## _wp14218

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---

### Introduction and motivation
- Kilian (2009): fluctuations in global crude oil spot prices reflect global economic conditions and supply shocks.
- Kilian and Murphy (2013): extend Kilian (2009) by identifying speculative demand shocks and including oil inventories as an additional variable.
- Motivation: because oil can be stored, changes in oil inventories (including speculative demand) can be a third driver of oil price fluctuations beyond flow production and flow demand.
- Null hypothesis: only oil market fundamentals (or news about them) induce low-frequency movements in oil prices; mispricing in futures markets is temporary and should not contribute to low-frequency price movements.
- Strategy: impose additional restrictions to bound the contribution of speculative demand shocks to oil price volatility by:
  - minimizing their long-run (20 years) contribution to the oil price forecast error variance (MFEV), and
  - an alternative Max Ratio restriction that maximizes the short- vs long-run oil price reaction to a speculative shock.

### Literature overview
- KM (Kilian and Murphy, 2013): use inventory data to identify speculative demand; main finding: speculative demand played only a modest role in 2003–08 oil price buildup.
- Alternative findings:
  - Juvenal and Petrella (2011): substantial role for financial speculation.
  - Knittel and Pindyck (2013): speculation decreased or left prices unchanged; reduced peak prices by roughly 5 percent.
  - Masters (2008); Alquist and Kilian (2010); Liu and Tang (2010); Tang and Xiong (2010); Singleton (2011): mechanisms/evidence linking financial flows and market structure to price deviations from fundamentals.
- Empirical microstudies (e.g., Büyükşahin and Robe, 2012): limited evidence that non-commercial players influenced commodity price movements.

### Storage model of speculation — theoretical predictions
- Model features:
  - refiners use oil to produce final good;
  - oil can be stored with storage cost and convenience yield;
  - futures prices relate to expectations of future spot prices plus risk premium.
- Fundamental system (no mispricing): futures prices are determined residually from fundamentals (no causality from futures to spot).
- Introducing mispricing via a stationary deviation in futures prices permits futures to affect spot and inventories.
- Testable implications:
  - Flow supply shocks:
    - negative production shock raises oil price;
    - inventories unambiguously fall initially;
    - global oil demand falls.
  - Flow demand shocks:
    - positive demand shock raises oil price;
    - inventories unambiguously fall;
    - global oil production rises.
  - News shocks (expectations of future supply shortfalls or demand increases):
    - increase inventories today and raise spot price;
    - inventories exert downward pressure on price once higher.
  - Financial speculation shock (mispricing):
    - movements in futures prices not justified by fundamentals affect oil prices, inventories, and production in the same direction;
    - oil demand moves opposite;
    - impact on spot prices and inventories resembles news shocks but is temporary under the null.

### VAR estimation, data, and model specification
- Sample period: 1983:Q1–2012:Q4.
- VAR specification: four-variable, four-lags, quarterly data.
  - Variables:
    - o_t: log-difference in global crude oil production (flow oil production).
    - y_t: log-difference of the global industrial production index (flow demand proxy).
    - p_t: log of the demeaned real price of oil (U.S. refiners’ acquisition cost deflated by U.S. CPI).
    - s_t: level change in OECD crude oil inventories (proxy for speculative demand).
- Inventory data: total OECD crude inventories from IEA; OECD data start in 1983.
- Global demand proxy: global industrial production (IP) index used (spliced with OECD IP prior to 1990).
- Identification: dynamic sign restrictions plus bounds on short-run oil supply elasticity and on the response of global demand.
  - Sign restrictions (intuitions):
    - Flow supply shock: negative response of oil production (for at least four quarters), positive real oil price, lower global activity on impact; inventories unrestricted.
    - Flow demand shock: increase real activity (for at least four quarters), positive real oil price, increase oil production on impact; inventories unrestricted.
    - Speculative demand shock: increase in crude oil inventories and real price; inventories accumulation requires oil production to increase and real activity to decline.
    - Cross-restriction: over the long term (defined as 20 years), declining oil prices must be associated with no increase in the level of inventories.
  - Boundary restrictions:
    - Upper bound on impact price elasticity of oil supply (conservative bound multiplied by three for quarterly data).
    - Impact price elasticity of oil demand negative and smaller in magnitude than long-run price elasticity (which ranges between 0.1 and 0.6).
- Admissible models reduced from approximately 5 million candidates to about 1,100 models after restrictions.

### Admissible impulse response behavior (selected)
- Shocks are one standard deviation.
- Flow supply shock:
  - persistent reduction in oil production, up to 5 percent.
  - persistent reduction in global industrial production.
  - oil price increases not necessarily very persistent.
  - inventories draw down (to increase effective supply).
- Flow demand shock:
  - persistent rise in industrial production between 2 and 5 percent.
  - real oil prices rise sharply initially between 20 and 50 percent, then fall.
  - inventories draw down.
- Speculative demand shock (admissible set):
  - impact increase in spot real oil price between 10 and 35 percent.
  - price then gradually declines.
  - oil production—restricted to rise at impact—eventually declines under admissible models, also bringing down global industrial production.

### When does speculative demand matter? (additional identification)
- Two selection strategies on admissible models:
  - MFEV: select model that minimizes the contribution of the speculative demand shock to the real oil price forecast error variance at 20 years.
  - Max Ratio: select model that maximizes the difference between the short- and long-run oil price reaction to a speculative shock (largest slope).
- MFEV results:
  - temporary speculative demand shocks imply large inventory accumulation but the real spot oil price moves little, by at most 10 percent.
  - only 3 percent of the oil price forecast error variance (FEV) is explained by speculative demand shocks at short horizons.
  - residual demand shock explains a larger share of real oil price variance under this restriction.
- Max Ratio results:
  - oil price response almost three times greater than under MFEV.
  - variance contribution of speculative shock in the short term increases to 22 percent.
  - contribution at longer horizons becomes 13 percent.
  - within the admissible set, the maximum contribution to the oil price FEV is 47 percent at the one-quarter horizon and 35 percent at the 20 year horizon.
- Bounded results across identifications:
  - estimated short-run impact response of oil price to speculative demand shocks: between 10 and 35 percent.
  - contribution of speculative demand shocks to short-term oil price volatility: between 3 and 22 percent.
  - comparative contributions:
    - flow demand shocks impact: between 40 and 45 percent.
    - flow supply shocks impact: 20 percent.
  - interpretation: news on temporary supply disruptions, movements in risk premiums, and potentially financial speculation have nonnegligible short-run roles and explain large part of inventory volatility.

### Historical decomposition and sensitivity to identification
- Historical decomposition components: cumulative effects through time of flow supply, flow demand, speculative demand, and residual demand shocks.
- MFEV identification:
  - flow demand shocks dominate across the full sample.
  - run-up during 2003–08 initially driven by flow demand; speculative demand joins after 2005; drivers re-emerge during 2011–12.
- Max Ratio identification:
  - flow demand loses some importance.
  - speculative demand and the residual demand shock play dominant roles; oil supply importance increases.
- Absolute contributions over time:
  - MFEV: flow demand most prominent; supply disruptions downplayed.
  - Max Ratio: speculative demand induces inventory demand shifts and becomes more prominent.
- Conclusion: identification and the set of restrictions materially affect inferred relative importance of shocks; all four shock types influenced real oil price movements.

### Conclusion — substantive implications and quantified bounds
- Additional restrictions on KM’s SVAR provide a plausible bound for the short-term impact of speculative demand shocks.
- Key quantified findings:
  - short-run real oil price response to speculative demand shocks: between 10 and 35 percent.
  - contribution of speculative demand shocks to short-term oil price variance: between 3 and 22 percent.
  - flow demand shocks explain between 40 and 45 percent of short-run real oil price variance.
  - flow supply shocks explain about 20 percent of short-run real oil price variance.
  - under Max Ratio, speculative shocks can contribute about 13 percent to long-run (20-year) real oil price FEV, indicating contamination by news shocks and persistent expectation shifts.
- Interpretation:
  - speculative demand shocks (broadly defined to include news, mispricing, and real interest rate effects) can materially affect short-run oil price volatility through inventory demand shifts.
  - under the null that mispricing is temporary, arbitrage should align prices with fundamentals in the long run; this motivates the MFEV-based lower bound.
  - identification choices matter: restricting speculative shocks to be short-lived yields a narrative where flow demand dominates the 2003–08 run-up; allowing larger persistent speculative effects reduces flow demand’s explanatory power.

### Appendix highlights
- Appendix 1: Analytical solution of the system of equations (1) to (8)
  - log-linearization around deterministic steady state; inventories constant in steady state.
  - fundamental system solved first; deviations denoted by lowercase log-deviations for prices and simple deviations for inventories.
  - model reduces to one endogenous state (inventories) and a jump variable (oil price).
  - closed-form solutions and parameter-dependent coefficients for s_t, p_t, and related tilde-variables provided in the source.
- Appendix 2: Differences between the Global Activity Index and Global Industrial Production
  - GAI and IP diverge at times; GAI incorporates bunker fuel prices.
  - empirical contemporaneous correlations reported:
    - correlation between GAI and Brent or WTI: about 0.3.
    - correlation between GAI and the bunker fuel: about 0.4.
- Appendix 3: Standard VAR(4) model representation
  - reduced-form VAR written; structural disturbances related to VAR innovations; structural form contains a (4 × 1) vector of serially and mutually uncorrelated structural innovations.
- Appendix 4: Implementation of the identification procedure
  - identification by searching over orthogonal matrices D where BB' = Σ and applying sign/bound restrictions.
  - Matlab procedure following Uhlig (2005) and Kilian and Murphy (2012):
    - draw N × N matrix K of NID(0, 1) random variables; derive QR decomposition K = Q・R with Q'Q = I.
    - let D = Q; compute impulse responses using orthogonalization.
    - retain D if implied impulse responses satisfy identifying restrictions; otherwise discard.
    - repeat many times and store admissible Ds and impulse responses.
  - estimation uncertainty assessed via Bayesian draws applying the identification to each draw.
- Appendix 5: Maximum and minimum impulse responses generated by the estimation (Quarterly frequency)
  - plotted maximum/minimum impulse responses over horizons with axes labelled in quarters (0,5,10,15,20) and response magnitudes (examples: Inventories responses range -200 to 200; Real price of oil -20 to 60; Oil production and Global IP -6 to 6).

*Source: _wp14218 (IMF PDF chapter/section).*

### 1. Evolution of the Real Oil Price and Political Events ........................................................3

### 1. Evolution of the Real Oil Price and Political Events ........................................................3

### Major sections
- 1. Evolution of the Real Oil Price and Political Events ........................................................3
- 2. Admissible Estimated Models–Impulse Response Functions ........................................17
- 3. Narrowing the Admissible Estimated Models–IRFs ......................................................19
- 4. Historical Decomposition of the Drivers of the Real Oil Price ......................................22
- 5. Absolute Drivers of the Real Oil Price ...........................................................................22

### Tables
- 1. Real Oil Price Variance Decomposition .........................................................................20

*Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2014/_wp14218.pdf*

### References .............................................................................................................

### _wp14218 - References .............................................................................................................

### Introduction
- Kilian (2009) highlighted that fluctuations in global crude oil spot prices reflect global economic conditions as well as supply shocks.
- Kilian and Murphy (2013) extend Kilian (2009) by identifying speculative demand shocks and including oil inventories as an additional variable.
- Motivation: because oil can be stored, changes in oil inventories (including speculative demand) can be a third driver of oil price fluctuations beyond flow production and flow demand.
- Null hypothesis: only oil market fundamentals (or news about them) induce low-frequency movements in oil prices; mispricing in futures markets is temporary and should not contribute to low-frequency price movements.
- Strategy: impose additional restrictions to bound the contribution of speculative demand shocks to oil price volatility by minimizing their long-run (20 years) contribution to the oil price forecast error variance (MFEV) and by an alternative Max Ratio restriction that maximizes the short- vs long-run oil price reaction to a speculative shock.

### Literature overview
- KM (Kilian and Murphy, 2013) use inventory data to identify speculative demand; main finding: speculative demand played only a modest role in 2003–08 oil price buildup.
- Alternative findings:
  - Juvenal and Petrella (2011) find a substantial role for financial speculation.
  - Knittel and Pindyck (2013) argue speculation decreased or left prices unchanged across their sample, reducing peak prices by roughly 5 percent.
  - Masters (2008), Alquist and Kilian (2010), Liu and Tang (2010), Tang and Xiong (2010), Singleton (2011) present mechanisms or evidence linking financial flows and market structure to price deviations from fundamentals.
- Empirical microstudies (e.g., Büyükşahin and Robe, 2012) find limited evidence that non-commercial players influenced commodity price movements.

### Storage model of speculation — theoretical predictions
- Model setup: refiners use oil to produce final good; oil can be stored with storage cost and convenience yield; futures prices relate to expectations of future spot prices plus risk premium.
- Fundamental system (no mispricing): futures prices are determined residually from fundamentals (no causality from futures to spot).
- Introduce mispricing via a stationary deviation in futures prices; dropping the inter-temporal Euler (refiners’ optimality) equation permits futures to affect spot and inventories.
- Testable implications summarized:
  - Flow supply shocks: negative production shock raises oil price; inventories unambiguously fall initially; global oil demand falls.
  - Flow demand shocks: positive demand shock raises oil price; inventories unambiguously fall; global oil production rises.
  - News shocks (expectations of future supply shortfalls or demand increases): increase inventories today and raise spot price; inventories exert downward pressure on price once higher.
  - Financial speculation shock (mispricing): movements in futures prices not justified by fundamentals affect oil prices, inventories, and production in the same direction, while oil demand moves opposite; impact on spot prices and inventories resembles news shocks but is temporary under the null.

### VAR estimation, data, and model specification
- Sample period: 1983:Q1–2012:Q4.
- VAR: four-variable, four-lags, quarterly data.
  - Variables:
    - o_t: log-difference in global crude oil production (flow oil production).
    - y_t: log-difference of the global industrial production index (flow demand proxy).
    - p_t: log of the demeaned real price of oil (U.S. refiners’ acquisition cost deflated by U.S. CPI).
    - s_t: level change in OECD crude oil inventories (proxy for speculative demand).
- Inventory data: total OECD crude inventories from IEA; OECD data start in 1983.
- Choice of global demand proxy: global industrial production (IP) index used (spliced with OECD IP prior to 1990).
- Identification: dynamic sign restrictions plus bounds on short-run oil supply elasticity and on the response of global demand.
  - Sign restrictions intuition:
    - Flow supply shock: negative response of oil production (for at least four quarters), positive real oil price, lower global activity on impact; inventories unrestricted.
    - Flow demand shock: increase real activity (for at least four quarters), positive real oil price, increase oil production on impact; inventories unrestricted.
    - Speculative demand shock: increase in crude oil inventories and real price; inventories accumulation requires oil production to increase and real activity to decline.
    - Cross-restriction: over the long term (defined as 20 years), declining oil prices must be associated with no increase in the level of inventories.
  - Boundary restrictions:
    - Upper bound on impact price elasticity of oil supply (conservative bound multiplied by three for quarterly data).
    - Impact price elasticity of oil demand negative and smaller in magnitude than long-run price elasticity (which ranges between 0.1 and 0.6).
- Admissible models reduced from ~5 million candidates to about 1,100 models after restrictions.

### Admissible impulse response behavior (selected)
- Shocks are one standard deviation.
- Flow supply shock:
  - Persistent reduction in oil production, up to 5 percent.
  - Persistent reduction in global industrial production.
  - Oil price increases not necessarily very persistent.
  - Inventories draw down (to increase effective supply).
- Flow demand shock:
  - Persistent rise in industrial production between 2 and 5 percent.
  - Real oil prices rise sharply initially between 20 and 50 percent, then fall.
  - Inventories draw down.
- Speculative demand shock (admissible set):
  - Impact increase in spot real oil price between 10 and 35 percent.
  - Price then gradually declines.
  - Oil production—restricted to rise at impact—eventually declines under admissible models, also bringing down global industrial production.

### When does speculative demand matter? (additional identification)
- Two strategies impose additional restrictions on admissible models:
  i. MFEV: select model that minimizes the contribution of the speculative demand shock to the real oil price forecast error variance at 20 years.
  ii. Max Ratio: select model that maximizes the difference between the short- and long-run oil price reaction to a speculative shock (largest slope).
- MFEV results:
  - Temporary speculative demand shocks imply large inventory accumulation but the real spot oil price moves little, by at most 10 percent.
  - Only 3 percent of the oil price forecast error variance (FEV) is explained by speculative demand shocks at short horizons.
  - Residual demand shock explains a larger share of real oil price variance under this restriction.
- Max Ratio results:
  - Oil price response almost three times greater than under MFEV.
  - Variance contribution of speculative shock in the short term increases to 22 percent.
  - Contribution at longer horizons becomes 13 percent.
  - Within the admissible set, the maximum contribution to the oil price FEV is 47 percent at the one-quarter horizon and 35 percent at the 20 year horizon.
- Overall bounded results for the role of speculative demand shocks:
  - Estimated short-run impact response of oil price to speculative demand shocks: between 10 and 35 percent.
  - Contribution of speculative demand shocks to short-term oil price volatility: between 3 and 22 percent.
  - Comparative contributions:
    - Flow demand shocks impact: between 40 and 45 percent.
    - Flow supply shocks impact: 20 percent.
  - Interpretation: news on temporary supply disruptions, movements in risk premiums, and potentially financial speculation have nonnegligible short-run roles and explain large part of inventory volatility.

### Historical decomposition and sensitivity to identification
- Historical decomposition examines cumulative effects through time of flow supply, flow demand, speculative demand, and residual demand shocks.
- Under MFEV identification:
  - Flow demand shocks dominate across the full sample.
  - Run-up during 2003–08 initially driven by flow demand; speculative demand joins after 2005; drivers re-emerge during 2011–12.
- Under Max Ratio identification:
  - Flow demand loses some importance.
  - Speculative demand and the residual demand shock play dominant roles; oil supply importance increases.
- Absolute contributions over time:
  - MFEV: flow demand most prominent; supply disruptions downplayed.
  - Max Ratio: speculative demand induces inventory demand shifts and becomes more prominent.
- Conclusion from decomposition: identification and the set of restrictions materially affect inferred relative importance of shocks; all four shock types influenced real oil price movements.

### Conclusion — substantive implications and quantified bounds
- Additional restrictions on KM’s SVAR provide a plausible bound for the short-term impact of speculative demand shocks.
- Key quantified findings:
  - Short-run real oil price response to speculative demand shocks: between 10 and 35 percent.
  - Contribution of speculative demand shocks to short-term oil price variance: between 3 and 22 percent.
  - Flow demand shocks explain between 40 and 45 percent of short-run real oil price variance.
  - Flow supply shocks explain about 20 percent of short-run real oil price variance.
  - Under Max Ratio, speculative shocks can contribute about 13 percent to long-run (20-year) real oil price FEV, indicating contamination by news shocks and persistent expectation shifts.
- Interpretation:
  - Speculative demand shocks (broadly defined to include news, mispricing, and real interest rate effects) can materially affect short-run oil price volatility through inventory demand shifts.
  - Under the null that mispricing is temporary, arbitrage should align prices with fundamentals in the long run; this motivates the MFEV-based lower bound.
  - Identification choices matter: restricting speculative shocks to be short-lived yields a narrative where flow demand dominates the 2003–08 run-up; allowing larger persistent speculative effects reduces flow demand’s explanatory power.

*Source: _wp14218 - References .............................................................................................................*

### REFERENCES

### _wp14218 - REFERENCES

### Appendix 1. Analytical solution of the system of equations (1) to (8)
- The non-linear system is log-linearized around the deterministic steady state. Since no trend growth in oil production is assumed, the existence of a steady state requires inventories to be constant.
- Using equations (4) and (5) the steady-state oil price equilibrating oil demand and supply is determined by the model (text gives the expression).
- Equation (3) determines the level of inventories as a function of the convenience yield and storage costs (text gives the expression).
- The fundamental system (variables with an asterisk) is solved first; deviations are denoted by lowercase log-deviations for prices and simple deviations for inventories.
- The model reduces to one endogenous state, inventories, and a jump variable, the oil price.
- The rational expectation equilibrium is characterized by the system summarized in the source (expressions with infinite sums and parameter groupings).
- It is proven in the text that under the authors' assumptions certain parameter relations hold (the source states: "given that 32 12 12 2 1. λ  λγ  ηϑ λ  λγ   +  =  +  +  =+").
- The log-linear futures price is determined by log-linearizing equation (7).
- The non-fundamental system, where futures prices can deviate from fundamentals, is written in deviation form (tilde variables) and has a closed-form solution given in the source:
  - The source provides explicit expressions for s_t, p_t, and related tilde-variables and parameter-dependent coefficients.

### Appendix 2. Differences between the Global Activity Index and Global Industrial Production
- GAI and IP diverge at times, including during structural change in the shipping sector (example: since 2011, freight costs collapsed with the onset of Chinamax and cape vessels coming on stream).
- The GAI incorporates bunker fuel prices (used for cargo freight shipping); the real oil price has a contemporaneous effect on the GAI at monthly and quarterly frequency.
- Empirical contemporaneous correlations reported in the source:
  - Correlation between GAI and Brent or WTI: about 0.3.
  - Correlation between GAI and the bunker fuel: about 0.4.
- Figure annotations in the source illustrate episodes:
  - "Economic booms missed by the GAI"
  - "Boom in GAI due to shipping shortages not present in IP"
  - "Major slump in GAI due to dry bulk shipping vessel oversupply"
  - "GAI co-moves sharply with fall in oil prices"
- Data sources cited for the figures: IMF WEO database; Kilian's webpage; authors' estimates.

### Appendix 3. Standard VAR(4) model representation
- Consider a 4-dimensional vector with l lags and matrices of coefficients; the VAR is written in the reduced-form and related to structural disturbances.
- Structural disturbances are related to VAR innovations; the structural VAR representation is described in matrix form in the source.
- The structural form contains a (4 × 1) vector of serially and mutually uncorrelated structural innovations and impact matrices at each lag where demand and supply elasticities are contained.
- To have orthogonalized innovations coincide with true structural disturbances certain matrix relations must hold (the source provides the formal constraints).

### Appendix 4. Implementation of the identification procedure
- Start from the reduced-form VAR: N-dimensional vector, finite-order autoregressive lag polynomial, and white-noise reduced-form innovations with variance–covariance matrix Σ.
- Structural VAR model innovations are related to reduced-form innovations via an N × N matrix B satisfying BB' = Σ.
- Because for any orthogonal matrix D, BD also satisfies BB' = Σ, identification proceeds by searching over orthogonal matrices.
- The set of admissible models is constructed by drawing rotation matrices and discarding candidate solutions that violate a priori restrictions on implied impulse response functions.
- Matlab procedure (following Uhlig (2005) and Kilian and Murphy (2012)) outlined in steps preserved verbatim:
  - Draw an N × N matrix K of NID(0, 1) random variables. Derive the QR decomposition of K such that K = Q・R and Q'Q = I.
  - Let D = Q. Compute impulse responses using the orthogonalization.
  - If all implied impulse response functions satisfy the identifying restrictions, retain D. Otherwise discard D.
  - Repeat the first two steps a large number of times, recording each D that satisfies the restrictions and storing the corresponding impulse response functions.
- The resulting set comprises the set of admissible structural VAR models.
- Estimation uncertainty can be assessed by Bayesian methods: specify priors for reduced-form parameters and the distribution for the rotation matrix; obtain the posterior by applying the identification procedure to each draw.
- The section notes it closely follows Kilian and Murphy (2013).

### Appendix 5. Maximum and minimum impulse responses generated by the estimation (Quarterly frequency)
- The source presents maximum and minimum impulse responses (quarterly) for three types of shocks and four endogenous variables. The plotted combinations in the source are:
  - Flow supply shock — Oil production
  - Flow supply shock — Global IP
  - Flow supply shock — Real price of oil
  - Flow supply shock — Inventories
  - Flow demand shock — Oil production
  - Flow demand shock — Global IP
  - Flow demand shock — Real price of oil
  - Flow demand shock — Inventories
  - Speculative demand shock — Oil production
  - Speculative demand shock — Global IP
  - Speculative demand shock — Real price of oil
  - Speculative demand shock — Inventories
- Plots in the source show impulse responses over a horizon labeled with quarter indices (e.g., "Quarters" and axes ticks 0,5,10,15,20) and response magnitudes (e.g., ranges shown as -200 to 200 for Inventories responses, -20 to 60 for Real price of oil responses, -6 to 6 for Oil production and Global IP responses).

*Source: _wp14218 - REFERENCES (IMF PDF chapter/section).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2014/_wp14218.pdf_