticity of substitution (CES) function for total labor
ξ
1+ξ 1+ξ 1+ξ
−1 N −1 T
lt = ω ξ lt ξ
+ (1 − ω ) ξ lt ξ
, (2.7)
where ω is the steady-state share of labor supply in the non-traded goods sector, which also
governs labor sectoral mobility in the economy. In equation [2.7], ξ (ξ > 0) is the elasticity of
substitution between the two types of labor. Then, the aggregate real wage index corresponds
to
1
N 1+ξ T 1+ξ 1+ξ
wt = ω wt + (1 − ω ) wt , (2.8)
N and w T are the real wage rate in the non-traded and traded goods sector, respectively.
where wt t
Eﬃcient allocation: Given the preferences and the budget constraint, the household’s
optimization problem consists of choosing ct , iN T N T
t , it , kt , kt , and bt for all t ∈ [0, ∞) to maximize
lifetime utility function, Ut (·). Finally, given [2.1] and [2.2], households
ψ
− λt (1 − τ l )wt = 0, (2.9)
1 − lt
Rt+1
− λt + βEt λt+1 = 0, (2.10)
πt+1
8
N N N 2
ktN λ kt kt ϕN kt
t+1 +1 +1 +1
1+ϕN N
−1 = βEt 1 − δ N + rt
N
+ ϕN N
−1 N
+ N
−1 ,
kt−1
λt kt kt 2 kt
(2.11)
T T T 2
ktT λ kt kt ϕT kt
t+1 +1 +1 +1
1 + ϕT T
−1 = βEt 1 − δ T + rt
T
+ ϕT T
−1 T
+ T
−1 .
kt−1
λt kt kt 2 kt
(2.12)
2.2 Firms
Non-traded good ﬁrms are assumed to be monopolistically competitive, while traded good sector
ﬁrms are perfectly competitive. In each sector, ﬁrms produce goods using labor lt , private
N or k T ) and public capital k G . In contrast to the natural resource sector, production
capital (kt t t
and oil prices are assumed to follow exogenous deterministic processes. These assumptions are
consistent and match clearly low-income and small-open economy frameworks since Uganda’s
oil production, as estimated, is relatively small in comparison to world’s oil supply.2 In the
following subsections, we describe the production chain in the tradable and non-tradable goods
sectors.
2.2.1 Non-traded Good Sector
The monopolistic producer i ∈ (0, 1) uses the following technology
N αN (1−αN ) αG
yt = aN N
t kt
N
· lt G
· kt (2.13)
where aN G
t is the sectoral total factor productivity (TFP), and kt−1 is the public capital stock
with an output elasticity of αG . This production technology is well received and documented
in neoclassical literature, featuring public capital as a key input. Following this literature,
Baxter and King (1993) and Kamps (2004) have considered a constant returns to scale function
associated with private inputs (private capital and labor) and an increasing returns to scale
technology, when considering all input factors including public capital. Relative to another
2
These assumptions and their quantitative implications are well documented in Ambler et al. (2004),
Cherif and Fuad (2012) and Jihad et al. (2012).
9
common speciﬁcation with constant return to scale to all production factors, this speciﬁcation
has the advantage that αT and αN can be calibrated to match income shares of labor and private
capital of an economy. Finally, this speciﬁcation has the advantage to facilitate the steady-state
computation. Private capital evolves by the law of motion
N 2
N N N ϕN kt+1 iN
kt+1 = (1 − δ )kt + 1 − −1 t (2.14)
2 ktN
N)
Θ(kt
N ), is the investment adjustment cost function, satisfying: Θ(1) = Θ (1) and Θ > 0.3
where, Θ(kt
As in Obstfeld and Rogoﬀ (2000), the monopolistic producer i faces a demand function for the
variety i
N pN
t (i) N
yt (i) = N
yt , (2.15)
pt
N is the aggregate non-traded demand. A representative non-traded good ﬁrm chooses
where yt
its price (pN N N
t (i)), labor demand (lt (i)), and capital stock (kt+1 (i)) to maximize its net present-
value proﬁts, weighted by the household’s marginal utility of consumption (λt ).
∞
Et β t λt (1 − ι)pN N N N N N N N
t (i)yt (i) − wt lt − Adjt (i) − rt kt (i) + ιpt yt (2.16)
t=0
subject to the production function deﬁned in equation [2.13] and the demand function in equation
[2.15]. ι captures distortions in developing countries that discourage ﬁrms from investing and
hiring further. ι may be viewed as a distorting tax on ﬁrms, but revenue collected remains in
the private sector and is distributed to households and proﬁts. Additionally, this tax helps to
match the relatively low investment to GDP ratios observed in developing countries. However,
this implicit tax is rebated back to the ﬁrms as lump-sum transfers.
Denoting by λN
t , the Lagrange multiplier associated with the optimization program, which
N , then the
also may be interpreted as the real marginal cost of producing one unit of output yt
3
Under this speciﬁcation, the steady-state level of capital stock is not aﬀected by the presence of
adjustment costs.
10
ﬁrst order conditions of a costs minimizing problem are given by
N
yt
N
rt = λN N
t α (1 − ι) N
,
kt
N
(2.17)
N yt
wt = λN
t (1
N
− α )(1 − ι) N ,
lt
a la Calvo. To this end, we
Price setting: Price rigidity is introduced following a strategy `
assume that in each period, a fraction φp of ﬁrms cannot change their prices. When allowed to
do so, ﬁrm in the non-tradable goods sector chooses the price of its output, pN
t (j ), in order to
maximize its discounted real proﬁts. All other ﬁrms can only index their prices to past inﬂation
of the composite good price. Indexation is controlled by χp ∈ (0, 1) (χp = 0 refers to a no
indexation case while χp = 1 is a perfect indexation). Intermediate good producer j chooses
the optimal price pN
t (j ) at the time t. Then, after h periods with no reoptimizing, ﬁrm’s price
would evolve over time according to the following recursive equation
h−1
pN
t+h (j ) = (πt+1 )
χp
× (πt+2 )χp × · · · × (πt+h−1 )χp × pN
t (j ) = (πt+i )χp pN
t (j ), (2.18)
i=1
where πt+h = pt+h /pt+h−1 . The problem of ﬁrm j is then:
∞ h−1
pN
t (j )
max Et (βφp )l λN
t+h (πt+i )χp − mct+h N
yt+h (j )
pN
t (j ) i=0 i=1
pN
t+h
−ξp (2.19)
h−1
pN (j )
s.c. N
yt+h (j ) = (πt+i )χp tN N
yt+h ,
i=1
pt+h
where λN
t+h is the marginal utility of wealth for a ﬁrm j after t + h periods. Assuming that all
ﬁrms of type j adopt a same strategy, then the ﬁrst order condition related to the optimal price
of a domestic intermediate good j is
∞ h−1 −ξpt
(πt+i )χp
Et (βφp )h λN
t+h
N
yt+h (j )
ξp πt+i+1
i=0 i=1
pN
t = 1−ξh,t
, (2.20)
ξp − 1 ∞ h−1
(πt+i )χp
Et (βφp )l λN
t+h
N
yt+h (j )
πt+i+1
i=0 i=1
11
In the case of a full indexation (χp = 1), equation [2.20] may be rewritten to derive the New
Keynesian Phillips curve given by: (pN 1−ξp = φ (pN )1−ξp + (1 − φ )(pN )1−ξp .
t ) p t−1 p t
Wage setting: Recall that households supply diﬀerentiated labor inputs used by interme-
diate good producers and set their nominal wage using Calvo’s partial indexation. We assume
that the aggregate labor is supplied by a representative competitive ﬁrm that hires labor sup-
plied by households individually. The diﬀerentiated labor inputs supplier aggregates labor using
ξw
ξw −1
N = 1 N ξw −1
a constant elasticity of substitution function given by lt 0 lt (i)
ξw di , where ξw
(ξw ∈ (0, ∞)) is the elasticity of substitution among diﬀerent types of labor. The diﬀerentiated
labor inputs supplier maximizes proﬁts subject to the production function given all diﬀerenti-
N (i), and the aggregate wage, w N . The ﬁrst order conditions are such that
ated labor wages, wt t
1
N (i) −ξw
wt 1 N 1−ξw
N (i) = N N =
and wt 1−ξw di
lt wtN lt 0 wt (i) . Following Calvo (1983), we include
nominal rigidities on households’ wage setting. Thus, in each period, a fraction 1 − φw can
change their wages, i.e., households only reset optimally the wage contract in states of nature
with a constant probability 1 − φw . All others are not able to lay out the optimal wage contract.
In that case, they can only partially index their wages to the past inﬂation of the composite
domestic goods. The level of indexation is captured by χw ∈ (0, 1). This nominal rigidity implies
that if the household cannot change its wage for h periods, then, its normalized wage is given
h χw N
πt +s−1 wt (i)
by .
πt+i pt
i=1
χw −ξw
N (i) = h πt N
+h−1 wt (i) N ), the
Recall that, under the labor supply constraint ( lt+h i=1 πt+h wN lt+h
t+h
eﬃcient wage can be written as a geometric average of past real wage and the new optimal wage
1−ξw N 1−ξw N 1−ξw 1−ξw 1−ξw N 1−ξw
in the case of full indexation πt wt = φ w wt−1 πt−1 + (1 − φw )πt wt .
2.2.2 Traded Good Sector (Exportable Goods)
Intermediate tradable good production:
The intermediate traded good sector is perfectly competitive and goods are produced using
12
a similar technology to that in the non-traded good sector.
iT αT (1−αT ) αG
yt = aT T
t kt
T
· lt G
· kt (2.21)
The total factor productivity (TFP) in the tradable good sector, aT
t , is subject to learning-by-
doing externalities, depending on the last period traded output: ln aT T T
t = ρzT ln at−1 + d ln yt−1 .
Private capital in the traded good sector also evolves by the law of motion
T 2
T T T ϕT kt+1 iT
kt+1 = (1 − δ )kt + 1 − −1 t . (2.22)
2 ktT
T)
Θ(kt
Each ﬁrm maximizes its weighted present-value proﬁts,
∞
Et β t λT T T T T T T T
t (1 − ι)st yt (i) − wt lt − Adjt (i) − rt kt (i) + ιst yt (2.23)
t=0
Let λT
t be the Lagrange multiplier associated with the production function constraint in the
tradable goods sector, which may be interpreted as the real marginal cost of producing one unit
T . The ﬁrst order conditions of a minimizing problem are given by
of output yt
iT
yt
T
rt = λT T
t α (1 − ι) T
,
kt
(2.24)
y iT
T
wt = λT
t (1 − α )(1 − ι) t
T
T
,
lt
T d , is used for
A part of the intermediate traded good production in the traded goods sector, yt
the domestic market and the remaining part, y T x , is exported in fully competitive market. So
that,
iT Td Tx
yt = yt + yt . (2.25)
The foreign demand for locally produced goods is as follows:
−µ
Tx px
t ∗
yt = yt , (2.26)
p∗
t
13
where (µ − 1)/µ captures the elasticity of substitution between the exported goods and
∗ and p∗ are,
foreign-produced goods in the consumption basket of foreign consumers, and yt t
respectively, foreign output and the price index. Both variables are exogenously given.
Final tradable good production:
There is a continuum of intermediate-good-importing ﬁrms in a monopolistic competition
market for, which are imperfect substitutes for each other in the production of the composite
M , produced by a representative competitive ﬁrm. We also assume Calvo-
imported good, yt
type staggered price setting in the imported goods sector to capture the empirical evidence on
incomplete exchange rate pass-through into import prices. The ﬁnal traded good is produced
T d , and imports goods,
by a competitive ﬁrm that uses domestically consumed traded goods, yt
M following a CES technology
yt
ν
1 ν −1 ν −1 ν −1
1
T Td ν M
yt = ν
φ m yt + (1 − φm ) ν yt ν
, (2.27)
where φm is the share of domestically consumed traded goods in the ﬁnal traded goods basket at
the steady state, and ν (ν > 0) is the elasticity of substitution between domestic and imported
goods. The ﬁrst-order conditions lead to
−ν
Td pd
t T
yt = φm yt , (2.28)
st
−ν
M pM
t T
yt = (1 − φm ) yt . (2.29)
st
The ﬁnal traded good price, pT , which corresponds to the numeraire of our economy is given
by
1
1−ν 1−ν 1−ν
1= φm pd
t + (1 − φm ) pM
t . (2.30)
2.2.3 Natural Resource Sector
Output in the natural resource sector is assumed to follow an exogenous process. This assump-
tion is consistent with the empirical observations since most natural resource production is in
14
reality capital intensive and does not depend on country’s endogenous factors. In addition, most
of resource investments in low-income countries is ﬁnanced by foreign direct investment (FDI)
that controls the level of oil exploitation. The production function is
O O
yt
yt −1 yo
ln = ρyo ln + t , (2.31)
yO yO
where the exogenous process returns to the steady-state level y O with the autoregressive param-
yo
eter ρyo . The resource production shock is assumed to be t ∼ i.i.d. and follows a standard
yo 2 )).
normal distribution with a standard deviation of σyo ( t ∼ N (0, σyo
The country’s resource output is assumed relatively small in the world market. Consequently,
Uganda’s resource production is assumed to not be able to aﬀect the international commodity
∗ ∗
price pO O (relative to the foreign goods)
t . As a result, the international commodity price pt
evolves according to an exogenous process deﬁned by
∗ ∗
pO
t pO
t−1 po
ln = ρpo ln + t , (2.32)
pO ∗ pO ∗
yo 2 ), and is an i.i.d. process. The
where the international commodity price shock t ∼ N (0, σyo
resource GDP from the natural resource sector in units of domestic composite consumption is:
∗
YtO = st pO O
t yt . (2.33)
As in many resource-rich economies, resource production in Uganda is subject to a royalty at a
rate of τto . Thus, the resource revenue collected from the natural resource sector is
∗ ∗
TtO = st τto pO O
t yt = st T O t . (2.34)
∗
where T O t is the resource revenue collected from the natural resource sector expressed in foreign
goods.
15
2.3 Public Sector
The model allows for ﬂexible public policy speciﬁcations, and we assume that the public sector
consists of a government and a central bank. In each period, government receives taxes and
C ), public
contracts domestic debt bt . Total expenditures include government consumption (gt
I ) and debt services. If capital letters denote the aggregate level of a variable, then
investment (gt
government budget constraint may be written as
st (1 + r∗ ) ∗ Rt−1 Bt−1
TtO + τtC Ct + τtl Wt Lt + Bt + ∗ Ft−1 = pg
t Gt + + st Ft∗ , (2.35)
πt πt
where Ft∗ is the asset value of resource fund, which generates a constant interest rate r∗ . In
[2.36], Gt is government purchases with a relative price to composite consumption goods of pg
t.
The model allows external assets accumulation, while we abstracts from external commercial
borrowing. Despite taxing revenues from the non-tradable and tradable goods sectors (ιpN
t Yt
N
and ιst YtT ), the government is unable to use this as an additional source of ﬁscal revenue.
Consequently, this tax does not appear as revenue in the government’s budget constraint (2.36).
By assuming that they are rebated to the ﬁrms, the model captures the ineﬃciencies of revenue
mobilization in Uganda. Including this feature, our speciﬁcation makes explicit the challenges
that ﬁscal authorities in developing economies face regarding tax revenue mobilization. However,
the government collects taxes on revenues from the natural resource sector and they account as
a ﬁnancing source for public infrastructures.
We deﬁne the non-oil ﬁscal balance that will be used for the ﬁscal stability measure in the
investigations about the optimal share of oil revenue to be used for public investment as follows:
Rt−1 Bt−1
NO
F Bt = τtC Ct + τtl Wt Lt + Bt − pg
t Gt − . (2.36)
πt
Finally, government purchases consist of expenditures on government consumption GC
t and
public investment GI . As in the private consumption, we assume that government purchases
are a CES function of traded and non-traded goods.
χ
1 χ−1 1 χ−1 χ−1
Gt = η χ GN
t
χ
+ (1 − η ) χ GT
t
χ
, (2.37)
16
where η is the degree of home bias in government purchases. The relative price of government
consumption to private consumption is
1
1−χ
pg + (1 − η ) (st )1−χ
N 1−χ
t = η pt . (2.38)
2.3.1 Absorptive Capacity Constraints and Ineﬃciency of Public Investment
In our framework, we introduce the concept of ineﬃciency of public investment to capture the
stylized fact of eﬀective public investment in low-income countries by allowing the model to take
into account potential investment ineﬃciencies and absorptive capacity constraints. As a result,
public investment generates capital accumulation following this law of motion
G G G G
kt+1 = (1 − δ )kt + GI
t, (2.39)
where 0 < (1 − G) ≤ 1 governs the ineﬃciency of public investment and δ G is the constant
depreciation rate of public capital.
2.3.2 Fiscal Policy
In this framework, we introduce three approaches to analyze ﬁscal policy in Uganda, which are
diﬀerent from the use of the fund from the natural resource sector. This involves three regimes of
management of the ﬁscal policy: the all-investing, the all-saving and the sustainable approaches.
Policy A: The All-Investing Approach.
Under this approach, the resource fund stays at its initial level, and all additional revenues from
the natural resources sector as well as wage and consumption taxes, and revenues from bonds
issuance are invested in public infrastructures and government consumption. Thus, Ft∗ = F ∗ ,
∀t, while public investment evolves as follows:
TtO TO
GI I
t =G + g − g , (2.40)
pt p
Gt = GC I
t + Gt , and (2.41)
17
Ft∗ = F ∗ , ∀t ∈ [0, ∞), (2.42)
g
where GI , T O and pg are, respectively, the steady state values of GI O
t , Tt and pt .
Policy B: The Saving in a Sovereign Wealth Fund.
Under this ﬁscal policy, all the resource revenues are saved externally in a sovereign wealth fund
for the future generation. Thus, the resource fund evolves as follows:
TtO TO
Ft∗ = Ft∗
−1 + − (2.43)
st s
Gt = GC I
t + Gt , and (2.44)
GI I
t =G , (2.45)
where s is the steady state values of the real exchange rate.
Policy C: The Sustainable Investing Approach.
This approach, which may be viewed as a combination of the ﬁrst two ﬁscal policies, allows
a constant share of the resource revenues to ﬁnance public investment and the remaining part
is saved in a sovereign wealth fund. Under this ﬁscal policy, the country’s foreign wealth and
public investment are deﬁned as follows:
TtO TO
GI I
t =G +φ
oil
g − g , (2.46)
pt p
Gt = GC I
t + Gt , and (2.47)
TtO TO
Ft∗ = Ft∗ oil
−1 + (1 − φ ) − , (2.48)
st s
where φoil is a ﬁscal policy parameter that satisﬁes 0 ≤ φoil ≤ 1. At this point, it’s worth
mentioning that the Sustainable Investing Approach and the all-investing approach produce the
same ﬁscal responses under φoil = 1, and the all-saving approach is obtained by setting φoil = 0.
18
2.3.3 Central Bank
Monetary policy is conducted by the central bank, which manages the short-term nominal
b ), in response to ﬂuctuations in domestic output gap and in consumer
interest rate Rt = (1 + rt
price inﬂation gap using a Taylor-type rule. This managing rule allows the central bank to
smooth nominal interest rates through open market operations.4
log Rt /R = λr log Rt−1 /R + (1 − λr ) λπ log (πt /π ) + λy log Yt /Y + ϕt , (2.49)
where Yt denotes the country’s growth domestic product (GDP) and ϕt are i.i.d. normal inno-
vations with a standard deviation of σr .
2.4 Rest of the World
Following the 2014 World Economic Outlook (WEO) released by the IMF, Uganda is considered
as a small open economy. Consequently, a plausible assumption is to assume that domestic
developments do not aﬀect the rest of the world economy. However, the foreign economy’s
dynamics (oil prices) have an impact on the domestic economy. For simplicity, we assume that
the foreign interest rate, foreign output and the world inﬂation rate are exogenous and follow
AR(1) processes.
2.5 Market Clearing and Competitive Equilibrium
In a competitive equilibrium, the markets for goods, labor and capital all clear. The goods
markets clears when the demand from the agents can be meet by the production of the ﬁnal
good. To do this, we deﬁne real aggregate GDP as the sum of value added in the three sectors,
measured by their steady state prices.
Yt = p N N T O
t Yt + st Y + Yt . (2.50)
4
The use of the previous period interest rate allows us to match the smooth proﬁle of the observed
interest rate in the data.
19
Then, the general equilibrium in the goods markets involves:
∗ ∗ ∗ ∗
(Ct + It + pG x Tx
t Gt ) + (pt Yt − pM M
t Yt ) + st Ft − Ft−1 = Yt + st r Ft−1 , (2.51)
N + I T is the private investment, and C = C N + C T is the total consumption.
where It = It t t t t
Recall that government purchases consist of expenditures on government consumption GC
t and
public investment GI , therefore Gt = GC I
t + Gt . Let denote by CAt the current account, then
the balance of payment condition is given by
CAt = px
t Yt
Tx
− pM M
t Yt + s t Ft∗ − Ft∗
−1 . (2.52)
Then, labor market clearing requires demand for labor by ﬁrms in both sectors to equal the
sector speciﬁc supply of labor. This implies that:
1 1
N T
Wt ≡ wt (i)di = (wt (i) + wt (i))di = WtN + WtT (2.53)
0 0
and
1 1
N T
Lt ≡ lt (i)di = (lt (i) + lt (i))di = LN T d
t + Lt = Lt , (2.54)
0 0
where Ld
t denotes total demand for labor by ﬁrms in both sectors.
Finally, capital market clearing conditions imply that:
1 1
N T N T
Kt ≡ kt (j )dj = (kt (j ) + kt (i))di = Kt + Kt , (2.55)
0 0
and
1
Bt (i)di = 0. (2.56)
0
2.6 Driving Forces
There are seven sources of uncertainty in our framework: One productivity shock in each of the
two sectors (tradable and non-tradable), an oil price shock that aims to capture the volatility
in the oil price markets, an oil production shock, a foreign demand shock, a foreign price shock
20
captured by foreign inﬂation and a domestic monetary policy shock. We assume that all shocks
follow autoregressive processes of order one. This assumption gives rise to the following laws of
motion:
ln(aN N
t ) = ρzN ln(at−1 ) +
N
Z,t : Productivity shock in the non-tradable sector
ln(aT T
t ) = ρzT ln(at−1 ) +
T
Z,t : Productivity shock in the tradable sector
ln(ϕt ) = ρϕ ln(ϕt−1 ) + ϕ,t : Monetary policy shock
yo
ln YtO /Y O = ρyo ln YtO
−1 /Y
O
+ t : Oil production shock (2.57)
∗ ∗ ∗ ∗ po
ln PtO /P O = ρpo ln PtO
−1 /P
O
+ t : Oil price shock
∗
ln(πt ∗
) = (1 − ρπ∗ ) ln(π ∗ ) + ρπ∗ ln(πt−1 ) + π∗ t : World price shock
ln(Yt∗ ) = (1 − ρY ∗ ) ln(Y ∗ ) + ρY ∗ ln(Yt∗
−1 ) + Y ∗t : Foreign demand shock
2.7 Competitive equilibrium
A competitive equilibrium is deﬁned as a set of sequences of functions for (i) households’ policies
Ct (i), Lt (i), Bt (i) and It (i) that solve the maximization problem of the household; (ii) ﬁrms’
policies Kt (j ), Ld
t (j ) and Wt (i) that solves ﬁrms maximization problem; (iii) aggregate prices
PtN , Ptx , St and Pt∗ ; (iv) saving and consumption decision rules for government; and (v) all
markets clear. The equilibrium system of the model consists of the private agents optimal-
ity conditions, the government budget constraint, ﬁscal policy, market clearing conditions, the
balance of payment condition, and the exogenous processes of the shocks.
3 Model Calibration
To evaluate the impact of ﬁscal responses to resource revenue on macroeconomic stability in
Uganda, we set the parameters of our model to reﬂect most of key features of a small-open
economy with abundant natural resources. The model is at the quarterly frequency, and Tables
1, 2 summarize the baseline calibrations and some steady-state ratios using macroeconomic
fundamentals of the Uganda. These parameters and ratios are consistent to those in line with the
enor and Aizenman (1999), Goldberg
evidence for low-income countries and calibrated in Ang´
21
enor (2014). Data sources used to match key ratios include the IMF’s World
(2011) and Ag´
Economic Outlook (WEO) database, the oil and revenue management policy framework provided
by the Uganda’s Ministry of Finance and various research papers such as Pritchett (2000),
enor and Aizenman (1999), Kopoin et al. (2013) and Ag´
Goldberg (2011), Ang´ enor (2014).
In the representative household’s utility function, the weight on leisure ψ is set to 3, which
leads to the steady-state value of household work eﬀort to be 40 percent of available time. The
household’s discount factor, β , is set 0.93, implying a long-run real interest rate of 9.68 percent
annually. This assumption is fairly reasonable and consistent regarding banks’ interest rates in
most of low-income countries (see African Development Indicators (ADI)). In addition, the share
of capital in the production function for intermediate goods in the non-traded goods sector, αN ,
is set to 0.45, while it is set to 0.3 in the traded goods sector. These values indicate that the
informal (non-tradable goods sector) sector is more intensive in labor than the tradable goods
sector. The depreciation rates of capital are ﬁxed to 0.1 in the informal sector and 0.075 in
the tradable goods sector. All these values are consistent with studies on Sub-Saharan African
enor (2014).
countries and reported in Jihad et al. (2012), Cherif and Fuad (2012) and Ag´
In our paper, we use the empirical evidence based on Mexican data from 1980 to 1994 by
Arestoﬀ and Hurlin (2006) to pin-down the parameter that governs the eﬃciency of public invest-
ment G. This paper shows that the coeﬃcient of regressing public capital produced (eﬀective
investment in our model) on investment expenditures falls between 0.4 and 0.65. This range of
investment eﬃciency is in line with the estimates in Pritchett (2000) for Sub-Saharan African
countries with a linear speciﬁcation between eﬀective investment and investment expenditures.
Based on these empirical papers and the macroeconomic eﬀorts undertaken by the government
to sustain public investment, we set G to 0.6.
The nominal price rigidity parameter in the non-traded goods sector, as well as the nominal
wage-setting parameter are set following Calvo’s model of staggered price and wage adjustment.
As in Christiano et al. (2005), the probability of not reoptimizing for price and wage setters in
the domestic country, φp and φw , are ﬁxed to 0.75 and 0.64, respectively. The degree of home
bias in private consumption, φ, and the elasticity of substitution between domestic labor types,
ξ , are set to 0.4 and 1, respectively. These values are estimated in Christiano et al. (2010) for
22
the U.S. economy and are commonly used in the literature of developing countries.
The domestic monetary policy parameters λr , λπ et λy are set to 0.8, 1.5 and 0.1/4, respec-
enor
tively. These values satisfy the Taylor principle and are consistent to those estimated in Ag´
(2014) and Kopoin et al. (2013). The standard deviation of both domestic and foreign mone-
tary policy shocks is ﬁxed to 0.0016, ρmp = ρRf = 0.0016, which ensures that a one-standard
deviation shock moves the interest rate by 0.6 percentage points. This value is consistent to the
empirical estimates reported in Christiano et al. (2005).
The model is solved using a second-order perturbation method around its deterministic
steady state.
4 Findings
The patterns of investment and saving out of income from the oil windfall in managing of the
optimal ﬁscal policy remain ambiguous for policymakers. In practice, the key issue for the
spending of oil revenue by the government, viewed as a Ramsey problem, is to scale up public
investment to meet huge needs in public infrastructure without generating higher public sector
deﬁcits and a Dutch disease in an uncertain oil production world, characterized by unexpected
shocks and prices volatility. To address this issue with our baseline DSGE model, we simulate
the eﬀects of oil production shocks and interpret it as a boom in the oil sector. Using the
parameters calibrated to reﬂect the key features of a small open economy such as Uganda, we
focus on the impulse response functions of some key variables. Throughout, we simulate and
compare the impulse responses to a one standard-deviation shock to the oil production.
Figures 1, 2 and 3 show impulse responses by illustrating macroeconomic dynamics under
three stylized ﬁscal policy approaches for managing a resource windfall: investing in public
capital, saving in a sovereign wealth and sustainable investing in public capital. In Table 1, the
solid lines present the responses under the ﬁscal policy A (investing in public capital), and the
dashed lines are under the ﬁscal policy B (saving in a sovereign wealth fund). Solid lines in
Figure 3 remain the responses under the ﬁscal policy A, while dashed lines present responses
23
Table 1: Baseline Parameter Calibration
Parameters Description Values
φ Degree of home bias in private consumption 0.3
χ Elasticity of substitution (traded and non-traded goods) 0.44
ξ Elasticity of substitution between labors 1
β Discount factor 0.93
αN Capital income share in non-traded goods sector 0.45
αT Capital income share in traded goods sector 0.3
αG Output elasticity of public capital 0.2
T
ϕ , ϕN Investment adjustment cost 10
φp Probability of not reoptimizing prices 0.75
φw Probability of not reoptimizing wages 0.64
ω Share of labor supplied to non-traded sector 0.55
δN Depreciation rate for K N 0.1
δT Depreciation rate for K T 0.075
δG Depreciation rate for public capital 0.07
ψ Inverse of Frisch elasticity of labor supply 3
η Home bias of government purchases 0.65
τl Eﬀective labor tax rates 0.1
τc Eﬀective consumption tax rates 0.1
G
Eﬃciency of public investment 0.6
r∗ Annual real return to a resource fund 0.015
λr Interest rate smoothing parameter 0.8
λπ Central banks’ inﬂation reaction parameter 1.5
λy Central banks’ output reaction parameter 0.025
φoil Share of oil revenues allocated to public investment 0.5
ρyo 0 0.95 0
Uncorrelated oil production and price shock parameters
0 ρpo 0 0.95
under the ﬁscal policy C (sustainable investing). In Figure 2, the solid lines are under the saving
in a sovereign wealth fund policy, and the dashed lines depict responses under the ﬁscal policy
C. Unless mentioned, the units in the y-axis are percentage deviations from the original steady
state and the x-axis denotes the number of quarters after the initial date of extraction.
24
Table 2: Steady-state Values in percentage of total output
Steady-state ratios Description Values
Y O /Y Oil revenues to GDP ratio in steady state 0.072
I /Y Total investment to GDP ratio in steady state 0.1468
Y T /Y Tradable to GDP ratio in steady state 0.329
Y N /Y Tradable to GDP ratio in steady state 0.665
LN /L Share of employment in non-tradable sector 0.583
LT /L Share of employment in tradable sector 0.417
C N /C Non-tradable goods consumption to C 0.316
GC /Y Government consumption to GDP ratio in steady state 0.53
GI /Y Public investment to GDP ratio in steady state 0.32
F ∗ /GDP Sovereign wealth fund to GDP ratio in steady state 0.08
4.1 All-investing and saving in a sovereign wealth fund
In response to an increase in the oil production, oil output and total output rise gradually,
and this drives up the oil revenue. Under the saving in a sovereign wealth fund policy, foreign
reserves increase permanently, reaching around 10 percent of GDP after 10 years (Figure 1,
panel A and C). As higher output means more income to households, under the all-investing
approach, this exogenous shock leads to an increase in the private consumption to reach about
0.25 percent after 5 years (Figure 1, panel A). On the other hand, since the government budget
constraint includes interest earnings from foreign reserves, private consumption also rises under
the saving in a sovereign wealth fund policy, reaching around 0.17 percent after 6 years. Higher
private consumption, in turn, leads households to reduce labor supply by about 0.25 percent and
lower the marginal product of private investment. Consequently, wages increase sharply in both
the tradable and the non-tradable goods sectors. Lower labor supply and private investment
lead to a decline of non-oil GDP (Figure 1, panel A and B). Public capital also rises sharply by
around 0.35 percent after 3 years and half under the all-investing approach, and remains at the
pre-windfall level under the all-saving approach because none of the resource income is allocated
for public investment (Figure 1, panel B).
25
7 Simulated results
3: Responses
TableFigure to a
1. Responses toone standard
a one deviation
standard deviation oil production
oil production shock
shock − ﬁscal − ﬁscal
policy A and policy
B A and B
Panel A
Aggregate Consumption Consumption Tradable Goods Consumption NonTradable Goods
0.25 1 0
Deviation from s.s. (%)
Deviation from s.s. (%)
Deviation from s.s. (%)
0.2 0.8 −0.5
0.15 −1
0.6
0.1 −1.5
0.4
−2
5 · 10 −2
0.2
0 −2.5
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
Total Output Private Investment Public Investment
4 0 0.8
Deviation from s.s. (%)
Deviation from s.s. (%)
Deviation from s.s. (%)
−0.2
3 0.6
−0.4
2 −0.6 0.4
−0.8
1 0.2
−1
0 −1.2 0
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
Public Capital Investment Tradable Sector Investment NonTradable Sector
0 0
Deviation from s.s. (%)
Deviation from s.s. (%)
Deviation from s.s. (%)
0.3 −0.1
−0.2
−0.2
0.2
−0.4 −0.3
0.1
−0.4
−0.6
0 −0.5
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
Under the All-investing in Public Capital Approach Under the Saving in a Sovereign Wealth Fund Approach
Notes Notes : The show
: The ﬁgures ﬁgures impulse
showresponse
impulse response
functions functions
from fromDSGE
the simulated the simulated DSGE model
model to illustrate the to
eﬀect of a one-standard-deviation oil production shock. Responses are expressed in percentage
illustrate the eﬀect of a one-standard-deviation oil production shock. Responses are deviation
from the steady-state values. The solid line shows the response of the ﬁscal policy A (All-Investing
expressed
Approach in percentage
) and Dashed lines show deviation from
the response the
of the steady-state
ﬁscal values. The
policy B (All-Saving solid line
Approach ). shows the
response of the ﬁscal policy A (All-Investing Approach) and Dashed lines show the
response of the ﬁscal policy B (All-Saving Approach).
26
49
Panel B
Output Tradable Sector Output NonTradable Sector Non Oil Revenues
0 0 0
Deviation from s.s. (%)
Deviation from s.s. (%)
Deviation from s.s. (%)
−5 · 10−2 −5 · 10 −2
−0.2
−0.1 −0.1
−0.15 −0.15 −0.4
−0.2 −0.2 −0.6
−0.25 −0.25
−0.8
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
Total Employment Employment Tradable Sector Employment NonTradable Sector
0 0 0
Deviation from s.s. (%)
Deviation from s.s. (%)
Deviation from s.s. (%)
−5 · 10−2 −5 · 10−2 −5 · 10−2
−0.1 −0.1 −0.1
−0.15 −0.15 −0.15
−0.2 −0.2 −0.2
−0.25 −0.25 −0.25
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
Wage Tradable Sector Wage NonTradable Sector Total Wage
·10−2
0.1
8 0.1
Deviation from s.s. (%)
Deviation from s.s. (%)
Deviation from s.s. (%)
8 · 10−2
8 · 10−2
6
6 · 10−2 6 · 10−2
4
4 · 10−2 4 · 10−2
2 2 · 10−2 2 · 10−2
0 0 0
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
Under the All-investing in Public Capital Approach Under the Saving in a Sovereign Wealth Fund Approach
Notes : The ﬁgures show impulse response functions from the simulated DSGE model to
Notes illustrate eﬀectimpulse
the show
: The ﬁgures response functions fromoil
of a one-standard-deviation production
the shock.
simulated DSGE Responses
model are the
to illustrate
expressed
eﬀect in percentage deviation
of a one-standard-deviation from the
oil production steady-state
shock. Responsesvalues. The solid
are expressed line shows
in percentage the
deviation
fromresponse of the ﬁscal policy A (All-Investing Approach) and Dashed lines show the
the steady-state values. The solid line shows the response of the ﬁscal policy A (All-Investing
Approach) and Dashed lines show
response of thethe response
ﬁscal of B
policy the ﬁscal policy BApproach
(All-Saving (All-Saving). Approach).
50
27
Panel C
Total Government Spending Gov. Spending Tradable Sector Gov. Spending NonTradable Sector
1.5
Deviation from s.s. (%)
Deviation from s.s. (%)
Deviation from s.s. (%)
−0.2
2
1
−0.4
0.5 1
−0.6
0
0
−0.8
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
Non Oil Exports Imports Sovereign Wealth Fund
0.4
0
Deviation from s.s. (%)
Deviation from s.s. (%)
Deviation from s.s. (%)
1 0.3
−0.5
0.5 0.2
0.1
−1 0
0
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
Inﬂation Exchange Rate Public Debt
0 2
Deviation from s.s. (%)
Deviation from s.s. (%)
1 1.5
Percentage Points
−0.5
−1 1
0.5
−1.5 0.5
−2 0
0
−2.5
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
Under the All-investing in Public Capital Approach Under the Saving in a Sovereign Wealth Fund Approach
Notes : The ﬁgures show impulse response functions from the simulated DSGE model to
illustrate the eﬀect of a one-standard-deviation oil production shock. Responses are
Notes : The ﬁgures show impulse response functions from the simulated DSGE model to illustrate the
expressed
eﬀect in percentage deviation
of a one-standard-deviation the steady-state
from shock.
oil production Responses arevalues. The in
expressed solid line shows
percentage the
deviation
response
from the of the values.
steady-state ﬁscal policy A (All-Investing
The solid Approach
line shows the response ) and
of the ﬁscalDashed
policy Alines show the
(All-Investing
Approach) and Dashed lines show
response the ﬁscal
of the response B ﬁscal
of the
policy All-Saving ).
policy B (Approach
(All-Saving Approach).
51
28
A boom in the oil sector makes the country a net exporter. Then, the wealth and income
accumulated from the resource windfall increase, generating more revenue for government. As
a result, demand in the non-tradable goods sector increases, leading to a substantial rise in
the prices of non-tradable goods. Since Uganda is considered as a small open economy and
a price taker in the international tradable goods market, the real exchange rate, deﬁned as
the relative price of non-tradable to tradable, appreciates consequently. This appreciation,
which is more pronounced under the all-investing approach, reduces the competitiveness of
the country’s exports and domestic imports-competing products. Therefore, imports become
relatively cheaper, leading to a rise in the total imports by about 1.2 percent and a fall of non-
oil exports by around 1.3 percent (Figure 1, panel C). Finally, under the all-saving approach,
the economy experiences smaller movements because resource income is directly saved into
a foreign account. In contrast, under the all-investing approach, the oil production shock is
more persistent and the return to the pre-windfall equilibrium is done more slowly. Comparing
these two stylized ﬁscal policies, simulations show that the boom in the oil production sector
generates sizeable macroeconomic activity under the all-investing approach. However, the all-
saving approach is much less susceptible to generate Dutch disease eﬀects.
4.2 The sustainable investing approach
In this subsection, we compare the ﬁrst two ﬁscal approaches to the sustainable investing ap-
proach. This latter ﬁscal policy, which may be viewed as a mixed policy, can conciliate public
investment and saving approach by proposing a new investment with external saving approach.
We allow the government to use half of the oil revenue for public investment (φoil = 0.5) and to
save the remaining half; Section 4.4 investigates the optimal value of φoil . As described in 2.48,
this new approach allows policymakers to choose an optimal scaling up magnitude given the size
of the oil production and economic characteristics. Figures 2 and 3 show impulse responses of
the main macroeconomic aggregates in comparison with the ﬁrst two ﬁscal policy approaches.
Under the three stylized ﬁscal policies, simulations show that the boom in the oil sector leads
to deteriorate employment in both the tradable and non-tradable goods sectors. This result,
which might be surprising, is resulting from two macroeconomic eﬀects: substitution and wealth
29
Responses
Table 4: Figure to a one
2. Responses to standard deviationoil
deviation
a one standard oil production shock
production shock − ﬁscal
− ﬁscal B and CB
policy policy and C
Panel A
Aggregate Consumption Consumption Tradable Goods Consumption NonTradable Goods
0.8
0.2 0
Deviation from s.s. (%)
Deviation from s.s. (%)
Deviation from s.s. (%)
0.15 0.6
−0.5
0.1 −1
0.4
−2
5 · 10
−1.5
0.2
0
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
Total Output Private Investment Public Investment
−0.2
3 0.4
Deviation from s.s. (%)
Deviation from s.s. (%)
Deviation from s.s. (%)
−0.4 0.3
2
−0.6 0.2
1
−0.8 0.1
0 −1 0
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
Public Capital Investment Tradable Sector Investment NonTradable Sector
−0.1 −0.1
Deviation from s.s. (%)
Deviation from s.s. (%)
Deviation from s.s. (%)
0.15 −0.2
−0.2
0.1 −0.3
−0.4 −0.3
5 · 10−2
−0.5
−0.4
0
−0.6
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
Under the Sustainable Investing Approach Under the Saving in a Sovereign Wealth Fund Approach
Notes
Notes : The
: The show show
ﬁgures
ﬁgures impulse
impulse response
response from the from
functions
functions the DSGE
simulated simulated DSGE
model modelthe
to illustrate to
of a one-standard-deviation
eﬀect illustrate oil production shock. Responses
the eﬀect of a one-standard-deviation are expressed
oil production in percentage
shock. Responses deviation
are
from the steady-state values. The dashed line shows the response of the ﬁscal policy B (All-Saving
expressed in percentage deviation from the steady-state values. The dashed line shows
Approach) and solid lines show the response of the ﬁscal policy C (Sustainable Investing Approach).
the response of the ﬁscal policy B (All-Saving Approach) and solid lines show the
response of the ﬁscal policy C (Sustainable Investing Approach).
52
30
Panel B
Output Tradable Sector Output NonTradable Sector Non Oil Revenues
0 0 0
Deviation from s.s. (%)
Deviation from s.s. (%)
Deviation from s.s. (%)
−2
−5 · 10 −5 · 10 −2
−0.1 −0.1 −0.2
−0.15 −0.15
−0.4
−0.2 −0.2
−0.25 −0.25
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
Total Employment Employment Tradable Sector Employment NonTradable Sector
0 0 0
Deviation from s.s. (%)
Deviation from s.s. (%)
Deviation from s.s. (%)
−5 · 10−2 −5 · 10−2 −5 · 10−2
−0.1 −0.1 −0.1
−0.15 −0.15 −0.15
−0.2 −0.2 −0.2
−0.25 −0.25 −0.25
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
Wage Tradable Sector Wage NonTradable Sector Total Wage
·10−2 ·10−2 ·10−2
5
4
Deviation from s.s. (%)
Deviation from s.s. (%)
Deviation from s.s. (%)
4
4
3
3
2
2 2
1 1
0 0 0
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
Under the Sustainable Investing Approach Under the Saving in a Sovereign Wealth Fund Approach
Notes : The ﬁgures show impulse response functions from the simulated DSGE model to
illustrate
Notes the eﬀect
: The ﬁgures show of a one-standard-deviation
impulse response functions from oil production
the shock.model
Responses
simulated DSGE are the
to illustrate
expressed
eﬀect in percentage deviation
of a one-standard-deviation from the
oil production steady-state
shock. Responsesvalues. The dashed
are expressed line shows
in percentage deviation
the response of the ﬁscal policy B (All-Saving Approach) and solid lines show the
from the steady-state values. The dashed line shows the response of the ﬁscal policy B (All-Saving
Approach lines
) and solidof
response theshow thepolicy
ﬁscal C of
response C (Sustainable
the ﬁscal policy Investing
(Sustainable Investing
Approach ). Approach).
53
31
Panel C
Total Government Spending Gov. Spending Tradable Sector Gov. Spending NonTradable Sector
2
−0.2
Deviation from s.s. (%)
Deviation from s.s. (%)
Deviation from s.s. (%)
1
1.5
−0.3
1
0.5
−0.4
0.5
0 −0.5
0
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
Non Oil Exports Imports Sovereign Wealth Fund
0 1 0.4
Deviation from s.s. (%)
Deviation from s.s. (%)
Deviation from s.s. (%)
−0.2 0.3
0.5
−0.4
0.2
−0.6
0 0.1
−0.8
0
−1
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
Inﬂation Exchange Rate Public Debt
1 0 1.5
Deviation from s.s. (%)
Deviation from s.s. (%)
0.8
Percentage Points
−0.5 1
0.6
0.4
−1 0.5
0.2
0 −1.5 0
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
Under the All-investing in Public Capital Approach Under the Saving in a Sovereign Wealth Fund Approach
Notes : The ﬁgures show impulse response functions from the simulated DSGE model to
illustrate
Notes : The ﬁgures the
showeﬀect of aresponse
impulse one-standard-deviation
functions from the production
oilsimulated shock.
DSGE Responses
model are the
to illustrate
eﬀect of expressed in percentage oil
a one-standard-deviation deviation from
production the steady-state
shock. Responses arevalues. Thein
expressed dashed line deviation
shows
percentage
from the the response of the ﬁscal policy B (All-Saving Approach) and solid lines show the
steady-state values. The dashed line shows the response of the ﬁscal policy B ( All-Saving
Approach) and solid lines show
response of thethe response
ﬁscal of the
policy ﬁscal policy C (Investing
C (Sustainable Sustainable Investing).
Approach Approach).
54
32
Table 5: Responses to a one
Figure 3. Responses tostandard deviation
a one standard oilproduction
oil
deviation shock
production shock − ﬁscal
− ﬁscal policy policy
A and CA and C
Panel A
Aggregate Consumption Consumption Tradable Goods Consumption NonTradable Goods
0.25 1 0
Deviation from s.s. (%)
Deviation from s.s. (%)
Deviation from s.s. (%)
0.2 0.8 −0.5
0.15 −1
0.6
0.1 −1.5
0.4
5 · 10−2 −2
0.2
0 −2.5
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
Total Output Private Investment Public Investment
4 0 0.8
Deviation from s.s. (%)
Deviation from s.s. (%)
Deviation from s.s. (%)
−0.2
3 0.6
−0.4
2 −0.6
0.4
−0.8
1
−1 0.2
0 −1.2
0
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
Public Capital Investment Tradable Sector Investment NonTradable Sector
0 0
Deviation from s.s. (%)
Deviation from s.s. (%)
Deviation from s.s. (%)
0.3 −0.1
−0.2
−0.2
0.2
−0.4 −0.3
0.1 −0.4
−0.6
−0.5
0
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
Under the All-investing in Public Capital Approach Under the Sustainable Investing Approach
Notes
Notes : The
: The ﬁgures
ﬁgures showshow impulse
impulse response
response functions
from the from
functions the simulated
simulated DSGE model DSGE modelthe
to illustrate to
eﬀectillustrate the eﬀect of a one-standard-deviation
of a one-standard-deviation oil production
oil production shock. Responses shock.
are expressed Responses
in percentage are
deviation
expressed
from in percentage
the steady-state values. deviation from
The solid line the steady-state
shows the response ofvalues. The
the ﬁscal solid
policy A line shows the
(All-Investing
Approach
response ) and Dashed
of the ﬁscallines show
policy Athe response of the Approach
(All-Investing ﬁscal policy )C and
(Sustainable Investing
Dashed lines Ap-
show the
proach). response of the ﬁscal policy C (Sustainable Investing Approach).
55
33
Panel B
Output Tradable Sector Output NonTradable Sector Non Oil Revenues
0 0
0
Deviation from s.s. (%)
Deviation from s.s. (%)
Deviation from s.s. (%)
−5 · 10−2 −5 · 10 −2
−0.2
−0.1 −0.1
−0.4
−0.15
−0.15
−0.6
−0.2
−0.2
−0.8
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
Total Employment Employment Tradable Sector Employment NonTradable Sector
−5 · 10−2
Deviation from s.s. (%)
Deviation from s.s. (%)
Deviation from s.s. (%)
−5 · 10−2 −5 · 10−2
−0.1 −0.1 −0.1
−0.15 −0.15 −0.15
−0.2 −0.2 −0.2
−0.25 −0.25 −0.25
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
Wage Tradable Sector Wage NonTradable Sector Total Wage
·10−2
0.1
0.1
8
Deviation from s.s. (%)
Deviation from s.s. (%)
Deviation from s.s. (%)
8 · 10−2
8 · 10−2
6
6 · 10−2
6 · 10−2
4
4 · 10−2 4 · 10−2
2 2 · 10−2
2 · 10−2
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
Under the All-investing in Public Capital Approach Under the Sustainable Investing Approach
Notes : The ﬁgures show impulse response functions from the simulated DSGE model to
illustrate
Notes : The the eﬀect
ﬁgures a one-standard-deviation
of impulse
show oil the
response functions from production
simulated shock. Responses
DSGE model are the
to illustrate
expressed in percentage deviation
eﬀect of a one-standard-deviation steady-state
from the shock.
oil production values.
Responses The solid
are expressed line shows
in percentage the
deviation
from the steady-state values. The solid line shows the response of the ﬁscal
response of the ﬁscal policy A (All-Investing Approach) and Dashed lines show the policy A (All-Investing
Approach) and Dashed lines show the response of the ﬁscal policy C (Sustainable Investing Ap-
response of the ﬁscal policy C (Sustainable Investing Approach).
proach).
56
34
Panel C
Total Government Spending Gov. Spending Tradable Sector Gov. Spending NonTradable Sector
1.5
Deviation from s.s. (%)
Deviation from s.s. (%)
Deviation from s.s. (%)
−0.2
2
1
−0.4
0.5 1
−0.6
0 0
−0.8
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
Non Oil Exports Imports Sovereign Wealth Fund
0.2
0
Deviation from s.s. (%)
Deviation from s.s. (%)
Deviation from s.s. (%)
1 0.15
−0.5
0.5 0.1
5 · 10−2
−1
0
0
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
Inﬂation Exchange Rate Public Debt
0 2
Deviation from s.s. (%)
Deviation from s.s. (%)
1 1.5
Percentage Points
−0.5
−1 1
0.5
−1.5 0.5
−2 0
0
−2.5
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
Under the All-investing in Public Capital Approach Under the Sustainable Investing Approach
Notes : The ﬁgures show impulse response functions from the simulated DSGE model to
illustrate the eﬀect of a one-standard-deviation oil production shock. Responses are
Notes : The ﬁgures show impulse response functions from the simulated DSGE model to illustrate the
expressed
eﬀect in percentage deviation
of a one-standard-deviation from the
oil production steady-state
shock. Responsesvalues. The solid
are expressed line shows
in percentage the
deviation
response
from of the ﬁscal
the steady-state policy
values. TheAsolid line shows the Approach
(All-Investing ) and
response of the Dashed
ﬁscal lines
policy A show the
(All-Investing
Approach) and Dashed
response lines
of the the response
show policy
ﬁscal of the ﬁscal policy
C (Sustainable C (Sustainable
Investing Approach Investing
). Ap-
proach).
57
35
eﬀects. Indeed, higher public capital increases the marginal product of labor in both sectors,
leading households to increase their labor supply. Then, oil revenue yields a wealth eﬀect on the
other hand. Consequently, households reduce labor supply and substitute their working hours
for leisure. As the income eﬀect outperforms that of substitution, the net eﬀect on labor supply
is negative. Nevertheless, this negative eﬀect is stronger under the all-investing approach. The
sustainable investing approach, in turn, yields a mixed result.
Compared to the all-investing approach, the sustainable-investing approach provides a lower
and a smoother path of scaling-up by generating less volatile eﬀect. Panel C of Figure 3 shows
that the real exchange rate appreciates in both cases but the magnitude is less pronounced
under the sustainable approach. The real exchange rate appreciates by 2.2 percent under the
all-investing approach and only by 1.6 percent under the sustainable approach. However, output,
non-tradable and tradable goods production, employment and wages rebound faster under the
sustainable approach.
Next, compared to the all-saving approach, the sustainable approach produces higher con-
sumption and public investment in the long run. Consumption increases by 0.22 percent un-
der the sustainable approach, 0.05 percentage point larger than the peak under the all-saving
approach (Figure 2, Panel A). Public capital is also 0.17 percentage point higher than the pre-
windfall level. Imports and exports display almost similar paths under these two stylized ﬁscal
policies.
Finally, the responses of the model economy under policy C, in which a constant share of the
resource income is allocated to a sustainable public investment and the rest saved in a sovereign
wealth fund, are less volatile. When the government saves a fraction of the oil revenue in a
sovereign wealth fund and invests each period the return of the fund plus a small additional
fraction, the economy displays a much milder and more prolonged expansion. Because a sus-
tainable share of the revenue from oil exports is saved, the trade balance improves substantially,
which displays an eﬃcient oil resource management. Overall, the sustainable approach proposes
a gradual scaling-up and a smooth investment path by minimizing macroeconomic volatility.
Our results is in line with Devarajan et al. (2015), which shows that the sustainable investment
approach is the less volatile and it engenders higher welfare, in an environment with positive
36
and negative commodity price shocks, using data from Niger.
4.3 Sensitivity Analysis
In this section, we consider changes in some key policy parameters to assess the robustness of the
simulated results under the sustainable investing approach − which is taken as benchmark. We
focus on the ﬁscal responses following these changes under an oil production shock. Specially,
we look at the ﬁscal responses by considering diﬀerent values of the parameter governing the
eﬃciency of public investment and diﬀerent values of the parameter capturing productivity of
public capital.
4.3.1 Absorption capacity constraints
The parameter capturing the eﬃciency of public investment is a fundamental factor in our frame-
work. In practice, this policy parameter captures all the weaknesses in public-sector management
and administration responsible for the failure to translate available resources into eﬀective public
investment. Figure 4 presents the macroeconomic responses given an oil production shock for
two values of G ( G = 0.25 and G = 0.95) around our benchmark value set to 0.6. Figure
4 shows that with much more public investment, households enjoy more consumption under
the sustainable investing approach. An interesting result is that without absorption constraints
( G → 1), tradable and non-tradable sector outputs decline less under an oil production shock,
mitigating the negative impact of a potential Dutch disease eﬀect.
4.3.2 Productivity of public capital
In addition to the absorptive capacity, another important policy parameter for savings and
investment decisions is the productivity of public capital − also viewed as the return to public
capital. In this subsection, we consider the impact of a higher and a lower return to public
capital (αG = 0.05 and αG = 0.5) around the baseline value set to 0.2. The results illustrated
in Figure 5 show that the supply-side responses of capital and labor are key determinants of
the output response to public investment. Panel A of Figure 5 shows that under a higher
return to public capital, households enjoy much more consumption, public sector records higher
37
Figure 4. Robustness
Table 6: Robustness checks:
checks: Absorptive
Absorptive capacity
capacity constraints
constraints under
under ﬁscal
ﬁscal policy
CC
policy
Aggregate Consumption Public Investment Private Investment
0.25
−0.2
0.6
Deviation from s.s. (%)
Deviation from s.s. (%)
Deviation from s.s. (%)
0.2
−0.4
0.15 0.4
−0.6
0.1
0.2 −0.8
5 · 10−2
−1
0
0
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
Public Capital Output Tradable Sector Output NonTradable Sector
0.3 0 0
Deviation from s.s. (%)
Deviation from s.s. (%)
Deviation from s.s. (%)
−5 · 10−2 −5 · 10−2
0.2
−0.1 −0.1
−0.15 −0.15
0.1
−0.2 −0.2
0 −0.25
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
Total Employment Total Wage Government Spending
·10−2
8
Deviation from s.s. (%)
Deviation from s.s. (%)
Deviation from s.s. (%)
−5 · 10−2 1
6
−0.1
4 0.5
−0.15
−0.2
2
0
−0.25
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
G G
Sustainable investing Approach, = 0.25 Sustainable investing Approach, = 0.95
Notes : : The
Notes ﬁgures
Theﬁgures show
show impulse
impulse response
response functions
functions from
from the the simulated
simulated DSGE modelDSGE model to
to illustrate the
eﬀect of a one-standard-deviation oil production shock. Responses are expressed in percentage
illustrate the eﬀect of a one-standard-deviation oil production shock. Responses are deviation
from the steady-state values. The solid line shows the response of the ﬁscal policy C (Sustainable
expressed in percentage deviation from the steady-state values. The solid line shows the
Investing Approach) under G = 0.25 and Dashed lines show the response under G = 0.95.
response of the ﬁscal policy C (Sustainable Investing Approach) under G = 0.25
and Dashed lines show the response under G = 0.95.
38
58
Figure 5. Robustness checks: Productivity of public capital under ﬁscal policy C
Table 7: Robustness checks: Productivity of public capital under ﬁscal policy C
Panel A
Aggregate Consumption Total Output Private Investment
0.4
Deviation from s.s. (%)
Deviation from s.s. (%)
Deviation from s.s. (%)
3
0.3
−0.5
2
0.2
1 −1
0.1
0
0
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
Public Investment Public Capital Output Tradable Sector
0.6 0
0.25
Deviation from s.s. (%)
Deviation from s.s. (%)
Deviation from s.s. (%)
−5 · 10−2
0.2
0.4
0.15 −0.1
0.2 0.1 −0.15
5 · 10−2
−0.2
0 0
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
Output NonTradable Sector Non Oil Revenues Public Debt
0 2
0.5
Deviation from s.s. (%)
Deviation from s.s. (%)
Deviation from s.s. (%)
−2 1.5
−5 · 10
0
1
−0.1
−0.5
0.5
−0.15
−1
0
−0.2
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
Sustainable investing Approach, αG = 0.05 Sustainable investing Approach, αG = 0.5
Notes : The ﬁgures show impulse response functions from the simulated DSGE model to
Notes : The ﬁgures show impulse response functions from the simulated DSGE model to illustrate the
illustrate
eﬀect the eﬀect of a one-standard-deviation
of a one-standard-deviation oil production
oil production shock. Responses shock.
are expressed Responses
in percentage are
deviation
expressed in percentage deviation from the steady-state values. The solid line shows
from the steady-state values. The solid line shows the response of the ﬁscal policy C (Sustainable the
G
response
Investing of the ﬁscal
Approach policy
) under G
α = C0.( Sustainable
05 Investing
and Dashed lines show theApproach ) under
response under α =α
G
0.5.= 0.05
and Dashed lines show the response under αG = 0.5.
59
39
Panel B
Total Employment Total Wage Government Spending
0
Deviation from s.s. (%)
Deviation from s.s. (%)
Deviation from s.s. (%)
0.15
1
−0.1
0.1
0.5
−0.2
5 · 10−2
0
−0.3 0
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
Gov. Spending Tradable Sector Gov. Spending NonTradable Sector Non Oil Exports
0 0
2
Deviation from s.s. (%)
Deviation from s.s. (%)
Deviation from s.s. (%)
−0.2
1.5 −0.2
−0.4
1 −0.4 −0.6
0.5 −0.8
−0.6
0 −1
−0.8
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
Imports Exchange Rate Sovereign Wealth Fund
1 0
Deviation from s.s. (%)
Deviation from s.s. (%)
Deviation from s.s. (%)
0.2
−0.5
0.15
0.5
−1 0.1
0 −1.5 5 · 10−2
−2 0
0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
Quarters Quarters Quarters
Sustainable investing Approach, αG = 0.05 Sustainable investing Approach, αG = 0.5
Notes : The ﬁgures show impulse response functions from the simulated DSGE model to
illustrate
Notes show of
the eﬀect
: The ﬁgures a one-standard-deviation
impulse theproduction
response functions from oil shock.
simulated DSGE Responses
model are the
to illustrate
expressed
eﬀect in percentage deviation
of a one-standard-deviation from the
oil production steady-state
shock. Responses values. The solid
are expressed line shows
in percentage the
deviation
G
response
from of the ﬁscal
the steady-state policy
values. TheCsolid
(Sustainable Investing
line shows the response ofApproach ) under
the ﬁscal policy C (α = 0.05
Sustainable
Investing Approach ) under
and αG = lines
Dashed 0.05 and
showDashed the response
lines showunder
the response αG = under
G
0.5. α = 0.5.
60
40
public investment and output in tradable and non-tradable sectors declines less compared to the
scenario where public is almost unproductive αG = 0.05. Panel B of Figure 5 shows that when
investment projects are almost unproductive (αG = 0.05), households are better oﬀ saving in a
sovereign wealth fund and consuming the interest income. Although investing natural resource
revenues in public infrastructures might be viewed as an attractive ﬁscal policy to accelerate
economic development in public capital-scarce economies, a better ﬁscal management is to save
the resource income in a sovereign fund for future generation when public capital is almost
unproductive.
4.4 Optimal allocation of natural resource revenues
The previous analysis has focused on the benchmark model in which the parameter governing
the share of resource windfalls allocated to public investment is exogenously set to 0.5. Under
this ﬁscal rule, half of the resource income is saved in a sovereign wealth fund and the remaining
half combined to the interest rate payments received are used to ﬁnance public infrastructure.
However, a key ﬁscal policy issue is the following: given the poor return to public capital and
signiﬁcant absorptive capacity constraints in the economy, what should be the optimal allocation
of resource revenues between public infrastructure ﬁnancing and saving in a sovereign wealth
fund? In other words what is the value of φoil that optimizes the objective function of the
policy maker? The answer to this question requires that the policy maker’s objective function
be deﬁned. To assess the optimal allocation of the resource income to public infrastructures
under the sustainable investing approach and come out with a well deﬁned loss function, we
focus on the volatility of four important macroeconomic variables: private consumption (σC ),
total employment (σL ), non-oil ﬁscal balance (σF B N O ) and real exchange rate (σs ).
Conceptually, we propose a criterion consisting to determine the value of φoil that minimizes
enor (2014); it is
a social loss function. Our loss function closely resembles that used by Ag´
indeed deﬁned as a weighted geometric average of a welfare measure and a ﬁscal/macroeconomic
stability measure. The welfare measure is either captured by the volatility of consumption or
by an equally weighted geometric average of the volatility of consumption and that of total
employment. In our model, households as risk averse agents dislike volatile private consumption
41
and working hours since these adversely aﬀect their welfare. Similarly, the ﬁscal stability measure
is captured by the volatility of the non-oil ﬁscal balance whereas the macroeconomic stability
measure is captured by an equally weighted geometric average of the volatility of the non-oil
enor (2014), movements
ﬁscal balance and that of the real exchange rate. As stressed by Ag´
in the real exchange rate capture the volatility of key relative prices which are important for
the competitiveness of the economy, and therefore for macroeconomic stability. In all cases
volatilities are computed along the simulated path of the model. We therefore consider the
following loss function:
oil µ oil 1−µ
L = Wφ Sφ
oil oil oil 0.5 oil 0.5
φ φ φ
Wφ ∈ σC , σC σL (4.1)
oil oil oil 0.5 oil 0.5
φ φ
Sφ ∈ σF BN O
, σF BN O
φ
σs
oil oil
where W φ and S φ are the variables that capture households’ welfare and macroeconomic/ﬁscal
φ oil
stability respectively, and F B N O is the non-oil ﬁscal balance. σX denotes the volatility of vari-
able X along the simulated path of the model featuring the Sustainable Investing ﬁscal rule,
with the share of resource windfalls allocated to investment set at φoil .
It is important to mention that this optimization criterion is an ad-hoc one, set by the
policy maker based on its priorities in terms of households’ welfare versus macroeconomic/ﬁscal
stability. Parameter µ controls the extent to which the policy maker cares about ﬂuctuations in
enor (2014), we vary
households’ welfare and macroeconomic stability. In our analysis, as in Ag´
this parameter in order to assess how optimal decisions vary with the policy maker’s preference
for macroeconomic/ﬁscal stability (1 − µ).
Given the above deﬁnition of our social loss function, we have four alternative criteria for
the analysis of the optimal allocation of oil windfalls, we denote the four corresponding loss
42
functions by L1 , L2 , L3 ,and L4 where:
oil µ oil 1−µ
φ φ
L1 = σC σF BN O
oil 0.5 oil 0.5 µ oil 1−µ
φ φ φ
L2 = σC σL σF BN O
oil µ oil 0.5 0.5 1−µ (4.2)
φ φ oil
L3 = σC σF BN O
φ
σs
oil 0.5 oil 0.5 µ oil 0.5 oil 0.5 1−µ
φ φ φ
L4 = σC σL σF BN O
φ
σs
As already mentioned above, social loss functions are computed using simulated data from
the model. In simulations, we have the choice between two diﬀerent sources of uncertainty for
oil revenues: the uncertainty stemming from the volatility of oil prices, and the one stemming
from the volatility of oil production. Note that unlike in Devarajan et al. (2015) where volatility
in the supply of resources mainly comes from oil price ﬂuctuations, our model considers that oil
production does not respond to ﬂuctuations in oil prices and sets the oil production function
exogenously. Oil production and oil price ﬂuctuations are therefore two separate and indepen-
dent sources of uncertainty in the model; This speciﬁcation allows us to put more emphasis on
oil price volatilities in our simulations as we are dealing with a developing countries who newly
discovered oil and may have a smooth production stream in the beginning of the production
process. Therefore, and for the sake of saving space, we show only the results obtained in the
case where oil price ﬂuctuations are the source of uncertainty in the model. However, we found
little diﬀerences between our baseline results and those based on simulations considering both
sources of uncertainty; these simulation results are available upon request.
Figure 6 shows the graphs of our four loss functions when the policy maker puts equal
weights on households’ welfare and on stability, and Figure 7 shows a 3-D plot of the social loss
enor (2014), the loss functions are decreasing in µ for φoil given. But
function L15 . As in Ag´
their shapes for a given value of µ depend on the policymakers preference for macroeconomic
stability. Indeed, for a very high preference for macroeconomic/ﬁscal stability (i.e. generally
for values of µ lower than 0.3 − 0.39) the loss functions are decreasing in φoil , but for values
5
The other loss functions have similar shapes.
43
Figure 6. Social loss functions for µ = 0.5
−3
x 10
9.5
L1
L2
9
L3
L4
8.5
8
Loss function (µ = 0.5)
7.5
7
6.5
6
5.5
5
0 0.2 0.4 0.6 0.8 1
φoil
Figure 7. Social loss function L1
44
of µ higher than 0.3 − 0.39 (meaning a fair or low preference for stability), the loss functions
have convex shapes in φoil . Low values of φoil lead to high volatility in the economy due to
higher return on savings in the sovereign wealth which yield higher government consumption.
But as φoil increases, the volatility decreases gradually and eventually (for values of µ higher
that 0.3 − 0.39) reaches its minimum and starts increasing due to higher public investment that,
again, generates volatility in the economy (Figure 6).
Figure 8. Optimal allocation rule under L1
1 1
0.8 0.8
0.6 0.6
φoil
φoil
0.4 Baseline 0.4 Baseline
εG = 0.95 αG = 0.4
0.2 0.2
G
ε = 0.25 αG = 0.1
0 0
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
µ µ
1 1
0.8 0.8
0.6 0.6
φoil
φoil
Baseline Baseline
0.4 0.4
ρyo = 0.975
δG = 0.125
0.2 0.2
G
δ = 0.05 ρ = 0.925
yo
0 0
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
µ µ
1 1
0.8 0.8
0.6 0.6 Baseline
φoil
φoil
Baseline r* = 0.05
0.4 0.4
ρpo = 0.975
r* = 0.005
0.2 0.2
ρpo = 0.925
0 0
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
µ µ
The shapes of the loss functions just discussed lead to the observation that when the policy
maker is too concerned about macro/ﬁscal stability and not much about households welfare, the
best option available to the policy maker is the very conservative ﬁscal strategy which consists
in saving the resource windfalls and spending only the interest income in order to prevent the
economy from the Dutch disease and from a boom-bust cycle due to ineﬃcient spending (see
Go et al. (2013) and Devarajan et al. (2015)). This clearly appears in Figures 8−11 which plot
the optimal allocation rule as functions of µ (blue solid lines); all four lost functions recommend
setting φoil = 0 for values of µ lower than 0.3 − 0.39. However, when the policy maker’s preference
for macro/ﬁscal stability is moderate or low, φoil varies between 0.55 and 0.85, meaning that 55
45
Figure 9. Optimal allocation rule under L2
1 1
0.8 0.8
0.6 0.6
φoil
φoil
Baseline Baseline
0.4 0.4
εG = 0.95 αG = 0.4
0.2 G
0.2
ε = 0.25 αG = 0.1
0 0
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
µ µ
1 1
0.8 0.8
0.6 0.6
Baseline
φoil
φoil
Baseline
0.4 0.4 ρyo = 0.975
G
δ = 0.125
0.2 0.2 ρyo = 0.925
δG = 0.05
0 0
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
µ µ
1 1
0.8 0.8
0.6 Baseline 0.6 Baseline
φoil
φoil
0.4 ρpo = 0.975 0.4 r* = 0.05
0.2 ρpo = 0.925 0.2 r* = 0.005
0 0
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
µ µ
Figure 10. Optimal allocation rule under L3
1 1
0.8 0.8
0.6 0.6
φoil
φoil
Baseline Baseline
0.4 0.4
εG = 0.95 αG = 0.4
0.2 0.2
εG = 0.25 αG = 0.1
0 0
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
µ µ
1 1
0.8 0.8
0.6 0.6
φoil
φoil
Baseline Baseline
0.4 0.4 ρyo = 0.975
δG = 0.125
0.2 0.2
δG = 0.05 ρyo = 0.925
0 0
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
µ µ
1 1
0.8 0.8
0.6 0.6 Baseline
φoil
φoil
Baseline r* = 0.05
0.4 ρpo = 0.975 0.4
r* = 0.005
0.2 0.2
ρpo = 0.925
0 0
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
µ µ
46
Figure 11. Optimal allocation rule under L4
1 1
0.8 0.8
0.6 0.6
φoil
φoil
0.4 Baseline 0.4 Baseline
εG = 0.95 αG = 0.4
0.2 0.2
G
ε = 0.25 αG = 0.1
0 0
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
µ µ
1 1
0.8 0.8
0.6 0.6
φoil
φoil
Baseline Baseline
0.4 0.4
G ρyo = 0.975
δ = 0.125
0.2 0.2
δG = 0.05 ρ = 0.925
yo
0 0
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
µ µ
1 1
0.8 0.8
0.6 Baseline 0.6 Baseline
φoil
φoil
0.4 ρpo = 0.975 0.4 r* = 0.05
0.2 ρpo = 0.925 0.2 r* = 0.005
0 0
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
µ µ
to 85 percent of oil windfalls should be used for public investment. This share increases with
µ and does not depend much on the loss function used. Although this range include values
that are very high compared to values generally found in the literature, we think that they are
reasonable for a country that newly discovered oil, and for which the oil production process is
not as volatile and uncertain as experienced oil producers. Being a new oil producer reduces
a the volatility stemming from oil production in the beginning of the extraction process and
therefore reduces the need for savings.
A welfare comparison of alternative ﬁscal rules in an economy enduring volatile and uncertain
resource price leads Devarajan et al. (2015) to recommend a combination of savings and public
investment as the best way to cope with volatile oil revenues due to unpredictable shocks. Their
analysis is a special case of ours (when µ = 1) but we go beyond their recommendation by
stressing that if households’ welfare is the only concern of the policy maker, then 80 percent to
85 percent of resource windfalls should be allocated to public investment instead of assuming
50 percent for saving and 50 percent investment as a sustainable approach. Public investment
improves households’ welfare mainly through the positive eﬀect that public infrastructure has
47
on private capital and labor productivity.
Robustness checks show that our ﬁndings do not on depend key parameters of the model
apart from those which directly aﬀect resource revenues such as the persistence of oil price
shocks (ρpo ) and the interest rate paid on sovereign funds (r∗ ). Indeed, the red dashed lines
and the green dotted lines in Figures 8−11 show the optimal allocation rule for two alternative
values of each of the parameters indicated. The middle right panels of these ﬁgures show that
the rules, under the alternative parameterizations of the persistence of the oil production shock,
are similar to the baseline as oil production is exogenously determined in our model. The top
panels and the middle left panel show that the eﬃciency of public investment, G, the output
elasticity of public capital, αG , as well as the depreciation rate of public capital, δ G , only play a
minor role in determining the optimal allocation of resource windfalls. However, the interest rate
paid on sovereign funds (bottom right panels) is an important driver of the resource allocation.
Our analysis suggests on the one hand that when funds saved abroad do not generate enough
income because of very low interest rates, then the policy maker should invest 20 percent of the
windfall if he is extremely worried about stability, but otherwise almost all (90 percent to 98
percent) the windfall should be used for public investment. On the other hand, if the interest
paid on sovereign funds are very high, the best strategy is to invest only if households’ welfare is
of very high concern; in this case, only up to 40 percent of the windfall should be invested, and
the remaining share saved. Additional robustness checks show that more windfalls should be
saved in the sovereign wealth fund when oil price shocks are very persistent (green dotted lines
in bottom left panels of Figures 8−11), or invested when oil price shocks are less persistent.
5 Concluding Remarks
In this paper we studied diﬀerent ﬁscal policy approaches of investing a resource windfall through
a small open economy DSGE model applied to Uganda. Speciﬁcally, we study macroeconomic
dynamics following three stylized ﬁscal policy approaches: the all-investing approach, the all-
saving approach and the sustainable-investing approach in which a constant share of the resource
income is allocated to public investment. The model accounts for several important features that
48
are common in the New Keynesian model literature applied to developing countries, including
Dutch disease eﬀects, investment ineﬃciencies and weak tax systems. The model is parameter-
ized following various empirical works and data from Uganda, and is used to simulate the eﬀects
of a one standard deviation oil production shock, interpreted as a boom in the energy sector.
Our results show that: (i) a better ﬁscal management is to save the resource income in a
sovereign wealth fund for future generation when public capital is almost unproductive; (ii) a
gradual scaling-up of public investment (The Sustainable-Investing Approach ) yields the best
outcomes as it minimizes macroeconomic volatility; e.g. the real exchange rate appreciation is
30 percent lower than in the all-investing approach, which might be viewed as an attractive ﬁscal
policy to accelerate economic development in public capital-scarce economies; the trade balance
improves substantially and impulse response functions suggest that output, non-tradable and
tradable goods production, employment and wages rebound faster.
We also deﬁne criteria to determine the optimal value of the oil share to invest in public
infrastructures by minimizing a social loss function; we use four loss functions that include a
households’ welfare indicator and a macroeconomic/ﬁscal stabilization indicator. We ﬁnd that
the loss functions have convex shapes with optimal values of φoil varying between 0.55 and
0.85, depending on the policy maker’s preference for macroeconomic stability. Furthermore,
our results show that the optimal share of oil revenues to be used for public investment is very
robust to the various parameter calibrations; only parameters that directly aﬀect these revenues
(such as interest rates on savings and the persistence of oil price shocks) play an important
role. In comparison with the recent literature, our optimal share to invest domestically in public
enor (2014), which ranges from 30
infrastructures is slightly higher than those estimated in Ag´
percent to 60 percent using oil price shocks.
A number of extensions could usefully be considered. First, the paper assumes an exogenous
oil sector, and the analysis can be extended to explore labor movements between non-oil and
oil sectors. In practice, oil sectors in developing countries use domestic labor and Dutch disease
eﬀects can be optimally analyzed using an endogenous oil production sector. Second, the paper
does not consider the eﬀect of foreign direct investments (FDI). Indeed, it’s well-known that
in low-income countries, FDI account substantially and may aﬀect macroeconomic dynamics.
49
Third, the model focuses on some standard government rules and our sustainable approach can
be improved to take into account a sovereign wealth fund that can serve as a stabilization buﬀer,
enabling households and government to smooth consumption and public investment paths over
negative economic shocks. Finally, our analysis suggests that a high proportion of oil revenues
should be invested, but does not specify which type of investment should be prioritized. The
analysis could be deepened so as to determine how much of the resources should be used to
increase soft/hard infrastructure.
References
enor, P. R. (2014). Optimal ﬁscal management of commodity price shocks. Centre for Growth
Ag´
and Business Cycle Research Discussion Paper Series, 197. Economics, The Univeristy of
Manchester.
Aikman, D. and Paustian, M. (2006). Bank capital, asset prices and monetary policy. Working
paper, Bank of England 2006-305.
Ambler, S., Dib, A., and Rebei, N. (2004). Optimal taylor rules in estimated model of small
open economy. Working paper, Bank of Canada 2004-36.
enor, P. R. and Aizenman, J. (1999). Macroeconomic adjustment with segmented labor
Ang´
markets. Journal of Development Economics, 58.
Arestoﬀ, F. and Hurlin, C. (2006). Estimates of government net capital stocks for 26 developing
countries 1970-2002. World Bank Policy Research Working Paper 3858.
Backus, D., Kehoe, P., and Kydland, F. (1994). Dynamics of the trade balance and the terms
of trade: the j-curve? American Economic Review 84 (1), pages 84–103.
Backus, D., Kehoe, P., and Kydland, F. (1995). International business cycles: theory and
evidence. In: Cooley, T.F. (Ed.), Frontiers of Business Cycle Research. Princeton University
Press, Princeton, pages 331–356.
50
Barnett, S. and Ossowski, R. (2003). Operational aspects of ﬁscal policy in oil-producing coun-
tries. in J. Davis, J. Ossowski, and A. Fedelino, eds., Fiscal Policy Formulation and Imple-
mentation in Oil-Producing Countries, (Washington, D.C.: International Monetary Fund.
Baunsgaard, T., Villafuerte, M., Poplawski-Ribeiro, M., and Richmond, C. (2012). Fiscal frame-
works for resource rich developing countries. Staﬀ Discussion Note, International Monetary
Fund, page 12/04.
Baxter, M. (1995). International trade and business cycles. In: Grossmann, G.M., Rogoﬀ, K.
(Eds.), Handbook of International Economics, pages 1801–1864.
Baxter, M. and King, R. (1993). Fiscal policy in general equilibrium. American Economic
Review, vol. 86, pages 1154–1174.
Berg, A., Portillo, R., Yang, S., and Zanna, L.-F. (2013). Public investment in resource-abundant
developing countries. IMF Economic Review, 61, pages 92–129.
Berms, R. and Irineu, C., F. (2011). The current account and precautionary savings for exporters
of exhaustible resources. Journal of International Economics, vol. 84, pages 48–64.
Cherif, R. and Fuad, H. (2012). Oil exporters’ dilemma: How much to save and how much to
invest. IMF Working Paper WP/12/4, International Monetary Fund.
Christensen, I. and Dib, A. (2008). The ﬁnancial accelerator in an estimated new keynesian
model. Review of Economic Dynamics.
Christiano, L., Eichenbaum, M., and Evans, C. (2005). Nominal rigidities and the dynamic
eﬀects of a shock to monetary policy. Journal of Political Economy.
Christiano, L., Motto, R., and Rostagno, M. (2010). Financial factors in economic ﬂuctuations.
European Central Bank Working Paper, pages 555–576.
Christopher, A. and Bevan, D. (2006). Aid and the supply side: Public investment, export
performance, and dutch disease in low-income countries. World Bank Economic Review,
pages 261–90.
51
Collier, P., van der Ploeg, F., Spence, M., and Venables, A. (2010). Managing resource revenues
in developing economies. IMF Staﬀ Papers, 51, pages 84–118.
Dagher, J., Gottschalk, J., and Portillo, R. (2012). The short-run impact of oil windfalls in
low-income countries: A dsge approach. Journal of African Economies, 21, pages 343–72.
Davis, J., Owssowski, J., Daniel, J., and Darnett, S. (2001). Stabilizing and saving funds
for non-renewable resources: Experience and ﬁscal policy implications. (Washington, D.C.:
International Monetary Fund). IMF Occasional Paper, no. 205.
Devarajan, S., Dissou, Y., Go, D., and Robinson, S. (2015). Budget rules and resource booms
and busts: A dynamic stochastic general equilibrium analysis. Policy Research Working Paper
Series 6984, The World Bank.
Economides, G., Park, H., and Philippopoulos, A. (2011). How should the government allo-
cate its tax revenues between productivity-enhancing and utility-enhancing public goods?
Macroeconomic Dynamics, 15, pages 336–64.
Gelb, A. and Grasmann, S. (2010). How should oil exporters spend their rents? Center for
Global Development, Working Paper No. 221.
Giovanni, M., Shu-Chun, S. Y., and Zanna, L.-F. (2014). Debt sustainability, public invest-
ment, and natural resources in developing countries: the dignar model. IMF Working Paper
WP/14/50.
Go, D., Robinson, S., Thierfelder, K., and Utz, R. (2013). Dutch disease and spending strategies
in a resource-rich low-income country – the case of niger. Policy Research Working Paper
Series 6691, The World Bank.
Goldberg, J. (2011). Kwacha gonna do? experimental evidence about labor supply in rural
malawi. Manuscript, Economics Department, University of Maryland.
Jihad, D., Gottschalk, J., and Portillo, R. (2009). What are the eﬀects of ﬁscal policy shocks?
Journal of Applied Econometrics, vol. 24, pages 960–992.
52
Jihad, D., Gottschalk, J., and Portillo, R. (2012). Oil windfalls in ghana: A dsge approach.
Journal of African Economies.
Kamps, C. (2004). The dynamic macroeconomic eﬀects of public capital. Berlin, Bermany:
Springer.
Kopoin, A., Moran, K., and Pare, J. P. (2013). Bank capital, credit market frictions and
e Laval.
international shocks transmission. Mimeo, Universit´
Lartey, E. K. (2008). Capital inﬂows, dutch disease eﬀects, and monetary policy in a small open
economy. Review of International Economics, 16, pages 971–89.
Lundgren, C., Thomas, A., and York, R. (2013). Boom, bust, or prosperity? managing sub-
saharan africa’s natural resource wealth. International Monetary Fund, Washington DC.
Maliszewski, W. (2009). Fiscal policy rules for oil-producing countries: A welfare-based assess-
ment. Working Paper No. 09/126, International Monetary Fund.
Matsen, E. and Torvik, R. (2005). Optimal dutch diseas. Journal of Development Economics,
78, pages 494–515.
Obstfeld, M. and Rogoﬀ, K. (2000). New directions in stochastic open economy models. Journal
of International Economics, pages 117–153.
Pieschacn, A. (2012). The value of ﬁscal discipline in oil-exporting countries. Journal of Mone-
tary Economics, 59, pages 250–68.
Pieschacon, A. (2011). The value of ﬁscal discipline in oil-exporting countries. Journal of
Monetary Economics, vol. 59, pages 250–268.
Pritchett, L. (2000). The tyranny of concepts: Cudie (cumulated, depreciated, investment eﬀort)
is not capital. Journal of Economic Growth, 5, pages 361–84.
Sachs, J. and Warner, A. (1999). The big push, natural resource booms and growth. Journal of
Development Economics.
53
e, S. and Uribe, M. (2003). Closing small open economy models. Journal of
Schmitt-Groh´
International Economics 61, pages 163–185.
Tilak, D., Joutz, F., Lakuma, P., Mayanja, L. M., and Manzano, B. (2015). The challenges of
macroeconomic management of natural resource revenues in developing countries: The case
of uganda. Research Series No. 124.
van den Bremer, S. and van der Ploeg, F. (2013). Managing and harnessing volatile oil windfalls.
OxCarre Research Paper No. 85.
van der Ploeg, F. (2011). Natural resources: Curse or blessing? Journal of Economic Literature,
49, pages 366–410.
6 Steady state Calculation
We need to solve the non-stochastic steady state of the model to pin-down equilibrium values
of the endogenous variables.
1 − βγ
− Λ (1 + τ c ) = 0 (6.1)
(1 − γ )C
ψ
− Λ(1 − τ l )W = 0 (6.2)
1−L
ξ
N WN
L −ω L=0 (6.3)
W
ξ
T WT
L − (1 − ω ) L=0 (6.4)
W
R
−1+β =0 (6.5)
π
1 = β 1 − δ N + RN (6.6)
1 = β 1 − δ T + RT (6.7)
αN (1−αN ) αG
Y N = KN · LN · KG (6.8)
54
YN
RN = ΛN αN (1 − ι) (6.9)
KN
YN
W N = ΛN (1 − αN )(1 − ι) (6.10)
LN
K N = (1 − δ N )K N + I N (6.11)
αT (1−αT ) αG
Y iT = K T · LT · KG (6.12)
T
Kt = (1 − δ T )K T + I T (6.13)
Y iT
RT = λT αT (1 − ι) (6.14)
KT
Y iT
W T = λT (1 − αT )(1 − ι) (6.15)
LT
Y iT = Y T d + Y T x (6.16)
Y T x = (s)−µ Y ∗ (6.17)
−ν
Ptd
YtT d = φm YtT (6.18)
St
−ν
PtM
YtM = (1 − φm ) YtT (6.19)
St
S (1 + r∗ )F ∗ RB
T O + τ C C + τ lW L + B + ∗
= P gG + + SF ∗ (6.20)
π π
Y = P N Y N + SY T + Y O . (6.21)
−χ
Y N = PN φ C + I N + I T + η (P g )χ G (6.22)
Y + Sr∗ F ∗ = C + I + P G G + SY T x − P M Y M . (6.23)
SY T x − P M Y M = S (F ∗ − F ∗ ) . (6.24)
55
First, begin with, (6.6) and (6.7), which imply that RN = 1/β − 1+ δ N and RT = 1/β − 1+ δ T .
Now go to (6.9), the ﬁrst order condition for labor supply in the production, we have
αN − 1
N YN KN g
R N N
= Λ α (1 − ι) N = ΛN αN (1 − ι) α
KG (6.25)
K LN
Then,
1
N N 1/β − 1 + δ N αN −1
K /L = αg (6.26)
ΛN αN (1 − ι)KG
and by analogy, the same expression holds in the tradable goods sector
1
T T 1/β − 1 + δ T αT −1
K /L = αg . (6.27)
ΛT αT (1 − ι)KG
Turning to the steady state of W N and W T , equations (6.10) and (6.15) yield
αN
N YN KN g
W N N
= Λ (1 − α )(1 − ι) N = ΛN (1 − αN )(1 − ι) α
KG , (6.28)
L LN
and
αT
T Y iT KT g
W T T
= Λ (1 − α )(1 − ι) T = ΛT (1 − αT )(1 − ι) α
KG . (6.29)
L LT
Then, using (6.26) and (6.27), the steady state values of W N and W T are
αN
N N N 1/β − 1 + δ N αN −1
α g
W = Λ (1 − α )(1 − ι) N N αg Kg (6.30)
Λ α (1 − ι)KG
and
αT
T T T 1/β − 1 + δ T αT −1
α g
W = λ (1 − α )(1 − ι) T T αg Kg . (6.31)
λ α (1 − ι)KG
Market clearing condition (6.24) leads to Y T x = Y M in the steady state. Recalling that in
the steady steady state, we impose that all prices are equal to 1. Then, equilibrium conditions
(6.18) and (6.19) imply the following steady-state conditions of importable and exportable goods
Y T x = φm Y T , (6.32)
and
Y T d = (1 − φm )Y T . (6.33)
These expressions and equilibrium condition (6.16) imply that
Y iT = Y T . (6.34)
56
G and the capital-labor ratio, we can ﬁnd directly the
Given the steady-state values of Lt , Kt
steady-state values of capital, investment and output.
ξ
N WN
L =ω L (6.35)
W
ξ
T WT
L = (1 − ω ) L (6.36)
W
1
N 1/β − 1 + δ N αN −1
K = αg LN (6.37)
ΛN αN (1 − ι)KG
and by analogy, the same expression holds in the tradable goods sector
1
T1/β − 1 + δ T αT −1
K = αg LT . (6.38)
ΛT αT (1 − ι)KG
Then,
ψ
Λ= (6.39)
(1 − τ l )(1 − L)W
and
(1 − βγ )
C= , (6.40)
(1 − γ )(1 + τ c )Λ
and therefore
C N = φC (6.41)
C T = (1 − φ)C (6.42)
The steady state value of government spending is given by
G = (1/η )(Y N − φ(C + I )) (6.43)
By setting Y O = θo Y , the equilibrium value of the sovereign wealth fund is
F ∗ = (1/r∗ )(−Y + C + I + G). (6.44)
Now, using (6.20), the steady state value of government debt is given by:
T O + τ C C + τ l W L − G + ((1 + r∗ )/π ∗ − 1) F ∗
B= (6.45)
(1/β − 1)
57