## 12. GDP (in logs) Forecast with Error Bands ## Source details **Canonical URL:** [12. GDP (in logs) Forecast with Error Bands](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12109.pdf) ## Other formats - [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12109.pdf.md) - [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12109.pdf.json) --- ### Introduction and key result - Recent literature: forecasting oil prices is difficult; Alquist, Kilian, and Vigfusson (2011) conclude commonly employed forecasting techniques cannot consistently beat a random-walk out-of-sample. - Two supply views combined in the paper: geological (Hubbert/Deffeyes) and economic/technological (price-responsive supply). - Key result: - Combining geological and economic/technological views in a simple macroeconomic model improves out-of-sample forecasts for oil prices and production relative to a random walk and to historical agency/advocate forecasts. - The geological, price-insensitive component of supply captures the underlying trend in prices and is the key reason for the model’s predictive accuracy. - Shocks to excess demand for goods and to demand for oil explain persistent and sizeable deviations from the underlying trend. - Projection highlighted: near doubling of real oil prices over the coming decade, with substantial uncertainty due to limited knowledge about ultimately recoverable reserves and long-run price elasticities. ### Historical forecasts and stylized facts - EIA forecasts (2001–2010) trend: almost continuous decline; forecast for 2020 declined by over 20%, or by 25 million barrels per day. - Real oil price normalization: real oil price in 2011 equals 104 (average 2011 nominal oil price equalled US$ 104). - Historical production growth benchmark: 1.5%-2% per annum growth that was not regained after 2005; world oil production has been on a plateau since. - Comparison with proponents: - Example: EIA 2001 overestimated 2010 by 8.7 Mbd; Colin Campbell 2003 underestimated by 4.5 Mbd. ### Model structure and estimation - Model components: - World oil demand equation. - World oil supply combining Hubbert linearization and price-sensitive supply. - Trend and gap equations for world GDP (separating output gap, potential level, and potential growth). - Data and sample: - Annual data 1983–2011; lags back to 1972 for oil prices. - Variables: world real GDP (IMF data), real quantity of oil produced (IEA definition), real oil price (U.S. CPI based). - Estimation method: - Nonlinear Bayesian estimation with priors informed by other studies to aid identification given short sample and nonlinearity. - Table 1 parameter posterior modes (selected): - Oil α_s: 507.6483 - Supply β_1: 0.2427 - β_2: 0.6238 - β_3: 0.0546 - Demand γ_1: 0.9098 - γ_2: 0.0213 - γ_3: 0.06 - Output λ_1: 0.8987 - g (steady-state world annual growth rate of potential GDP): 0.04 - ρ (average annual growth rate of real oil prices): 0.07 ### Oil supply specification and implications - Supply equation (levels with auxiliary relationship) as displayed: - qt/Qt = αs (507.7) − β1 (0.243) Qt + β2 (0.624) pt + β3 (0.056) (1/3) Σ_{k=4}^{6} p_{t−k} - Qt = Qt−1 + qt - Implied price elasticities of supply (levels-dependent): - Pre-2003: elasticity w.r.t. current prices ≈ 0.05; elasticity w.r.t. lagged prices well below 0.01. - Recent period: elasticity w.r.t. current prices ≈ 0.15; elasticity w.r.t. lagged prices ≈ 0.02. - Economic interpretation: - Positive β2 and β3 flatten and shift upward the Hubbert linearization, delaying and raising the production peak. - Contemporaneous response dominated by use of spare capacity rather than expansion of long-run capacity. ### Oil demand specification and implications - Demand equation (differences form) as displayed: - Δln qt = αd (−0.018) + γ1 (0.910) Δln gdp_t − γ2 (0.021) ln(p_t / p_{t−1}) − γ3 (0.06) (ln(p_{t−1} / p_{t−10}) / 9) - Estimated parameters shown: αd = −0.018; γ1 = 0.910; γ2 = 0.021; γ3 = 0.06. - Elasticities: - Estimated short-run price elasticity of demand ≈ 0.02. - Estimated long-run (after 10 years) price elasticity of demand ≈ 0.08. - Elasticities allowed to rise up to 2.5 times at very high oil prices (scaling examples provided in text). ### GDP potential, output gap, and feedbacks - Potential GDP level dynamics: - ∆lnpot_t = lng_t + ǫ_pot_t - lng_t = λ1 (0.899) lng_{t−1} + (1−λ1) g (0.04) − λ2 (0.005) (∆lnp_t − ρ (0.07)) − λ3 (0.005) (∆lnp_{t−1} − ρ (0.07)) + ǫ_g_t - λ1 posterior mode: 0.8987 implies highly persistent deviations. - Output gap dynamics: - ∆lny_t = (φ1 (0.956) − 1) lny_{t−1} + φ2 (0.257) ∆lny_{t−1} − φ3 (0.005) (∆lnp_t − ρ (0.07)) − φ4 (0.005) (∆lnp_{t−1} − ρ (0.07)) + ǫ_y_t - φ1 posterior mode: 0.9556; φ2 posterior mode: 0.2565. - Interpretation: - Oil price growth above ρ (0.07) has a small but significant negative effect on potential growth. - Oil price increases reduce excess demand; both gap and potential growth effects are persistent due to high lag coefficients. ### Impulse Response Functions (IRFs) — summary of shock effects - Five shocks analyzed: oil supply, oil demand, output gap, potential growth rate, potential level. - Oil supply shocks: - Relatively small and transitory in recent data. - Negative supply shock produces a five year cycle of output below potential. - Contraction in GDP is about half the contraction in oil supply. - Very low short-run elasticities cause oil prices to spike dramatically: increase by more than 30 times the magnitude of the supply contraction, then return to trend. - Oil demand shocks: - Larger and more persistent contributors to high oil prices pre-Great Recession and in partial recovery. - More persistent effects on oil production and GDP than supply shocks. - Output gap shocks: - Main shocks explaining oil price behavior during the crisis; large, persistent, and negative during the Great Recession, explaining roughly half of the 2009 oil price drop according to the model. - Potential growth and potential level shocks: - Potential growth shocks are smaller in magnitude than output gap shocks but much more persistent. - Potential level shocks contribute little to overall variability but, when present, effects are highly persistent. ### Historical decomposition (post-2002) — oil prices and production - Oil prices: - By 2008, oil prices were 60% higher than predicted using 2002 information. - Early drivers: very strong oil demand (booming emerging economies) and a positive world output gap. - From 2005 onward world oil production plateaued; by 2008 insufficient supply became the major factor behind high prices. - Great Recession (2009) price drop: model attributes roughly half to a negative output gap shock and half to a positive oil supply shock (increase in excess capacity). - By 2011, real prices regained 2008 average levels, largely attributed to negative oil supply shocks. - Underlying upward trend in oil prices would occur even in a no-shocks scenario due to Hubbert coefficient β1. - Oil production: - Except for 2009, production was consistently above the model’s 2002-predicted trend. - Major drivers of above-trend production: booming oil demand and positive output gaps (2006–2008); oil supply shocks minor. - Price mechanism added to Hubbert linearization is key to explaining post-2003 deviations from pure geological explanations. ### Relative forecast performance (out-of-sample rolling forecasts 2001–2011) - Predicted average annual growth rates of oil output: below EIA historical forecasts, but above pure geological proponents’ forecasts. - Forecast trade-off: - Positive trend in oil production requires a large increase in real oil price — nearly doubling over the coming decade to maintain modest output expansion. - Such high prices could be economically damaging (e.g., threaten airlines, long-distance tourism). - RMSE comparisons (period 2003–2011) — selected statements: - Production RMSEs: lower than EIA historical forecasts at all but the one-year horizon; less than half as large at longer horizons. - Prices RMSEs: model gains larger; at the five-year horizon the model’s RMSE is about a quarter of a random walk RMSE. - GDP RMSEs: gains are substantial though less dramatic. - Table 2 entries preserved exactly in source (note: table entries as presented). ### Current forecasts (2012–2021 projections) - Oil production (Figure 10): - Point forecast mean annual growth rate ≈ 0.9% over the coming decade. - Historical growth reference: around 1.5%–2.0%. - 90% confidence interval: lower band indicates flat oil output for the decade; upper band indicates annual output growth rates almost as large as historical ones. - Point forecast growth rate approximately as large as recent EIA forecasts, but with much higher oil price forecast. - Oil prices (Figure 11): - Point forecast implies near doubling of real oil prices over the coming decade. - Even the lower 90% confidence interval shows prices increasing over recent high levels. - Concern: world economy has not experienced such sustained high prices historically; potential for nonlinear, convex GDP effects at very high prices. - GDP (Figure 12): - 2011 world real GDP normalized to one. - Point forecast: roughly 4% per annum real GDP growth. - 90% confidence interval: average growth rates as low as 3% per annum and as high as 5% per annum. - Sensitivity: at more pessimistic coefficient values for recoverable reserves and elasticities, average world growth would be one percentage point lower. ### Alternative scenario — tighter supply response (β2 lower 90% band) - Baseline β2 = 0.624; alternative β2 = 0.505. - Effects reported: - Average oil output growth drops from 0.9% to 0.5% per annum. - Oil price fully doubles by 2021. - GDP path approximates the lower 90% confidence band — one percentage point lower world output growth due to this single parameter change. ### Open questions, nonlinearities, and research priorities - Two key questions under lower oil output growth hypothesis: - Importance of availability of oil inputs for continued overall GDP growth. - Substitutability between oil and other factors of production. - Debate on energy’s contribution: - Conventional production functions imply low vulnerability due to low cost shares (U.S. oil cost share ~3.5%; total energy cost share ~7% for U.S.). - Natural-science–based aggregate production functions (Ayres and Warr; Hall and Klitgaard; Kümmel) suggest energy output contributions up to around 50%. - If the latter are correct, lower oil output growth implications for GDP could be very large. - Elasticities of substitution concerns: - Possible pattern: very low elasticities short run; higher elasticities medium run; much lower elasticities long run if supply shock is large due to finite substitutability. - Incorporating such nonlinear elasticity behavior would increase forecasted oil prices after large, persistent supply shocks and magnify GDP effects. - Research priorities: studying nonlinear output responses, energy’s true contribution to GDP, and long-run substitutability limits. ### Conclusion — main takeaways - The paper’s world oil market model combining Hubbert linearization and price-responsive supply: - Outperforms competing models in out-of-sample prediction of oil production and oil prices. - Provides partial support for both geological and economic/technological views while rejecting pure extremes. - Future outlook per model: - Small further increases in world oil production projected, but require a near doubling, permanently, of real oil prices over the coming decade. - Modeled GDP effects of such prices are perceptible but small and transitory based on historical data. - Caveats: - Potential nonlinear, convex effects of very high oil prices on GDP are a major concern. - Possibility that lack of oil availability acts like a negative technology shock. - Further study of nonlinear output responses and energy’s role in production is a priority. *Source: _wp12109 - 12. GDP (in logs) Forecast with Error Bands . . . . . . . . . . . . . .* ### 1. Potential Level of GDP . . . . . . . . . . . . . . . . . . . . . . . . . 10 ### 1. Potential Level of GDP ### Major sections covered - 1. Potential Level of GDP . . . . . . . . . . . . . . . . . . . . . . . . . . 10 - 2. Potential Growth Rate of GDP . . . . . . . . . . . . . . . . . . . . . . . 10 - 3. Output Gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 ### Analysis (Section IV) - IV. Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 - A. Impulse Response Functions . . . . . . . . . . . . . . . . . . . . . . . . 11 - B. Interpretation of History . . . . . . . . . . . . . . . . . . . . . . . . . 12 - C. Relative Forecast Performance . . . . . . . . . . . . . . . . . . . . . . 13 - D. Current Forecasts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 - E. Oil and Output - Open Questions . . . . . . . . . . . . . . . . . . . . . 15 ### Conclusion and references - V. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 - References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 ### Tables (listed) - 1. Parameter Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 - 2. Root Mean Square Errors - Comparisons . . . . . . . . . . . . . . . . . . 20 ### Figures (listed) - 1. EIA Forecasts 2001-2010 (EIA Definition of World Total Oil Supply, in Mbd)21 - 2. World Real Oil Prices and Spare Capacity . . . . . . . . . . . . . . . . 22 - 3. Colin Campbell Forecasts 2003-2010 (Campbell Definition of Regular Conven- tional Oil, in Mbd) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 - 4. Oil Production Forecasts in the Deffeyes (2005) Model (Q in gigabarrels, q in gigabarrels p.a.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 - 5. Impulse Responses (in percent level deviation from control) . . . . . . 25 - 6. Historical Residuals (in percent) . . . . . . . . . . . . . . . . . . . . . . 26 - 7. Contributions of Different Shocks to Oil Prices (in real 2011 US dollars) . . . 27 - 8. Contributions of Different Shocks to Oil Production (in gigabarrels p.a.) . . . 28 - 9. Rolling Forecasts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 - 10. Oil Output Forecast with Error Bands (in gigabarrels p.a.) . . . . . . . . 30 - 11. Oil Price Forecast with Error Bands (in real 2011 US dollars) . . . . . 31 *Source: _wp12109 - 1. Potential Level of GDP . . . . . . . . . . . . . . . . . . . . . 10* ### 12. GDP (in logs) Forecast with Error Bands . . . . . . . . . . . . . . . . . . . . . 32 ### 12. GDP (in logs) Forecast with Error Bands ### Introduction - Recent literature finds forecasts of oil prices difficult; Alquist, Kilian, and Vigfusson (2011) conclude commonly employed forecasting techniques cannot consistently beat a random-walk out-of-sample. - Two broad views of supply dynamics: - Economic/technological view: higher prices spur production and substitutes, implying prices eventually induce increased production. - Geological view: finite, easy-to-access oil is produced first, leading to increasing difficulty and cost of extraction as cumulative production grows; proponents argue a peak in conventional production is plausible before 2020. - Key result from this paper: - Combining geological and economic/technological views in a simple macroeconomic model improves out-of-sample forecasts for oil prices and production relative to a random walk and to historical agency/advocate forecasts. - The geological, price-insensitive component of supply captures the underlying trend in prices and is the key reason for the model’s predictive accuracy. - Shocks to excess demand for goods and to demand for oil explain persistent and sizeable deviations from the underlying trend. - Projection: both geological constraints and demand factors point to a near doubling of real oil prices over the coming decade, but substantial uncertainty remains due to limited knowledge about ultimately recoverable reserves and long-run price elasticities. ### Historical forecasts of world oil production — key observations - EIA forecasts (2001–2010) showed an almost continuous decline; forecast for 2020 declined by over 20%, or by 25 million barrels per day. - Real oil prices (2011 U.S. dollars, normalized so 2011 = 104) rose markedly after 2003 as OPEC spare capacity dropped below 2 Mbd; spare capacity below 2 Mbd is considered a critical constraining mark. - World oil production did not regain the historical growth rate of 1.5%-2% per annum after 2005 and has been on a plateau since. - Comparison with geological proponents: - Colin Campbell’s forecasts were pessimistic but closer to realized production than some EIA forecasts (example: EIA 2001 overestimated 2010 by 8.7 Mbd; Campbell 2003 underestimated by 4.5 Mbd). - Curve-fitting / Hubbert linearization approach summary: - Notation: qt = annual oil production at time t; Qt = cumulative production until t; Q̄ = ultimately recoverable reserves. - Hubbert logistic form: qt = αs Qt (Q̄ − Qt)/Q̄. - Linearized form: qt/Qt = αs − β Qt. - Deffeyes (2005) fit world data well until 2003 and predicted a peak in late 2005; post-2003 higher prices produced positive deviations from that straight-line fit, yielding a plateau rather than renewed historical growth. ### The model — overview and estimation approach - Model components: - Conventional equation for world oil demand. - World oil supply equation combining geological (Hubbert linearization) and economic/technological (price-sensitive) views. - Trend and gap equations for world GDP (reduced-form production function separating output gap, potential output level, and potential output growth). - Data and sample: - Annual data 1983–2011, with lags using data back to 1972 for oil prices. - Variables: world real GDP (IMF data), real quantity of oil produced (IEA definition), real oil price (U.S. CPI based). - Estimation: - Nonlinear Bayesian estimation techniques with priors based on other studies to aid identification given the short sample and model nonlinearity. - Table 1 (not reproduced here) summarizes key parameters, prior/posterior modes, and 90% confidence intervals. ### Oil supply (model specification and findings) - Supply equation (levels specification with auxiliary relationship): - qt/Qt = αs (507.7) − β1 (0.243) Qt + β2 (0.624) pt + β3 (0.056) (1/3) Σ_{k=4}^{6} p_{t−k} - Qt = Qt−1 + qt - Parameter interpretations and priors: - αs < 1 indicates speed of production increase in early years before depletion constrains growth. - β1 > 0 indicates effect of depleted reserves on production; prior for β1 taken from Deffeyes (2005) and given a fairly loose uniform distribution. - β2 > 0 and β3 > 0 indicate production increases with current and lagged oil prices; priors for β2 and β3 set uniformly and loosely because supply response to price is less well known. - Estimated parameters: - β1 = 0.243 (posterior mode shown in text). - Coefficients in equation displayed as αs (507.7), β1 (0.243), β2 (0.624), β3 (0.056). - Implied price elasticities of supply (depend on levels of production and prices): - Pre-2003 period: elasticity w.r.t. current prices (from β2) ≈ 0.05; elasticity w.r.t. lagged prices (from β3) well below 0.01. - Recent period: elasticity w.r.t. current prices ≈ 0.15; elasticity w.r.t. lagged prices ≈ 0.02. - Economic interpretation: - Positive β2 and β3 flatten and shift upward the Hubbert linearization, delaying and raising the production peak. - The dominant contemporaneous response to price suggests producers mainly used spare capacity to meet higher prices rather than expanding longer-run capacity via exploration/technology; this option may be limited in a future with persistently low spare capacity. ### Oil demand (specification and findings) - Demand equation (differences form): - Δln qt = αd (−0.018) + γ1 (0.910) Δln gdp_t − γ2 (0.021) ln(p_t / p_{t−1}) − γ3 (0.06) (ln(p_{t−1} / p_{t−10}) / 9) - Variables and interpretation: - Demand driven by economic activity (GDP) and oil prices; includes both current oil prices and a 10-year moving average to capture slower adjustments (e.g., vehicle stock turnover). - Priors: γ1 set tightly reflecting robust GDP–oil link; γ2 and γ3 set tightly reflecting literature consensus that short-run elasticity < long-run elasticity. - Elasticities allowed to rise up to 2.5 times at very high oil prices (with scaling examples: at average pre-2008 prices elasticities unaffected; at average 2008 and 2011 prices elasticities rise by roughly factor 1.75; at much higher projected prices out to 2021 elasticities can rise by maximally factor 2.5). - Estimated parameters and elasticities: - αd = −0.018 (displayed in equation). - γ1 = 0.910 (displayed in equation). - γ2 = 0.021 (displayed in equation). - γ3 = 0.06 (displayed in equation). - Estimated short-run price elasticity of demand ≈ 0.02. - Estimated long-run (after 10 years) price elasticity of demand ≈ 0.08. - Implication: - The combination of low price elasticities of supply and demand implies that inadequate supply growth relative to past trends must lead to much higher oil prices or economic contraction, or both. ### GDP equations and feedbacks - Reduced-form production function separates: - shocks to the output gap (transitory shocks), - shocks to potential output (permanent level shocks), - shocks to potential output growth (permanent growth shocks). - Formulation (displayed): - gdp_t = pot_t * y_t - The specification allows trend and gap declines if oil prices increase, capturing complicated interactions of oil price movements and GDP. - Identification approach: - Bayesian priors are used to help identify the three separate shocks to output given limited variation in historical data. ### Key quantitative statements and projections - Historical production growth benchmark: 1.5%-2% per annum historical growth rate that was not regained after 2005. - EIA forecast revision magnitude: forecast for 2020 declined by over 20%, or by 25 million barrels per day (2001–2010). - Normalization of real oil price figures in figures: real oil price in 2011 equals 104 (average 2011 nominal oil price equalled US$ 104). - Model projection highlighted in text: near doubling of real oil prices over the coming decade (with substantial uncertainty tied to recoverable reserves and long-run elasticities). *Source: _wp12109 - 12. GDP (in logs) Forecast with Error Bands . . . . . . . . . . . . . . . . . . . . . . . . 32* ### 1. Potential Level of GDP ### 1. Potential Level of GDP ### Model specification and key parameters - Potential GDP level dynamics: - ∆lnpot_t = lng_t + ǫ_pot_t - ǫ_pot_t is a shock to the level of potential output. - Oil prices do not enter this equation directly; their dynamic effects are captured via the potential growth rate. - Potential growth rate specification (fluctuates around exogenous long-run trend; oil price changes amplify fluctuations; oil price effects are persistent but not permanent): - lng_t = λ1 (0.899) lng_{t−1} + (1−λ1) g (0.04) − λ2 (0.005) (∆lnp_t − ρ (0.07)) − λ3 (0.005) (∆lnp_{t−1} − ρ (0.07)) + ǫ_g_t - ǫ_g_t is a shock to the growth rate of potential output. - g (steady-state world annual growth rate of potential GDP) = 0.04 (four percent). - ρ (average annual growth rate of real oil prices) = 0.07 (seven percent). - Estimated lag on lng is 0.899, implying highly persistent deviations from long-run value. ### Findings on potential growth - An oil price growth rate higher than ρ (0.07) has a small but significant negative effect on potential growth. - Both exogenous shocks ǫ_g_t and oil price fluctuations generate persistent deviations because of the high lag coefficient (0.899). ### 2. Output Gap ### Model specification and coefficients - Output gap dynamics: - ∆lny_t = (φ1 (0.956) − 1) lny_{t−1} + φ2 (0.257) ∆lny_{t−1} − φ3 (0.005) (∆lnp_t − ρ (0.07)) − φ4 (0.005) (∆lnp_{t−1} − ρ (0.07)) + ǫ_y_t - ǫ_y_t represents a shock to the level of aggregate demand. - Coefficients indicate persistence and that higher oil prices have a small but significant negative effect on excess demand. ### Implication - Fluctuations in output gap are modeled as persistent; oil price increases reduce excess demand with highly persistent effects. ### 3. Impulse Response Functions (IRFs) ### Shock categories analyzed - Five shocks: oil supply shocks, oil demand shocks, output gap shocks, potential growth shocks, potential level shocks. - IRFs shown in percent deviations from control, after trend removal. ### Key IRF findings - Oil supply shocks: - Relatively small and transitory in recent data. - Negative oil supply shock produces a five year cycle of output below potential. - Contraction in GDP is about half the contraction in oil supply. - Due to very low short-run demand and supply elasticities, oil prices spike dramatically in the short run: increase by more than 30 times the magnitude of the supply contraction, but return quickly to trend. - Oil demand shocks: - Significantly larger in size and a major contributor to high oil prices pre-Great Recession and in partial recovery. - More persistent effects on oil production and GDP than supply shocks; price effects less sharp but more persistent. - Output gap shocks: - Main shocks explaining oil price behavior during the crisis. - Large and persistent effects on GDP and oil demand. - The dominant crisis shock was negative, reducing activity and demand and contributing substantially to the steep drop in oil prices following the Great Recession. - Potential growth rate shocks: - Smaller in magnitude than output gap shocks but much more persistent effects on output and oil production. - Less dramatic effects on real oil price (gradual increase in oil demand). - Potential level shocks: - Do not contribute much to overall variability. - When present, effects on output, oil demand, and oil prices are highly persistent. ### 4. Interpretation of History (post-2002 decomposition) ### Oil prices (Figure 7 summary) - By 2008, oil prices were 60% higher than predicted using 2002 information. - Early drivers: very strong oil demand (booming emerging economies) and a positive world output gap. - Until around 2005, oil supply helped keep prices lower ceteris paribus; from 2005 onward world oil production plateaued. - By 2008 insufficient world oil supply became the major factor behind high oil prices. - Great Recession (2009) caused oil prices to drop below the 2002 forecast: - Model attributes roughly half of this drop to a negative output gap shock and half to a positive oil supply shock (increase in oil excess capacity in 2009). - By 2011, real oil prices regained their 2008 average levels, largely attributed to negative oil supply shocks. - The model indicates the underlying upward trend in oil prices would occur even in a no-shocks scenario due to the Hubbert linearization coefficient β1. ### Oil production (Figure 8 summary) - Except for 2009, production was consistently above the model’s 2002-predicted trend. - Major drivers of above-trend production: booming oil demand and positive output gaps (2006–2008); oil supply shocks played only a minor role. - Price mechanism added to Hubbert linearization is key to explaining post-2003 deviations from pure geological explanations. - Geological explanation (Hubbert linearization) accounts for strong underlying trends, especially the upward trend in oil prices. ### 5. Relative Forecast Performance ### Out-of-sample rolling forecasts (2001–2011) findings - Predicted average annual growth rates of oil output: - Below EIA historical forecasts, but above pure geological proponents’ forecasts. - Model accommodates both geological and economic/technological views; rejects pure versions of either. - Forecast trade-off: - Positive trend in oil production requires a large increase in real oil price — nearly doubling over the coming decade to maintain modest output expansion. - Such high prices could be economically damaging (e.g., threaten airlines, long-distance tourism). ### Forecast accuracy (RMSE comparisons, period 2003–2011) - Production RMSEs: - Lower than EIA historical forecasts at all but the one-year horizon; less than half as large at longer horizons. - Prices RMSEs: - Larger relative gains; at the five-year horizon the model’s RMSE is about a quarter of a random walk RMSE. - GDP RMSEs: - Gains are substantial though less dramatic. ### 6. Current Forecasts (2012–2021 projections) ### Oil production (Figure 10) - Point forecast mean annual growth rate ≈ 0.9% over the coming decade. - Historical growth rate reference: around 1.5%–2.0%. - 90% confidence interval is very wide: - Lower 90% band indicates flat oil output for the decade. - Upper 90% band indicates annual output growth rates almost as large as historical ones. - The point forecast growth rate is approximately as large as recent EIA forecasts, but the corresponding oil price forecast is far higher. ### Oil prices (Figure 11) - Point forecast implies near doubling of real oil prices over the coming decade. - Even the lower 90% confidence interval shows prices increasing over recent high levels. - World economy has not experienced such sustained high prices historically; potential for nonlinear, convex GDP effects at very high prices is a concern. ### GDP (Figure 12) - 2011 world real GDP normalized to one. - Point forecast: roughly 4% per annum real GDP growth. - 90% confidence interval: average growth rates as low as 3% per annum and as high as 5% per annum. - At more pessimistic coefficient values for recoverable reserves and elasticities, average world growth would be one percentage point lower. ### Alternative scenario on supply elasticity (β2 lower 90% confidence band) - Baseline β2 = 0.624; alternative β2 = 0.505 (drop fairly modest). - Effects: - Average oil output growth drops from 0.9% to 0.5% per annum. - Oil price fully doubles by 2021. - GDP path approximates the lower 90% confidence band — one percentage point lower world output growth due to this single parameter change. ### 7. Open Questions: Oil, Output, and Nonlinearities ### Two key questions under lower oil output growth hypothesis - Importance of availability of oil inputs for continued overall GDP growth. - Substitutability between oil and other factors of production. ### Issues raised - Conventional production functions imply equality of cost shares and output contributions of oil; historically low cost share (~3.5% for U.S. oil; total energy cost share ~7% for U.S.) has led economists to conclude limited GDP vulnerability. - Natural-science–based aggregate production functions (Ayres and Warr; Hall and Klitgaard; Kümmel) suggest energy output contributions up to around 50%, despite low cost shares. - If confirmed, lower oil output growth implications for GDP could be very large. - IMF (April 2011 WEO) DSGE simulations with oil’s output contribution far above cost share generate much larger negative output effects after permanent declines in oil output growth. ### Elasticities of substitution concerns - Questioning economists’ assumption that long-run elasticities of substitution between oil and other factors will be much higher than short-run elasticities. - Alternative plausible pattern: - Very low elasticities in the short run (rigidities, adjustment costs). - Significantly higher elasticities in the medium run. - Much lower elasticities again in the long run if there is a sufficiently large shock to growth of world oil supply (finite limits to substitutability). - Incorporating such nonlinear elasticity behavior would increase forecasted oil prices after large, persistent supply shocks and magnify GDP effects. ### 8. Conclusion ### Main points - The paper proposes and empirically evaluates a world oil market model that combines: - Hubbert linearization (Deffeyes (2005)) representing geological/resource constraints. - A price mechanism where higher oil prices increase oil output. - Empirical performance: - Model outperforms competing models in out-of-sample prediction of oil production and oil prices. - Results provide partial support for both geological and economic/technological views, rejecting pure extremes. - Future outlook per model: - Small further increases in world oil production are projected, but require a near doubling, permanently, of real oil prices over the coming decade. - Current modeled GDP effects of such prices are perceptible but small and transitory based on historical data. - Caveats and research priorities: - Potential nonlinear, convex effects of very high oil prices on GDP are a major concern. - Possibility that lack of oil availability acts like a negative technology shock (technology dependent on fossil fuel availability). - Studying nonlinear output responses, energy’s true contribution to GDP, and long-run substitutability limits will be a priority of future research. *Source: _wp12109 - 1. Potential Level of GDP* ### References ### References ### Bibliographic Sources - Alquist, R., Kilian, L. and Vigfusson, R. (2011), “Forecasting the Price of Oil”, Working Paper. - Ayres, R. (2007), “On the Practical Limits to Substitution”, Ecological Economics, 61, 115-128. - Ayres, R. and Warr, B. (2005), “Accounting for Growth: The Role of Physical Work”, Structural Change and Economic Dynamics, 16, 181-209. - Ayres, R. and Warr, B. (2010), The Economic Growth Engine - How Energy and Work Drive Material Prosperity, Edward Elgar Publishing. - Deffeyes, K. (2005), Beyond Oil: The View from Hubbert’s Peak, Hill and Wang. - Government Accountability Office (2007), “Crude Oil: Uncertainty about Future Oil Supply Makes It Important to Develop a Strategy for Addressing a Peak and Decline in World Oil Production”, Report to Congressional Requesters. - Hall, C. and Klitgaard, K. (2011), Energy and the Wealth of Nations: Understanding the Biophysical Economy, Springer Verlag (forthcoming, June 2011). - Hamilton, J. (2009), “Causes and Consequences of the Oil Shock of 2007-08”, Brookings Papers on Economic Activity, 215-261. - Hirsch, R., Bezdek, R. and Wendling, R. (2005), “Peaking of World Oil Production: Impacts, Mitigation and Risk Management”, United States Department of Energy. - Hirsch, R., Bezdek, R. and Wendling, R. (2010), The Impending World Energy Mess, Apogee Prime. - Hubbert, M.K. (1956), “Nuclear Energy and the Fossil Fuels”, American Petroleum Institute Drilling and Production Practice Proceedings, pp. 5-75. - Hubbert, M.K. (1982), “Techniques of Prediction as Applied to the Production of Oil and Gas”, in: S.I. Gass, ed., Oil and Gas Supply Modeling, Special Publication 631, Washington, National Bureau of Standards, pp. 16-141. - IMF (2011), “Oil Scarcity, Growth and Global Imbalances”, World Economic Outlook, April 2011, Chapter 3, International Monetary Fund. - Kilian, L. (2009), “Not All Oil Price Shocks Are Alike: Disentangling Demand and Supply Shocks in the Crude Oil Market”, American Economic Review, 99(3), 1053-1069. - Kümmel, R. (2011), The Second Law of Economics - Energy, Entropy, and the Origins of Wealth, Springer Verlag. - Kümmel, R., Henn, J. and Lindenberger, D. (2002), “Capital, Labor, Energy and Creativity: Modeling Innovation Diffusion”, Structural Change and Economic Dynamics, 13, 415-433. - Reynolds, D. (2002), Scarcity and Growth Considering Oil and Energy: An Alternative Neo-Classical View, Edwin Mellen Press. - Simmons, M. (2005), Twilight in the Desert: The Coming Saudi Oil Shock and the World Economy, Hoboken, New Jersey: John Wiley & Sons. - Smil, V. (2010), Energy Transitions - History, Requirements, Prospects, Praeger. - Sorrell, S., Miller, R., Bentley, R. and Speirs, J. (2010), “Oil Futures: A Comparison of Global Supply Forecasts”, Energy Policy, 38, 4990-5003. - UK Energy Research Centre (2009), “Global Oil Depletion - An Assessment of the Evidence for a Near-Term Peak in Global Oil Production”. - United States Joint Forces Command (2010), “The Joint Operating Environment 2010”. ### Table 1. Parameter Estimates - Parameter | Distribution Prior Mode | Prior (or Bounds) | Prior St. Dev. | Posterior Mode | 90% Confidence Interval - Oil α_s | uniform | 500 | [0 1000] | 507.6483 | [501.9955 514.8299] - Supply β_1 | uniform | 0.25 | [0 100] | 0.2427 | [0.2353 0.2538] - β_2 | uniform | 0.25 | [0 100] | 0.6238 | [0.5053 0.7422] - β_3 | uniform | 0.25 | [0 100] | 0.0546 | [0.0043 0.1322] - Oil α_d | uniform | 0 | [-0.1 0.1] | -0.0177 | [-0.0237 -0.0119] - Demand γ_1 | lognormal | 0.9 | 0.09 | 0.9098 | [0.7844 1.0352] - γ_2 | invgamma | 0.02 | 0.002 | 0.0213 | [0.0181 0.0252] - γ_3 | invgamma | 0.06 | 0.006 | 0.06 | [0.0507 0.0707] - Output λ_1 | beta | 0.9 | 0.009 | 0.8987 | [0.8833 0.9128] - Growth λ_2 | normal | 0.005 | 0.0005 | 0.0048 | [0.0039 0.0056] - λ_3 | normal | 0.005 | 0.0005 | 0.0048 | [0.0040 0.0056] - Output φ_1 | normal | 0.85 | 0.085 | 0.9556 | [0.9058 0.9873] - Gap φ_2 | normal | 0.25 | 0.025 | 0.2565 | [0.2156 0.2967] - φ_3 | normal | 0.005 | 0.0005 | 0.005 | [0.0042 0.0058] - φ_4 | normal | 0.005 | 0.0005 | 0.005 | [0.0042 0.0058] ### Table 2. Root Mean Square Errors - Comparisons - Real Price of Oil | Oil Production | GDP Level - Horizon: 1 year - Model: 14.72 | Random Walk: 7.71 | Model EI A: 1.69 | Model WEO: 1.59 | 1.82 | 1.83 - Horizon: 2 years - 17.64 | 7.41 | 1.97 | 2.57 | 3.03 | 3.41 - Horizon: 3 years - 19.95 | 7.92 | 2.31 | 3.51 | 3.62 | 4.69 - Horizon: 4 years - 22.47 | 9.02 | 2.41 | 4.66 | 3.74 | 5.55 - Horizon: 5 years - 25.11 | 100.02 | 2.69 | 5.72 | 3.05 | 5.00 (Note: table entries preserved exactly as presented.) ### Figures and Captions (selected) - Figure 1. EIA Forecasts 2001-2010 (EIA Definition of World Total Oil Supply, in Mbd) - Horizontal axis markers: 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 - Vertical axis range labels include: 70 75 80 85 90 95 100 105 110 115 120 - Year ticks listed: 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 - Figure 2. World Real Oil Prices and Spare Capacity - Time range: 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 - Oil Price (Average of UK Brent, Dubai, and West Texas) (In U.S. dollars per barrel divided by U.S. CPI; 2011 CPI=1) - Two highlighted dates: February 2003 and November 2008 - OPEC Spare Capacity (In millions of barrels per day) (Source: EIA) - Figure 3. Colin Campbell Forecasts 2003-2010 (Campbell Definition of Regular Conventional Oil, in Mbd) - Time axis: 2000 through 2020 - Vertical axis labels: 40 45 50 55 60 65 70 - Forecast series: 2003 Forecast, 2005 Forecast, 2010 Forecast - Figure 4. Oil Production Forecasts in the Deffeyes (2005) Model (Q in gigabarrels, q in gigabarrels p.a.) - Q axis markers: 400 600 800 1000 1200 1400 1600 1800 2000 2200 - q/Q vertical axis ticks: 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045 - Series: Actual, Fitted; q/Q vs. Q; Q over years 1985 1990 1995 2000 2005 2010 2015 2020; Oil Production (q) for 2003–2010 - Figure 5. Impulse Responses (in percent level deviation from control) - Panels include responses for: Oil Production, Real Price of Oil, GDP, Output Gap, Pot. Growth, Pot. Level, and shocks labeled Oil Supply Shock, Oil Demand Shock, Output Gap Shock, Pot. Growth Shock, Pot. Level Shock - Time axis markers: 2011 2014 2017 2020 - Example axis values shown: −0.1 0.0; 0 2 4 6; −0.05 0.00; 0.0 0.5 1.0; −0.2 −0.1 0.0; 0.0 0.5 1.0; 0 5; 0 2 4; 0.0 0.5 1.0; 0.0 0.1 0.2; 0.00 0.02 0.04; 0.0 0.1 0.2; 0.00 0.05 - Figure 6. Historical Residuals (in percent) - Time axis: 1983 1988 1993 1998 2003 2008 - Panels for Oil Supply Shocks, Oil Demand Shocks, Output Gap Shocks - Example axis ranges: −2 0 2 4; −3 −2 −1 0 1 2; −4 −3 −2 −1 0 1 - Figure 7. Contributions of Different Shocks to Oil Prices (in real 2011 US dollars) - Time axis: 2002 2005 2008 2011 - Panels for All Shocks, Oil Demand Shocks, Oil Supply Shocks, Output Gap Shocks - Vertical axis labels include: 40 60 80 100 120 - Figure 8. Contributions of Different Shocks to Oil Production (in gigabarrels p.a.) - Time axis: 2002 2005 2008 2011 - Panels for All Shocks, Oil Demand Shocks, Oil Supply Shocks, Output Gap Shocks - Vertical axis labels: 28 29 30 31 32 - Figure 9. Rolling Forecasts - Time axis: 1990 1995 2000 2005 2010 2015 2020 - Panels show Oil Production (24–34), Real Price of Oil (0–150 range shown with ticks 50 100 150), GDP Growth Rate (0 2 4) - Figure 10. Oil Output Forecast with Error Bands (in gigabarrels p.a.) - Time axis: 2000 through 2020 - Vertical axis labels: 28 29 30 31 32 33 34 35 36 37 - Series: Point forecast; 90 pct interval; 70 pct interval; 50 pct interval; Tighter Oil Supply - Figure 11. Oil Price Forecast with Error Bands (in real 2011 US dollars) - Time axis: 2000 through 2020 - Vertical axis labels: 40 60 80 100 120 140 160 180 200 220 240 - Series: Point forecast; 90 pct interval; 70 pct interval; 50 pct interval; Tighter Oil Supply - Figure 12. GDP (in logs) Forecast with Error Bands - Time axis: 2000 through 2020 - Vertical axis labels: 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 - Series: Point forecast; 90 pct interval; 70 pct interval; 50 pct interval; Tighter Oil Supply *Source: _wp12109 - References (PDF).* --- _Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12109.pdf_