## _wp12256 — Baseline Scenario (sections I–V; Technology Externality; Technical Substitutability; Scenarios)

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### I. Introduction — Purpose and main conclusions
- Purpose:
  - Analyze implications of potential further downward shifts in the growth rate of world oil production for the world economy, focusing on GDP, current account imbalances, and oil prices.
  - Use simulation analysis based on the IMF’s Global Integrated Monetary and Fiscal Model (GIMF), a six-region dynamic general equilibrium model.
- Key model assumptions highlighted up front:
  - Oil is a separate and exhaustible factor of production in addition to capital and labor.
  - Demand and supply elasticities for oil are empirically based and very low.
- Principal findings summarized:
  - Baseline (modest, persistent) negative oil supply shocks need not become a major constraint on global growth nor dramatically worsen current account imbalances under a conventional CES specification.
  - If long-run price elasticities of oil demand are increasing functions of the oil price (they double or triple following a permanent doubling of the real price of oil), effects on growth and current account imbalances are even smaller — termed the Growing Elasticity Scenario.
  - Downside scenarios can produce much larger adverse effects, especially when combined:
    - Entropy Boundary and Falling Elasticity Scenarios: substitutability between oil and other factors is limited by a factor space boundary; price elasticity of oil demand decreases under increasing scarcity.
    - Technology Externality Scenario: oil’s output contribution is higher than indicated by cost share because oil provides external productivity benefits not captured in cost shares.
    - Larger Shock Scenario: reduction in the growth rate of world oil production of 4 percentage points rather than 1 percentage point.
  - Combined downside scenarios can lead to reductions in world GDP growth of several percentage points and predict oil prices so large that the model’s assumed smooth adjustment may not hold.
- Empirical/Motivational points:
  - Observed downward shifts in trend growth rate of world oil production since late 1960s; latest trend break occurred in late 2005 when average growth rate of 1.8 percent per annum (1981-2005) could no longer be sustained and production entered a fluctuating plateau.
  - Benes and others (2012) estimate:
    - estimated long-run price elasticity of oil demand equals 0.08
    - estimated long-run price elasticity of oil supply equals 0.02 (under assumption that significant spare capacity will not be available)
    - a fairly small reduction in the world economy’s ability to draw on spare capacity could take a full percentage point off world growth.
- Recommended research direction:
  - Multidisciplinary modeling that better represents dependence of production technologies on physical processes.

### II. The Model — GIMF structure and extensions used
- Model overview:
  - GIMF documented in Kumhof and others (2010).
  - Features: finite planning horizons; gradual adjustment of prices, nominal wages, consumption, investment and imports; financial system with borrower constraints via higher financing costs; fully specified fiscal sector.
  - Six economic regions used: oil exporters, the United States, the euro area, Japan, emerging Asia, and remaining countries; reported as “Oil Exporters”, “USA and the Euro Area” and “Rest of the World”.
  - All regions assumed to have flexible exchange rates.
  - Real variables detrended by world technology growing at an exogenous and constant rate of 1.5 percent per annum.
- Model extensions specific to this analysis:
  - Allow elasticities of substitution between oil and other factors to (a) rise with the oil price or (b) fall with the available quantity of oil.
  - Introduce entropy boundaries in production and consumption that limit substitution away from oil.
  - Include technology externalities from oil in production that raise the output contribution of oil and give oil supply shocks aspects of technology shocks.
- Oil as endowment:
  - Each region’s supply of oil is exogenous except for a quantitatively small elasticity of oil supply with respect to the oil price.

### III. Oil Supply specification
- Supply equation (text preserved):
  - log(Osup_t) = log(Osup*_t)+ǫ_s log ( p_O,avg_t / p_O ), where p_O,avg_t = ( p_O_t ( p_O,avg_{t−1} )^3 )^{1/4}.
- Interpretation and calibration notes:
  - Osup_t is an individual region’s oil production; p_O_t is oil price in local currency.
  - Osup*_t is exogenous part; normalized by trend growth in initial steady state.
  - Simulations subject Osup*_t to exogenous shocks where oil output grows, for three decades, at a significantly lower rate than the historic trend growth rate.
  - Long-run price elasticity of oil supply is ǫ_s: oil output rises by ǫ_s percent for a one percent deviation of the lagged moving average of oil prices p_O,avg_{t−4} from steady state oil price p_O.
  - Moving average begins to fully reflect permanent changes after around 5 years; moving average term enters with a four-year lag to capture exploration and field development lead times.
  - Model omits responsiveness to the current oil price (spare capacity utilization).
- Spare capacity note (text preserved):
  - "Spare capacity is the amount of oil that producers could technically bring to market immediately if prices (and politics) justified it. The evidence shows that when officially reported spare capacity drops below 2 million barrels per day, oil prices start to increase sharply."

### IV. Oil Demand — sectoral production and scenarios
- Sectoral structure:
  - Three sectors require oil: nontradables (superscript N), tradables manufacturing (superscript T), and consumption (superscript C). General J ∈ {N,T,C}.
- Baseline production/consumption aggregator (CES with quasi-share and adjustment costs):
  - Baseline production function (preserved formula):
    - Z_Jt = ( (1−η_J)^{1/ǫ_d} (M_Jt)^{(ǫ_d−1)/ǫ_d} + (η_J)^{1/ǫ_d} (O_Jt)^{(1−G_JO,t)}^{(ǫ_d−1)/ǫ_d} )^{ǫ_d/(ǫ_d−1)}
    - M_Jt = (K_Jt)^{1−α} (L_Jt)^α
    - G_JO,t = φ_O / 2 * ( (O_Jt − O_Jt−1) / O_Jt−1 )^2
  - η_J is quasi-share parameter for oil.
  - ǫ_d is elasticity of substitution (long-run price elasticity of oil demand), assumed equal across sectors in baseline.
  - Adjustment cost G_JO,t makes rapid variation in oil use costly, lowering short-run elasticity relative to ǫ_d.
- Growing Elasticity Scenario:
  - Same functional form as baseline, but ǫ_d replaced by time-varying ǫ_d,t:
    - log(ǫ_d,t) = log(ǫ_d) + ǫ_pǫ log( p_O,avg_t / p_O ).
  - ǫ_pǫ equals 0 in Baseline, and equals 1 or 2 in Growing Elasticity Scenario.
  - For ǫ_pǫ = 1, a doubling of the oil price relative to initial steady state leads to a doubling of long-run price elasticity.
- Entropy Boundary and Falling Elasticity Scenarios:
  - Alternative production function (Stone-Geary term) preserved in source:
    - Z_Jt = ( (1−η_J)^{1/ǫ_Jd} (M_Jt)^{(ǫ_Jd−1)/ǫ_Jd} + (η_J)^{1/ǫ_Jd} ( O_Jt (1−G_JO,t)^{−β ( ̄O_J / ̄M_J ) ̃M_Jt } )^{(ǫ_Jd−1)/ǫ_Jd} )^{ǫ_Jd/(ǫ_Jd−1)}
  - ̄O_J / ̄M_J denotes initial steady state ratio of oil inputs to other factor inputs.
  - β denotes proximity of the entropy boundary to that ratio (β = 0 reverts to standard specification; as β → 1 initial steady state moves closer to the boundary).
  - ̃M_Jt denotes macroeconomic scale of production measured by capital-labor bundle; producers take ̃M_Jt as exogenous when choosing inputs (in equilibrium ̃M_Jt = M_Jt).
  - Long-run elasticity becomes time-varying and can decline towards zero after an oil supply shock:
    - ε_Jd,t = ǫ_Jd ( O_Jt / M_Jt − β ̄O_J / ̄M_J ) / ( O_Jt / M_Jt ) < ǫ_Jd.
  - Reduced-form Falling Elasticity Scenario:
    - log(ǫ_d,t) = log(ǫ_d) + ǫ_oǫ log( O_avg_t / O ), where O_avg_t = ( O_t ( O_avg_{t−1} )^3 )^{1/4}.

### V. Scenarios enumerated (definitions)
- Baseline Scenario:
  - Negative oil supply shock: reduction in trend growth rate of world oil output persistent and modest at 1 percentage point.
  - CES aggregators used; elasticities constant (except short-run effects from adjustment costs).
- Growing Elasticity Scenario:
  - Long-run price elasticity of oil demand increases with oil price (ǫ_pǫ = 1 or 2). For ǫ_pǫ = 1: doubling of oil price → doubling of long-run elasticity.
- Entropy Boundary Scenario:
  - Stone-Geary-type boundary limits substitutability; elasticity declines with scarcity (β controls proximity).
- Falling Elasticity Scenario:
  - Reduced-form where price elasticity of oil demand is an increasing function of oil availability (parameter ǫ_oǫ).
- Technology Externality Scenario:
  - Oil provides external productivity benefits not fully reflected in cost shares; output contribution of oil higher than cost share.
- Larger Shock Scenario:
  - Reduction in growth rate of world oil production equals 4 percentage points (vs 1 percentage point in Baseline).

### Key calibration and institutional assumptions (from Technology Externality section)
- Elasticities:
  - Long-term price elasticity of oil demand in production and consumption assumed 0.08.
  - Short-term elasticity (interaction of long-term elasticity and adjustment costs) around 0.02.
- Oil cost shares:
  - Calibrated at 2 to 5 percent depending on sector and region.
- Balanced growth assumption:
  - Long-run income elasticity of oil demand set equal to one (model assumption); contrasts with Helbling and others (2011) estimate ≈ one third.
- Oil supply elasticities:
  - Literature short-run estimates between 0.05 and 0.15; long-run ǫ_s estimates between 0.005 and 0.02.
  - Model omits short-run price elasticities; calibration sets ǫ_s = 0.03.
- Oil revenue and fiscal treatment:
  - Prior to decline in growth rate, 40 percent of oil revenue used to pay for intermediate goods.
  - Thereafter, real extraction cost per barrel increases at a constant annual rate of 2 percent.
  - Remainder is oil rent distributed between private sector and government.
  - In net oil-importing regions, government receives only a very small portion of oil rent.
  - In oil exporters government receives 90 percent of oil rent.
  - Governments accumulate additional funds in a U.S. dollar—based fund spent gradually at 3 percent per annum.
  - One key effect of higher oil price is dramatic increase in world savings due to low propensity to consume out of oil exporters’ governments’ revenues.

### Technical substitutability — overview and sectoral limits
- Main uses of oil today: liquid transportation fuel and chemical feedstock.
- Critical substitutability considerations: storability, transportability, ability to deliver useful energy.
- Transportation:
  - Properties of oil/liquid fuels are far superior for transportation; transitions to electricity, natural gas, or liquid fuels derived from non-oil sources are technically possible but:
    - Enormously expensive in dollars, energy, and time.
    - Require several decades; Hirsch and others (2005) estimate lead time of at least 20 years to prepare alternatives for the U.S.
  - Gas filling stations require greater safety precautions.
  - Coal-to-liquids and gas-to-liquids industries not established at large scale except in isolated countries.
- Chemical feedstock:
  - Oil derivatives are pervasive; few easy substitutes exist for many applications.

### Energy alternatives and supply limitations (preserved findings)
- Renewable electricity (solar and wind):
  - Intermittency limits substitution at required scale.
  - Electricity grids collapse when supply cannot match demand to within around 0.5 percent.
  - On current knowledge, solar and wind cannot supply more than 20%-30% of overall electricity without serious grid stability problems.
  - Storage or smart grids might raise this percentage, but at great cost and not to eliminate intermittency; renewables depend on oil-based components and costly backup fossil-fuel plants.
  - These factors contribute to much lower EROEI for renewables compared with conventional oil.
- Biofuels:
  - Blending limits typically 5% to 15%.
  - Problems: extremely low EROEI, heavy water use, competition with food production.
- Coal, natural gas, nuclear:
  - Coal:
    - Some authors claim coal reserves overstated; global peak of coal production about 20 years away in some assessments.
  - Natural gas:
    - Fracking has pushed out gas production in some regions; fracking faces environmental concerns and fast decline rates requiring constant new drilling.
    - Berman (2012) documents potential acceleration of decline rates and overstatement of field reserves.
    - Switching to gas/electricity requires costly power plants and fueling infrastructure with long amortization.
  - Nuclear:
    - Dittmar (2011) estimates large-scale substitution toward nuclear power would hit a peak in uranium production quickly; trend away from nuclear due to fears of low-probability, high-cost events.
- Summary:
  - Non-renewable alternatives may also face supply limits; possibility exists that they cannot provide long-run energy security.

### Simulation framework and Baseline Scenario — setup and core results
- Simulation design:
  - Variables shown relative to trend where applicable.
  - Aggregations use PPP weights.
  - Shock year denoted τ; agents surprised by the shock but thereafter perfectly foresee future evolution of world oil production.
- Baseline shock:
  - Decline in the average growth rate of world oil production by 1 percentage point below its historical trend growth rate starting in year τ, with eventual return to initial growth rate in year τ+30.
- Baseline dynamics and magnitudes:
  - Shock generates an immediate oil price spike of over 60 percent.
  - Because the decline is persistent, cumulative oil price increases over 10- and 20-year horizons amount to just over 100 percent and 200 percent, respectively.
  - Reduced oil availability and higher oil prices reduce GDP levels and enlarge current account deficits in oil importers; cause wealth transfer from importers to exporters.
  - Oil exporters:
    - Domestic absorption increases ahead of GDP, at an initial rate of over 2 percent annually.
    - Output in tradables (other than oil) reduces, lowering GDP by up to 7 percent below trend over first five years, and by almost 10 percent after 20 years.
    - Current account improvement up to 4 percent of GDP in very short run and almost 8 percent after 20 years; improvement due entirely to higher value of oil exports.
  - Oil importers:
    - Absorption contracts over time due to negative wealth effect, at an average rate of around 0.5 percent per annum.
    - GDP declines moderately, by 0.2 to 0.4 percent per annum.
  - World real interest rates:
    - Gradually drop; after 20 years are 60 basis points below initial value.
    - Mechanism: oil exporters’ additional oil revenue accrues primarily to governments, leading to higher saving.
  - Global imbalances:
    - Worsen in short to medium term: United States and euro area current accounts deteriorate immediately; other regions’ current accounts strengthen for a lengthy transition but eventually deteriorate.
    - Long-run effects modest: oil importers’ current account-to-GDP ratios on average deteriorate by at most a little over 1 percentage point by year τ+20.

### Growing Elasticity Scenario — rationale and key simulation outcomes
- Rationale:
  - Some substitution technologies are technically feasible; price elasticities of demand may rise for a number of years despite supply limitations.
- Mechanism:
  - ǫ_{d,t} given by log(ǫ_d,t) = log(ǫ_d) + ǫ_pǫ log( p_O,avg_t / p_O ); cases ǫ_pǫ = 1 and ǫ_pǫ = 2 examined (focus often on ǫ_pǫ = 2).
- Key simulated outcomes (ǫ_pǫ = 2):
  - Oil price needs to rise by half as much as in Baseline to induce substitution.
  - Effects on GDP are positive everywhere relative to Baseline:
    - Roughly 50 percent smaller contractions in oil exporters, the United States and the euro area.
    - In the Rest of the World, an 8 percent output loss over 20 years (Baseline) turns into a 2 to 3 percent output gain.
  - Drivers of Rest of the World turnaround:
    - Surge in goods exports to oil importers (emerging Asia and Japan benefit).
    - Surge in investment demand due to lower world real interest rates; particularly strong in emerging Asia because of a higher steady state investment-to-GDP ratio.
  - Global current account imbalances are less severe.

### Entropy Boundary and Falling Elasticity Scenarios — sensitivity to substitution limits
- Entropy Boundary Scenario (β ∈ {0, 0.3, 0.6, 0.9}):
  - β = 0 identical to Baseline; larger β implies tighter entropy boundary.
  - Average elasticity ε_{d,t} moves closer to zero as constraint tightens.
  - For β = 0.9 oil price increases by almost 300 percent after 20 years (versus 200 percent in Baseline).
  - Oil exporters: larger wealth effects, larger absorption, larger real appreciation, larger initial tradables contraction, eventual rebound as governments spend surpluses.
  - Oil importers: worse contractions in absorption and output; current account imbalances get larger but size of effects fairly small.
  - Computational note: Entropy Boundary Scenario simulations relied on numerical linearization, understating real effects when oil prices rise very high.
- Falling Elasticity Scenario (reduced-form):
  - Captures quantity-driven decline in elasticity.
  - Worst case: overall elasticity declines similar to worst entropy case; oil price increase around 250 percent after 20 years (smaller than Entropy Boundary worst case).
  - Output effects are significantly worse in some regions (e.g., Rest of World reduction in annual GDP growth rate rises from 0.4 percent to 0.6 percent).

### Technology Externality Scenario — specification and effects
- Production function:
  - Oil-augmenting technology term (̃O_J_t / ̄O_J)^{ξ_J} is treated as external by agents; in equilibrium ̃O_J_t = O_J_t.
  - When ξ_J > 0, cost share of oil remains below its output contribution.
  - Beneficial effects of oil shared by all factors (factor-augmenting).
- Calibration/assumption for illustrative simulation:
  - Contribution of oil to output set at 25 percent in tradables sector and 20 percent in nontradables (versus baseline 5 percent and 2 percent).
- Key simulated outcomes:
  - Oil prices increase by almost 400 percent after 20 years (versus 200 percent in Baseline).
  - Deterioration in all oil-importing regions’ GDP larger by around a factor of three relative to Baseline.
  - Oil importers’ current accounts deteriorate in the longer run by almost twice as much as in Baseline.
  - World real interest rates drop by approximately twice as much as in Baseline.
  - Both oil and oil-dependent technologies have very low elasticity of substitution with other factors under this specification, limiting compensation for oil contraction.

### Larger Shock Scenario and combined downside outcomes
- Larger Shock parameters:
  - Consider a 3.8 percent rather than 1 percent annual decline in world oil output growth.
  - Given initial growth rate of 1.8 percent per annum, this implies oil production declines by 2 percent annually (except small supply response to price).
  - Real extraction costs per barrel increase by 4 percent annually rather than 2 percent.
- Key simulated effects (relative to baseline):
  - Longer-term output and current account effects approximately four times as large as in Baseline.
  - Declines in absorption in oil importers average around 2 percent annually (vs 0.5 percent in Baseline).
  - Annual GDP growth rates in the United States and the euro area drop by around one percentage point (vs 0.25 percentage points in Baseline).
  - Current account deteriorations in oil importers average 5 percentage points of GDP on average in long term in both the United States and the euro area.
  - Supply reductions require more than 200 percent increase of oil price on impact, and an 800 percent increase over 20 years; such changes likely produce nonlinear GDP effects beyond the model’s scope.
  - Implied increase in world savings so large that several regions could see nominal interest rates approach zero after first few years, complicating monetary policy.
- Combined downside (Technology Externality + Larger Shock):
  - Real oil prices increase by over 400 percent on impact, and by around 1400 percent after 20 years.
  - Model yields a steady, crisis-free reduction in annual GDP growth rates in oil importers equal to 3 percentage points.
  - Authors note real-world responses could include much higher elasticities of substitution and/or much sharper aggregate demand contraction (not captured by model).
- Combined Downside + Growing Elasticity (ǫ_pǫ = 2):
  - Increase in oil price is half as large and output effects approximately half as large relative to combined downside without growing elasticity.
  - Still yields an oil price increase of 800 percent after 20 years.
  - Conclusion: unless elasticity increases are extreme, worst downside scenarios force unprecedented oil price rises; a more likely outcome would combine higher elasticities and larger output contraction.

### Assumptions, caveats, and structural considerations
- Assumption of unitary income elasticity:
  - Model assumes income elasticity of oil demand = 1.
  - Empirical evidence suggests around one third; a lower income elasticity exacerbates supply-constraint problems.
  - Illustration: if 1/3 of 0.1 percentage point increase in oil supply supports 1 percentage point GDP growth, then a 1/3 of 0.1 percentage point decrease would reduce GDP growth by 1 percentage point.
- Assumption of smooth reallocation:
  - Model assumes smooth transition: oil exporters absorb surpluses; financial markets intermediate savings efficiently; businesses reallocate; workers accept lower real wages.
  - Real-world caveats:
    - Inefficient intermediation of large net capital flows could increase risk premia and prevent some regions from benefiting from lower risk-free interest rates.
    - Sectoral interdependencies: car manufacturing, airlines, trucking, long-distance trade, tourism affected earlier and more severely.
    - Large-scale bankruptcies could spread via corporate and bank balance sheets, reducing credit availability.
    - Workers may resist real wage cuts under larger/persistent price increases, increasing output costs.
    - Some oil exporters could withhold growing share of oil for domestic use (fuel subsidies), shrinking oil available to importers faster than world oil output and worsening importers’ growth consequences.

### Conclusion — conditional outcomes and critical determinants
- The extent to which persistent oil scarcity could constrain global growth and current account imbalances depends critically on:
  - Magnitude and persistence of decline in trend growth rate of oil output.
  - Elasticities of substitution between oil and other factors and whether they rise with oil price (Growing Elasticity) or fall with scarcity (Entropy Boundary / Falling Elasticity).
  - Whether oil’s output contribution substantially exceeds its cost share (Technology Externality).
  - Income elasticity of oil demand (unitary in model vs empirical estimate ≈ one third).
- Summary of possibilities:
  - Modest decline + standard production function → world output suffers but perhaps not dramatically.
  - Rising substitutability with price → smaller effects.
  - Pessimistic scientific studies + limited substitutability + higher oil output contribution → effects could be extremely large, potentially dramatic to outright implausible if combined.

*Italic: Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12256.pdf*

### 1. Baseline Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . .    7

### 1. Baseline Scenario

### I. Introduction — Purpose and main conclusions
- Purpose:
  - Analyze implications of potential further downward shifts in the growth rate of world oil production for the world economy, focusing on GDP, current account imbalances, and oil prices.
  - Use simulation analysis based on the IMF’s Global Integrated Monetary and Fiscal Model (GIMF), a six-region dynamic general equilibrium model.
- Key model assumptions highlighted up front:
  - Oil is a separate and exhaustible factor of production in addition to capital and labor.
  - Demand and supply elasticities for oil are empirically based and very low.
- Principal findings summarized:
  - Baseline (modest, persistent) negative oil supply shocks need not become a major constraint on global growth nor dramatically worsen current account imbalances under a conventional CES specification.
  - If long-run price elasticities of oil demand are increasing functions of the oil price (they double or triple following a permanent doubling of the real price of oil), effects on growth and current account imbalances are even smaller — termed the Growing Elasticity Scenario.
  - Downside scenarios can produce much larger adverse effects, especially when combined:
    - Entropy Boundary and Falling Elasticity Scenarios: substitutability between oil and other factors is limited by a factor space boundary; price elasticity of oil demand decreases under increasing scarcity.
    - Technology Externality Scenario: oil’s output contribution is higher than indicated by cost share because oil provides external productivity benefits not captured in cost shares.
    - Larger Shock Scenario: reduction in the growth rate of world oil production of 4 percentage points rather than 1 percentage point.
  - Combined downside scenarios can lead to reductions in world GDP growth of several percentage points and predict oil prices so large that the model’s assumed smooth adjustment may not hold.
- Motivation and empirical support:
  - Observed downward shifts in trend growth rate of world oil production since late 1960s; latest trend break occurred in late 2005 when average growth rate of 1.8 percent per annum (1981-2005) could no longer be sustained and production entered a fluctuating plateau.
  - References to geological view of finite reserves, entropy limits, Hubbert peak concept, and empirical/modeling support (Benes and others (2012) cited) which estimates:
    - estimated long-run price elasticity of oil demand equals 0.08
    - estimated long-run price elasticity of oil supply equals 0.02 (under assumption that significant spare capacity will not be available)
    - a fairly small reduction in the world economy’s ability to draw on spare capacity could take a full percentage point off world growth.
- Recommended research direction:
  - Multidisciplinary modeling that better represents dependence of production technologies on physical processes.

### II. The Model — GIMF structure and extensions used in the paper
- Model overview:
  - GIMF documented in Kumhof and others (2010).
  - Features include finite planning horizons for households and firms; gradual adjustment of prices, nominal wages, consumption, investment and imports; financial system where losses constrain borrowers via higher financing costs; fully specified fiscal sector.
  - Six economic regions in the version used: oil exporters, the United States, the euro area, Japan, emerging Asia, and remaining countries. For reporting aggregated as “Oil Exporters”, “USA and the Euro Area” and “Rest of the World”.
  - All regions assumed to have flexible exchange rates.
  - Real variables detrended by the level of world technology growing at an exogenous and constant rate of 1.5 percent per annum.
- Model extensions specific to this analysis:
  - Allow elasticities of substitution between oil and other factors to (a) rise with the oil price or (b) fall with the available quantity of oil.
  - Introduce entropy boundaries in production and consumption that limit substitution away from oil.
  - Include technology externalities from oil in production that raise the output contribution of oil and give oil supply shocks aspects of technology shocks.
- Oil as an endowment: each region’s supply of oil is exogenous except for a quantitatively small elasticity of oil supply with respect to the oil price.

### III. Oil Supply specification
- Supply equation (text excerpt preserved):
  - log(Osup_t) = log(Osup*_t)+ǫ_s log ( p_O,avg_t / p_O ), where p_O,avg_t = ( p_O_t ( p_O,avg_{t−1} )^3 )^{1/4}.
- Interpretation and calibration notes:
  - Osup_t is an individual region’s oil production; p_O_t is oil price in local currency.
  - The exogenous part Osup*_t is assumed constant when normalized by trend growth in initial steady state (i.e., oil output prior to simulated shock grows at same trend rate as output).
  - Simulations subject Osup*_t to exogenous shocks where oil output grows, for three decades, at a significantly lower rate than the historic trend growth rate.
  - Long-run price elasticity of oil supply is ǫ_s. Equation implies oil output rises by ǫ_s percent for a one percent deviation of the lagged moving average of oil prices p_O,avg_{t−4} from steady state oil price p_O.
  - The moving average begins to fully reflect permanent changes in p_O_t after around 5 years; the moving average term enters with a four-year lag to capture exploration and field development lead times.
  - The model omits responsiveness to the current oil price (spare capacity utilization) because persistently high spare capacity is unlikely under studied scenarios.
- Spare capacity note (text excerpt preserved):
  - "Spare capacity is the amount of oil that producers could technically bring to market immediately if prices (and politics) justified it. The evidence shows that when officially reported spare capacity drops below 2 million barrels per day, oil prices start to increase sharply."

### IV. Oil Demand — sectoral production and scenarios
- Sectoral structure:
  - Three sectors require oil: nontradables (superscript N), tradables manufacturing (superscript T), and consumption (superscript C). General notation J ∈ {N,T,C}.
- Baseline production/consumption aggregator (CES with quasi-share and adjustment costs):
  - Baseline production function (preserved formula):
    - Z_Jt = ( (1−η_J)^{1/ǫ_d} (M_Jt)^{(ǫ_d−1)/ǫ_d} + (η_J)^{1/ǫ_d} (O_Jt)^{(1−G_JO,t)}^{(ǫ_d−1)/ǫ_d} )^{ǫ_d/(ǫ_d−1)}
    - M_Jt = (K_Jt)^{1−α} (L_Jt)^α
    - G_JO,t = φ_O / 2 * ( (O_Jt − O_Jt−1) / O_Jt−1 )^2
  - Features:
    - η_J is quasi-share parameter for oil.
    - ǫ_d is elasticity of substitution (long-run price elasticity of oil demand), assumed equal across sectors in baseline.
    - Adjustment cost G_JO,t makes rapid variation in oil use costly, lowering short-run elasticity relative to ǫ_d.
- Growing Elasticity Scenario:
  - Same functional form as baseline, but the long-run elasticity ǫ_d is replaced by time-varying ǫ_d,t given by:
    - log(ǫ_d,t) = log(ǫ_d) + ǫ_pǫ log( p_O,avg_t / p_O ).
  - Parameter ǫ_pǫ equals 0 in Baseline, and equals 1 or 2 in the Growing Elasticity Scenario.
  - For ǫ_pǫ = 1, a doubling of the oil price relative to initial steady state leads to a doubling of the long-run price elasticity of oil demand.
- Entropy Boundary and Falling Elasticity Scenarios:
  - Alternative production function with Stone-Geary term representing an entropy boundary (preserved formula excerpt):
    - Z_Jt = ( (1−η_J)^{1/ǫ_Jd} (M_Jt)^{(ǫ_Jd−1)/ǫ_Jd} + (η_J)^{1/ǫ_Jd} ( O_Jt (1−G_JO,t)^{−β ( ̄O_J / ̄M_J ) ̃M_Jt } )^{(ǫ_Jd−1)/ǫ_Jd} )^{ǫ_Jd/(ǫ_Jd−1)}
  - Interpretation of parameters:
    - ̄O_J / ̄M_J denotes initial steady state ratio of oil inputs to other factor inputs.
    - β denotes proximity of the entropy boundary to that ratio (β = 0 reverts to standard specification (2); as β → 1 the initial steady state moves closer to the boundary).
    - ̃M_Jt denotes macroeconomic scale of production measured by capital-labor bundle; producers take ̃M_Jt as exogenous when choosing inputs (in equilibrium ̃M_Jt = M_Jt).
  - Key mechanistic implication:
    - Production isoquants become upward-sloping before approaching the entropy boundary, reducing economically feasible region; substitutability between oil and other inputs is limited by boundary.
  - Long-run elasticity becomes time-varying and can decline towards zero after an oil supply shock:
    - ε_Jd,t = ǫ_Jd ( O_Jt / M_Jt − β ̄O_J / ̄M_J ) / ( O_Jt / M_Jt ) < ǫ_Jd.
  - Reduced-form Falling Elasticity Scenario:
    - log(ǫ_d,t) = log(ǫ_d) + ǫ_oǫ log( O_avg_t / O ), where O_avg_t = ( O_t ( O_avg_{t−1} )^3 )^{1/4}.
    - This captures the notion that available quantities of oil could affect elasticities of substitution in the opposite direction to price effects in the Growing Elasticity Scenario.
  - Practical note:
    - Results for Falling Elasticity Scenario will be presented alongside Entropy Boundary Scenario partly because of computational limits when solving the model under the Entropy Boundary Scenario.

### V. Scenarios enumerated (as defined in the text)
- Baseline Scenario:
  - A negative oil supply shock where the reduction in trend growth rate of world oil output is persistent and relatively modest at 1 percentage point.
  - CES aggregators used; elasticities constant (except short-run effects from adjustment costs).
- Growing Elasticity Scenario:
  - Long-run price elasticity of oil demand increases with the oil price (parameter ǫ_pǫ = 1 or 2).
  - For ǫ_pǫ = 1: doubling of oil price leads to doubling of long-run elasticity.
- Entropy Boundary Scenario:
  - Explicit Stone-Geary-type boundary in factor space limits substitutability; elasticity of substitution declines with scarcity (parameter β controls proximity).
- Falling Elasticity Scenario:
  - Reduced-form where price elasticity of oil demand is an increasing function of oil availability (parameter ǫ_oǫ).
- Technology Externality Scenario:
  - Oil provides external productivity benefits not fully reflected in cost shares; output contribution of oil is higher than indicated by cost share.
- Larger Shock Scenario:
  - Reduction in growth rate of world oil production equals 4 percentage points (vs 1 percentage point in Baseline).

*Source: _wp12256 - 1. Baseline Scenario (PDF chapter/section) — content excerpt provided from the source PDF.*

### 4.  Technology Externality Scenario

### 4.  Technology Externality Scenario

### Production function specification
- The production function takes the form (equation (6) reproduced in source) involving parameters η_J, ǫ_J^d, ξ_J, and an oil-augmenting technology term:
  - The term  ̃O_J_t / ̄O_J  raised to ξ_J represents oil-augmenting technology, where ̄O_J denotes steady state oil use and ̃O_J_t represents actual oil use.
  - Agents treat ̃O_J_t as external when equating the value of the marginal product of oil to the price of oil, while in equilibrium ̃O_J_t = O_J_t.
  - The specification implies that the cost share of oil remains below its output contribution when ξ_J > 0.
  - Beneficial effects of oil under this specification are shared by all factors of production, analogous to other factor-augmenting technological change.

### World oil market equilibrium
- Market clearing condition for the world oil market:
  - Σ_{i=1}^6 O^sup_t(i) = Σ_{i=1}^6 [O^N_t(i) + O^T_t(i) + O^C_t(i)] (equation (7)).
- The world oil price adjusts to equilibrate oil supply and oil demand.

### Calibration
- Elasticities:
  - Long-term price elasticity of oil demand in both production and consumption assumed to equal 0.08.
  - Short-term elasticity, reflecting interaction of long-term elasticity and adjustment costs, is around 0.02.
  - These elasticities are consistent with estimates for 1990—2009 in Helbling and others (2011) and with Bayesian estimation in Benes and others (2012).
- Oil contribution and cost share:
  - In the baseline the contribution of oil to output is determined by the oil cost share.
  - Based on historical data for six regions, the oil cost share has been calibrated at 2 to 5 percent, depending on sector and region.
- Balanced growth assumption:
  - Model assumes balanced growth, implying long-run income elasticity of oil demand equal to one.
  - This contrasts with Helbling and others (2011) who estimate a long-run income elasticity of around one third at the world level (short-term income elasticity 0.68) based on post-1990 data.
- Oil supply elasticities and specification choices:
  - Literature estimates for short-run price elasticities of supply (ability to utilize spare capacity) between 0.05 and 0.15 (Benes and others (2012)).
  - Long-run price elasticities corresponding to coefficient ǫ_s estimated between 0.005 and 0.02 (Benes and others (2012)).
  - The model omits short-run price elasticities, assuming decline in growth rate of world oil output will eliminate spare capacity.
  - Calibration sets long-run price elasticity of oil supply at ǫ_s = 0.03.
- Oil revenue allocation and fiscal treatment:
  - Prior to decline in growth rate of oil supply, 40 percent of oil revenue used to pay for intermediate goods inputs.
  - Thereafter, real extraction cost per barrel increases at a constant annual rate of 2 percent.
  - The remainder of oil revenue is oil rent, distributed between the private sector and the government.
  - In net oil-importing regions, government receives only a very small portion of the oil rent.
  - In oil exporters government is assumed to receive 90 percent of oil rent.
  - Governments are assumed not to immediately spend additional funds; they accumulate them in a U.S. dollar—based fund that is spent gradually over time at a rate of 3 percent per annum.
  - One key effect of an increase in the oil price is a dramatic increase in world savings due to the low propensity to consume out of oil revenues of oil exporters’ governments.

### Discussion of the alternative specifications: Entropy Boundary and Falling Elasticity Scenarios
- General context:
  - Standard economic view: elasticities of substitution between oil and other factors are higher in the long run than in the short run.
  - Reasons:
    - Adjustment costs drive short-run elasticity below constant long-run elasticity ǫ_d.
    - For persistently very high oil prices, ǫ_d may grow with oil prices (Growing Elasticity Scenario).
  - Contrasting natural science objections:
    - Claims that constant or growing long-run elasticity is inconsistent with historical facts (Smil (2010)), practical limits to substitution (Ayres (2007)), or the laws of thermodynamics—entropy (Reynolds (2002)).
- Entropy boundary formalization:
  - Reynolds’ entropy boundary is formalized as a Stone-Geary production function requiring oil use to exceed a certain minimum multiple of other factors.
  - Implications:
    - After an oil supply shock: elasticities are very low in the short run (adjustment costs), significantly higher in the medium run, but potentially much lower again in the long run if the shock is sufficiently large because of finite limits to substitution of machines (and labor) for oil.
    - The Falling Elasticity Scenario attempts to capture this logic in reduced form.
- Physical/engineering argument:
  - Entropy pertains to energy broadly, affecting energy-capital/labor factor space.
  - The Second Law of Thermodynamics implies capital substituting for energy needs a continuing minimum energy input to remain useful; only energy in excess of that minimum adds to output.
  - This places a boundary on accessible factor space; near-zero energy input is not an option.
  - As factor use approaches that boundary, elasticity of substitution between energy and other factors must go to zero.
- Relation between oil and energy:
  - If oil and other forms of energy must be used in proportions that cannot change sufficiently or rapidly, an entropy boundary for energy implies an entropy boundary for oil.
  - Critical questions:
    - Can other energy sources technically substitute for oil over realistic time horizons (years rather than decades) and at required scale?
    - Do such energy sources have their own supply limitations?
  - Hirsch and others (2005) estimate a lead time of at least 20 years to prepare alternatives to an oil-based economy for the U.S., with shorter preparation times implying serious transition problems.
  - For the automotive sector, alternatives include natural gas and electricity, especially in densely populated areas.

### Energy alternatives and supply limitations
- Renewable electricity (solar and wind):
  - Intermittency limits substitution for other forms of electricity generation at required scale.
  - Electricity grids collapse when supply cannot match demand to within around 0.5 percent.
  - On current knowledge, solar and wind cannot supply more than 20%-30% of overall electricity without causing serious grid stability problems.
  - Storage or smart grids might raise this percentage, but at great cost and not to the point where intermittency ceases to be an issue altogether.
  - Solar and wind production/operation depend on oil-based components, oil-based transportation infrastructure, and costly backup fossil-fuel power plants to match demand when there is no wind or sun.
  - These issues contribute to much lower EROEI for renewables compared with conventional oil.
- Biofuels:
  - More substitutable for oil than electricity, but blending limits typically 5% to 15%.
  - Problems include extremely low EROEI, heavy water use, and competition with food production.
- Coal, natural gas, nuclear:
  - Coal:
    - Several authors claim coal reserves have been greatly overstated in a number of countries, putting global peak of coal production about 20 years away, with some countries reaching peak much earlier.
    - Attempted large-scale substitution toward coal would accelerate the peak.
  - Natural gas:
    - Global gas production peak may be further away, especially with hydraulic fracturing (“fracking”).
    - In the United States, additional gas production from fracking has been budgeted for planned fuel switch from coal to natural gas in electricity generation.
    - Fracking faces environmental pollution concerns and has been stopped in some jurisdictions.
    - Fracking wells and fields exhibit extremely fast decline rates and require constant new drilling, raising extraction costs.
    - Berman (2012) documents potential acceleration of sector-wide average decline rates and overstatement of field reserves; if correct, natural gas prices could rise rapidly, reducing cost advantage over oil and the incentive to switch.
    - Switching to electricity from natural gas requires building costly power plants with amortization periods of 30 years or more.
    - Direct switch to natural gas as a transportation fuel requires installation of a costly network of filling stations.
  - Nuclear:
    - Dittmar (2011) estimates that large-scale substitution toward nuclear power would hit a peak in uranium production in short order; this finding is controversial with counterarguments about reactor types eliminating fuel supply problems.
    - Worldwide trend appears to move away from nuclear power due to fears of low-probability, high-cost events such as Fukushima.
- Summary finding:
  - Other non-renewable energy sources may also have supply limits, and there is at least a possibility that they may not be able to provide energy security over the long run.

*Source: _wp12256 - 4.  Technology Externality Scenario*

### 2.  Technical Substitutability

### 2.  Technical Substitutability

### A. Limits to technical substitutability: overview
- Main uses of oil today: as a liquid transportation fuel and as a feedstock for the chemical industry.
- Critical considerations for technical substitutability (relative to any specific application): storability, transportability, and the ability to deliver useful energy.
- Example: impossibility of running an airplane with coal due to coal’s physical properties rather than simply its energy content.
- Transportation:
  - Properties of oil/liquid fuels in transportation are far superior to alternatives.
  - Transition to transportation infrastructure based on electricity, natural gas and/or liquid fuels derived from non-oil sources may be technically possible via retrofits or new equipment but:
    - Would be enormously expensive in terms of dollars, in terms of energy, and most importantly in terms of time.
    - Would require several decades.
    - Cited scientific evidence indicates this is time that may not be available (Hirsch and others (2005), UK Energy Research Centre (2009)).
  - Note: Gas filling stations require significantly greater safety precautions than conventional filling stations.
  - Coal-to-liquids or gas-to-liquids industries have not been established on a significant scale except in countries facing economic sanctions or economic isolation.
- Chemical feedstock:
  - Oil derivatives are present in virtually every product consumed either directly or via mining, transportation, or processing.
  - In most cases there is no easy substitute for oil derivatives, though in some specific cases chemicals can be derived from coal or gas instead.

### B. Growing Elasticity Scenario: rationale and mechanics
- Rationale:
  - Some substitution technologies (e.g., gas-powered vehicles; to a lesser extent coal-to-liquids and gas-to-liquids) are technically feasible.
  - Therefore price elasticities of demand may be able to rise for a number of years despite supply limitations and entropy-imposed limits on economizing oil use.
  - It is impossible to determine ex ante which effects on price elasticities will dominate or for how long, motivating inclusion of the Growing Elasticity Scenario.
- Mechanism in simulations:
  - Price elasticity of demand for oil ǫ_{d,t} is elastic with respect to the oil price per equation (3).
  - Cases shown: ǫ_p^ǫ = 1 (red) and ǫ_p^ǫ = 2 (green); focus often on ǫ_p^ǫ = 2.
- Key simulated outcomes (case ǫ_p^ǫ = 2):
  - Oil price needs to rise by half as much as in the Baseline Scenario to bring about necessary substitution.
  - Effects on GDP are positive everywhere relative to Baseline:
    - Roughly 50 percent smaller contractions in oil exporters, the United States and the euro area.
    - In the Rest of the World, an 8 percent output loss over 20 years (Baseline) turns into a 2 to 3 percent output gain.
  - Drivers of Rest of the World turnaround:
    - Surge in goods exports to oil importers (emerging Asia and Japan benefit disproportionately).
    - Surge in investment demand due to lower world real interest rates; particularly strong in emerging Asia because of a higher steady state investment-to-GDP ratio.
  - Global current account imbalances are less severe: smaller surpluses for oil exporters and emerging Asia, and smaller deficits for large oil importers.

### C. Technology Externality Scenario: alternative production-function specification
- Motivation:
  - Conventional production functions imply equality of cost shares and output contributions of oil, leading to the conclusion that oil (with historically low cost share around 3.5% for the U.S. economy) cannot cause massive output contraction.
  - Counterarguments:
    - Permanent sharp oil price rises could raise cost shares enough to be consequential.
    - Alternative production functions based on engineering and thermodynamics suggest output contributions of energy/oil need not equal cost shares (Ayres and Warr (2005, 2010); Hall and Klitgaard (2011); Kümmel (2011); Kümmel and others (2002)).
- Model implementation:
  - Oil enters externally in a similar fashion to technology; output contributions of oil can exceed cost shares when ξ_J > 0.
- Simulation assumption illustrated:
  - Contribution of oil to output set at 25 percent in the tradables sector and 20 percent in the nontradables sector, rather than 5 percent and 2 percent as in the baseline.
- Key simulated outcomes:
  - Oil prices increase by almost 400 percent after 20 years (versus 200 percent in Baseline).
  - Deterioration in all oil-importing regions’ GDP larger by around a factor of three relative to Baseline.
  - With the specification both oil and oil-dependent technologies have very low elasticity of substitution with other factors, so sizeable contraction in oil output cannot easily be compensated by replacements.
  - Oil importers’ current accounts deteriorate in the longer run by almost twice as much as in Baseline.
  - World real interest rates drop by approximately twice as much as in Baseline.

### D. Simulation framework and Baseline Scenario: setup and core results
- Simulation design:
  - Variables shown relative to trend where applicable.
  - First column: world oil supply, the real oil price (in terms of U.S. goods), and the world average real interest rate.
  - Second column: real GDP, real absorption, and current account-to-GDP ratio for oil exporters.
  - Third and fourth columns: same three variables for the United States plus Euro Area region, and for the Rest of the World.
  - Aggregations use purchasing power parity (PPP) weights.
  - Shock year denoted τ; agents are surprised by the shock but thereafter perfectly foresee future evolution of world oil production.
- Baseline shock:
  - Decline in the average growth rate of world oil production by 1 percentage point below its historical trend growth rate starting in year τ, with eventual return to the initial growth rate in year τ+30.
  - For technical reasons it is not possible to simulate a completely permanent shock to this growth rate.
- Baseline key dynamics and magnitudes:
  - Shock generates an immediate oil price spike of over 60 percent.
  - Because the decline is persistent, real oil price continues to increase: cumulative oil price increases over 10- and 20-year horizons amount to just over 100 percent and 200 percent, respectively.
  - Reduced oil availability and higher oil prices:
    - Reduce GDP levels and enlarge current account deficits in oil importers.
    - Cause a wealth transfer from oil importers to oil exporters, affecting trade and capital flows.
  - Oil exporters:
    - Experience sustained increases in income and wealth.
    - Domestic absorption increases ahead of GDP, at an initial rate of over 2 percent annually.
    - Higher spending causes upward domestic price pressures and a large real appreciation (“Dutch disease”).
    - Output in tradables (other than oil) reduces, lowering GDP by up to 7 percent below trend over the first five years, and by almost 10 percent after 20 years.
    - Current account improvement up to 4 percent of GDP in the very short run and almost 8 percent after 20 years; improvement due entirely to higher value of oil exports.
    - Goods exports fall substantially relative to GDP; non-oil current account deteriorates but government low propensity to consume from oil fund limits deterioration.
  - Oil importers:
    - Absorption contracts over time due to negative wealth effect, at an average rate of around 0.5 percent per annum.
    - GDP declines moderately, by 0.2 to 0.4 percent per annum.
  - World real interest rates:
    - Gradually drop; after 20 years are 60 basis points below their initial value.
    - Mechanism: oil exporters’ additional oil revenue accrues primarily to governments, leading to higher saving (reminiscent of international lending boom in 1970s/1980s).
  - Global imbalances:
    - Worsen over short to medium term.
    - United States and euro area current accounts deteriorate immediately.
    - Other regions’ current accounts strengthen for a lengthy transition (they export more to oil exporters) but eventually deteriorate.
    - Long-run effects modest: oil importers’ current account-to-GDP ratios on average deteriorate by at most a little over 1 percentage point by year τ+20, explained by relatively low aggregate cost share of oil.

### E. Entropy Boundary Scenario and Falling Elasticity Scenario: sensitivity to substitution limits
- Entropy Boundary Scenario (technology per equation (4)):
  - Simulations for β ∈ {0, 0.3, 0.6, 0.9}; β = 0 identical to Baseline.
  - Larger β implies tighter entropy boundary (closer to initial steady state factor allocation) so substitution away from oil becomes harder faster.
  - Observations:
    - Average elasticity of substitution ε_{d,t} moves closer to zero as supply constraint worsens.
    - For β = 0.9 oil price increases by almost 300 percent after 20 years (versus 200 percent in Baseline).
    - Oil exporters experience larger positive wealth effects, larger absorption, larger real exchange rate appreciation, larger initial “Dutch disease” output contraction, but eventually larger rebound as governments spend larger accumulated surpluses.
    - Oil importers experience worse contractions in absorption and output when economy is closer to entropy boundary; current account imbalances get larger but size of effects is fairly small.
    - Computational note: Entropy Boundary Scenario simulations relied on numerical linearization (unlike other fully nonlinear simulations), which understates real effects when oil prices rise to very high levels.
- Falling Elasticity Scenario (reduced-form relation per equation (5)):
  - Captures same idea as Entropy Boundary Scenario by relating price elasticity of demand to quantity of available oil.
  - Worst-case in Figure 6:
    - Overall elasticity of substitution declines to a level very similar to worst case in Figure 5.
    - Increase in oil price is significantly smaller than Entropy Boundary worst case, at around 250 percent after 20 years.
    - Output effects are significantly worse, especially in Rest of World where reduction in annual GDP growth rate rises from 0.4 percent to 0.6 percent.

*Italic: Source: _wp12256 - 2.  Technical Substitutability*

### 1.2 percentage points after 20 years.

### _wp12256 - 1.2 percentage points after 20 years.

### Larger Shock Scenario
- Several studies conclude world oil production is currently on a temporary and fluctuating plateau and forecast future decline rates of around 2 percent per annum.
- Scenario parameters:
  - Consider a 3.8 percent rather than 1 percent annual decline in world oil output growth.
  - Given an initial growth rate of 1.8 percent per annum in the data, this implies oil production declines by 2 percent annually (except for the small supply response to higher oil prices).
  - Real extraction costs per barrel increase by 4 percent annually rather than 2 percent.
- Key simulated effects (relative to baseline):
  - Longer-term output and current account effects are approximately four times as large as in the baseline.
  - Declines in absorption in oil importers average around 2 percent annually over the period shown, rather than 0.5 percent as in the baseline.
  - Annual GDP growth rates in the United States and the euro area drop by around one percentage point, rather than 0.25 percentage points as in the baseline.
  - Current account deteriorations in oil importers average 5 percentage points of GDP on average in the long term in both the United States and the euro area.
- Oil price implications:
  - Supply reductions of this magnitude require a more than 200 percent increase of the oil price on impact, and an 800 percent increase over 20 years.
  - Relative price changes of this magnitude would be unprecedented and would almost certainly have nonlinear effects on GDP that the model cannot capture adequately.
- Financial/monetary consequences:
  - The implied increase in world savings is so large that several regions could, after the first few years, experience nominal interest rates that approach zero, creating difficulties for the conduct of monetary policy.

### Combined Downside Scenarios (Technology Externality + Larger Shock)
- The paper analyzes the combination of the Technology Externality Scenario with the Larger Shock Scenario.
- Model simulation outcomes:
  - Real oil prices increase by over 400 percent on impact, and by around 1400 percent after 20 years.
  - Despite extreme price increases, there is no sharp short-run crisis in the model; the subsequent reduction in annual GDP growth rates in oil importers equals a steady, crisis-free 3 percentage points.
- Real-world response mechanisms to extreme price increases could include:
  - A much more urgent search for alternatives to oil, reflected in much higher elasticities of substitution.
  - A much sharper contraction in aggregate demand (not captured by the model); if output contracted far more sharply the required increase in oil prices could be limited by demand destruction.
- The model cannot fully capture possible nonlinear demand-side contractions; the question is revisited in Section IV.I of the source.

### Combined Downside and Growing Elasticity Scenario
- Combines the worst case of the combined downside scenario with the Growing Elasticity Scenario.
- For the case of ǫ p ǫ = 2:
  - The increase in the oil price is only half as large, and so are approximately the output effects.
  - Even so, this still yields an oil price increase of 800 percent after 20 years.
- General conclusion:
  - Unless the increase in the price elasticity of demand in response to higher oil price is extreme, the worst downside scenarios would still force the economy to cope with unprecedented increases in oil prices.
  - A more likely real-world outcome would include not only higher elasticities of substitution but also a larger output contraction.

### The Assumption of Unitary Income Elasticity
- Model assumption:
  - The model assumes a unitary income elasticity of oil demand.
- Empirical evidence:
  - Data suggest a much lower income elasticity of around one third.
  - Much recent growth worldwide has been due to the services sector, which uses less oil per unit of output.
- Implication:
  - A low income elasticity exacerbates supply-constraint problems because low price elasticities limit substitution away from oil.
  - Illustration: if a one third of one percentage point increase in oil supply per annum supports additional GDP growth of one percentage point, then a one third of one percentage point decrease in oil supply growth would reduce GDP growth by a full percentage point.
  - Declines in oil supply growth being discussed in the literature are far larger than one third of one percentage point.

### The Assumption of Smooth Reallocation
- Model assumes smooth transition to a new equilibrium: consumers in oil exporters absorb surpluses, financial markets efficiently intermediate savings, businesses reallocate resources flexibly, and workers accept lower real wages.
- Real-world caveats:
  - Historical experience suggests caution about efficient intermediation of large net capital flows from oil exporters’ governments; inefficient allocation could increase risk premia in vulnerable borrowers’ regions, preventing them from taking advantage of lower risk-free interest rates.
  - If private and public saving rates increase in oil-exporting countries, the problem could intensify.
  - Real economies have many interdependent industries; sectors like car manufacturing, airlines, trucking, long-distance trade, and tourism would be affected earlier and more seriously than others.
  - Large-scale bankruptcies in affected industries could spread via corporate and bank balance sheets, reducing credit availability.
  - Labor market flexibility has helped absorb past oil shocks (Blanchard and Galí (2007)), but larger and more persistent price increases could lead workers to resist real wage cuts, raising the output cost of the shock during the transition.
  - Some oil exporters might withhold an increasing share of stagnating or decreasing oil output for domestic use (e.g., fuel subsidies to support energy-intensive industries and forestall unrest); if so, oil available to importers could shrink faster than world oil output, worsening growth consequences for importers.

### Conclusion
- The extent to which persistent oil scarcity could constrain global economic growth and current account imbalances depends critically on a few key factors:
  - If the trend growth rate of oil output declined only modestly and the economy is well represented by a standard production function in capital, labor and oil, world output would eventually suffer but perhaps not dramatically.
  - If substitutability between oil and other factors of production increased with oil price, the effect would be smaller.
  - If reductions in oil output align with more pessimistic scientific studies, effects could be extremely large.
  - Standard production functions may miss important aspects of oil’s economic role under scarcity; three possibilities discussed:
    - An entropy-imposed lower limit of oil use when substituting away from oil.
    - Oil’s contribution to output could be much larger than its cost share because oil is an essential precondition for many modern technologies.
    - The income elasticity of oil demand might be around one third rather than one.
  - If two or more aggravating factors occur in combination, effects could range from dramatic to outright implausible.

*Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12256.pdf*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12256.pdf_