## Abstract

Building on recent work on the role of speculation and inventories in oil markets, the paper embeds a competitive oil storage model within a DSGE model of the U.S. economy. This enables us to formally analyze the impact of a (speculative) storage demand shock and to assess how the effects of various demand and supply shocks change in the presence of oil storage facility. The paper finds that business-cycle-driven oil demand shocks are the most important drivers of U.S. oil price fluctuations during 1982–2007. Disregarding the storage facility in the model causes a considerable upward bias in the estimated role of oil supply shocks in driving oil price fluctuations. The results also confirm that a change in the composition of shocks helps explain the resilience of the macroeconomic environment to the oil price surge after 2003. Finally, speculative storage is shown to have a mitigating or amplifying role depending on the nature of the shock.

This is a preview of subscription content, log in to check access.

## Notes

- 1.
The modern storage theory was pioneered by Williams (1936), Kaldor (1939), and Working (1948).

- 2.
The speculative storage shock in our setup could be interpreted as a reduced form way of modeling the precautionary shock in Alquist and Kilian (2010). In Alquist and Kilian (2010), the precautionary demand shock is modeled as an exogenous shock to uncertainty regarding the future production of oil, which in effect increases the demand for storage. In our case, we take a more direct approach, and allow an exogenous shock to oil storage demand. This oil-specific demand shock by construction captures fluctuations in precautionary demand for oil driven by uncertainty about future oil shortfalls. See also Kilian (2009a) and Kilian and Park (2009).

- 3.
We estimate the model also for the 2000–07 period in which the macroeconomic resilience to the oil price hikes has been seen unprecedented. During this period, inflation remained low and growth has been high and stable around the world despite high oil prices, unlike what happened in the previous episodes of oil price surges.

- 4.
Kilian (2009a) makes the case that due to adjustment costs and uncertainty about the future oil demand, oil-producing countries will not revise their production level in response to demand shocks within the same month. Obviously, the oil supply might give an endogenous response to oil demand in longer horizons. In this paper, for the sake of simplicity, we take oil supply as exogenous in a quarterly model. However, future research should relax this assumption. There are various papers which account for endogenous oil production. For example, Backus and Crucini (2000) model oil supply partially endogenously, in a neoclassical setup, by assuming that OPEC supply is exogenous. See also Nakov and Pescatori (2010), which also distinguish between OPEC and non-OPEC supply, but supply is determined endogenously in both.

- 5.
In its current form, the model features a closed economy. Hence, it abstracts from the open economy channels of the transmission of oil price shocks. An obvious extension in the future would be to embed our model of storage within a model of the global economy. Bodenstein and Guerrieri (2011) incorporate an open economy dimension and discuss the effects of various domestic and foreign oil demand and supply shocks on oil price fluctuations. However, their model excludes speculative storage.

- 6.
The existence of convenience yield is a common assumption in commodity storage literature. The nonexhaustive list includes Brennan (1991), Fama and French (1988), and Gibson and Schwartz (1990). More recently, Alquist and Kilian (2010) also adopt this modeling device.

- 7.
The level of storage is always positive in our framework as the steady-state level is positive and sufficiently high and

*deviations*of storage from its steady state are sufficiently small (within the neighborhood of the steady state). Incorporating nonlinearities associated with storage technology is beyond the scope of this paper. Although conceptually appealing, this would make solution and estimation of the model considerably more complicated without providing any additional insight for the issues we focus here. - 8.
For the sake of simplicity, we assume that the profits from selling and storing oil are distributed evenly among the consumers and are included in the lump-sum transfers in the budget constraints of households.

- 9.
See Lubik and Schorfheide (2006) and An and Schorfheide (2007) for details of the methodology and its advantages over other methods in estimating DSGE models.

- 10.
See Appendix for the full set of linearized equilibrium conditions of the model.

- 11.
The estimation is done using Dynare 4.2.4. The posteriors are based on 250,000 draws of the Metropolis-Hastings algorithm.

- 12.
Parameter ψ is a function of

*a*, κ and some steady-state ratios (see Appendix for details). Hence, we do not need to calibrate or estimate ψ. - 13.
In order to calculate this steady-state ratio, we use the data for 1973–2011, which is the longest period available.

- 14.
For the model without storage, we exclude one of the observables (oil storage) and one of the shocks (speculative demand) from the estimation. In the absence of oil storage, oil supply directly equals the total oil usage (oil in consumption plus oil in production), and hence the model excludes parameters

*a*and κ. The prior distributions are the same for the models with and without storage. - 15.
There is no clear consensus regarding the value of ρ

_{ v }. As reported by Chirinko (2008), the estimated elasticities in the literature generally vary within the range from 0.15 to 0.75. Our low estimate for ρ_{ v }could reflect the difficulty of estimating this parameter with aggregate data. - 16.
Bodenstein and Guerrieri (2011) reach different outcomes than ours in their historical decomposition exercise. This is mostly brought by important differences in the model setups. By incorporating an open economy dimension, they are able to account for both U.S. specific and foreign shocks. Besides, different from us, they also analyze the effects of oil efficiency shocks and their model excludes speculative oil storage. In particular, they find that oil efficiency shocks and foreign productivity shocks were the key drivers of fluctuations in oil prices between 1984–2008 and 2003–2008, respectively. In our variance decomposition exercise, productivity shocks explain the majority of the oil price fluctuations. This could be partly brought by the absence of the foreign dimension in the model such that the effects of this missing channel (foreign demand) are captured by the productivity shocks. Note, however, that the decomposition is more balanced in shorter horizons. Notice also that, the presence of storage technology in the model elevates the estimated contribution of productivity shocks at every horizon.

- 17.
Note that, as in the case of a negative oil supply shock, the endogenous component of the storage demand decreases, which causes a hump shape in the response of the total oil storage.

- 18.
In order to make the comparison, we estimate the models with and without storage separately. This allows us to reveal the effects of ignoring oil storage when studying the cause and consequences of oil price changes. Notice that there are two factors that cause the impulse responses differ under the cases with and without storage. One comes from differences in estimated parameters, the other from the direct effect of taking or not taking into account storage.

## References

Alquist, R., and L. Kilian, 2010, “What Do We Learn From the Price of Crude Oil Futures?” Journal of Applied Econometrics, Vol. 25, No. 4, pp. 539–573.

An, S., and F. Schorfheide, 2007, “Bayesian Analysis of DSGE Models,” Econometric Reviews, Vol. 26, No. 2–4, pp. 113–172.

Backus, D.K., and M.J. Crucini, 2000, “Oil Prices and the Terms of Trade,” Journal of International Economics, Vol. 50, No. 1, pp. 185–213.

Bodenstein, M., C.J. Erceg, and L. Guerrieri, 2011, “Oil Shocks and External Adjustment,” Journal of International Economics, Vol. 83, No. 2, pp. 168–184.

Bodenstein, M., and L. Guerrieri, 2011, “Oil Efficiency, Demand, and Prices: a Tale of Ups and Downs,” International Finance Discussion Papers No.1031, Board of Governors of the Federal Reserve System.

Brennan, M.J, 1991, “The Price of Convenience and the Valuation of Commodity Contingent Claims,” in Stochastic Models and Option Values, ed. by D. Lund and B. Øksendal (Amsterdam, North-Holland), pp. 135–57.

Calvo, G, 1983, “Staggered Prices in a Utility-Maximizing Framework,” Journal of Monetary Economics, Vol. 12, No. 3, pp. 383–98.

Chirinko, R.S, 2008, “σ: The Long and Short of It,” Journal of Macroeconomics, Vol. 30, No. 2, pp. 671–686.

Clarida, R., J. Gali, and M. Gertler, 2001, “Optimal Monetary Policy in Open vs Closed Economies: An Integrated Approach,” American Economic Review, Vol. 91, No. 2, pp. 248–252.

Deaton, A., and G. Laroque, 1992, “On the Behavior of Commodity Prices,” Review of Economic Studies, Vol. 59, No. 1, pp. 1–23.

Deaton, A., and G. Laroque, 1996, “Competitive Storage and Commodity Price Dynamics,” Journal of Political Economy, Vol. 104, No. 5, pp. 896–923.

Dvir, E., and K.S. Rogoff, 2009, “The Three Epochs of Oil,” Boston College Working Paper in Economics, No. 706.

Fama, E.F., and K.R. French, 1988, “Permanent and Temporary Components of Stock Prices,” Journal of Political Economy, Vol. 96, No. 2, pp. 246–273.

Fattouh, B., L. Kilian, and L. Mahadeva, 2012, “The Role of Speculation in Oil Markets: What Have We Learned So Far?,” mimeo, University of Michigan.

Gali, J, 2002, “New Perspectives on Monetary Policy, Inflation, and the Business Cycle,” NBER Working Paper No.8767.

Gali, J., F. Smets, and R. Wouters, 2011, “Unemployment in an Estimated New Keynesian Model,” NBER Chapter in: NBER Macroeconomics Annual 2011, 26.

Gibson, R., and E.S. Schwartz, 1990, “Stochastic Convenience Yield and the Pricing of Oil Contingent Claims,” Journal of Finance, Vol. 45, No. 3, pp. 959–976.

Hamilton, J.D, 2009, “Causes and Consequences of the Oil Shock of 2007–2008,” NBER Working Paper No.150002.

Kaldor, N, 1939, “Speculation and Economic Stability,” Review of Economic Studies, Vol. 7, No. 1, pp. 1–27.

Kilian, L, 2008, “The Economic Effects of Energy Price Shocks,” Journal of Economic Literature, Vol. 46, No. 4, pp. 871–909.

Kilian, L, 2009a, “Not All Price Shocks are Alike: Disentangling Demand and Supply Shocks in the Crude Oil Market,” American Economic Review, Vol. 99, No. 3, pp. 1053–69.

Kilian, L, 2009b, “Comment on ‘Causes and Consequences of the Oil Shock of 2007–08’’ by James D. Hamilton,” Brookings Papers on Economic Activity, Vol. 1 (Spring), pp. 267–278.

Kilian, L., and B. Hicks, 2012, “Did Unexpectedly Strong Economic Growth Cause the Oil Price Shock of 2003–2008?,”

*Journal of Forecasting*, advance online publication, 10 April, 2012; doi:10.1002/for.2243.Kilian, L., and D.P. Murphy, 2010, “The Role of Inventories and Speculative Trading in the Global Market for Crude Oil,” CEPR Discussion Paper, No. 7753.

Kilian, L., and D.P. Murphy, 2012, “Why Agnostic Sign Restrictions Are Not Enough: Understanding the Dynamics of Oil Market VAR Models,”

*Journal of the European Economic Association*, Vol. 10, No. 5, pp. 1166–88.Kilian, L., and C. Park, 2009, “The Impact of Oil Price Shocks on the U.S. Stock Market,” International Economic Review, Vol. 50, No. 4, pp. 1267–1287.

Kilian, L., A. Rebucci, and N. Spatafora, 2009, “Oil Shocks and External Balances,” Journal of International Economics, Vol. 77, No. 2, pp. 181–194.

Lippi, F., and A. Nobili, 2012, “Oil and the Macroeconomy: A Quantitative Structural Analysis,”

*Journal of the European Economic Association*, Vol. 10, No. 5, pp. 1059–83.Lubik, T.A., and F. Schorfheide, 2004, “Testing for Indeterminacy: An Application to U.S. Monetary Policy,” The American Economic Review, Vol. 94, No. 1, pp. 190–217.

Lubik, T.A., and F. Schorfheide, 2006, “A Bayesian Look at New Open Economy Macroeconomics,” in NBER Macroeconomics Annual 2005, ed. by G. Mark and K. Rogoff (Cambridge: The MIT Press), pp. 313–366.

Nakov, A., and A. Pescatori, 2010, “Monetary Policy Trade-Offs with a Dominant Oil Supplier,” Journal of Money, Credit, and Banking, Vol. 42, No. 1, pp. 1–32.

Raurich, X., H. Sala, and V. Sorollae, 2012, “Factor Shares, the Price Markup, and the Elasticity of Substitution between Capital and Labor,” Journal of Macroeconomics, Vol. 34, No. 1, pp. 181–198.

Ríos-Rull, J.V., and R. Santaeulàlia-Llopis, 2010, “Redistributive Shocks and Productivity Shocks,” Journal of Monetary Economics, Vol. 57, No. 8, pp. 931–948.

Sahuc, J.-G., and F. Smets, 2008, “Differences in the Interest Rate Policy at the ECB and the Fed: An Investigation with a Medium Scale DSGE Model,” Journal of Money, Credit, and Banking, Vol. 40, No. 2–3, pp. 505–521.

Unalmis, D., I. Unalmis, and D.F. Unsal, 2009, “On the Sources of Oil Price Fluctuations,” IMF Working Paper, No.9285.

Williams, J.B, 1936, “Speculation and the Carryover,” Quarterly Journal of Economics, Vol. 50, No. 3, pp. 436–55.

Williams, J.C., and B. Wright, 1982, “The Roles of Public and Private Storage in Managing Oil Import Disruptions,” Bell Journal of Economics, Vol. 13, No. 2, pp. 341–353.

Williams, J.C., and B. Wright, 1984, “The Welfare Effects of the Introduction of Storage,” Quarterly Journal of Economics, Vol. 99, No. 1, pp. 169–192.

Williams, J.C., and B. Wright, 1991, Storage and Commodity Markets (Cambridge: Cambridge University Press).

Working, H, 1948, “Theory of the Inverse Carrying Charge in Futures Markets,” Journal of Farm Economics, Vol. 30, No. 1, pp. 1–28.

## Additional information

^{*}Deren Unalmis is an Economist at the Central Bank of the Republic of Turkey; Ibrahim Unalmis is a Specialist at the Central Bank of the Republic of Turkey; Derya Filiz Unsal is an Economist at the International Monetary Fund. The authors are grateful to the editor Pierre-Olivier Gourinchas, two anonymous referees of the *IMF Economic Review*, Harun Alp, Nese Erbil, Refet Gurkaynak, Hande Kucuk, Andrea Pescatori, and Steven Phillips, for valuable contributions, comments, and suggestions. They also thank the participants at the conference on “Policy Responses to Commodity Price Movements”; particularly Olivier Blanchard, Tommaso Monacelli, Roland Straub and Rafael Portillo for insightful discussions and comments.

## Appendix

### Appendix

### A.I. Equilibrium Conditions

In what follows, small letters denote percentage deviations of the respective variables from their steady-state levels. Households' maximization of Equation (1) subject to Equations (7) and (8) yields the following (log-linearized) optimality conditions:

where is the real rental rate of capital, =*w*_{
t
}−*p*_{
t
} is the real wage, log *R*_{
t
}=log(1+*r*_{
t
})≈*r*_{
t
} is the nominal interest rate, π_{z, t+1}=*p*_{z, t+1}−*p*_{z,t} is the non-oil CPI inflation between *t* and *t*+1, and π_{t+1}=*p*_{t+1}−*p*_{
t
} is the CPI inflation between *t* and *t*+1. The law of motion for capital in log-linearized form is as follows:

Oil used in consumption (Equation (5)) is log-linearized as:

where =*p*_{o, t}−*p*_{
t
} is the real price of oil.

Firms will minimize *R*_{
t
}^{K}*K*_{
t
}+*W*_{
t
}*N*_{
t
}+*P*_{o, t}*O*_{y, t} subject to Equation (12). Log-linearized F.O.C.s are as follows:

where *pr*_{z, t}=*p*_{z, t}−*p*_{
t
} is the relative price. Equation (A.7) presents the determinants of the oil used in production.

The (log-linearized) real marginal cost (*mc*_{
t
}=*mc*_{
t
}^{n}−*p*_{z, t}) that is faced by the firms is:

We assume that firms set prices according to Calvo (1983) framework, in which only a randomly selected fraction (1−θ) of the firms can adjust their prices optimally in each period. Thus, θ is the probability that firm *i* does not change its price in period *t*. These firms of fraction θ can only adjust the price according to a partial indexation scheme:

where Π_{z, t}=*P*_{z, t}/*P*_{z, t−1}. For firms who do not have chances to reoptimize prices, the prices are adjusted according to past inflation of core goods. ς captures the degree of inflation indexation in the economy.

The firm *i* who has opportunity to reoptimize the price chooses the price (*P̃*_{z, t}(*i*)) so that it maximizes the stream of profits discounted by *Q*_{t, t+k}:

subject to the demand function faced by the firm:

where ɛ is the elasticity of substitution among the core goods.

Therefore, *P̃*_{H, t}(*i*) should satisfy the following first-order condition:

Hence, the firms’ optimal price-setting strategy implies the marginal cost-based (log-linearized) Phillips curve:

Log-linearization of goods market equilibrium condition around the symmetric steady state gives:

where *z*_{
t
}=*c*_{
t
}−ρ_{
c
}*pr*_{z, t}. and are the steady-state shares of government spending and investment in output, where letters with a bar above indicate the steady-state levels.

In the oil market, oil supply (*o*_{s, t}) is assumed be exogenous, while oil demand and oil storage are endogenously determined. The (log-linearized) equilibrium conditions are:

where and the oil supply shock (*o*_{s, t}) and storage demand shock (*sd*_{
t
}) are assumed to follow stationary AR(1) processes.

Notice that at steady state, , , and

## Rights and permissions

## About this article

### Cite this article

Unalmis, D., Unalmis, I. & Unsal, D. On Oil Price Shocks: The Role of Storage.
*IMF Econ Rev* **60, **505–532 (2012). https://doi.org/10.1057/imfer.2012.18

Published:

Issue Date:

### JEL Classifications

- C68
- E12
- Q43