metadata: authors: 0: author: Loayza,Norman V.
1: author: Galego Mendes,Arthur
2: author: Mendez Ramos,Fabian
3: author: Pennings,Steven Michael
count: World
docna: 0: docna: Assessing the Effects of Natural Resources
            on Long-Term Growth : An Extension of the World Bank Long
            Term Growth Model
docty: Policy Research Working Paper
subtopic: Public Finance Decentralization and
            Poverty Reduction,Public Sector Economics,Economic Adjustment and Lending,Macro-Fiscal Policy,Macroeconomics and Economic Growth,Economic Policy, Institutions and Governance,Fiscal & Monetary Policy,Energy Demand,Energy and Mining,Energy and Environment,Coastal and Marine Resources,Energy and Natural Resources
teratopic: Public Sector Development,Water Resources,Energy,Macroeconomics and Economic Growth
abstracts: cdata!: This paper extends the World Bank's
            Long-Term Growth Model (LTGM) with the addition of a natural
            resource sector to analyze how long-run growth evolves in
            resource-rich countries and the growth impacts of price
            shocks and resource discoveries. In the LTGM-Natural
            Resource Extension (LTGM-NR), commodity price shocks affect
            long-term economic growth through physical investment rates.
            As a large share of resource income typically accrues to the
            government, the size of the boost to investment in a price
            boom depends on the government’s fiscal rule. Fiscal rules
            that prioritize public investment, like a Hartwick Rule,
            generally lead to the largest increases in long-term growth.
            However, structural surplus rules, which save commodity
            revenues, can also boost growth if they free up savings for
            private investment. The response of growth to discoveries of
            natural resources is similar to the response to price
            shocks, although discoveries also produce a direct effect on
            real GDP, in addition to an indirect effect through
            investment. The LTGM¬-NR also captures the effect of other
            (non-resource) growth fundamentals in resource-rich
            economies, and it is better suited to general growth
            analysis in these countries than the standard LTGM. However,
            the LTGM-NR is a supply-side model, and so does not capture
            the short-run effects of price and discovery shocks that
            operate through aggregate demand.
repnme: repnme: Assessing the Effects of Natural Resources
            on Long-Term Growth : An Extension of the World Bank Long
            Term Growth Model
display_title: Assessing the Effects of Natural
            Resources on Long-Term Growth : An Extension of the World
            Bank Long Term Growth Model
listing_relative_url: /research/2022/03/33757729/assessing-effects-natural-resources-long-term-growth-extension-world-bank-long-term-growth-model
topicv3: Natural Resources m1326446 1979,Energy and Extractives m1326595 507,Fiscal Stimulus and Fiscal Rules m1326652 1073,Environment, Natural Resources and Blue
            Economy m1327391 566,Fiscal Rules m1584062 4486
publishtoextweb_dt: 2022-03-14T00:00:00Z
dois: 10.1596/1813-9450-9965
historic_topic: Public Sector Development,Water Resources,Energy,Macroeconomics and Economic Growth
origu: Off of Sr VP Dev Econ/Chief Econ (DECVP)
no_of_pages: 61
author_keys: 0: author_key: 97109
1: author_key: 1464295
2: author_key: 1247803
3: author_key: 1324256
model_extractions: Policy Research Working Paper 9965 Assessing the Effects of Natural Resources on Long-Term Growth An Extension of the World Bank Long Term Growth Model _Norman Loayza Arthur Mendes Fabian Mendez Ramos Steven Pennings_ Development Research Group & Global Indicators Group March 2022
Policy Research Working Paper 9965

# **Abstract**

This paper extends the World Bank’s Long-Term Growth Model (LTGM) with the addition of a natural resource sector to analyze how long-run growth evolves in resourcerich countries and the growth impacts of price shocks and resource discoveries. In the LTGM-Natural Resource Extension (LTGM-NR), commodity price shocks affect long-term economic growth through physical investment rates. As a large share of resource income typically accrues to the government, the size of the boost to investment in a price boom depends on the government’s fiscal rule. Fiscal rules that prioritize public investment, like a Hartwick Rule, generally lead to the largest increases in long-term growth. However, structural surplus rules, which save commodity revenues, can also boost growth if they free up savings for private investment. The response of growth to discoveries of natural resources is similar to the response to price shocks, although discoveries also produce a direct effect on real GDP, in addition to an indirect effect through investment. The LTGM-NR also captures the effect of other (non-resource) growth fundamentals in resource-rich economies, and it is better suited to general growth analysis in these countries than the standard LTGM. However, the LTGM-NR is a supply-side model, and so does not capture the short-run effects of price and discovery shocks that operate through aggregate demand.

This paper is a product of the Development Research Group and the Global Indicators Group, Development Economics. 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://www.worldbank.org/prwp. The authors may be contacted at nloayza@worldbank.org, agalegomendes@worldbank.org, fabianmendezr@gmail.com, and spennings@worldbank.org.

_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
# **Assessing the Effects of Natural Resources on Long-Term Growth: An Extension of the World Bank Long Term Growth Model**

Norman Loayza, Arthur Mendes, Fabian Mendez Ramos, and Steven Pennings<sup>1</sup> JEL: O13, O41, 023, Q33, Q43. Keywords: long-term growth, neoclassical model, natural resources, fiscal rules.

> 1 The views expressed here are the authors’ and do not necessarily reflect those of the World Bank, its executive directors, or the countries they represent.

> ∗ World Bank, 1818 H St NW, Washington DC 20433, USA. Loayza: nloayza@worldbank.org; Mendes: agalegomendes@worldbank.org; Mendez Ramos: fabianmendezr@gmail.com; Pennings: spennings@worldbank.org. The authors appreciate helpful comments from Sharmila Devadas, Lay Lian Chuah, Jorge Luis Guzman, Young Eun Kim, and seminar participants at the World Bank’s Development Research Group hub in Kuala Lumpur, Bank of Mexico, and Economic Commission for Latin America and the Caribbean.
# **I. Introduction**

The celebrated Solow-Swan neoclassical growth model analyzes how long-run economic growth depends on growth fundamentals like productivity, savings, investment, human, and physical capital and demographic trends (Solow 1956; Swan 1956; Mankiw et al. 1992; Hall and Jones 1999). The World Bank’s Long Term Growth Model (LTGM; Loayza and Pennings 2018) is in this tradition, though it is applied to simulations of future growth in developing countries. However, standard neoclassical models are inappropriate for economies where the natural resource sector is sufficiently large to have a first-order effect on growth, including many developing countries. Traditional neoclassical models are also silent on how commodity price shocks and resource discoveries affect long-term growth for commodity exporters, and the economic consequences of government policies that manage resource wealth.

The Long Term Growth Model–Natural Resource Extension (LTGM-NR) seeks to fill this gap by augmenting an otherwise-standard neoclassical growth model with a natural resource sector and government fiscal policy. The model is designed to be accessible and transparent—a spreadsheet-based toolkit (without macros) is freely downloadable at <u>https://www.worldbank.org/LTGM</u> with preloaded data for 56 resource-rich countries (see Appendix Table 1 for a list of available countries). The LTGM-NR first allows for the evaluation of how commodity price shocks and discoveries of natural resources affect a country’s medium to long-term economic growth and how it depends on different fiscal frameworks. Second, the model analyzes how standard growth fundamentals affect growth in resource-rich economies, like human capital, demographics, and productivity. The LTGM-NR allows for a more accurate analysis of the effect of these fundaments than one-sector models as those models do not account for heterogeneity across sectors or the consequences of depleting reserves of natural resources. However, as the LTGM-NR is a supply-side model, it does not capture the short-run effects of price and discovery shocks that operate through aggregate demand.

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The first step in analyzing country-specific commodity price shocks or discoveries is a resource-accounting exercise that evaluates the size of resource exports and reserves in each country, and hence the scale of the direct impact of a given change in commodity prices or a resource discovery. We make this easier by providing preloaded data on the resource sector in 56 countries. Our simulations incorporate some often-misunderstood accounting identities, such as the fact that commodity price fluctuations only directly affect gross domestic income (GDI), whereas real gross domestic product (GDP) changes only indirectly (as real GDP fixes the price of exports, see Kehoe and Ruhl 2008).

The second step is to trace out how higher GDI and government resource revenues affect investment rates and long-term growth. As in a standard neoclassical model, a higher income boosts private savings (assumed to be a fixed share of GDI) and, consequentially, private investment. But more important—since a large share of the resource income typically accrues to the government—is how the government’s fiscal policy affects investment.<sup>2</sup> In short, fiscal rules that generate the largest increases in investment will generate the fastest growth in the medium and long terms.

The LTGM-NR has two submodels: the _LTGM-NR-Default_ , in which public investment responds directly to fiscal policy via a simple fiscal rule, and the _LTGMNR-External-Balance_ that considers more sophisticated fiscal rules and the relationship between public savings and the international capital flows.

The fiscal rules in both submodels are classified by whether the government saves or spends any extra resource revenues; and if it spends them, whether that spending falls on public investment or government consumption. For a temporary commodity price shock, a _Balanced Budget Rule (BBR)_ is when the government spends the extra revenues and a _Structural Surplus Rule (SSR)_ when they are mostly saved in financial assets. We usually assume that the spending allocation across investment/government consumption is kept constant, but if all the extra spending is on public investment, we call it a _Hartwick Rule (HR)._ This yields four rules with

> 2 Cross-country evidence suggests that governments retain on average 65-85 percent of rents in the hydrocarbons sector and 40-60 percent of rents in the mining sector (IMF 2012).

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different combinations of spending/savings and spending allocations: BBR, BBRHR, SSR, and SSR-HR (see Table 1).<sup>3</sup>

**<u>Table 1: Taxonomy of fiscal rules for Government resource revenues</u>**

|||**Spending**<br>|**allocation**<br>|
|---|---|---|---|
|||**Mostly Govt. consumption**<br>(Historical budget shares)|**Public investment**<br>(Hartwick rule)|
|**ng of**<br>**ding**|**Spent on impact**<br>(Balanced budget rule)|BBR|BBR-HR<br>(“HR” in Default submodel)|
|**imi**<br>**pen**|**Save for the future**||SSR-HR|
|**T**<br>**s**|(Structural surplus rule)|SSR|(Not in Default submodel)|

BBR=Balanced Budget Rule; SSR=Structural Surplus Rule; HR=Hartwick Rule The LTGM-NR-External-Balance also analyzes how resource revenues and different fiscal rules interact with international capital flows. This mostly affects the SSR, which often leads to large movements in international borrowing/lending. Most important is the effect on the current account balance and private investment. If the current account and private savings are relatively fixed, the extra public savings through an SSR can crowd in private investment dollar-for-dollar, leading the SSR to have a similar path for investment and growth as a BBR-Hartwick rule. In contrast, without crowding-in of investment (full adjustment of the current account), the SSR in the External-Balance model performs similarly to that of the simple model (which abstracts from international flows). Of course, real-world countries are somewhere in between these two extremes, and so the strength of crowding in is chosen via a parameter that is calibrated to match the data. In addition, the reduced international borrowing generated by a fiscal surplus under an SSR can reduce the government’s interest bill–through reduced borrow and lower interest rates–which can free up funds for public investment in the long-run under the SSRs.

**Angola Case Study.** To illustrate how the LTGM-NR works, we discuss three simulations with the model calibrated to Angola. First, we simulate the baseline

> 3 The difference between the SSR and SSR-HR depends on the timing of the analysis. In the short term, revenues are mostly saved, and, consequentially, both rules yield a similar allocation of spending. However, they diverge substantially in the medium and long terms, as fiscal surpluses under the SSRs can improve the government net asset position, freeing up funds for extra spending. In this case, the SSR-HR would lead a higher path of public investment than the SSR.

4
“business-as-usual” growth path for Angola over the next three decades. We find that, in the absence of major economic shocks or reforms, potential GDP per capita growth declines slightly in the medium term but is expected to pick up in the longer term. A growth decomposition shows that these “U-shaped” dynamics is driven by the interaction of improving demographic trends, depleting oil reserves, and a transition of the economy away from oil. Finally, we show that an unadjusted (“naïve”) calibration of the standard LTGM would generate an overly optimistic growth path for Angola. This is because a one-sector model cannot account for the depletion of oil reserves that is a drag on growth and the fact that the oil sector is much more capital intensive than the non-oil sector.

Second, we evaluate the effects of a hypothetical oil-price boom-and-bust cycle in Angola under each fiscal rule. At the end of the oil price simulation (when oil prices are back at their original level), GDP per capita is highest under the BBRHR at 20%-25% above the baseline, as all of the higher government oil revenues are invested during the boom years. However, under the other fiscal rules, GDP is only 5%-12% above baseline because of a much smaller increase in investment. The SSR-HR is the only rule that supports faster growth for several years after the end of the oil price cycle. This is because the interest from the extra savings during the oil-price cycle is recycled into the budget, releasing resources for an almost permanent increase in public investment. Third, we find that discoveries have a large and persistent impact on Angola’s growth rate, especially under HRs. As before, the LTGM-NR only simulates the supply-side effects of these price shocks and discoveries, not their short effects through aggregate demand.

**Related literature** While there is a rich literature on managing the short-term cyclical effects of commodity booms (for example, Kumhof and Laxton 2013, Mendes and Pennings 2020, Pieschacón 2012) and whether natural resources are a curse or a blessing for development (see Van der Ploeg 2011 for a survey), the mechanics of medium-to-long-term growth in individual resource-rich economies are much less frequently studied.<sup>4</sup> The closest work is the modeling sections of

> 4 For empirical evidence on the resource curse in developing countries, see Terry Lynn (1999) and Wood (1999). For individual country experience with the resource curse (Ghana and Angola), see

5
Hansen and Gross (2018) and Arezki et al. (2018), who evaluate the effect of exploration and discoveries on medium-term macroeconomic aggregates. While these models share some similarities with ours (in particular, the setup of the resource sector), their purposes are very different. Those papers seek to explain estimated empirical relationships, whereas we propose a simple and accessible tool for country-specific growth simulations and policy analysis. Our model is simpler but is calibrated to 56 countries individually, rather than to one representative small open economy.<sup>5</sup> The remainder of the paper is organized as follows. Section II describes the theoretical underpinnings of the LTGM-NR, and Section III discusses a general calibration. Section IV presents the applications to Angola, and Section V concludes.

# **II. Model Description**

The point of departure of the LTGM-NR from a standard neoclassical model (like the standard LTGM), is the disaggregation of the economy into non-resource sector (Sector 0) and resource sector (Sector ). **The non-resource sector.** The structure of the non-resource sector is identical RR

**The non-resource sector.** The structure of the non-resource sector is identical to the standard LTGM. A representative firm employs physical capital and effective labor with a constant returns to scale Cobb-Douglas production function to generate 0 non-resource output, , 0 0 0 tt (h ) ) (1) YY where 0 is the total factor productivity (TFP) in sector 0, tt tt tt tt ββ tt−1 1−ββ 0 is the physical YY = AA LL (KK ,    0 < ββ< 1 capital in sector 0 at the end of period tt , and is the labor share in the non-tt−1 AA KK resource sector. Effective labor, h , is decomposed into h , human capital per tt−1 ββ worker, and , the labor force (number of workers). The labor force is defined as tt tt tt LL . Where tt is total population, is the working-age to population LL tt tt tt tt tt tt LL = ρρ ωω NN NN ωω

> Cust and Mihalyi (2017) for Ghana and Richmond et al. (2013) for Angola. For countries that avoided the resource curve (Chile and Botswana), see Medina and Soto (2007) and AfDB (2016). 5 Importantly, our model lacks forward-looking decision-making by agents, as this is difficult to incorporate in a spreadsheet-based model.

6
ratio, and is the labor force participation rate (labor force to working-age population ratio). The variables tt 0, h , and are exogenous and evolve at ρρ 0 h the following annual growth rates: tt tt tt tt tt , respectively. Throughout AA , NN , ωω ρρ AA NN ωω ρρ the model, exogenous variables are indicated with a bar index notation (as in tt tt tt tt tt ). gg̅ , gg̅ , gg̅ , gg̅ , gg̅ **The natural resource sector.** The setup of the natural resource sector builds gg̅

**The natural resource sector.** The setup of the natural resource sector builds on Hansen and Gross (2018) and Arezki et al. (2017) in being a Cobb-Douglas function of proven reserves (R) and physical capital (K), with decreasing returns in both R and K (equation (2)).<sup>6</sup> This production function has the desired property that the first reserves are relatively easy to extract – for example, being close to the surface—but later reserves require more and more capital (or technology) to generate the same output as firms are forced to drill further underground or in less accessible locations.<sup>7</sup>

accessible locations.<sup>7</sup> As countries produce multiple commodities, the natural resource sector, , is further disaggregated into non-renewable resource industries (e.g., RR oil, natural gas, copper, gold, and others). As shown in equation (2), the output of NN ii∈{1, ... , NN} resource industry , , is produced using reserves and physical capital ii ii ii in that industry, tt tt−1 tt−1 ii QQ RR KK � � (2) 1−γγii γγii ii ii ii ii where QQtt = AA is the TFP in industry tt�KKtt−1 �RRtt−1 —which grows at exogenous rate , 0 < γγii < 1 and ii∈{1, ... , NN} — and is ii AAii the share of resource rents in industry tt (then, is the capital income share). tt ii AA ii gg̅ γγ Capital and reserves are state variables determined in the previous year ii . ii 1 −γγ The dynamics of reserves in each industry obey the following law of motion, tt−1 (3) ii ii ii ii tt tt−1 tt tt RR = RR −QQ + DD� , ii∈{1, ... , N}

> 6 Hansen and Gross (2018) and Arezki et al. (2017) also include labor in the production function, but its share is very small (0.13); so for simplicity we exclude it.

> 7 Alternatively, can be interpreted as a quality-adjusted index of reserves, that takes into consideration geological factors such as ore grade (for minerals) or the composition of hydrocarbons ii tt (for petroleum and natural gas). As the highest quality mines and oil fields tend to be explored first, RR further extraction and depletion reduces the quality of the remaining reserves, scaling down the industry marginal product of capital (see Cochilco 2017). However, our default calibration of the model is not adjusted for the quality of reserves.

7
where reserves in industry at the end of period , , increases with an exogenous ii stream of discoveries, , and is endogenously depleted by the production of good tt ii tt RR ii , . tt ii DD<sup>�</sup> ttEquations (4) and (5) describe the evolution of physical capital in activity ii QQ (non-resource sector plus resource industries) and at the aggregate jj∈ level, respectively, {0, 1, ... , NN} (4) jj jj jj tt tt−1 tt KK = (1 −δδ)KK + II , jj∈{0, 1, ... , NN} (5) = �NN jj tt tt where is the annual depreciation rate (common across all activities), KK jj=0KK is the jj investment in activity , and is the aggregate capital at the end of period tt . δδ II **National income/output and prices.** tt The model economy represents a small, jj KK tt

**National income/output and prices.** The model economy represents a small, price taking, commodity exporter. The non-resource good is freely traded with a constant price of $1 (the numeraire), and is used for private and government consumption, investment, and imports. All the proceeds from the resource sector are exported at exogenous international prices in constant dollars. ii **Real GDP and real GDI.** There are two measures of the “size” of an open tt pp̅

**Real GDP and real GDI.** economy, Real Gross Domestic Product (RGDP) and Real Gross Domestic Income (RGDI) (also known in the US as “Command-basis GDP”).<sup>8</sup> While these two are identical in a closed economy, they are often very different in countries with volatile terms of trade like commodity exporters. The key difference between the measures is how exports are deflated (Kehoe and Ruhl 2008).<sup>9</sup>

> For RGDP, exports are deflated by the export price index, which for a country exporting one commodity is simply 1 01 (the current commodity price relative to its price in the base year, ). _This means that changes in commodity prices have_ tt pp /pp tt= 0

> 8 The term “Real Gross Domestic Income” from the international System of National Accounts (SNA), see https://stats.oecd.org/glossary/detail.asp?ID=2244. The nomenclature can be confusing as the US Bureau of Economic Analysis (BEA) departs from the SNA. The BEA calls GDP(I) (gross domestic product calculated using the income method) GDI, see <u>https://www.bea.gov/resources/learning-center/what-to-know-income-saving, which is why it need</u> to use the term “Command-basis GDI”: see <u>https://www.bea.gov/help/glossary/command-basisgross-domestic-product</u>

> 9 RGDP and RGDI are equivalent in a closed economy.

8
>)

-y
In the LTGM-NR, private investment is an exogenous share of GDI (usually a fixed share), and public investment depends on the government’s fiscal rule. The assumption of a fixed share of private investment is a generalization of the SolowSwan tradition.<sup>12</sup> This generalization is an important departure from the literature (Hansen and Gross 2018 and Arezki et al. 2017), where agents are forward looking and allocate investment intertemporally based on its costs and benefits. However, the assumption of a fixed share of private investment keeps the LTGM-NR simple and its mechanisms straightforward. The public investment assumption stems from our application to resource-rich economies, where public investment is often funded by commodity revenues. The determinants of investment vary across the LTGM-NR Default and External-Balance submodels, which are discussed further below.

We also need to determine the allocation of aggregate investment across the non-resource and different resource industries. Again, to keep the model simple, this is done via a rule of thumb where investment is allocated across the different activities proportionally to the marginal efficiency of capital and (i ) the sector’s relative size (in terms of capital shares), as below: (ii)

> 12 More specifically, in the closed economy Solow-Swan model (without a government), savings are fixed as a share of GDP, which means that investment is also a fixed share of GDP.

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Dixit-Stiglitz (DS) aggregator of the MRPK across all activities.<sup>13</sup> The aggregator weights each activity by their capital shares, . jj While the rule of thumb is not derived from an optimizing framework, it is tt−1 tt−1 KK /KK constructed to allocate investment to more efficient and larger industries (as would be the case in an optimizing framework) and has two other appealing properties. First, across same-size industries, if activity is 1% more efficient than activity , it receives more investment (i.e., if → ii jj ii jj � μμ% � )). Second, investment is allocated so that KKtt−1 = KKtt−1 ii jj ii jj capital shares remain constant across sectors with the same marginal efficiency of tt tt tt tt ln (ii ii ) = μμ ln ( MMRRPPKK MMRRPPKK capital (i.e., if � � ). Moreover, this rule of ii jj ii jj ii jj thumb is simple enough to be solved in a spreadsheet. We usually calibrate tt tt tt tt tt−1 tt−1 . MMRRPPKK = MMRRPPKK →KK KK = KK KK μμ= 1

# _A. The LTGM-NR Default_

In this subsection, we describe the LTGM-NR-Default submodel which is a simplified version of the LTGM-NR-External-Balance (presented in subsection B) and designed to be more user-friendly. In the LTGM-NR-Default, investment is determined directly—like Model 1 in the standard LTGM—rather than indirectly via international and domestic savings. The simplifications fall into two categories, which are related to the determinants of private and public investment, respectively.

First, private investment is assumed to be an exogenous fraction of GDI, which is our analogue of the standard assumption in a Solow-Swan model. Second, public investment as a share of GDI responds to fluctuations in resource revenues according to the following rule: (13) gg gg RR RR where are cyclical government resource revenues (as a share GDI)—i.e., iitt = ıı̅tt + θθ(zztt −zz̆tt ) + εεtt RR RR the deviation of actual resource revenues tt tt from their “structural” or long-run zz −zz̆ RR values (discussed below). The parameter tt is the marginal propensity to invest zz RR tt zz̆ θθ

> 13 Note that equation (10) does not apply for the non-resource sector (0) but equations (11) and (12) do. Investment in the non-resource sector is determined residually as 0 −∑ . However, the normalization of equation (10) by D ensures that it also holds for the non-resource sector.  NN ii tt tt ii=1 tt II = II II

> MMRRPPKKtt 11
The purpose of defining a structural revenue is to smooth out transitory fluctuations in actual revenues. As discussed in section III, structural prices are usually set at their (perceived) long-term levels. When production is not the focus of the analysis, to keep the model simple, we set structural production equal to actual production or a moving average. However, the LTGM-NR toolkit provides other specifications, such as using baseline as reference production.<sup>16</sup> **Fiscal rules.** The marginal propensity to invest, , captures the pro-cyclicality of fiscal policy. The user can choose any value of , although more common values θθ range between 0 and 1. This range nests three popular fiscal rules: θθ • captures a SSR (Structural Surplus Rule), as cyclical resource revenues are saved (when prices are high) and do not affect public investment.<sup>17</sup> θθ= 0

> 14 The LTGM-NR spreadsheet also allows the parameter to vary over time. 15 Capturing, for example, royalties from the concessions of exploration of natural resources, taxreceipts from private extractive enterprises and profits from state-owned companies. θθ 16 An equilibrium is defined as a collection of 15 endogenous trajectories

> 0 , R 0 D � where with each endogenous variable specified as a function of the exogenous paths ii ii jj ii jj gg RR RR tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt �YY , QQ , RRh , KK , KK DDPP , YY , ii , ii , ii , MMRRPPKK} and initial conditions , MMRRPPKK �  �ii , zz , zz̆ jj∈{0,1, ... , NN} ttAAjj 0 tt ttNN0 ttωω0 ttρρ0 ttii0 ttii 0 pptt 0ttgg 0ttii 0ttii� that satisfy equations (1)—(15) for all _t_ . 17{gg̅ In the LTGM-NR-default the SSR and SSR-HR are very similar (given that spending is mostly , gg̅ , gg̅ , gg̅jj , gg̅ , DD�jj , pp̅ii , ıı̅ii , ıı̅ , pp� , QQ� constant). Hence, we focus on the SSR in the applications of the Default submodel. �RRDDPP , RRDDPP , KK , KK , RR , pp , NN , ωω , ρρ

12
- captures a BBR (Balanced Budget Rule), where is the historical

- <sup>tttt</sup>

- fraction of the expenditure that is spent on public investment. In this case, when θθ= θθ<sup>hi</sup> θθ<sup>hi</sup> the cyclical resource revenue increases by one dollar, all windfall is spent, but only the fraction in extra spending is channeled to investment (the<sup>tt</sup>

- remaining falling on government consumption). ). . θθ<sup>tthi</sup>

- • When , all cyclical resource revenue is spent, but it falls only on public 1 −θθ<sup>hi</sup>

- remaining falling on government consumption). ). .

- • When , all cyclical resource revenue is spent, but it falls only on public<sup>hi</sup>

- investment, as prescribed under a BBR-HR (Balanced Budget-Hartwick Rule). θθ= 1

# _B. The LTGM-NR External Balance_

The LTGM-NR External Balance submodel keeps the structure of the Default submodel but accounts for the public sector in more detail and allows for a relationship between the public and private investment via the availability of savings.

**The external sector.** A key equation in this submodel is the constraint which imposes that aggregate investment must be equal to domestic savings less the current account balance (CAB), −c (16) pp gg where and denote private and public savings, respectively, and iitt = ss̅tt + sstt bbtt c is the pp gg current account balance, all expressed as a share of GDI. Public savings are tt tt tt ss̅ ss bb endogenously determined by the fiscal rule in place (details below), and private savings are assumed to be an exogenous share of GDI. The CAB is financed by (exogenous) foreign direct investment (FDI) or newly created external debt (we abstract from other forms of portfolio investment, as they are less common in developing countries):

13
growth rate of GDI in period . Equation (18) decomposes external debt into private and public, and , respectively. tt pp gg The relationship between the CAB and fiscal policy is an active debate in the tt tt dd dd literature and is likely to change substantially from country to country.<sup>18</sup> Much of this literature is about the response of private savings to various shocks (e.g., Loayza et al. 2000), though in our model we assume private savings are simply a fixed share of GDI. In countries with open capital accounts, an increase in public deficits can be funded by foreign savings—a larger current account deficit, resulting in what is known as the “twin deficits.”<sup>19</sup> In contrast, if the current account is relatively fixed as a share of GDI—for example, due to thin capital markets or capital controls—then an increase in public savings could free-up financial resources for private investment. Ultimately, we let users choose the degree of crowding in of private investment via a parameter : −<sup>dd</sup> −<sup>dd</sup> λλ pp gg � � (19) �����������pp tt−1 �����������gg tt−1 pp P tt tt tt �dd YY = −λλ�dd YY + dd̅ 1 + gg 1 + gg where is the exogenous component of private external debt. Equation (19) iiP ttPP−iiPPssttssPP ddPPddiissiitt FFi ssPPFF ddPPddiissiitt pp implies that a one-dollar fall in public net borrowing crowds in tt dollars of private dd̅ investment (funded by private net borrowing).<sup>20</sup> λλ **The public sector.** The public sector in the External Balance submodel is also more realistic than that in the Default model. The government collects shares and 0 of the resource and non-resource sectors, respectively (equations (20) and RR ττ (21)). Total revenue is the sum of resource and non-resource revenue (equation ττ (22)). Revenues are used to finance a stream of public expenditure, which is decomposed into government consumption ( )—which does not affect growth— gg tt cc

> 18 Some empirical studies find that higher budget deficits lead to higher current account deficits, others show evidence of the opposite, or show no significant impact. For a literature review on this subject, see Bussiere et al. (2005) or Cavallo (2005).

> 19 Abbas et al. (2011) find that a one percentage point of GDP improvement in the fiscal balance is associated with 1/3 percentage point improvement in the current account, though it is unclear how much of this adjustment is through private savings.

> 20 Note that ����� − <u>tpp 1</u> �, where and ����� are exogenous. In this case, a fall in pp pp pp dd t− pp the fiscal deficit must be matched by a one-to-one increase in private investment on the left side.  iitt = ss̅tt + ffddııtt + �ddtt 1+ggYY ss̅tt ffddııtt

14
The primary balance is the difference between revenues and non-interest expenditure and represents the government’s net borrowing or net lending, excluding interest payments on the outstanding debt (equation (25)). Public savings is defined as revenues less government consumption and represents the amount of resources generated by the government to finance public investment or to pay off the external public debt (equation (26)). Equation (27) describes the evolution of public external debt (as a share of GDI). Each period, the debt grows at the gross rate ), due to payments on the principal and interest on the YY outstanding bonds, but decreases one-to-one with the primary balance, tt−1 tt (1 + ff )/(1 + gg 15
where is the debt-elasticity of the interest-rate spread, and is the long-run external debt to GDI ratio.<sup>21</sup> If , the government can issue debt at the ψψ dd world interest rate, . If tt−1, an increase in debt of 1 percent of GDI leads dd ≤dd to percentage points increase in the country spread. WW tt−1 ff dd > dd **Fiscal rules.** As in the Default submodel, a fiscal rule determines both the ψψ

**Fiscal rules.** As in the Default submodel, a fiscal rule determines both the timing and composition of government expenditure. The LTGM-NR External Balance allows for four types of rules: BBR, BBR-HR, SSR, and SSR-HR (see Table 1), up from three types of rules in the Default submodel (where there is no SSR-HR). The External Balance submodel defines the timing aspect of fiscal rules in terms of how the primary balance evolves. The BBR fixes the headline primary balance as a share of GDI at a target (usually fixed but could vary over time exogenously) (see top line of equation (29)). tt bb<sup>�</sup> This policy leads to pro-cyclical spending: a one-dollar increase (fall) in resource revenues leads to (almost) exactly one dollar increase (fall) in expenditure.

The SSR mitigates pro-cyclicality by fixing the _structural_ primary balance at target the primary balance tends to increase (decrease) in periods of high (low) tt<sup>_._The structural primary balance adjusts for the commodity cycle so that</sup> bb<sup>��</sup> commodity prices. More specifically, the structural primary balance is computed based on structural resource revenues, −e , where the structural revenue, , is defined as in the default model (equation (15)). The following tt tt tt bb<sup>�</sup> = zz̆ pp equation summarizes the fiscal target under BBRs and SSRs: tt zz̆ [Fiscal Rule] (29) �<sup>B</sup> S<sup>RR: bbtt= bb�tt+ eett</sup> where � adjusts the target by a fraction tt tt<sup>+ ee</sup> tt of the deviation of the gg RR: bb<sup>�</sup> = bb<sup>��</sup> public debt-to-GDI ratio from its long-run level, tt tt−1 gg , thus ensuring debt ee = φφ�dd −dd φφ sustainability. The parameter ensures the stability of the public debt and controls gg dd its volatility.<sup>22</sup> φφ

> 21 For simplicity, the parameter is usually set to zero or 0 but the user can choose other values.

> 22 Condition )⁄ ) ensures that the debt-to-GDI ratio fluctuates within bounds around the long-run level. In the limit dd YY the fiscal rule collapses to a debt-rule: dd . WW φφ> (1 + ff (1 + gg gg tt gg

> φφ→∞ 16 dd = dd
The BBR and SSR can either keep the composition of spending constant or try to increase investment as in Table 1. As in the Default submodel, the highinvestment rule is called a Hartwick Rule (HR), though its application here is more complicated and closer to how it is applied in practice. The principle behind HRs is to prevent extra revenues earned from exhaustible natural resource from being used to finance government consumption. Accordingly, under an HR, all cyclical resource revenue must be invested either in physical or financial assets.<sup>23</sup> The rule is implemented by adding the following inequality to the model: ⁄ 0 ����� (usually, ����� = 1) gg this inequality states that the Sustainable Budget Index (SBI, the ratio of tt tt tt tt tt SSBBII ≡cc zz ≤SSBBII SSBBII government consumption to non-resource revenues) must be equal or lower than an exogenously determined threshold ����� (typically set to one for all ). An >1 means that government consumption is being financed at least partially by resource tt tt SSBBII tt SSBBII revenues. An <1 means that resource revenues are being invested either in physical or financial assets, while consumption is being financed only from non-tt SSBBII resource revenues. Capping the to one ensures that assets are being preserved (for a detailed discussion, see Lange and Wright 2004).tt<sup>24</sup> SSBBII The standard SBI rule (with ����� = 1) works well for governments with moderate dependence on resource revenues but might be too restrictive for tt SSBBII countries where resource revenues represent a large part of the budget. For example, Angola’s fiscal oil revenues account for more than 80 percent of total revenues. In this case, it is inevitable that oil revenues are partially consumed to run basic functions of the government. For that reason, the user of the LTGM-NR can choose any positive value for ����� . A possibility is to set ����� to 0 ⁄ 00 implying gg that the cannot increase over time (as in section IV.B).tt tt<sup>25</sup> Although this SSBBII SSBBII cc zz configuration does not match perfectly the asset-preservation principle, it prevents tt SSBBII the government from increasing consumption in times of high resource revenues.

> 23 Some countries consider spending on education and health as investment in human capital, so the HR would not constrain this type of expenditure.

> 24 Botswana is the most celebrated country to incorporate the SBI rule in its fiscal framework for diamond revenues (AfDB 2016). 25 Another possible application is to set ����� to match historical SBI values.

> SSBBIItt 17
On the surface, it seems that the HR has no effect when coupled with an SSR, as this rule already saves most of the transitory windfalls in the short run. However, the HR prevents the government from increasing consumption over time as the financial returns on the invested assets start to improve the fiscal budget.<sup>26</sup>

# **III. General Baseline Calibration**

In this section, we describe how to calibrate the LTGM-NR to a generic oil exporter for a “business-as-usual” baseline simulation. The discussion below intends to be comprehensive and provide a detailed description of the calibration. The general reader that is more interested in how the LTGM-NR works in practice can jump ahead to the Angolan exercise in section IV.

The baseline simulation runs from 2021 to 2050 (though the simulation horizon can be changed). “Flow” variables are usually calibrated to a 20-year average (2000-2019) to reduce year-to-year volatility—also, 2019 is before COVID-19— and slow-moving “stock” variables are calibrated to the most recent year available. Many of the parameters are common to the standard LTGM (indicated with a red cross on Table 2) and so are not discussed further here (see Loayza and Pennings 2018). However, other similar parameters need to be adjusted, as aggregate data sets like the Penn World Tables (PWT) do not include a resource sector. The user has the ability to override the default calibration if they have better data. If the data are missing, we suggest using an average within the same income group or region. Table 2 provides an overview of the calibration and data sources.

> 26 An equilibrium in the External-Balance submodel is defined as a collection of 12 endogenous trajectories 0 , R 0 D � plus 14 endogenous variables (that are specific to this submodel) tt ttii ttii ttjj tt tt tt tt, c tt ttii ttjj 0 tt , e � where with each endogenous variable specified as a function of the exogenous paths �YY , QQ , RR , KK , KK DDPP , YYpp , iigg , ii , ii , MMRRPPKKpp gg, MMRRPPKKRR gg gg tt tt tt�����tt tt tt tt tt tt tt tt tt tt h �ii , ss bb , dd , dd , dd , zz , zz , zz pp , cc , ii , bb , ff jj∈ } and � as well as initial conditions {0,1, ... , NN}AAjj NN ωω ρρ ii ii ii ii pp tt 0 tt tt 0 tt 0 tt0 tt 0 tt 0 tt 0 tt 0 0 0 0tt� that satisfy equations (1)—(12) and equations tt tt tt ����� (16)—(29) for every period{gg̅ , gg̅ , gg̅ , gg̅jj , gg̅ , DD�jj , pp̅ii , pp�ii _t_ . For HRs, the SBI inequality must also hold for a specified path , QQ� pp �ss̅gg , ffddıı , ηη̅ , bb� �RRDDPPat all periods. , RRDDPP , KK , KK , RR , pp , NN , ωω , ρρ , dd , dd tt SSBBII

18
**Parameters.** The labor share is set to match the average share of labor compensation in non-resource GDP over 2000-2019. This requires adjusting the PWT labor share, which applies to the whole economy, usually less labor intensive than the non-resource sector. Specifically: t ⁄ 0 PPWWPP where t is the share of labor compensation in GDP in period tt tt tt _t_ , taken from Penn ββ = ββ x RRDDPP RRDDPP PPWWPP 0 World Table 10 (PWT10), and is non-resource GDP in period _t_ . The baseline ββ calibration sets equal to the average value of tt over recent years. RRDDPP To calibrate the resource rents in resource industry tt , , we use information on ββ ββ natural resource rents shares, provided by the Global Trade Analysis Project ii ii γγ (GTAP), and averaged over 2004, 2007, 2011, and 2014.<sup>27</sup> The tax rate in the resource sector, , is calibrated using data on government natural resource revenues and resource GDP from the IMF’s World Commodity RR ττ Exporters Dataset (IMF-WCE). Specifically, is set to match the longest available historical average of resource revenues as a share of resource GDP since 2000. RR ττ

The fiscal rule in the Default submodel requires the calibration of the marginal propensity to invest, (see equation (13)). For BBR-HR and SSR, is set to one and zero, respectively. For BBR, is the average ratio of public investment to total θθ θθ expenditure over 2000-2019, taken from the IMF-WEO and the Investment and θθ Capital Stock Dataset provided by the IMF Fiscal Affairs Department (IMF-FAD). The External-Balance model requires five additional parameters: the private investment crowd-in parameter the average tax rate on the non-resource economy 0, the debt-elastic interest spread , the world real interest rate , and how the λλ, budget balance responds to debt . measures the response of private investment WW ττ ψψ ff to the fiscal balance (equation (19)). Its default value is set to 0.15 (a one-dollar φφ λλ increase in net government borrowing crowds in 15 cents of private investment) based on the average of estimates for both industrial and less developed countries (see Chinn et al. 2011). 0 is set to match the average ratio of non-resource revenue ττ

> 27 We can map parameter into the measure of natural resource rents from GTAP as it quantifies the total income that can be generated from the extraction of natural resources, less the cost of ii extraction, including the return on capital employed on the extractive activity. γγ

19
to non-resource GDP over 2000 (or most recent historical average). Non-resource revenue is calculated as the difference between total revenue and resource revenue,

**Table 2: Baseline set-up of the LTGM-NR** :

Selected parameters, initial conditions & trajectories of exogenous variables <u>(Symbol + indicates the parameter is taken from the standard LTGM)</u>

||**Model**|**SOURCE**|**TIME SERIES**|
|---|---|---|---|
|A. Parameters<br><br>||||
|Depreciation rate (δ)+<br><br>|Both|PWT 10|2000–2019 average|
|Labor share, non-res. sector (β0)<br><br>|Both|PWT 10|2000–2019 average|
|Resource rents share (γi)<br><br>|Both|GTAP|2004–2014 average|
|Resource tax rate (τR)<br><br>|Both|IMF-WCE|2000–2016 average|
|Non-resource tax rate (τ0) <br><br>|EBM*|WEO/WCE|2000–2016 average|
|World real interest rate (fW)<br><br>|EBM|FRED|US long-run real interest rate≈2%|
|Debt-elasticity of spread (ψ)<br><br>|EBM|SGU (2003)|Ranges between 0.001 and 0.1|
|Private investment crowd-in (λ)<br>|EBM|Chinn et al.|Average of industrial and EMDEs|
|Marginal propensity to invest(θ)|Default|<br>IMF-FAD|BBR: 2000–2017 average of<br>investment to expenditure ratio;<br>SSR:θ = 0;HR:θ = 1|
|B. Initial conditions||||
|GDP per capita+|Both|WB-WDI|2020 (or most recent)|
|Exports of oil (% of GDP)**|Both|UN-CT|2002–2019 average|
|Capital to GDP ratio:+|Both|PWT 10|2019 or most recent|
|Non-R sector|Both|Endogenous|Equalize initial MRPK|
|R sector (oil)|Both|Endogenous|Equalize initial MRPK|
|Reserves of oil|Both|BP/USGS|Most recent|
|External public debt (% GDP)|EBM|WB-WDI|2020 (or most recent)|
|External private debt (% GDP)|EBM|WB-WDI|2020 (or most recent)|
|C. Trajectoryof exogenous variabl|es,2021–|2050||
|Price of oil (2010 US$/barrel)|Both|WB-CPD|Most recent or 2000–2019 average|
|Discoveries of oil (barrels/year)|Both|BP/USGS|2000–2019 average|
|TFP growth, non-R sector|Both|PWT 10|2000–2019 average|
|TFP growth, oil sector|Both|--|Country-specific|
|Human capital+|Both|PWT 10|2000–2019 average|
|Population+(total, working-age)|Both|ILO|Forecast for 2021–2050|
|Private savings (% GDI)|EBM|WB-CPD|2000–2019 average|
|FDI+(% GDI)|EBM|WB-WDI|2000–2019 average|
|Private investment (% GDI)|Default|<br>IMF-FAD|2000–2019 average|
|Exogenous public investment∔|Both|IMF-FAD|2000–2019 average|
|Target primary balance (% GDI)|EBM|IMF-WEO|Country-specific|
|Exogenousprivate external debt<br>|EBM<br>|--<br>|Country-specific<br>|
|* EBM denotes External-Balance Model<br>** For simplicity, we assume that the reso<br>three industries from the set of commoditi<br>∔Default model: exogenous public inves<br>of total expenditure).|urce sector<br>es: coal, co<br>tment (% of|has one industry: oil (<br>pper, diamond, gas, g<br>GDP); External-Bal|N= 1). In practice, the user can choose up to<br>old, iron, lead, nickel, oil, silver, tin, and zinc.<br>ance Model: exogenous public investment (%|

20
provided by IMF-WEO and IMF-WCE, respectively.<sup>28</sup> Likewise, non-resource GDP is computed as the difference between GDP and resource GDP. The baseline world annual real interest rate, , is set to two percent, which is in line with the 10-year inflation-indexed US Treasury bond yields averaged over 2000-2019 from WW ff the St Louis Federal Reserve Bank Economic Data (Series: WLTIIT). The baseline debt-elasticity of the interest spread is set to , which implies that a ten percent of GDI increase in the external debt leads to a one ψψ= 0.1 percentage point increase in the country’s interest rate.<sup>29</sup> Finally, we set , which is sufficient to prevent any explosive paths for public debt as . φφ= 0.05 **Initial conditions.** GDP for 2020 is taken from World Bank’s World WW φφ> ff

**Initial conditions.** Development Indicators (WB-WDI), in constant 2010 U.S. Dollars.<sup>30</sup> In the absence of a data set containing comprehensive information on GDP at the industry level for several commodity-exporting countries, we proxy GDP in resource industry by exports of the resource good . More specifically, GDP in industry is set to match the average value of exports as a share of GDP.<sup>31</sup> The export data is ii ii ii taken from the UN-Comtrade Database (UN-CT), which provides information on export value for all 11 commodities and all 56 countries pre-loaded in the LTGMNR, with a time series that usually starts in 2002.<sup>32</sup>

28 As a complementary data set for government revenues (total, resource and non-resource), we use ICTD/UN-WIDER Government Revenue Dataset (UN-GRD). 29 The range of estimates for in literature varies widely across countries and papers. For example, while Schmitt-Grohe and Uribe (2003) set to match the volatility of the observed current-account-to-GDP ratio for Canada, Schmitt-Grohe and Uribe (2016) estimate ψψ for Argentina. We adopt as a compromise between these two seemingly extreme estimates. ψψ= 0.001 30 LTGM-NR spreadsheet since updated to constant 2015 USD. ψψ= 1 31 Initial GDP in industry ψψ= 0.1is computed as a share of total 2020 GDP. The default method is to use average value of exports in industry as a share of GDP since 2000. The following expression describes how the default initial real GDP in industry ii is computed: ii <u>�</u> 2010⁄ <u>� ,</u> 2020 � ii ii ii UUNNUUPP 2020 ii = ����������������������������<sup>1</sup> tt ii tt ~~�~~ WWDDWW pp pp x EEeeppf ttss P P i WWDDWW RRDDPP tt≥2000 tt x RRDDPP where is the real price (2010 U.S. dollars) of resource good NN RRDDPP in period taken from the World PPggPP iihP PP ssdd GGDDPP i ddi ttPPii ii i iissPP 2000 Bank Commodity Markets Outlook.ii is exports value (current U.S. dollars) of resource tt good in period pp , and is real GDP in period UUNNUUPP As ii tt is measured in current ii,tt U.S. dollars, it is deflated by WWDDWW 2010EEeeppf. ttss UUNNUUPP 32 Alternatively, we provide a measure of GDP in industry ii tt RRDDPPtt ii ii tt. derived directly from production data, EEeeppf ttssii,tt tt pp /pp 21 ii
As in the standard LTGM, the initial stock of capital-to-GDP ratio is calculated using the most recent observation from PWT 10 (although earlier versions of PWT are also available).<sup>33</sup> The initial capital stock is split across activities to equalize the initial marginal revenue product of capital across .<sup>34</sup> Information on the initial stock of reserves in industry is taken from the BPjj∈{0, ... NN} Energy Dataset for oil, natural gas and coal, and from the U.S. Geological Survey ii Database (USGS) for mining industries, such as copper, gold, and iron. As a stock variable, initial reserves are set to match the most recent observation (usually 2017).

The External-Balance Model also requires initial public and private external debt. Reliable data on the decomposition of external debt into private and public debt is often unavailable for developing commodity-exporting countries. Hence, in the baseline calibration, we assume that all initial external debt is public, and initial private external debt is zero. This is obviously an extreme assumption, and countryspecific data should be used where available. We calibrate public external debt equal to the most recent observation on total external debt taken from WB-WDI.

**Trajectory of exogenous variables** . The LTGM-NR requires the trajectories of a number of exogenous variables from 2021 until 2050. The key assumption of baseline simulations is that recent trends will continue in the long-term. In this case, we assume that historical averages (such as 2000-2019) will continue until 2050.

The first assumptions are the paths for actual and structural commodity prices. A structural price should reflect its perceived long-term value, so the user could use a long historical average or a proper estimate of the long-run price. For example, in
section IV, we set the structural price of oil to US$50/barrel, which is the estimated unconditional mean of oil prices from 1960 to 2020. The actual path of commodity prices can be set to any value. Again, in section IV, we analyze the consequences of an increase in oil prices from US$50 to US$80/barrel. The default data source for commodity prices is the World Bank’s Commodities Prices Dataset (WB-CPD– _The Pink Sheet_ ), although other sources are available (e.g., USGS and BP-Energy). Also, the structural production of resources is usually assumed to follow N-year moving average of actual production.

Discoveries of natural resources are calibrated using data on annual production and reserves of the resource good , taken from the BP-Energy (for energy industries) and the USGS (for mining). The time series of discoveries of good in ii period is computed as the change in reserves from period to plus ii production in period (as in equation (3)). In the baseline, the trajectory of tt tt−1 tt discoveries of good from 2020 to 2050 can be set to match the historical average tt over the past 20 years. Naturally, predicting future discoveries of natural resources ii is no trivial task and using historical averages can be misleading. In this case, country-specific data based on experts’ knowledge should be used when available.

The LTGM-NR requires paths for future TFP growth in each sector and industry. TFP data at the industry level is usually unavailable for most developing countries. A simple approach is to assume that TFP growth is homogenous across sectors. In this case, we can set TFP growth in each sector/industry equal to the average aggregate TFP growth over 2000-2019, from PWT 10. When available, the user should use information on sectoral TFP growth.<sup>35</sup> In the Default submodel, private- and public-sector investment data are taken from IMF-FAD, which decomposes total investment into private and public from 1960 to 2017. The paths for private investment, , and the exogenous component pp tt ıı̅

> 35 For example, the Chilean 2016 Annual Report of the National Productivity Commission documents a large heterogeneity of TFP growth across the copper and non-copper sectors over 20002015, with an average fall of one percent in the copper sector and average growth of 1.4 percent in the non-copper sector.

23
of public investment, , are set equal their historical averages over 2000-2017, gg reflecting “business as usual” investment rates. tt ıı̅ In the External Balance submodel, private savings, , are set to match the pp observed average of private savings (% of GDP) in 2000-2019, computed using tt ss̅ data from the IMF-WEO and IMF-FAD. Similarly, the share of public investment in total expenditure, , is set to match the average ratio of public investment to total expenditure over 2000-2017 (also IMF- WEO & IMF-FAD). For simplicity, tt ηη̅ the default fiscal rule is the BBR-Default, with a zero target for the primary balance ( = 0) and stable external public debt ( 2020), though the user can refer to gg the IMF-FAD for actual targets for the fiscal balance and debt in specific countries. tt bb<sup>�</sup> dd<sup>gg</sup> = dd Finally, the exogenous component of the private debt, , is set to zero by default. pp tt dd̅

# **IV. Application of the LTGM-NR to Angola**

In this section, we illustrate how to apply the LTGM-NR in practice with three exercises for Angola. After a brief discussion of the calibration, we assess the baseline business-as-usual growth path over the next three decades (subsection A), how the long-term growth would be affected by higher oil prices (subsection B) and higher oil discoveries (subsection C). Subsection A compares the LTGM-NRDefault with the standard LTGM (submodel 1). Subsections B and C consider all fiscal rules (BBR, SSR, BBR, SSR-HR) and submodels (Default & External Balance). As before, the LTGM-NR only capture supply-side of the economy, and not the short-run response of the economy to shocks via aggregate demand.

**Calibration to Angola (Default submodel).** The calibration to Angola follows the logic of the generic calibration presented in section III. To keep the description brief, we discuss here only the most important parameters and variables of the Default submodel (for details, see Table 3). We calibrate the model with data up to 2020 but the simulation runs from 2023 to 2050. The years 2021-2022 are excluded from the simulation because the LTGM-NR is not suited to account for the shortterm volatility induced by the COVID-19 pandemic. Instead, we refer to the IMF’s official forecasts for 2021-2022 (see IMF 2021).

24
<!-- Start of picture text --> —1)xshare of oil in 2020 GDP<br><!-- End of picture text -->
UN’s forecast of demographic trends for Angola, which suggests that population growth will fall from about 3 percent in 2020 to 2 percent by 2050. The workingage population is predicted to rise from 52 percent of total population in 2020 to 58 percent in 2050. Moreover, based on recent trends, the labor force participation rate is assumed to remain constant at around 80 percent of the working-age population until 2050 (WB-WDI).

**Table 3: Baseline calibration to Angola (Default model)** <u>Selected Parameters, Initial Conditions & Trajectories of Exogenous Variables</u>

||**VALUE**|**SOURCE**|**TIME SERIES**|
|---|---|---|---|
|_A. Parameters_<br>||||
|Depreciation rate (δ) <br>|4.4%|PWT 10|2000-2019 average|
|Labor share total (β<sup>PWP</sup>)|0.34|PWT 10|2015-2019 average|
|Labor share, non-oil (β)|0.56|Calculation|2015-2019 average oil share|
|Oil rents (γ)<br> <br><br>|0.33|GTAP|Median oil-exporters 2004-14|
|_Government:_<br><br>||||
|Tax rate in oil sector (τR)<br><br>|0.7|IMF-WCE|2001-2013 average|
|LR public investment (e)<br>|6→2% of GDI|IMF-FAD|2015-2017 average|
|MPI (θ)<br>|0.2<br>|IMF-FAD|BBR: 2000-2017 average;<br>SSR (θ = 0);HR (θ = 1)|
|Sectoral investment elasticity (μ)|1|Assumption||
|_B. Initial conditions_<br>||||
|Real GDP per capita<br>|US$2,890*|WB-WDI|2020|
|Exports of oil(I= 1)|50.8% of GDP|UN-CT|2007-2015 average|
|<br>_Capital to GDP ratio:_|2|PWT/MFMod|2011|
|<br>Non-oil sector|1|Endogenous|Equalize initial MRPKs|
|Oil sector|1|Endogenous|Equalize initial MRPKs|
|Reserves of oil|9.5 Bi/barrels|BP-Energy|2017|
|Participation rate,_% of working_|_-age population_|||
|Male / Female|80.2 / 76.4|WB-WDI|2017|
|Base year for oil prices|2010||User choice|
|Initial year of simulation|2020||User choice|
|_C. Trajectory of exogenous var_<br>|_iables, 2023-2050_<br>|<br>||
|Price of oil|US$50/barrels|World Bank|Estimated mean 1960-2019|
|Private investment|20% of GDI|IMF-FAD|2000-2017 average|
|TFP growth, non-oil sector|1%|PWT 10|Median of LMCs, 2000-19|
|TFP growth, oil sector|0%|PWT 10|Median oil exporters, 2000-19|
|Human capital growth|0.7%|PWT 10|2000-2019 average|
|Oil Discoveries||||
|Baseline & Discovery Shock|400m bbl/year|BP-Energy|25<sup>th</sup>percentile 1990-2017|
|Price shock|Endogenous**|Assumption||
|_Demographics:_||||
|Population growth|3.4→2.3%|ILO|Forecast for 2023–2050|
|Working-age population|51→59% pop.|ILO|Forecast for 2023–2050|
|Population, male|49.1% of pop.|ILO|Forecast for 2023–2050|
|Participation rate(M&F)|≈0 growth|WB-WDI|2000-2019 average|

*Real US Dollars of 2010. **Discoveries are set to keep reserves constant in per worker terms.

26
We set the government share in the oil sector = 0.7, which is the historical average of oil revenues (as share of oil GDP) in Angola over 2001-2013 (IMF-RR ττ WEC, most recent data available). Private investment is set to 20 percent of GDP to match the average observed in 2000-2017 (IMF-FAD). Due to exceptionally large investments in energy infrastructure, public investment has been historically very high in Angola (above 10 percent of GDP), but is expected to fall significantly over time, especially due to the likely decline in oil revenues. Accordingly, we assume that public investment falls from 6 percent of GDI in 2023 to 2 percent by 2050. The marginal propensity to spend under the BBR is set to B = 0.2, as public investment averaged 20 percent of total government expenditure from 2000 RR θθ to 2017 (IMF-FAD) (recall D = 0.2 and = 1). Finally, in the baseline we set the actual and structural price of oil to 50 dollars RR HHRR θθ θθ per barrel, which is the estimated unconditional mean estimated with data since 1960 (see Appendix Figure 5 for details). Also, we assume discoveries of 400 million barrels of oil per year in the baseline, equal to the 25<sup>th</sup> percentile over 19902017 (BP-Energy data, see Figure 6 panel A).

**Calibration to Angola (External Balance submodel).** For the External Balance submodel, we set the private savings rate and FDI to 19 and 1 percent of GDP, respectively, similar to their averages over the past 20 years. The public investment share in expenditure is set = 0.2 until 2050 (also the historical average). Finally, we assume that = 0, which means a balanced budget for the tt ηη BBR and a structural balance for the SSR. We assume the default private tt bb<sup>�</sup> investment crowd-in parameter (Chinn and Ito 2011). For more details of the calibration of the External Balance submodel refer to Appendix Table 4. λλ= 0.15

# _A. Baseline Growth in Angola: LTGM-NR versus Standard LTGM_

In this subsection, we (i) present the baseline GDP per capita growth simulated by the LTGM-NR-default until 2050, (ii) discuss how this baseline is explained by each of the variables of the model, and (iii) illustrate the importance of using a model with a resource sector (by comparing it with a naïve calibration using the standard LTGM).

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<!-- Start of picture text --> 4.3%<br>4% Baseline (standard LTGM<br>3.6% — { Residual growth<br>3% | Overestimated TFP growth<br>aaaaarit ee Underestimated laboreccccccccseceesshare {<br>ay om<br>1.5% Overestimated growth<br>due to depleting reserves<br>1%<br>Baseline (LTGM-NR)<br>Covid-19 Medium/long-term forecasts<br>+—__ —___><br>0% _ Ee ee ee Se |<br>2020 2025 2030 2035 2040 2045 2050<br>— Baseline +++e+eA = Baseline + constant reserves<br>— —B=A + low labor share — -C=B + high oil TFP growth<br><!-- End of picture text -->
Second, the Standard LTGM naïve calibration distorts the impact of growth fundamentals by ignoring the heterogeneity in the labor share across sectors. In the standard LTGM, we set to match the labor compensation share in total income from PWT. This particularly low aggregate labor share is the outcome of ββ= 0.34 an economy highly dependent on oil, which is typically a capital-intensive industry.<sup>44</sup> The LTGM-NR specification is more suitable for large oil producers as it allows the user to choose the labor share specific to the non-oil sector. Recall that in the baseline we set , which is a more conventional value for this parameter—see Appendix Figure 4—but also consistent with the aggregate labor ββ= 0.56 share from PWT (0.56 x initial non-oil share in GDI = 0.34).

The “distorted” low labor share in the naïve calibration of the standard LTGM boosts the effect of investment in physical capital on growth. As physical capital is reproducible, this makes growth much easier. In the limit where the labor share is zero, the standard LTGM becomes an “AK” model that delivers perpetual endogenous growth. To assess the net effect of the low labor share on growth, we run counterfactual B: equal counterfactual A (baseline + constant reserves) but with the labor share lowered to 0.34 (as in the standard LTGM). Not surprisingly, as investment is the main driver in Angola, the net effect is positive and substantial: the distorted labor share leads to extra 0.5ppts of growth on average (as shown by the vertical distance between the dotted and dashed lines).

Third, in the naïve calibration of the standard LTGM we set _aggregate_ TFP growth to 1 percent to match the average in lower-middle-income countries over the past two decades. However, there is large heterogeneity in TFP growth across sectors. Recall that in the LTGM-NR we set TFP growth in the _non-oil sector_ to one percent but, based on evidence from large oil exporters, we assume no TFP gains in the oil sector (see Appendix Figure 2). To assess the effect of overestimated TFP growth rates, we run counterfactual D: equal counterfactual C (baseline with

> 44 Appendix Figure 4 shows that Angola reported the lowest average labor share over 2000-2019 among LMCs (PWT10). It also shows that large oil exporters tend to have low labor shares, which is in line with the empirical evidence of low labor shares in resource industries (see Lebdioui 2021).

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constant reserves and low labor share) but with 1 percent oil TFP growth, so aggregate TFP is also 1 percent, as in the standard LTGM. The excessive TFP growth leads to extra 0.6ppts of growth on average over 2023-2050.

# _B. The Effects of Oil Price Shocks in Angola_

In this section, we assess the effects of oil prices on Angola’s long-term growth. Note that oil prices shocks have potentially very large effects on short-medium run growth through Keynesian effects. However, those mechanisms are not part of neoclassical growth models like the LTGM-NR, and while important, are not considered here. Moreover, it can be the case that the best fiscal rule for long-run growth produces excessive volatility in the medium term.

More specifically, we consider a ten-year boom-and-bust cycle, in which the price of oil increases from $50 to $80/barrel from 2025 to 2030 and then returns to $50 by 2035, remaining at that level thereafter (see Figure 4, Panel A). This scenario is assessed relative to the baseline oil price of $50 until 2050. We also set $50/barrel as the reference price to determine structural revenues.<sup>45</sup> To isolate the price effect, we assume that oil reserves are held constant in per worker terms by setting discoveries equal production (both in per worker terms) and the structural production of oil is set equal to actual production.

In this section, most variables are expressed as deviation from the baseline. For example, Panel B of Figure 4 displays incremental GDI as percent of baseline GDI, defined as: 100 x [(Scenario real GDI in US$)/(Baseline real GDI in US$) − 1] Each line represents the simulation of GDI under a specific fiscal rule (BBR, SSR, BBR-HR, and SSR-HR) and submodel (Default and External Balance). Likewise, panels C, E, and F display incremental GDP, public and private investment, respectively. Finally, panel D shows incremental GDP growth _,_ defined as the difference in growth rates between scenario and baseline, in percentage points. Below we briefly discuss the impact of oil prices in each variable. Appendix Table 6 through Appendix Table 8 provide a detailed summary of the results.

> 45 These assumptions are based on the estimated forecast distribution of oil prices, using the World Bank’s Commodity Markets Outlook data from 1960 to 2019. The price of $80 is the 75<sup>th</sup> percentile of the distribution and $50 is the unconditional mean. See Appendix Figure 5 for details.

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—o— BBR (Default model) -——SSR (Default model) —>— BBR (EB model) ——SSR (EB model) — — HR (Default model) - — BBR-HR (EB model) +++**SSR-HR (EB model) <!-- Start of picture text --> 90<br>80 «Baseline<br>—Scenario<br>70<br>60<br>50<br>40<br>30<br>20<br>10<br>0 _ OO ee |<br>2020 2025 2030 2035 2040 2045 2050<br><!-- End of picture text -->

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**Impact on GDI** . The first thing to notice is that, under any specification, the oil price shock leads to large increases in GDI of around 25%-35% (see Figure 4, Panel B). Around 25ppts of this increase is mechanical: oil accounts for around 40 percent of GDI at the start of the simulation, and at the peak, the oil price increases 60 percent (=$80/$50-1), with 40% x 60% ≈ 25%. The excess (depending on the submodel and fiscal rule) is due to (i) reallocation of capital towards the oil sector (which is more productive in dollar terms), and (ii) higher investment. Of course, when the oil price falls over 2030-2035, the effect goes into reverse, and GDI falls sharply.

The paths for different fiscal rules fall into two groups. First, the HR in the Default and BBR-HR in External-Balance models have the largest increase in GDI, hitting around 35 percent above baseline in the early-2030s. This is because the vast majority of commodity revenues are spent on public investment. The second group contains all the other rules: BBR, SSR, and SSR-HR. As discussed below, these rules lead to much smaller increases in investment.

**Impact on GDP.** In the very short run, the effect of the oil price shock on the level of real GDP is zero because commodity prices do not directly affect GDP (Figure 4, Panel C): for example, by 2026, real GDP is the same as in the baseline, even though oil prices are $6/barrel higher. Instead, GDP only increases after a few years when the productive capacity of the economy expands through higher investment. The flipside of the muted increase in real GDP is the muted _decrease_ in GDP when oil prices fall: whereas real GDI (relative to baseline) falls sharply, most measures of GDP only fall slightly and with a delay.<sup>46</sup> The rules that generate a larger increase in GDP are the ones with the higher GDI in Panel B: BBR-HR in both models, with peak GDP about 20-25ppts above the baseline in 2035 (which is five years after the peak oil price). In contrast, the BBR and SSR have a smaller boost to GDP, with a peak of 5-10ppts above the baseline in 2035. The SSR-HR in the Extended Balance submodel generates a boost to GDP that is more sustainable

> 46 Note that in reality, large movements in aggregate demand associated with the commodity price shock will cause disruption to domestic non-traded goods production. But these demand side effects are not in this type of neoclassical model.

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and lasts well beyond the duration of the price cycle. Moreover, the SSR-HR outperforms the BBR-HR (Default model) in the long run.

While the different rules do have a differential effect on GDP growth rates, it is perhaps less than might be expected (see Figure 4, Panel D). The peak increment to real GDP growth (relative to the baseline) is about 5ppts in 2030 in the BBR-HR (for both submodels). In contrast, the other rules lead to a peak increase in GDP growth of only about 1-2 ppts in 2030—despite a large increase in government revenue (discussed below). Perhaps surprisingly, the increment to real GDP growth continues to be positive as oil prices fall over 2030-2035, and only turns negative after 2035. For the SSR-HR incremental GDP growth remain positive until 2042.<sup>47</sup> Another surprising result is that the BBR and SSR yield almost exactly the same growth path in External-Balance submodel. As we will discuss below, under this calibration with and it does not make a large difference if oil revenues are saved or spent under these two rules: each extra dollar of oil revenue ηη= 0.2 λλ= 0.15 becomes 20c of public investment if spent; or 15c of private investment if saved.

**Impact on public investment.** The oil price shock triggers GDP growth mostly because it leads to higher public investment. In the Default submodel, the increase in public investment as a share of baseline GDI is approximately (the marginal propensity to invest times the change in revenues). As oil revenues account for tt θθΔzz almost 30 percent of GDI in 2020 ( 2020 = 0.7x0.4), a 60 percent increase in oil ssiiFF prices would boost revenues by nearly 20 percent of baseline GDI (see Appendix RR ττ yy Figure 8, Panel A). Under the SSR , so public investment is unchanged, which is shown by the black line in Figure 4, panel E. In the BBR-HR, , so all the θθ= 0 additional revenues are spent, leading to an increase in public investment by around θθ= 1 20 percent of baseline GDI at the peak, as shown by the grey dashed line. Finally, under a BBR , so 20 cents in the dollar windfall oil revenue is invested, yielding an increase in public investment of about 4 percent of baseline GDI (black θθ= 0.2 circled line). In all cases, public investment nearly returns to baseline levels after the end of the price cycle in 2035. This feature stems from the assumption that

> 47 The reason is that oil prices have no direct effect on real GDP—only an indirect effect via investment, which continues to be elevated as long as oil prices are above their steady-state level.

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structural production of oil equals actual production, implying that ) = RR RR = 0 for all after 2035 as returns to $50 (equation (13)). tt tt θθ(zz −zz̆ ssiiFF ssiiFF ssiiFF In the External-Balance submodel, the paths for public investment under the tt tt tt θθ�PP −$50�QQ θθ PP BBR and SSR are fairly similar to their Default submodel counterparts. However, the deviations of BBR-HR and SSR-HR are worth noting, as they both lead to persistently higher public investment, though for different reasons.

Under the BBR-HR, the oil sector expands rapidly during the oil price cycle, generating higher oil revenues that are reinvested under the BBR-HR. Though this effect is present in other simulations, it is especially strong for the BBR-HR. For example, in 2035, incremental revenues stand at 10 ppts of baseline GDP under the BBR-HR, more than double the value generated by the BBR or SSR (see Appendix Table 6 and Appendix Figure 8).

The SSR-HR (red dotted line) generates high public investment for many years after the end of the oil cycle (extra 5ppts on average in 2036-2050, see Appendix Table 8). This is because the extra interest savings from paying down government debt are recycled into the budget, releasing extra resources for higher public investment (for details, see Appendix Figure 8).

**Impact on private investment and spillovers** . Private investment increases in all simulations, though can be much larger in the External Balance submodel than the Default submodel. In the Default submodel, private investment is 20% of GDI, so as GDI increases by 25-40 percent, private investment increases by 5-8ppts of baseline GDI (Figure 4, Panel F).  In the External Balance model we assume that if the public sector runs a surplus of one dollar, this will free up dollars for private investment. However, it is only the SSR and SSR-HR that generate substantial λλ changes in the budget balance, and hence it is only these two rules that feature larger increases in private investment with .<sup>48</sup> With our default calibration of 0.15, private investment increases further to peak at 8ppts above baseline by 2030 λλ> 0 λλ= in the SSR and SSR-HR.

> 48 Under the BBR the budget is balanced, so there is almost no increase in the fiscal surplus. In practice there is sometimes a small increase in fiscal savings, because the BBR is specified as a share of GDI, which increases with an oil price shock.

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—o— BBR (Default model) -——SSR (Default model) — — HR (Default model) —>— BBR (EB model) ——SSR (EB model) - — BBR-HR (EB model) +++**SSR-HR (EB model) <!-- Start of picture text --> 25%<br>20%<br>15%<br>10%<br>4.<br>5% ye RR SETS<br>SS ELL serene,<br>0% cooeed— SSS Ss<br>2020 2025 2030 2035 2040 2045 2050<br><!-- End of picture text --> <!-- Start of picture text --> 35% oys°%iS<br>30% :,<br>fl \.<br>ve<br>20% 5 wae,<br>1% / \ ——<br>10% 4 \ =< :<br>SSSeccog.<br>5% f SSS Sg SS oS SCC,<br>0% eooced<br>2020 2025 2030 2035 2040 2045 2050<br><!-- End of picture text -->
calibration of . This means the path for GDI with either SSR in the External-Balance submodel is now similar to the BBR-HR (Figure 5, panel B), λλ= 0.15 achieving a 35ppt increase in GDI by 2030 (though through higher private rather than public investment). Moreover, the SSR-HR achieves the highest growth path—also peaks at 35ppts of baseline GDI in 2030—but outperforms the other rules in the longer-term. Finally, note that different from the default calibration, the BBR and SSR yield very different trajectories with . λλ= 1

# _C. The Effects of a Large Discovery of Oil in Angola_

In this section, we assess the effects of a large discovery of oil in Angola. Specifically, we assume a discovery of 2.7 billion barrels of oil in 2025, calibrated to match the 2002 discovery, which was the largest over the last 30 years. In all other years, as in the baseline, we assume discoveries of 400 million barrels, equal to the 25<sup>th</sup> percentile of the distribution over 1990-2017 (see Figure 6 panel A).

Note that in reality, discoveries often become useable “reserves” over a period of many years. While we assume an immediate transition here for analytical purposes—to clarify the effect of the shock—we advise that users of the LTGMNR smooth the discovery over several years.

To isolate the effect of the 2025 discovery, we assume constant oil prices at $50/barrel, as in the baseline. This last assumption means that real GDI and real GDP—which had large differences in section B—will have similar growth profiles, so in this subsection we only report results for GDP. Finally, to allow the discovery shock to generate cyclical oil revenues—and, hence, different spending profiles across fiscal rules—we set structural (long run) oil production equal to the baseline oil production.<sup>50</sup>

> 50 Note that this assumption is different from section IV.B, where structural production of oil was set equal to actual production. That assumption was designed to isolate the effect of oil price shocks on the government spending profile. However, we now want to explore the effects of higher oil output across different fiscal rules, keeping oil prices constants. This can be done assuming that structural production is equal the baseline, although similar results would be achieved by assuming that structural production follows an N-year moving average of actual production.

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—S— BBR (Default model) ——SSR (Default model) — — HR (Default model) —>-— BBR (EB model) ——SSR (EB model) - — BBR-HR (EB model) +++**SSR-HR (EB model) <!-- Start of picture text --> 3.0<br>BP-En data 4 Scenario,<br>25 erey 4 large discovery<br>t<br>2.0 "<br>iy<br>15 it<br>it<br>i<br>1.0 it<br>it<br>i 04<br>0.5 it<br>Baseline, 25th percentile since 1990<br>1990 2000 2010 2020 2030 2040 2050<br><!-- End of picture text --> <!-- Start of picture text --> 12<br>10 As<br>SB Xs<br>8 S —e<br>Xe<br>S<br>6 S<br>_<br>XQ<br>4 ‘A<br>Se<br>Se<br>2 ks <<br>" She, @<br>2020 2025 2030 2035 2040 2045 2050<br><!-- End of picture text --> <!-- Start of picture text --> 2.6<br>24 ae<br>. Ze<br>22. aa ~ SSS,<br>g R.,<br>2.0 a; ‘ . ‘<br>1.8 \<br>x x<br>WAY<br>14 a<br>12<br>1.0 _ OOO ee |<br>2020 2025 2030 2035 2040 2045 2050<br><!-- End of picture text -->

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to baseline. In 2026, higher reserves boost oil production to nearly 2.2 million barrels per day, a 9 percent increase relative to baseline ( 2025, see Panel ssiiFF C) in almost all models. As oil accounts for about half of Angola’s economy, the ≈γγ x %ΔRR increase in oil production boosts total GDP by about four percentage points in 2026 (see Panel D).

After 2026, the impact on growth depends mostly on public investment, which, in turn, depends on how the government spends/saves the windfall revenue generated by the discovery (Panel E). The shock leads to extra revenues of 2-3 percent of baseline GDI until 2040 but declines sharply after that due to depleting oil reserves (see Appendix Figure 9).<sup>51</sup> This path is very similar across models and rules, except from the BBR-HR, which generate higher growth and, hence, higher oil revenues in the 2030s.

The BBR-HRs (both models) are the only rules that yield a faster growth rate for several years after the discovery shock. As above, the BBR-HRs invest all windfall oil revenue, which increases GDP growth (oil and non-oil) and private investment vis-à-vis the baseline.<sup>52</sup> In contrast, the simple BBRs (either model), invest only 20 percent of the windfall, leading to a modest impact on growth after 2026.

The SSRs also generate a relatively small boost to public investment and longterm growth because the extra revenues are mostly classified as cyclical and so are saved. The SSR in the Default submodel generates the lowest growth path after 2026 as public investment remains constant and private investment increases only modestly vis-à-vis baseline. As above, the SSRs in the External-Balance submodel also generate a small amount of crowding-in of private investment (15 cents per dollar of fiscal surplus, see Panel F).

Over the long term, the differences in public and private investment accumulate to modest differences in the capital stock and GDP across the different fiscal rules. In the BBR-HRs (both submodel), GDP is about 8 percent above baseline by 2040,

> 51 For example, in 2026, oil revenues increased by just above 2 percent of baseline GDI: a 9% increase in oil production x 35% oil as share of total GDI in 2025 x 70% oil tax rate. 52 Recall that private investment increases in absolute terms because it is a fixed fraction of GDI, which increases relative to baseline after 2025 due to the discovery.

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which is double the mechanical increase in 2026 (see Panel D). However, by 2040, GDP under the non-HRs are similar to the initial shock in 2026 of 4 ppts above baseline (variation 3.5-4.5ppts, depending on the rule). Finally, as above, the SSRHR recycles interest savings into higher public investment. While the increase in investment (public and private) does boost the productive capacity of the economy under these rules, a higher rate of extraction reduces reserves, which is roughly offsetting. Consequently, by 2040 around 3/4 of the initial discovery has been depleted (see Panel B). See Appendix Table 9 and Appendix Table 10 for further details.

# **V. Conclusion**

This paper develops the Natural Resource extension of the World Bank’s LongTerm Growth Model (LTGM-NR), which evaluates the effects of commodity price shocks and discoveries of natural resources on medium- and long-term growth in resource-rich economies. The LTGM-NR augments a relatively standard neoclassical model (the LTGM) by adding a resource sector and a government whose fiscal rule determines how to spend or save resource revenues. The model is designed to be simple enough so that its mechanisms are clearly understood, and its solution can be implemented in a spreadsheet (without macros). The accompanying toolkit is preloaded with data for 56 commodity-rich economies and 11 resource industries and can be adjusted to the needs of users.

In a calibrated version of the model to Angola, we find that population growth, depleting oil reserves, and a reallocation of the economy towards the non-oil sector leads to a medium-term growth slowdown and subsequent recovery in the long term. This non-linearity is difficult to capture in standard one-sector neoclassical models. Failing to account for sectoral heterogeneity, naïve calibrations could lead to large differences in growth projections.

Next, we find that an increase in commodity prices can substantially affect real income (real GDI), though only while prices remain elevated. In contrast, the effect on real GDP is smaller and delayed because only the increase in the volume of production is counted (not the price effect). The boost to GDP is more persistent— outlasting the price boom—but its size depends on the government fiscal rule. Not 42
surprisingly, Hartwick rules that invest all extra resource revenues generate the largest increase in GDP. Structural surplus rules (SSRs) can potentially yield large growth rates in countries where higher public surpluses crowd-in private investment. However, in our default calibration for Angola, the crowd-in is small and so SSRs perform similarly to balanced-budget rules where the fraction of extra spending on public investment is equal to the historical average.

In contrast with price shocks, when resource discoveries become available for production there is the same immediate boost to GDP and GDI. The size of the gain largely depends on the share of resource rents in resource production. The subsequent evolution of GDP depends on the fiscal rules in a similar way to price shocks.

In closing, it is important to mention several caveats. First, the LTGM-NR is a simple neoclassical growth model and so omits some mechanisms connecting the commodity sector and growth that are outside this framework. Most important is the lack of an aggregate demand side, which means there is no stimulatory effect of extra commodity-related spending on the local economy in the short run. Our model also lacks channels through which commodity wealth might reduce longterm growth, such as Dutch Disease or a growth-sapping political economy.

Second, governments may have many different objectives in designing fiscal rules governing the use of resource revenues, beyond long-term growth. Other objectives include intergenerational equity (particularly in countries with limited reserves), consumption smoothing, and reducing business-cycle volatility. Often these objectives are conflicting. For example, our rule that delivers the fastest longterm growth (a Hartwick rule) can also result in procyclical spending that exacerbates the business cycle in the short term. As such, the findings in this paper regarding the ranking of different rules reflect only one dimension of performance – medium and long-term growth – and are not a blanket recommendation.

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