metadata: authors: 0: author: Zeufack,Albert G.
1: author: Kopoin,Alexandre
2: author: Nganou,Jean-Pascal
3: author: Tchana Tchana,Fulbert
4: author: Kemoe,Laurent
count: Uganda
docna: 0: docna: Optimal allocation of natural resource
            surpluses in a dynamic macroeconomic framework : a DSGE
            analysis with evidence from Uganda
docty: Policy Research Working Paper
subtopic: Global Environment Facility,Labor Markets,Coastal and Marine Resources,Economic Development,Energy and Natural Resources,Global Environment
teratopic: Macroeconomics and Economic Growth,Public Sector Development
abstracts: cdata!: In low-income, capital-scarce economies
            that face financial and fiscal constraints, managing
            revenues from newly found natural resources can be a
            daunting challenge. The policy debate is how to scale up
            public investment to meet huge needs in infrastructure
            without generating a higher public deficit, and avoid the
            Dutch disease. This paper uses an open economy dynamic
            stochastic general equilibrium model that is compatible with
            low-income economies and calibrated on Ugandan's data
            to tackle this problem. The paper explores macroeconomic
            dynamics under three stylized fiscal policy approaches for
            managing resource windfalls: investing all in public
            capital, saving all in a sovereign wealth fund, and a
            sustainable-investing approach that proposes a constant
            share of resource revenues to finance public investment and
            the rest to be saved. The analysis finds that a gradual
            scaling-up of public investment yields the best outcome, as
            it minimizes macroeconomic volatility. The analysis then
            investigates the optimal oil share to use for public
            investment; the criterion minimizes a loss function that
            accounts for households' welfare and macroeconomic
            stability in an environment featuring oil price volatility.
            The findings show that, depending on the policy maker's
            preference for stability, 55 to 85 percent of oil windfalls
            should be invested.
geo_reg_key: 517191
repnme: repnme: Optimal allocation of natural resource
            surpluses in a dynamic macroeconomic framework : a DSGE
            analysis with evidence from Uganda
display_title: Optimal allocation of natural
            resource surpluses in a dynamic macroeconomic framework : a
            DSGE analysis with evidence from Uganda
listing_relative_url: /research/2016/12/27010396/optimal-allocation-natural-resource-surpluses-dynamic-macroeconomic-framework-dsge-analysis-evidence-uganda
topicv3: Environmental Sustainability m1325984 1786,Natural Resources m1326446 1979,Environment, Natural Resources and Blue
            Economy m1327391 566,Labor Supply m1504055 2751,Dutch Disease m1583679 4708
publishtoextweb_dt: 2016-12-13T00:00:00Z
historic_topic: Macroeconomics and Economic Growth,Public Sector Development
no_of_pages: 59
author_keys: 0: author_key: 142139
1: author_key: 1297627
2: author_key: 167885
3: author_key: 660265
4: author_key: 1484195
model_extractions: 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 and fiscal constraints, managing revenues from newly found natural resources can be a daunting challenge. The policy debate is how to scale up public investment to meet huge needs in infrastructure without generating a higher public deficit, and avoid the Dutch disease. This paper uses an open economy dynamic stochastic general equilibrium model that is compatible with low-income economies and calibrated on Ugandan’s data to tackle this problem. The paper explores macroeconomic dynamics under three stylized fiscal policy approaches for managing resource windfalls: investing all in public capital, saving all in a sovereign wealth fund, and a sustainable-investing approach that proposes a constant share of resource revenues to finance public investment and the rest to be saved. The analysis finds that a gradual scaling-up of public investment yields the best outcome, as it minimizes macroeconomic volatility. The analysis then investigates the optimal oil share to use for public investment; the criterion minimizes a loss function that accounts for households’ welfare and macroeconomic stability in an environment featuring oil price volatility. The findings show that, depending on the policy maker’s preference for stability, 55 to 85 percent of oil windfalls should be invested.

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<sup>_∗_</sup> Alexandre Kopoin<sup>_†_</sup> Jean-Pascal Nganou<sup>_‡_</sup> Fulbert Tchana Tchana<sup>_§_</sup> Laurent Kemoe<sup>_¶_</sup> 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 revenues 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 without 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 production 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 aggregates 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 sustainable 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 vulnerable 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 constraints, 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 assessment of several scenarios based on the country’s specific macroeconomic strengths and weaknesses. 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 re3
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 under resource price uncertainty. Ag ́enor (2014) provides a characterization of the optimal fiscal 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 different 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 share to invest is slightly higher than the values estimated in Ag ́enor (2014), which ranges 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.

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, **E** 0 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: 6
where _τt_<sup>_c_and</sup><sup>_τ l_</sup> _t_<sup>denotethetaxratesonconsumptionandincomefromlaborsupply.Total</sup> private investment _−_ defined as the sum of private investment in the tradable sector and that in non-tradable sector _−_ is given by: _it_ = _i_<sup>_T_</sup> _t_<sup>+</sup><sup>_iN_</sup> _t_<sup>.</sup><sup>_bt_isthedomesticgovernmentdebtpaying</sup> a gross nominal rate of _Rt_ = (1 + _rt_<sup>_b_),</sup><sup>_πt_isthedomesticinflationand</sup><sup>_wt_istherealwageindex</sup> expressed in units of consumptions goods. _zt_ denotes total government transfers to households, whereas Ω<sup>_N_</sup> _t_<sup>andΩ</sup><sup>_T_</sup> _t_<sup>areprofitsfromthenon-tradedandtradedgoodssectors.</sup><sup>_r_</sup> _t_<sup>_Nk_</sup> _t_<sup>_N_</sup> _−_ 1<sup>+</sup><sup>_r_</sup> _t_<sup>_Tk_</sup> _t_<sup>_T_</sup> _−_ 1 is capital income. Throughout the analysis, we assume that households do not have access to foreign loans.<sup>1</sup> 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: Finally, the consumption basket is a composite of traded goods and non-traded goods, aggregated using a constant-elasticity-of-substitution (CES) technology.

with _χ_ and _φ_ denoting the intratemporal elasticity of substitution and the degree of home consumption 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

> 1Most 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 lowincome countries’ obligation bonds.

7
() Yo ~~)~~ Yo ~~)~~ ( ()~ ()~) (( ) () <u>)-</u> ( ~~—)~~
<!-- Start of picture text -->
[— ) (— J )<br>[J [— J—- )<br><!-- End of picture text -->
common specification with constant return to scale to all production factors, this specification has the advantage that _α_<sup>_T_</sup> and _α_<sup>_N_</sup> 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 where, Θ( _kt_<sup>_N_), is the investment adjustment cost function, satisfying:Θ(1) = Θ</sup><sup>_′_(1) and Θ</sup><sup>_′′>_0.3</sup> As in Obstfeld and Rogoff (2000), the monopolistic producer _i_ faces a demand function for the variety _i_ where _yt_<sup>_N_</sup> is the aggregate non-traded demand. A representative non-traded good firm chooses its price ( _p_<sup>_N_</sup> _t_<sup>(</sup><sup>_i_)),labordemand(</sup><sup>_l_</sup> _t_<sup>_N_(</sup><sup>_i_)),andcapitalstock(</sup><sup>_k_</sup> _t_<sup>_N_</sup> +1<sup>(</sup><sup>_i_))tomaximizeitsnetpresent-</sup> value profits, weighted by the household’s marginal utility of consumption ( _λt_ ).

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 _λ_<sup>_N_</sup> _t_<sup>,theLagrangemultiplierassociatedwiththeoptimizationprogram,which</sup> also may be interpreted as the real marginal cost of producing one unit of output _yt_<sup>_N_,thenthe</sup> 3Under this specification, the steady-state level of capital stock is not affected by the presence of adjustment costs.

10
em ~~)~~ ( ~~)~~ ~~<u>=)</u> >~~ ( ~~n—)~~
In the case of a full indexation ( _χp_ = 1), equation [2.20] may be rewritten to derive the New Keynesian Phillips curve given by: ( _p_<sup>_N_</sup> _t_<sup>)1</sup><sup>_−ξp_=</sup><sup>_φp_(</sup><sup>_pN_</sup> _t−_ 1<sup>)1</sup><sup>_−ξp_+ (1</sup><sup>_−φp_)(</sup><sup>_p_�</sup><sup>_N_</sup> _t_<sup>)1</sup><sup>_−ξp_.</sup>

**_Wage setting:_** Recall that households supply differentiated labor inputs used by intermediate 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 supplied by households individually. The differentiated labor inputs supplier aggregates labor using 1 _<u>ξw</u> −_ 1 _ξwξw−_ 1 a constant elasticity of substitution function given by _lt_<sup>_N_</sup> = 0<sup>_l_</sup> _t_<sup>_N_(</sup><sup>_i_)</sup> _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 differentiated labor wages, _wt_<sup>_N_(</sup><sup>_i_),andtheaggregatewage,</sup><sup>_w_</sup> _t_<sup>_N_.Thefirstorderconditionsaresuchthat</sup> _lt_<sup>_N_(</sup><sup>_i_)=</sup> � _wwt_<sup>_N_</sup> _t_<sup>_N_</sup><sup><u>(</u></sup><sup>_i_</sup><sup><u>)</u></sup> � _−ξw ltN_ and _wt_<sup>_N_</sup> = ��01<sup>_w_</sup> _t_<sup>_N_(</sup><sup>_i_)1</sup><sup>_−ξwdi_</sup> � 1 _−_ <u>1</u> _ξw_ . 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 πt_<sup>_χ_</sup> <u>+</u><sup>_w_</sup> _s−_ 1 _wt_<sup>_N_</sup><sup><u>(</u></sup><sup>_i_</sup><sup><u>)</u></sup> by � _πt_ + _i pt_ . _i_ =1

_−ξw_ Recall that, under the labor supply constraint ( _lt_<sup>_N_</sup> + _h_<sup>(</sup><sup>_i_) =</sup> �� _hi_ =1 _ππt_<sup>_χw_</sup> <u>+</u> _t_ + _<u>h−h</u>_ <u>1</u> _wwt_<sup>_N_</sup> _t_<sup>_N_</sup> +<sup><u>(</u></sup> _h_<sup>_i_</sup><sup><u>)</u></sup> � _lt_<sup>_N_</sup> + _h_<sup>),the</sup> efficient wage can be written as a geometric average of past real wage and the new optimal wage in the case of full indexation _πt_<sup>1</sup><sup>_−ξw_</sup> � _wt_<sup>_N_</sup> �1 _−ξw_ = _φw_ � _wt_<sup>_N_</sup> _−_ 1�1 _−ξw πt_ 1 _−−_ 1 _ξw_<sup>+(1</sup><sup>_−φw_)</sup><sup>_π_</sup> _t_<sup>1</sup><sup>_−ξw_</sup> � _w_ � _t_<sup>_N_</sup> �1 _−ξw_ .

# **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.

The total factor productivity (TFP) in the tradable good sector, **a**<sup>_T_</sup> _t_<sup>,issubjecttolearning-by-</sup> doing externalities, depending on the last period traded output: ln **a**<sup>_T_</sup> _t_<sup>=</sup><sup>_ρzT_ln</sup><sup>**a**</sup><sup>_T_</sup> _t−_ 1<sup>+</sup><sup>_d_ln</sup><sup>_y_</sup> _t_<sup>_T_</sup> _−_ 1<sup>.</sup> Private capital in the traded good sector also evolves by the law of motion Each firm maximizes its weighted present-value profits, Let _λ_<sup>_T_</sup> _t_<sup>betheLagrangemultiplierassociatedwiththeproductionfunctionconstraintinthe</sup> tradable goods sector, which may be interpreted as the real marginal cost of producing one unit of output _yt_<sup>_T_.Thefirstorderconditionsofaminimizingproblemaregivenby</sup> A part of the intermediate traded good production in the traded goods sector, _yt_<sup>_Td_,isusedfor</sup> the domestic market and the remaining part, _y_<sup>_Tx_</sup> , is exported in fully competitive market. So that, The foreign demand for locally produced goods is as follows:
where ( _μ −_ 1) _/μ_ captures the elasticity of substitution between the exported goods and foreign-produced goods in the consumption basket of foreign consumers, and _yt_<sup>_∗_and</sup><sup>_p∗_</sup> _t_<sup>are,</sup> 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 imported good, _yt_<sup>_M_</sup> , produced by a representative competitive firm. We also assume Calvotype 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 by a competitive firm that uses domestically consumed traded goods, _yt_<sup>_Td_,andimportsgoods,</sup> _yt_<sup>_M_</sup> following a CES technology 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 The final traded good price, _p_<sup>_T_</sup> , which corresponds to the numeraire of our economy is given by

# **2.2.3 Natural Resource Sector**

Output in the natural resource sector is assumed to follow an exogenous process. This assumption 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 where the exogenous process returns to the steady-state level _y_<sup>_O_</sup> with the autoregressive parameter _ρyo_ . The resource production shock is assumed to be _ε_<sup>_yo_</sup> _t ∼ i.i.d._ and follows a standard normal distribution with a standard deviation of _σyo_ ( _ε_<sup>_yo_</sup> _t ∼ N_ (0 _, σyo_<sup>2)).</sup> 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 _p_<sup>_O_</sup> _t_<sup>_∗_.Asaresult,theinternationalcommodityprice</sup><sup>_pO_</sup> _t_<sup>_∗_</sup> (relative to the foreign goods) evolves according to an exogenous process defined by where the international commodity price shock _ε_<sup>_yo_</sup> _t ∼ N_ (0 _, σyo_<sup>2),andisan</sup><sup>_i.i.d._process.The</sup> resource GDP from the natural resource sector in units of domestic composite consumption is: As in many resource-rich economies, resource production in Uganda is subject to a royalty at a rate of _τt_<sup>_o_.Thus,theresourcerevenuecollectedfromthenaturalresourcesectoris</sup> where _T_<sup>_O∗_</sup> _t_<sup>is the resource revenue collected from the natural resource sector expressed in foreign</sup> 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 contracts domestic debt _bt_ . Total expenditures include government consumption ( _gt_<sup>_C_),public</sup> investment ( _gt_<sup>_I_) and debt services.If capital letters denote the aggregate level of a variable, then</sup> government budget constraint may be written as where _Ft_<sup>_∗_istheassetvalueofresourcefund,whichgeneratesaconstantinterestrate</sup><sup>_r∗_.In</sup> [2.36], _Gt_ is government purchases with a relative price to composite consumption goods of _p_<sup>_g_</sup> _t_<sup>.</sup> The model allows external assets accumulation, while we abstracts from external commercial borrowing. Despite taxing revenues from the non-tradable and tradable goods sectors ( _ιp_<sup>_N_</sup> _t_<sup>_Y_</sup> _t_<sup>_N_</sup> and _ιstYt_<sup>_T_),thegovernmentisunabletousethisasanadditionalsourceoffiscalrevenue.</sup> 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: Finally, government purchases consist of expenditures on government consumption _G_<sup>_C_</sup> _t_<sup>and</sup> public investment _G_<sup>_I_</sup> . As in the private consumption, we assume that government purchases are a CES function of traded and non-traded goods.

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where _η_ is the degree of home bias in government purchases. The relative price of government consumption to private consumption is

# **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 where 0 _<_ (1 _− ε_<sup>_G_</sup> ) _≤_ 1 governs the inefficiency of public investment and _δ_<sup>_G_</sup> 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_<sup>_∗_=</sup><sup>_F ∗_,</sup> _∀t_ , while public investment evolves as follows:
# ▶ _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: 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: where _φ_<sup>_oil_</sup> is a fiscal policy parameter that satisfies 0 _≤ φ_<sup>_oil_</sup> _≤_ 1. At this point, it’s worth mentioning that the Sustainable Investing Approach and the all-investing approach produce the same fiscal responses under _φ_<sup>_oil_</sup> = 1, and the all-saving approach is obtained by setting _φ_<sup>_oil_</sup> = 0.

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## **2.3.3 Central Bank**

Monetary policy is conducted by the central bank, which manages the short-term nominal interest rate _Rt_ = (1 + _rt_<sup>_b_),inresponsetofluctuationsindomesticoutputgapandinconsumer</sup> price inflation gap using a Taylor-type rule. This managing rule allows the central bank to smooth nominal interest rates through open market operations.<sup>4</sup> where _Yt_ denotes the country’s growth domestic product (GDP) and _φt_ are _i.i.d._ normal innovations 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.

> 4The use of the previous period interest rate allows us to match the smooth profile of the observed interest rate in the data.

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Then, the general equilibrium in the goods markets involves: where _It_ = _It_<sup>_N_</sup> + _It_<sup>_T_</sup> is the private investment, and _Ct_ = _Ct_<sup>_N_</sup> + _Ct_<sup>_T_</sup> is the total consumption. Recall that government purchases consist of expenditures on government consumption _G_<sup>_C_</sup> _t_<sup>and</sup> public investment _G_<sup>_I_</sup> , therefore _Gt_ = _G_<sup>_C_</sup> _t_<sup>+</sup><sup>_GI_</sup> _t_<sup>.Letdenoteby</sup><sup>_CAt_thecurrentaccount,then</sup> the balance of payment condition is given by Then, labor market clearing requires demand for labor by firms in both sectors to equal the sector specific supply of labor. This implies that: and where _L_<sup>_d_</sup> _t_<sup>denotestotaldemandforlaborbyfirmsinbothsectors.</sup> Finally, capital market clearing conditions imply that: and

# **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:

## **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_ ), _L_<sup>_d_</sup> _t_<sup>(</sup><sup>_j_)and</sup><sup>_Wt_(</sup><sup>_i_)thatsolvesfirmsmaximizationproblem;(iii)aggregateprices</sup> _Pt_<sup>_N_,</sup><sup>_P_</sup> _t_<sup>_x_,</sup><sup>_St_and</sup><sup>_P ∗_</sup> _t_<sup>;(iv)savingandconsumptiondecisionrulesforgovernment;and(v)all</sup> markets clear. The equilibrium system of the model consists of the private agents optimality 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 evidence for low-income countries and calibrated in Ang ́enor and Aizenman (1999), Goldberg 21
(2011) and Ag ́enor (2014). Data sources used to match key ratios include the IMF’s World 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), Goldberg (2011), Ang ́enor and Aizenman (1999), Kopoin et al. (2013) and Ag ́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, _α_<sup>_N_</sup> , 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 countries and reported in Jihad et al. (2012), Cherif and Fuad (2012) and Ag ́enor (2014).

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 investment _ε_<sup>_G_</sup> . 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 _ε_<sup>_G_</sup> 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, respectively. These values satisfy the Taylor principle and are consistent to those estimated in Ag ́enor (2014) and Kopoin et al. (2013). The standard deviation of both domestic and foreign monetary 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<br>|0.3|
|_χ_|Elasticity of substitution (traded and non-traded goods)|0.44|
|_ξ_|Elasticity of substitution between labors|1|
|_β_<br>|Discount factor|0.93|
|_α_<sup>_N_</sup><br>|Capital income share in non-traded goods sector|0.45|
|_α_<sup>_T_</sup><br>|Capital income share in traded goods sector|0.3|
|_α_<sup>_G_</sup><br>|Output elasticity of public capital|0.2|
|_φ_<sup>_T_</sup>, _φ_<sup>_N_</sup>|Investment adjustment cost|10|
|_φp_|Probability of not reoptimizing prices<br>|0.75|
|_φw_|Probability of not reoptimizing wages|0.64|
|_ω_|Share of labor supplied to non-traded sector|0.55|
|_δ_<sup>_N_</sup><br>|Depreciation rate for _K_<sup>_N_</sup><br>|0.1|
|_δ_<sup>_T_</sup><br>|Depreciation rate for _K_<sup>_T_</sup>|0.075|
|_δ_<sup>_G_</sup>|Depreciation rate for public capital|0.07|
|_ψ_|Inverse of Frisch elasticity of labor supply|3|
|_η_<br>|Home bias of government purchases|0.65|
|_τ _<sup>_l_</sup>|Efective labor tax rates<br>|0.1|
|_τ _<sup>_c_</sup><br>|Efective consumption tax rates|0.1|
|_ε_<sup>_G_</sup>|Efciency of public investment|0.6|
|_r_<sup>_∗_</sup>|Annual real return to a resource fund|0.015|
|_λr_|Interest rate smoothing parameter|0.8|
|_λπ_|Central banks’ infation reaction parameter|1.5|
|_λy_|Central banks’ output reaction parameter|0.025|
|_φ_<sup>_oil_</sup><br><br>|Share of oil revenues allocated to public investment|0.5<br><br>|
|�_ρyo_<br>0<br>0<br>_ρpo_<br>�|Uncorrelated oil production and price shock parameters|�0_._95<br>0<br>0<br>0_._95<br>�|

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.

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**Table 2:** Steady-state Values in percentage of total output

|**Steady-state rati**|**os**<br>**Description**|**Values**|
|---|---|---|
|_Y _<sup>_O_</sup>_/Y_<br>|Oil revenues to GDP ratio in steady state|0.072|
|_I_<sup>_/_</sup>_Y_<br>|Total investment to GDP ratio in steady state|0.1468|
|_Y _<sup>_T_</sup>_/Y_<br>|Tradable to GDP ratio in steady state|0.329|
|_Y _<sup>_N_</sup>_/Y_<br>|Tradable to GDP ratio in steady state|0.665|
|_L_<sup>_N_</sup>_/L_<br>|Share of employment in non-tradable sector|0.583|
|_L_<sup>_T_</sup>_/L_|Share of employment in tradable sector|0.417|
|_C_<sup>_N_</sup>_/C_<br>|Non-tradable goods consumption to C|0.316|
|_G_<sup>_C_</sup>_/Y_<br>|Government consumption to GDP ratio in steady state|0.53|
|_G_<sup>_I_</sup>_/Y_|Public investment to GDP ratio in steady state|0.32|
|_F _<sup>_∗_</sup>_/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).

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**Figure 1.** Responses to a one standard deviation oil production shock _−_ fiscal policy A and B

<!-- Start of picture text --> Panel A<br>Aggregate Consumption Consumption Tradable Goods Consumption NonTradable Goods<br>0 . 25 1<br>0<br>0 . 2 0 . 8 − 0 . 5<br>0 . 15 − 1<br>0 . 6<br>0 . 1 − 1 . 5<br>0 . 4<br>5 · 10 − 2 − 2<br>0 . 2<br>0 − 2 . 5<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>Total Output Private Investment Public Investment<br>4 0 0 . 8<br>− 0 . 2<br>3 0 . 6<br>− 0 . 4<br>2 − 0 . 6 0 . 4<br>− 0 . 8<br>1 0 . 2<br>− 1<br>0 − 1 . 2 0<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>Public Capital Investment Tradable Sector Investment NonTradable Sector<br>0 0<br>0 . 3 − 0 . 1<br>− 0 . 2<br>− 0 . 2<br>0 . 2<br>− 0 . 4 − 0 . 3<br>0 . 1<br>− 0 . 4<br>− 0 . 6<br>0 − 0 . 5<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>Under the All-investing in Public Capital Approach Under the Saving in a Sovereign Wealth Fund Approach<br>(%) (%) (%)<br>s.s. s.s. s.s.<br>from from from<br>Deviation Deviation Deviation<br>(%) (%) (%)<br>s.s. s.s. s.s.<br>from from from<br>Deviation Deviation Deviation<br>(%) (%) (%)<br>s.s. s.s. s.s.<br>from from from<br>Deviation Deviation Deviation<br><!-- End of picture text --> _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 expressed in percentage deviation from the steady-state values. The solid line 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** ).

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**Panel B**

<!-- Start of picture text --> Output Tradable Sector Output NonTradable Sector Non Oil Revenues<br>0 0<br>0<br>− 5 · 10 − 2 − 5 · 10 − 2<br>− 0 . 2<br>− 0 . 1 − 0 . 1<br>− 0 . 15 − 0 . 15 − 0 . 4<br>− 0 . 2 − 0 . 2 − 0 . 6<br>− 0 . 25 − 0 . 25<br>− 0 . 8<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>Total Employment Employment Tradable Sector Employment NonTradable Sector<br>0 0 0<br>− 5 · 10 − 2 − 5 · 10 − 2 − 5 · 10 − 2<br>− 0 . 1 − 0 . 1 − 0 . 1<br>− 0 . 15 − 0 . 15 − 0 . 15<br>− 0 . 2 − 0 . 2 − 0 . 2<br>− 0 . 25 − 0 . 25 − 0 . 25<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>· 10 − Wage Tradable Sector 2 Wage NonTradable Sector Total Wage<br>0 . 1<br>0 . 1<br>8<br>8 · 10 − 2<br>8 · 10 − 2<br>6<br>6 · 10 − 2<br>6 · 10 − 2<br>4<br>4 · 10 − 2 4 · 10 − 2<br>2 2 · 10 − 2 2 · 10 − 2<br>0 0 0<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>Under the All-investing in Public Capital Approach Under the Saving in a Sovereign Wealth Fund Approach<br>(%) (%) (%)<br>s.s. s.s. s.s.<br>from from from<br>Deviation Deviation Deviation<br>(%) (%) (%)<br>s.s. s.s. s.s.<br>from from from<br>Deviation Deviation Deviation<br>(%) (%) (%)<br>s.s. s.s. s.s.<br>from from from<br>Deviation Deviation Deviation<br><!-- End of picture text --> _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 expressed in percentage deviation from the steady-state values. The solid line 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** ).

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# **Panel C**

<!-- Start of picture text --> Total Government Spending Gov. Spending Tradable Sector Gov. Spending NonTradable Sector<br>1 . 5<br>− 0 . 2<br>2<br>1<br>− 0 . 4<br>0 . 5 1<br>− 0 . 6<br>0<br>0<br>− 0 . 8<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>Non Oil Exports Imports Sovereign Wealth Fund<br>0 . 4<br>0<br>1<br>0 . 3<br>− 0 . 5<br>0 . 5 0 . 2<br>− 1 0 0 . 1<br>0<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>Inflation Exchange Rate Public Debt<br>2<br>0<br>1 − 0 . 5 1 . 5<br>− 1 1<br>0 . 5<br>− 1 . 5 0 . 5<br>0 − 2 0<br>− 2 . 5<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>Under the All-investing in Public Capital Approach Under the Saving in a Sovereign Wealth Fund Approach<br>(%) (%) (%)<br>s.s. s.s. s.s.<br>from from from<br>Deviation Deviation Deviation<br>(%) (%) (%)<br>s.s. s.s. s.s.<br>from from from<br>Deviation Deviation Deviation<br>(%) (%)<br>s.s. s.s.<br>Points<br>from from<br>Percentage<br>Deviation Deviation<br><!-- End of picture text --> _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 expressed in percentage deviation from the steady-state values. The solid line 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** ).

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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 nonoil 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 allsaving 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 approach. 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 ( _φ_<sup>_oil_</sup> = 0 _._ 5) and to save the remaining half; Section 4.4 investigates the optimal value of _φ_<sup>_oil_</sup> . 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
**Figure 2.** Responses to a one standard deviation oil production shock _−_ fiscal policy B and C

# **Panel A**

<!-- Start of picture text --> Aggregate Consumption Consumption Tradable Goods Consumption NonTradable Goods<br>0 . 8<br>0 . 2 0<br>0 . 15 0 . 6 − 0 . 5<br>0 . 1 0 . 4 − 1<br>5 · 10 − 2 − 1 . 5<br>0 . 2<br>0<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>Total Output Private Investment Public Investment<br>− 0 . 2<br>3 0 . 4<br>− 0 . 4 0 . 3<br>2<br>− 0 . 6 0 . 2<br>1<br>− 0 . 8 0 . 1<br>0 − 1 0<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>Public Capital Investment Tradable Sector Investment NonTradable Sector<br>− 0 . 1 − 0 . 1<br>0 . 15 − 0 . 2<br>− 0 . 2<br>− 0 . 3<br>0 . 1<br>− 0 . 4 − 0 . 3<br>5 · 10 − 2<br>− 0 . 5<br>− 0 . 4<br>0<br>− 0 . 6<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>Under the Sustainable Investing Approach Under the Saving in a Sovereign Wealth Fund Approach<br>(%) (%) (%)<br>s.s. s.s. s.s.<br>from from from<br>Deviation Deviation Deviation<br>(%) (%) (%)<br>s.s. s.s. s.s.<br>from from from<br>Deviation Deviation Deviation<br>(%) (%) (%)<br>s.s. s.s. s.s.<br>from from from<br>Deviation Deviation Deviation<br><!-- End of picture text --> _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 expressed in percentage deviation from the steady-state values. The dashed line shows the response of the fiscal policy B ( **All-Saving Approach** ) and solid lines show the response of the fiscal policy C ( **Sustainable Investing Approach** ).

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**Panel B**

<!-- Start of picture text --> Output Tradable Sector Output NonTradable Sector Non Oil Revenues<br>0 0 0<br>− 5 · 10 − 2 − 5 · 10 − 2<br>− 0 . 1 − 0 . 1 − 0 . 2<br>− 0 . 15 − 0 . 15<br>− 0 . 2 − 0 . 2 − 0 . 4<br>− 0 . 25 − 0 . 25<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>Total Employment Employment Tradable Sector Employment NonTradable Sector<br>0 0 0<br>− 5 · 10 − 2 − 5 · 10 − 2 − 5 · 10 − 2<br>− 0 . 1 − 0 . 1 − 0 . 1<br>− 0 . 15 − 0 . 15 − 0 . 15<br>− 0 . 2 − 0 . 2 − 0 . 2<br>− 0 . 25 − 0 . 25 − 0 . 25<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>· 10 − Wage Tradable Sector 2 · 10Wage NonTradable Sector − 2 · 10 − 2 Total Wage<br>5<br>4<br>4<br>4<br>3<br>3<br>2<br>2 2<br>1 1<br>0 0 0<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>Under the Sustainable Investing Approach Under the Saving in a Sovereign Wealth Fund Approach<br>(%) (%) (%)<br>s.s. s.s. s.s.<br>from from from<br>Deviation Deviation Deviation<br>(%) (%) (%)<br>s.s. s.s. s.s.<br>from from from<br>Deviation Deviation Deviation<br>(%) (%) (%)<br>s.s. s.s. s.s.<br>from from from<br>Deviation Deviation Deviation<br><!-- End of picture text --> _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 expressed in percentage deviation from the steady-state values. The dashed line shows the response of the fiscal policy B ( **All-Saving Approach** ) and solid lines show the response of the fiscal policy C ( **Sustainable Investing Approach** ).

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**Panel C**

<!-- Start of picture text --> Total Government Spending Gov. Spending Tradable Sector Gov. Spending NonTradable Sector<br>2 − 0 . 2<br>1<br>1 . 5<br>− 0 . 3<br>1<br>0 . 5<br>− 0 . 4<br>0 . 5<br>0 − 0 . 5<br>0<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>Non Oil Exports Imports Sovereign Wealth Fund<br>0 1 0 . 4<br>− 0 . 2 0 . 3<br>0 . 5<br>− 0 . 4<br>0 . 2<br>− 0 . 6<br>0 0 . 1<br>− 0 . 8<br>0<br>− 1<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>Inflation Exchange Rate Public Debt<br>1<br>0 1 . 5<br>0 . 8<br>0 . 6 − 0 . 5 1<br>0 . 4 − 1 0 . 5<br>0 . 2<br>− 1 . 5<br>0 0<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>Under the All-investing in Public Capital Approach Under the Saving in a Sovereign Wealth Fund Approach<br>(%) (%) (%)<br>s.s. s.s. s.s.<br>from from from<br>Deviation Deviation Deviation<br>(%) (%) (%)<br>s.s. s.s. s.s.<br>from from from<br>Deviation Deviation Deviation<br>(%) (%)<br>s.s. s.s.<br>Points<br>from from<br>Percentage<br>Deviation Deviation<br><!-- End of picture text --> _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 expressed in percentage deviation from the steady-state values. The dashed line shows the response of the fiscal policy B ( **All-Saving Approach** ) and solid lines show the response of the fiscal policy C ( **Sustainable Investing Approach** ).

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**Figure 3.** Responses to a one standard deviation oil production shock _−_ fiscal policy A and C

# **Panel A**

<!-- Start of picture text --> Aggregate Consumption Consumption Tradable Goods Consumption NonTradable Goods<br>0 . 25 1 0<br>0 . 2 0 . 8 − 0 . 5<br>0 . 15 − 1<br>0 . 6<br>0 . 1 − 1 . 5<br>0 . 4<br>5 · 10 − 2 − 2<br>0 . 2<br>0 − 2 . 5<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>Total Output Private Investment Public Investment<br>4 0 0 . 8<br>− 0 . 2<br>3 − 0 . 4 0 . 6<br>2 − 0 . 6 0 . 4<br>− 0 . 8<br>1<br>− 1 0 . 2<br>0 − 1 . 2<br>0<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>Public Capital Investment Tradable Sector Investment NonTradable Sector<br>0 0<br>0 . 3 − 0 . 1<br>− 0 . 2<br>− 0 . 2<br>0 . 2<br>− 0 . 4 − 0 . 3<br>0 . 1 − 0 . 4<br>− 0 . 6<br>− 0 . 5<br>0<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>Under the All-investing in Public Capital Approach Under the Sustainable Investing Approach<br>(%) (%) (%)<br>s.s. s.s. s.s.<br>from from from<br>Deviation Deviation Deviation<br>(%) (%) (%)<br>s.s. s.s. s.s.<br>from from from<br>Deviation Deviation Deviation<br>(%) (%) (%)<br>s.s. s.s. s.s.<br>from from from<br>Deviation Deviation Deviation<br><!-- End of picture text --> _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 expressed in percentage deviation from the steady-state values. The solid line shows the response of the fiscal policy A ( **All-Investing Approach** ) and Dashed lines show the response of the fiscal policy C ( **Sustainable Investing Approach** ).

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**Panel B**

<!-- Start of picture text --> Output Tradable Sector Output NonTradable Sector Non Oil Revenues<br>0 0<br>0<br>− 5 · 10 − 2 − 5 · 10 − 2<br>− 0 . 2<br>− 0 . 1 − 0 . 1<br>− 0 . 4<br>− 0 . 15 − 0 . 15<br>− 0 . 6<br>− 0 . 2 − 0 . 2<br>− 0 . 8<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>Total Employment Employment Tradable Sector Employment NonTradable Sector<br>− 5 · 10 − 2 − 5 · 10 − 2 − 5 · 10 − 2<br>− 0 . 1 − 0 . 1 − 0 . 1<br>− 0 . 15 − 0 . 15 − 0 . 15<br>− 0 . 2 − 0 . 2 − 0 . 2<br>− 0 . 25 − 0 . 25 − 0 . 25<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>· 10 − Wage Tradable Sector 2 Wage NonTradable Sector Total Wage<br>0 . 1<br>0 . 1<br>8<br>8 · 10 − 2<br>8 · 10 − 2<br>6<br>6 · 10 − 2<br>6 · 10 − 2<br>4<br>4 · 10 − 2 4 · 10 − 2<br>2<br>2 · 10 − 2 2 · 10 − 2<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>Under the All-investing in Public Capital Approach Under the Sustainable Investing Approach<br>(%) (%) (%)<br>s.s. s.s. s.s.<br>from from from<br>Deviation Deviation Deviation<br>(%) (%) (%)<br>s.s. s.s. s.s.<br>from from from<br>Deviation Deviation Deviation<br>(%) (%) (%)<br>s.s. s.s. s.s.<br>from from from<br>Deviation Deviation Deviation<br><!-- End of picture text --> _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 expressed in percentage deviation from the steady-state values. The solid line shows the response of the fiscal policy A ( **All-Investing Approach** ) and Dashed lines show the response of the fiscal policy C ( **Sustainable Investing Approach** ).

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# **Panel C**

<!-- Start of picture text --> Total Government Spending Gov. Spending Tradable Sector Gov. Spending NonTradable Sector<br>1 . 5<br>− 0 . 2<br>2<br>1<br>− 0 . 4<br>1<br>0 . 5<br>− 0 . 6<br>0<br>0<br>− 0 . 8<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>Non Oil Exports Imports Sovereign Wealth Fund<br>0 . 2<br>0<br>1 0 . 15<br>− 0 . 5<br>0 . 1<br>0 . 5<br>− 1 5 · 10 − 2<br>0<br>0<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>Inflation Exchange Rate Public Debt<br>2<br>0<br>1 − 0 . 5 1 . 5<br>− 1 1<br>0 . 5<br>− 1 . 5 0 . 5<br>0 − 2 0<br>− 2 . 5<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>Under the All-investing in Public Capital Approach Under the Sustainable Investing Approach<br>(%) (%) (%)<br>s.s. s.s. s.s.<br>from from from<br>Deviation Deviation Deviation<br>(%) (%) (%)<br>s.s. s.s. s.s.<br>from from from<br>Deviation Deviation Deviation<br>(%) (%)<br>s.s. s.s.<br>Points<br>from from<br>Percentage<br>Deviation Deviation<br><!-- End of picture text --> _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 expressed in percentage deviation from the steady-state values. The solid line shows the response of the fiscal policy A ( **All-Investing Approach** ) and Dashed lines show the response of the fiscal policy C ( **Sustainable Investing Approach** ).

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 consumption and public investment in the long run. Consumption increases by 0.22 percent under 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 prewindfall 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 sustainable 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 framework. 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 _ε_<sup>_G_</sup> ( _ε_<sup>_G_</sup> = 0 _._ 25 and _ε_<sup>_G_</sup> = 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 ( _ε_<sup>_G_</sup> _→_ 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 ( _α_<sup>_G_</sup> = 0 _._ 05 and _α_<sup>_G_</sup> = 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 checks: Absorptive capacity constraints under fiscal policy C

<!-- Start of picture text --> Aggregate Consumption Public Investment Private Investment<br>0 . 25 − 0 . 2<br>0 . 6<br>0 . 2 − 0 . 4<br>0 . 15 0 . 4<br>− 0 . 6<br>0 . 1<br>0 . 2 − 0 . 8<br>5 · 10 − 2<br>− 1<br>0<br>0<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>Public Capital Output Tradable Sector Output NonTradable Sector<br>0 . 3 0 0<br>− 5 · 10 − 2 − 5 · 10 − 2<br>0 . 2<br>− 0 . 1 − 0 . 1<br>− 0 . 15 − 0 . 15<br>0 . 1<br>− 0 . 2 − 0 . 2<br>0 − 0 . 25<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>Total Employment · 10 − 2 Total Wage Government Spending<br>8<br>− 5 · 10 − 2 1<br>6<br>− 0 . 1<br>− 0 . 15 4 0 . 5<br>− 0 . 2<br>2<br>0<br>− 0 . 25<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>Sustainable investing Approach, ε G = 0 . 25 Sustainable investing Approach, ε G = 0 . 95<br>(%) (%) (%)<br>s.s. s.s. s.s.<br>from from from<br>Deviation Deviation Deviation<br>(%) (%) (%)<br>s.s. s.s. s.s.<br>from from from<br>Deviation Deviation Deviation<br>(%) (%) (%)<br>s.s. s.s. s.s.<br>from from from<br>Deviation Deviation Deviation<br><!-- End of picture text --> _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 expressed in percentage deviation from the steady-state values. The solid line shows the response of the fiscal policy C ( **Sustainable Investing Approach** ) under _ε_<sup>_G_</sup> = 0 _._ 25 and Dashed lines show the response under _ε_<sup>_G_</sup> = 0 _._ 95.

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**Figure 5.** Robustness checks: Productivity of public capital under fiscal policy C

# **Panel A**

<!-- Start of picture text --> Aggregate Consumption Total Output Private Investment<br>0 . 4<br>3<br>0 . 3<br>− 0 . 5<br>2<br>0 . 2<br>1 − 1<br>0 . 1<br>0<br>0<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>Public Investment Public Capital Output Tradable Sector<br>0 . 6 0<br>0 . 25<br>− 5 · 10 − 2<br>0 . 2<br>0 . 4<br>0 . 15 − 0 . 1<br>0 . 2 0 . 1 − 0 . 15<br>5 · 10 − 2 − 0 . 2<br>0 0<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>Output NonTradable Sector Non Oil Revenues Public Debt<br>0 2<br>0 . 5<br>− 5 · 10 − 2 1 . 5<br>0<br>− 0 . 1 1<br>− 0 . 5<br>− 0 . 15 0 . 5<br>− 1<br>0<br>− 0 . 2<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>Sustainable investing Approach, α G = 0 . 05 Sustainable investing Approach, α G = 0 . 5<br>(%) (%) (%)<br>s.s. s.s. s.s.<br>from from from<br>Deviation Deviation Deviation<br>(%) (%) (%)<br>s.s. s.s. s.s.<br>from from from<br>Deviation Deviation Deviation<br>(%) (%) (%)<br>s.s. s.s. s.s.<br>from from from<br>Deviation Deviation Deviation<br><!-- End of picture text --> _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 expressed in percentage deviation from the steady-state values. The solid line shows the response of the fiscal policy C ( **Sustainable Investing Approach** ) under _α_<sup>_G_</sup> = 0 _._ 05 and Dashed lines show the response under _α_<sup>_G_</sup> = 0 _._ 5.

39
**Panel B**

<!-- Start of picture text --> Total Employment Total Wage Government Spending<br>0<br>0 . 15<br>1<br>− 0 . 1<br>0 . 1<br>0 . 5<br>− 0 . 2<br>5 · 10 − 2<br>0<br>− 0 . 3 0<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>Gov. Spending Tradable Sector Gov. Spending NonTradable Sector Non Oil Exports<br>0 0<br>2<br>− 0 . 2<br>1 . 5 − 0 . 2<br>− 0 . 4<br>1 − 0 . 4 − 0 . 6<br>0 . 5 − 0 . 6 − 0 . 8<br>0 − 1<br>− 0 . 8<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>Imports Exchange Rate Sovereign Wealth Fund<br>1 0<br>0 . 2<br>− 0 . 5<br>0 . 15<br>0 . 5<br>− 1<br>0 . 1<br>0 − 1 . 5 5 · 10 − 2<br>− 2 0<br>0 10 20 30 40 0 10 20 30 40 0 10 20 30 40<br>Quarters Quarters Quarters<br>Sustainable investing Approach, α G = 0 . 05 Sustainable investing Approach, α G = 0 . 5<br>(%) (%) (%)<br>s.s. s.s. s.s.<br>from from from<br>Deviation Deviation Deviation<br>(%) (%) (%)<br>s.s. s.s. s.s.<br>from from from<br>Deviation Deviation Deviation<br>(%) (%) (%)<br>s.s. s.s. s.s.<br>from from from<br>Deviation Deviation Deviation<br><!-- End of picture text --> _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 expressed in percentage deviation from the steady-state values. The solid line shows the response of the fiscal policy C ( **Sustainable Investing Approach** ) under _α_<sup>_G_</sup> = 0 _._ 05 and Dashed lines show the response under _α_<sup>_G_</sup> = 0 _._ 5.

40
public investment and output in tradable and non-tradable sectors declines less compared to the scenario where public is almost unproductive _α_<sup>_G_</sup> = 0 _._ 05. Panel _B_ of Figure 5 shows that when investment projects are almost unproductive ( _α_<sup>_G_</sup> = 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 _φ_<sup>_oil_</sup> 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 ( _σFBNO_ ) and real exchange rate ( _σs_ ).

Conceptually, we propose a criterion consisting to determine the value of _φ_<sup>_oil_</sup> that minimizes a social loss function. Our loss function closely resembles that used by Ag ́enor (2014); it is 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 fiscal balance and that of the real exchange rate. As stressed by Ag ́enor (2014), movements 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: where _W_<sup>_φoil_</sup> and _S_<sup>_φoil_</sup> are the variables that capture households’ welfare and macroeconomic/fiscal stability respectively, and _FB_<sup>_NO_</sup> is the non-oil fiscal balance. _σX_<sup>_φoil_</sup> denotes the volatility of variable _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 _φ_<sup>_oil_</sup> .

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 households’ welfare and macroeconomic stability. In our analysis, as in Ag ́enor (2014), we vary 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
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of _μ_ higher than 0 _._ 3 _−_ 0 _._ 39 (meaning a fair or low preference for stability), the loss functions have convex shapes in _φ_<sup>_oil_</sup> . Low values of _φ_<sup>_oil_</sup> lead to high volatility in the economy due to higher return on savings in the sovereign wealth which yield higher government consumption. But as _φ_<sup>_oil_</sup> 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 _L_<sup>1</sup>

<!-- Start of picture text --> 1 1<br>0.8 0.8<br>0.6 0.6<br>0.4 Baseline 0.4 Baseline<br>ε G = 0.95 α G = 0.4<br>0.2 0.2<br>ε G = 0.25 α G = 0.1<br>0 0<br>0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1<br>μ μ<br>1 1<br>0.8 0.8<br>0.6 0.6<br>Baseline<br>0.4 Baseline 0.4<br>δ G = 0.125 ρyo = 0.975<br>0.2 0.2<br>0 δ G = 0.05 0 ρyo = 0.925<br>0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1<br>μ μ<br>1 1<br>0.8 0.8<br>0.6 0.6 Baseline<br>0.4 Baseline 0.4 r * = 0.05<br>ρpo = 0.975 r * = 0.005<br>0.2 0.2<br>0 ρpo = 0.925 0<br>0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1<br>μ μ<br>oil oil<br>φ φ<br>oil oil<br>φ φ<br>oil oil<br>φ φ<br><!-- End of picture text --> 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 _φ_<sup>_oil_</sup> = 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, _φ_<sup>_oil_</sup> varies between 0.55 and 0.85, meaning that 55 45
# **Figure 9.** Optimal allocation rule under _L_<sup>2</sup>

<!-- Start of picture text --> 1<br>0.8<br>0.6<br>Baseline<br>0.4<br>ε G = 0.95<br>0.2<br>ε G = 0.25<br>0<br>0 0.2 0.4 0.6 0.8 1<br>μ<br>1<br>0.8<br>0.6<br>Baseline<br>0.4<br>δ G = 0.125<br>0.2<br>δ G = 0.05<br>0<br>0 0.2 0.4 0.6 0.8 1<br>μ<br>1<br>0.8<br>0.6 Baseline<br>0.4 ρ po = 0.975<br>0.2 ρ po = 0.925<br>0<br>0 0.2 0.4 0.6 0.8 1<br>μ<br>oil<br>φ<br>oil<br>φ<br>oil<br>φ<br><!-- End of picture text --> <!-- Start of picture text --> 1<br>0.8<br>0.6<br>Baseline<br>0.4<br>α G = 0.4<br>0.2<br>α G = 0.1<br>0<br>0 0.2 0.4 0.6 0.8 1<br>μ<br>1<br>0.8<br>0.6<br>Baseline<br>0.4 ρ yo = 0.975<br>0.2<br>ρyo = 0.925<br>0<br>0 0.2 0.4 0.6 0.8 1<br>μ<br>1<br>0.8<br>0.6 Baseline<br>0.4 r * = 0.05<br>0.2 r * = 0.005<br>0<br>0 0.2 0.4 0.6 0.8 1<br>μ<br>oil<br>φ<br>oil<br>φ<br>oil<br>φ<br><!-- End of picture text -->

**Figure 10.** Optimal allocation rule under _L_<sup>3</sup>

<!-- Start of picture text --> 1<br>0.8<br>0.6<br>Baseline<br>0.4<br>ε G = 0.95<br>0.2<br>ε G = 0.25<br>0<br>0 0.2 0.4 0.6 0.8 1<br>μ<br>1<br>0.8<br>0.6<br>Baseline<br>0.4<br>δ G = 0.125<br>0.2<br>δ G = 0.05<br>0<br>0 0.2 0.4 0.6 0.8 1<br>μ<br>1<br>0.8<br>0.6<br>Baseline<br>0.4<br>ρpo = 0.975<br>0.2<br>0 ρpo = 0.925<br>0 0.2 0.4 0.6 0.8 1<br>μ<br>oil<br>φ<br>oil<br>φ<br>oil<br>φ<br><!-- End of picture text --> <!-- Start of picture text --> 1<br>0.8<br>0.6<br>Baseline<br>0.4<br>α G = 0.4<br>0.2<br>α G = 0.1<br>0<br>0 0.2 0.4 0.6 0.8 1<br>μ<br>1<br>0.8<br>0.6<br>Baseline<br>0.4<br>ρyo = 0.975<br>0.2<br>0 ρyo = 0.925<br>0 0.2 0.4 0.6 0.8 1<br>μ<br>1<br>0.8<br>0.6 Baseline<br>r * = 0.05<br>0.4<br>r * = 0.005<br>0.2<br>0<br>0 0.2 0.4 0.6 0.8 1<br>μ<br>oil<br>φ<br>oil<br>φ<br>oil<br>φ<br><!-- End of picture text --> 46
**Figure 11.** Optimal allocation rule under _L_<sup>4</sup>

<!-- Start of picture text --> 1 1<br>0.8 0.8<br>0.6 0.6<br>0.4 Baseline 0.4 Baseline<br>ε G = 0.95 α G = 0.4<br>0.2 0.2<br>ε G = 0.25 α G = 0.1<br>0 0<br>0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1<br>μ μ<br>1 1<br>0.8 0.8<br>0.6 0.6<br>Baseline<br>0.4 Baseline 0.4<br>δ G = 0.125 ρyo = 0.975<br>0.2 0.2<br>0 δ G = 0.05 0 ρyo = 0.925<br>0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1<br>μ μ<br>1 1<br>0.8 0.8<br>0.6 Baseline 0.6 Baseline<br>0.4 ρpo = 0.975 0.4 r * = 0.05<br>0.2 ρ po = 0.925 0.2 r * = 0.005<br>0 0<br>0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1<br>μ μ<br>oil oil<br>φ φ<br>oil oil<br>φ φ<br>oil oil<br>φ φ<br><!-- End of picture text --> 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_<sup>_∗_</sup> ). 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, _ε_<sup>_G_</sup> , the output elasticity of public capital, _α_<sup>_G_</sup> , as well as the depreciation rate of public capital, _δ_<sup>_G_</sup> , 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 allsaving 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 parameterized 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 _φ_<sup>_oil_</sup> 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 infrastructures is slightly higher than those estimated in Ag ́enor (2014), which ranges from 30 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**

- Ag ́enor, P. R. (2014). Optimal fiscal management of commodity price shocks. _Centre for Growth 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.

- Ang ́enor, P. R. and Aizenman, J. (1999). Macroeconomic adjustment with segmented labor 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 countries. _in J. Davis, J. Ossowski, and A. Fedelino, eds., Fiscal Policy Formulation and Implementation in Oil-Producing Countries, (Washington, D.C.: International Monetary Fund_ .

- Baunsgaard, T., Villafuerte, M., Poplawski-Ribeiro, M., and Richmond, C. (2012). Fiscal frameworks 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 allocate 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 investment, 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 international shocks transmission. _Mimeo, Universit ́e Laval_ .

- 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 subsaharan africa’s natural resource wealth. _International Monetary Fund, Washington DC_ .

- Maliszewski, W. (2009). Fiscal policy rules for oil-producing countries: A welfare-based assessment. _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 Monetary 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
- Schmitt-Groh ́e, S. and Uribe, M. (2003). Closing small open economy models. _Journal of 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.

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[ J 0]

[ |

~~(-)~~ ~~(—)~~ ( ) [¢ )
First, begin with, (6.6) and (6.7), which imply that _R_<sup>_N_</sup> = 1 _/β−_ 1+ _δ_<sup>_N_</sup> and _R_<sup>_T_</sup> = 1 _/β−_ 1+ _δ_<sup>_T_</sup> . Now go to (6.9), the first order condition for labor supply in the production, we have Then, and by analogy, the same expression holds in the tradable goods sector Turning to the steady state of _W_<sup>_N_</sup> and _W_<sup>_T_</sup> , equations (6.10) and (6.15) yield and Then, using (6.26) and (6.27), the steady state values of _W_<sup>_N_</sup> and _W_<sup>_T_</sup> are and Market clearing condition (6.24) leads to _Y_<sup>_Tx_</sup> = _Y_<sup>_M_</sup> 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 and These expressions and equilibrium condition (6.16) imply that
Given the steady-state values of _Lt_ , _Kt_<sup>_G_andthecapital-laborratio,wecanfinddirectlythe</sup> steady-state values of capital, investment and output.

and by analogy, the same expression holds in the tradable goods sector Then, and and therefore The steady state value of government spending is given by By setting _Y_<sup>_O_</sup> = _θ_<sup>_o_</sup> _Y_ , the equilibrium value of the sovereign wealth fund is Now, using (6.20), the steady state value of government debt is given by: 57