Oil prices in a general equilibrium model with precautionary demand for oil

Accepted Manuscript Oil prices in a general equilibrium model with precautionary demand for oil

Conny Olovsson

PII: DOI: Reference:

S1094-2025(18)30021-8 https://doi.org/10.1016/j.red.2018.11.003 YREDY 898

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Review of Economic Dynamics

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22 January 2018 5 November 2018

Please cite this article in press as: Olovsson, C. Oil prices in a general equilibrium model with precautionary demand for oil. Review of Economic Dynamics (2018), https://doi.org/10.1016/j.red.2018.11.003

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Oil prices in a general equilibrium model with precautionary demand for oil Conny Olovsson∗ November 23, 2018

Abstract This paper analyzes the interaction between oil prices and macroeconomic outcomes by incorporating oil as an input in production alongside a precautionary motive for holding oil in a general equilibrium model. The driving forces are factor-specific technology shocks, oil supply shocks, and news shocks about future oil supply. Storage and the zero lower bound on stored oil are crucial for the model to match observed business-cycle statistics, the relationship between oil price changes and recessions, and for generating state-dependent responses to shocks. Large oil-price increases are mainly driven by increasing precautionary/smoothing demand for oil. Most of the time, oil-related shocks are of limited importance for the business cycle, but when oil inventories are low, negative news about the future oil supply can drive the economy into a recession that is triggered by oil scarcity.

Keywords: Oil prices, business cycles JEL: E32; Q43

The post-war period features highly volatile oil prices and several episodes of fast and dramatic swings in the oil price. The most famous examples are probably the “oil shocks” of 1973/74 and 1978/79, when the real oil price increased by almost 220 and 105 percent, respectively, from the first year to ∗

Conny Olovsson: Sveriges Riksbank, SE-103 37 Stockholm. Email: [email protected]. I am grateful for comments from Jonathan Heathcote, Per Krusell, Kjetil Storesletten, participants at the Nordic Summer Symposium in Macroeconomics, and three anonymous referees. The opinions expressed in this article are the sole responsibility of the author and should not be interpreted as reflecting the views of Sveriges Riksbank.

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the next, but at least six more occasions with large oil-price increases have occurred since World War II.1 In general, the volatility of the oil price is roughly one order of magnitude larger than that of output. The observation that a majority of the episodes with large oil-price increases since the early 1970s have been followed by recessions have raised questions about why the oil price is so volatile, and to what extent oil is important for the business cycle. Among other things, increases in oil prices have been suggested to cause recessions, excessive inflation, and reduced productivity.2 Early papers simply viewed oil-price changes as exogenous to the U.S. economy but today, the consensus view is that there is reverse causality from macroeconomic aggregates to oil prices.3 The empirical literature has then identified three types of shocks to be important determinants of oilprice changes: shocks to the amount of oil that is extracted from the ground (“flow supply for oil”), to the amount of oil that is consumed (“flow demand for oil”), and fear of future supply shocks that increase the precautionary demand for oil.4 This paper sets up a general equilibrium model with oil that incorporates all the specific shocks that have been identified in the empirical literature, and quantifies their individual importance for the oil price and the business cycle. The model differs from basically all existing models with oil in that it allows for storage of oil. Since stored quantities of oil cannot be negative, the possibility of storage introduces an occasionally binding constraint into the model: a zero lower bound on stored oil. In the model, the oil supply has two components: one exogenous part 1

Examples include the Iran-Iraq War initiated in 1980, the first Persian Gulf War in 1990/91, and the oil-price spike of 2007/08. 2 See Jones, Leiby and Paik (2004) and Baumeister and Kilian (2016) for reviews about oil-price fluctuations and the economy. 3 Examples of papers with exogenous oil prices include Pierce and Enzler (1974), Rasche and Tatom (1977), Bruno and Sachs (1982), and Kim and Loungani (1992). Later contributions with a similar approach include Rotemberg and Woodford (1996) and Finn (2000). The view with exogenous oil prices was first seriously challenged by Barsky and Kilian (2002). 4 There is, however, less agreement about the relative importance of these shocks. Basically, Hamilton argues that oil-price changes are largely caused by shocks to the flow supply, whereas Kilian instead finds shocks to flow demand, and to the uncertainty about future shortfalls that increase the precautionary demand for oil to be the most important factors. See, for instance, Barsky and Kilian (2002), Hamilton (2003, 2009, 2011), Kilian (2009), and Kilian and Murphy (2014).

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that is extracted from the ground and is subject to stochastic shocks and one endogenous part that is drawn from the oil stock that has been kept in storage from previous periods. Future supply levels can then be forecasted with the help of noisy signals - or news shocks - that agents receive about the future supply of ground oil. These news shocks contain information about big and potentially important events, such as wars and political instability in the oil-supplying region that may affect the variance and/or the mean of the distribution of the future supply of ground oil.5 The model also features factor-specific technology shocks that directly affect flow demand. To evaluate the importance of nonlinear and potentially asymmetric effects, the model is solved with global solution methods. The results show that storage and the zero lower bound on stored oil are crucial for the model to match observed business-cycle statistics and the relationship between oil price changes and recessions, as well as for replicating features that have been argued to be important in the empirical literature, such as state-dependent responses to shocks and asymmetric responses to positive and negative shocks. Specifically, when storage is allowed, the considered shocks can account for a large number of observed business-cycle properties. In particular, the model replicates the fact that oil use is more volatile than both output and hours worked. In addition, the distribution of oil prices is similar in the model and the data, implying that the model economy endogenously goes through episodes with dramatic swings in the oil price. The model distribution of prices also captures the empirical pattern of relatively few but huge price increases and relatively many but small price decreases. Consistent with the empirical findings in Kilian (2009), the most important channel by which wars and revolutions affect the oil price is through their effect on the precautionary demand for oil. Shocks that lead to increasing precautionary demand for oil have eight times larger an effect on oil-price changes than supply shocks do.6 Indeed, this is the most impor5

As far as I know there are only two previous papers that allow for storing in general equilibrium, and none of them consider news shocks. Arseneau and Leduc (2013), first, focuses mainly on the effect of storage on the persistence of the price for different commodities. Second, Unalmis, Unalmis, and Unsal (2012) analyzes storing in a New Keynesian closed economy that features exogenous disturbances to oil stocks. In contrast, the level of oil inventories is fully endogenous in the model in this paper. 6 Bornstein, Krusell, and Rebelo (2017) abstracts from storing and finds that demand

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tant reason for large oil-price increases in the model. Most of the time, oil and the oil-related shocks are of limited importance for understanding the business cycle. In these “normal” times, oil scarcity is not an issue because additional oil can easily be drawn from the inventories if necessary. About fifteen percent of the time, however, the economy is either at the zero lower bound on stored oil or close to this constraint, and the oil-related shocks can then have substantial effects on the business cycles. Negative news about the future oil supply and/or an oil-supply shock that hits the economy can then drive the economy into a deep recession that is triggered by oil scarcity. Specifically, the realization of a negative news shock when the amount of oil in storage is less than or equal to five percent of the average annual oil consumption - as it was in 1973 - generates a four percent contraction in output and a six percent reduction in labor supply. The reason for these nonlinear effects comes from the kink introduced by the zero lower bound on stored oil. Intuitively, oil is necessary for production and highly complementary to capital/labor. Hence, when the economy approaches the zero lower bound on stored oil, this input becomes scarce and dampens production. A related result is that, as the model economy approaches the zero lower bound on stored oil, the responses in output and labor supply become increasingly asymmetric to positive and negative shocks. Specifically, shocks that generate contractions in labor supply and output then have stronger effects than shocks that lead to expansions of these variables. The reason is that the constraint on the zero lower bound on stored oil is binding, and either output cannot be expanded enough in response to positive shocks or that the contraction becomes larger than what it would have been without the binding constraint.7 Overall, these results indicate that models with oil that are linearized around a steady state might miss important nonlinear and asymmetric effects that are introduced by the zero lower bound on stored oil. Finally, the model is consistent with the empirical observation that and supply shocks contribute equally to the volatility of the oil price. 7 Several empirical papers have suggested an asymmetric relationship between oil prices and economic variables, meaning that positive oil-price shocks would have larger effects on GDP growth and labor supply than negative oil-price shocks. See, for instance, Mork (1989), Bernanke, Gertler, and Watson (1997), and Hamilton (1996, 2003).

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sharp increases in the oil price tend to be followed by recessions.8 The intuition is that a sharp increase in the oil price following a bad news shock is a signal of potential future oil scarcity. The direction of causality then runs from expectations of a contraction - due to oil scarcity - to the oil price and not from the increase in the oil price to the contraction. Allowing for storage is crucial for this prediction because only then does the oil price contain the important forward-looking component that allows precautionary demand to adjust. The model abstracts from many features, such as nominal frictions, monopolistic competition, habit formation, etc., and is kept relatively simple in order to quantify the non-linear effects of oil-related shocks on output and labor supply. Given that many New Keynesian models build on a core from real-business-cycle models, however, it is useful to analyze modifications of this core separately as a first step. Nominal frictions and other features can then straightforwardly be introduced as a next step. The paper is structured as follows. Section 1 sets up the model, Section 2 describes the data, and the results are then presented in Section 3. The effects of the considered shocks are evaluated in Section 4, and the main assumptions are discussed in Section 5. Section 6, finally, concludes.

1

The model

The ambition is now to set up a general equilibrium model with oil that can quantify the importance of all the shocks that have been identified in the empirical literature for the oil price and the business cycle. Motivated by the findings reported in Section 2 below, there is one energy input in the model, and it is thought of as oil. The model is set up as a closed economy where a representative agent derives utility from consumption and leisure. I omit time subscripts and use  to denote next period’s variables. The agent has one unit of productive time per period, which must be divided between work and leisure. To specify the model as simply as possible, I abstract from households’ oil consumption. Oil is, thus, purely used as an input into production. This assumption is standard in the literature 8

See Hamilton (1983, 2003), and Kilian and Vigfusson (2017).

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and made mainly for simplification.9 Assuming that oil is also used for consumption requires a more complicated utility function, preferably with durables that require oil. The instantaneous utility function is given by u (c, 1 − l) = (1 − μ) log (c) + μ log (1 − l) ,

(1)

where l denotes hours worked and 1 − l is leisure. Output is produced with labor, capital (k), and oil (o), according to the following CES function  ε    ε−1 ε−1 ε−1 y ≡ F (a, ao , k, l, o) = (1 − γ) ak α l1−α ε + γ (ao o) ε ,

(2)

where a ≡ exp (z) and ao ≡ exp (zo ), respectively, denote the separate shocks to the productivity of capital/labor and oil and ε is the elasticity of substitution between capital/labor and oil. The production function in (2) ensures that the relative shares of capital and labor inherit their properties from the usual Cobb-Douglas form used in growth studies.10 The shocks a and ao directly affect the demand for capital, labor and oil.11 These non-Hicks-neutral shocks are motivated by findings in Hassler, Krusell, and Olovsson (2017) that show that technologies that save on capital/labor and energy typically grow at distinct rates and also have different volatilities. They will, therefore, interchangeably be referred to as productivity and demand shocks.12 The processes for z and zo are assumed to obey the following laws of 9 Ideally, the direct usage of oil should be deducted from the data on total oil use. The main category of direct oil use is transportation services provided by the private use of cars. Since the existing data on petroleum consumption contains breaks and also includes fuel used for professional services, I follow Hassler, Krusell, and Olovsson (2017) by not deducting the oil used by passenger cars. Because the correlation between overall oil use and petroleum for passenger cars is as high as 0.96, however, the only moment that is affected by its inclusion is the standard deviation of oil use. 10 A similar function is used in Hassler, Krusell, and Olovsson (2017), Stern and Kander (2012) and Gars and Olovsson (2015). 11 Bodenstein and Guerrieri (2011b) also considers factor-specific productivity shocks in a model without storing and news shocks. 12 The model is set up so that a and ao can decrease from one period to the next. It is, however, straightforward to add positive trends to the productivity processes to make sure that the probability is small that productivity levels will actually decrease.

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motion: z  = ρz z + z , and zo = ρzo zo + zo ,

(3)

with 0 ≤ ρz ≤ 1, and 0 ≤ ρzo ≤ 1 and where z and zo are both independent and normally distributed with mean zero and variances respectively given by σ z and σ zo . Finally, the aggregate resource constraint is given by c + k  = y + (1 − δ) k,

(4)

where δ denotes the depreciation rate for capital.

1.1

The supply of fossil fuel

The oil used in production can be sourced from two different suppliers: it can be pumped out of the ground and it can be sourced from inventories of stored oil. For simplicity, the supply of ground oil just follows an exogenous process. This assumption is standard in the literature and is, for instance, found in Backus and Crucini (2000), Bodenstein, Erceg and Guerrieri (2011a) and Arezki, Ramey, and Sheng (2016). The assumption effectively implies a vertical short-run supply curve for ground oil (but not for the total supply of oil), and it is motivated by the fact that oil-producing countries seem to be slow to respond to demand shocks due to adjustment costs and uncertainty about the oil market.13 Appendix A.6.3, however, shows that the results are not particularly sensitive to the assumption of inelastic ground oil by allowing for the possibility, at a cost, to expand this supply in some states of the world. Since inelastic ground oil is a simpler set-up, I abstract from elastic ground oil in the benchmark version of the model. 13

See Kilian (2009). He argues further that the unresponsive oil supply is consistent with evidence from interviews of Saudi officials in the early 1980s, and that the fact that state-owned Saudi oil company producers only produce forecasts for demand once a year. See also Anderson et al. (2018), which shows that producers should not change oil production in response to demand shocks, as well as the supply elasticity estimate close to zero in Bornstein, Krusell and Rebelo (2017).

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1.1.1

Ground oil

In a given period, the supply of ground oil, og , is given by og = ϕ exp (η) ,

(5)

where ϕ is a parameter and η is a random shock to the supply of ground oil. Next period’s value of η  can be imprecisely forecasted with the noisy signal, ξ, that arrives in each period and contains imperfect information about the future supply of ground oil. Hence, ξ is a news shock about big and potentially important events that might affect the supply. Good news implies zero risk of a supply shortfall in the next period. Bad news, however, is thought of as wars and political instability in the oil-supplying region and signals a positive probability of a supply shortfall in the subsequent period.14 The news shock is assumed to be state-independent, thus implying that bad news is realized with the constant probability π ξ :  ξ=

ξb ξg

w/prob π ξ w/prob 1 − π ξ .

(6)

The shock to the supply of ground oil then obeys the following process  η  (ξ) =

η l w/prob π η , and η h w/prob 1 − π η η h w/prob 1

if ξ = ξ b if ξ = ξ g .

(7)

The specification in (7) has the characteristic that, if the news shock is good (ξ = ξ g ), agents know with certainty that next period’s supply is high and equals η h . However, if the news shock is bad (ξ = ξ b ) then next period’s supply is low and equals η l with probability π η and next period’s supply is high and equals η h with probability 1 − π η . A bad shock, thus, implies a higher level of uncertainty about the future but also a lower expected value for the supply of ground oil.15 14

It would be straightforward to also allow for positive shocks to the oil supply. One example could be the recent shale oil boom, which is analysed in Çakir Melek, Plante, and Yücel (2017). Potentially, this “shock” is more permanent than the transitory shocks modelled in this paper. 15 A previous version of the paper also considered a specification where bad news generated a mean-preserving spread in the distribution for the supply of ground oil.

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The supply process for ground oil deserves some comments. First, it does not allow for serially correlated shocks. This assumption is supported by the empirical estimates of supply shortfalls that are provided in Kilian (2008a). Specifically, it finds exogenous oil supply shocks to be serially uncorrelated. I also abstract from autocorrelated shocks to the supply of ground oil in good times. With elastic oil supply, however, deviations from trend are endogenously autocorrelated in good times. As shown in Appendix A.6.3, this does not change the results. Second, the process does not allow for positive shocks to the supply. This is purely for simplicity, but it is straightforward to extend (7) to also allow for positive shocks. Third, there is a tight link between news and supply shocks in that all supply shocks are preceded by noisy news. This assumption is discussed and relaxed in the sensitivity analysis in Section A.6.2. Fourth and finally, Barsky and Kilian (2002) and Hamilton (2003) both point out that exogenous drops in oil extraction often are followed by endogenous increases in oil supply from other sources.16 Such an endogenous response can potentially come in the model from the supply of stored oil, which is the topic of the next section. 1.1.2

Stored oil

It is possible to store oil above ground between periods. The stock of stored oil, R, must then obey the following law of motion: R = R − os ,

(8)

where os is the net outtake of fossil fuel from storage. The amount of stored oil must, naturally, be positive, i.e., it is required that R ≥ 0.

(9)

There is a constant marginal cost to storing oil, which is denoted by κ. Note that even if there would be no physical cost to storing oil, there Results with that specification were similar to those derived from (7). 16 See also Nakov and Nuño (2013).

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would still be an opportunity cost in the form of delayed production and consumption. The total amount of oil available for production is equal in each period to the sum of the oil from the ground and the net outtake from storage, i.e.,  o = og + R − (10)  R . os

1.2

Equilibrium

Since there are no market failures in the model, the problem, without a loss of generality, can be formulated in recursive form as a social planning problem. The state variables are the factor-specific shocks, the capital stock, the stock of oil inventories, the shock to the current supply of ground oil, and the news shock. Denoting the Lagrange multiplier on the zero lower bound on stored oil (9) by λ, the planning problem is given by (11)

(1 − μ) log max  

k ,R ,l

V (a, ao , k, R, η, ξ) =



(1 − γ) (ak α l1−α )

ε−1 ε

+ γ (ao (og + R − R ))

ε−1 ε

ε  ε−1

+ (1 − δ) k − k  ) + μ log (1 − l) − κR} + βEt V (a , ao , k  , R , η  , ξ  ) −λR , s.t.(3), (6), and (7). (11) The first-order conditions to (11) deliver an Euler equation for capital, an equation that governs the return to storing oil and an intra-temporal equation for labor supply. These equations are laid out in Appendix A.2. The unknown variables are k  , R , l, os , ct and λ, and the equations that characterize the equilibrium are (4), (8), (9), (17), (18), (19), as well as laws of motions for factor productivity (3), and for news and the supply of ground oil (6)-(7). The price of oil (po ) is given in each period by the marginal product of oil in that period. Formally, this price is given by

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po = (og + R − R ) (1 − γ) (ak α l1−α )

ε−1 ε

−1 ε

×

+ γ (ao (og + R − R ))

ε−1 ε

1  ε−1

ε−1

γao ε .

(12)

Given that oil is storable, the price of oil now depends on flow demand and flow supply but also on the demand for oil inventories (R ) through the news shock ξ.

1.3

Calibration and numerical approximation of the model

The model is annual and calibrated as follows.17 The discount factor is set at β = 0.98 to generate an interest rate of around two percent. The utility weight on leisure is set to μ = 0.65, which implies that the representative agent dedicates roughly 1/3 of her time to work. There are three production parameters: α, γ and ε. The parameter α is set at α = 0.32 to generate a capital share of income of 0.3. The weight on energy in production, γ, is set to 0.05. The elasticity of substitution between capital/labor and fossil energy, ε, has been analyzed in a large number of studies. Early empirical investigations are Hudson and Jorgenson (1974) and Berndt and Wood (1975), who both use time-series data to estimate the substitutability of energy with other inputs. Both studies find capital and energy to be gross complements. Griffin and Gregory (1976), instead, uses pooled international data to capture the long-run relationships between capital and energy. The finding is that capital and energy are substitutes in the long-run. Koetse et al. (2008) carries out a meta-regression analysis and concludes that the demand for energy-saving capital is affected by energyprice increases, but that it generally takes a significant period of time before demand reacts. Another approach to estimate the elasticity is applied in Hassler, Krusell, and Olovsson (2017). Specifically, the authors consider a production function similar to (2) and allow the short-run elasticity to differ from the 17

Papers on the business cycle typically concentrate on quarterly data. The results for the annual model, however, should not be expected to differ materially from those from a quarterly model.

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long-run elasticity. The short-run elasticity is governed by the parameter ε, whereas the possibility to substitute in the long-run is affected by endogenous investments into the levels of a and ao .18 The authors then estimate the short-run, i.e., one-year, elasticity of substitution between capital/labor and fossil energy and find it to be close to zero. Since the setting in Hassler, Krusell, and Olovsson is close to the one in this paper, and given the fact that this paper is concerned with the short run and all studies find capital and fossil energy to be short-run complements, ε is set to 0.03.19 Since the long-run elasticity of substitution is not allowed to differ from that in the short run, the model is less suitable for deriving long-run implications. Results are also reported for higher elasticities, and the elasticity of substitution is discussed further in Section 5. The marginal cost for storing oil is set to κ = 0.000625 to match the average observed level of reserves relative to oil use between 2010 and 2014.20 This average is also close to the average for the last 25 years. The observed level of oil reserves relative to oil use was 15.75 between 2010 and 2014, and it is 15.66 in the benchmark version of the model.21 The scarcity of energy is determined by the parameter ϕ. This value is set so that energy’s share of income on average equals 2.5 percent. I turn now to the calibration of the input-saving shocks. Hassler, Krusell, and Olovsson (2017) shows that the level of the technologies that save on capital/labor and oil, respectively, can be computed from the following two equations: 18 Since technological progress can change the amounts of capital/labor that need to be combined with energy, the long-run elasticity of substitution will be higher than the short-run elasticity. Even though there are important distinctions, the setting with a low value for the short run and a higher value for the long run bears some resemblance to the the putty-clay setting in Atkeson and Kehoe (1999). 19 An elasticity of substitution close to zero is also employed in Rotemberg and Woodford (1996), Backus and Crucini (2000), and Unalmis, Unalmis, and Unsal (2012). 20 The reason for matching the ratio of reserves relative to oil use is that oil use has been increasing over time, thus implying that an inventory of 100 million barrels in 2015 was a relatively smaller buffer than in 1970. Scaling reserves by average oil use removes this problem. 21 The ratio was 14.25 between 1990 and 2014.

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log At = log yt −log



ktα lt1−α



ε + log ε−1



w t lt ε − log ((1 − α) (1 − γ)) yt ε−1 (13)

and log Ao,t

ε log = log (yt ) − log ot + ε−1



pot ot yt

−

ε log γ. ε−1

(14)

The standard procedure when computing the shock processes for z and zo is to fit linear trends to (13) and (14) and then use the residuals from these regressions to estimate ρz , ρzo , σ z and σ zo . A potential problem here is Hassler, Krusell, and Olovsson’s finding of directed technical change. Specifically, they show that average growth rates for capital/labor and energy are changing over time in a negatively related fashion. The capital/labor-saving technology, for instance, grew relatively fast before 1973 and relatively slowly for almost a decade after 1973 with the opposite being true for the energy-saving technology. This negative trade-off for the medium-term is present throughout the whole sample period, implying that the standard assumption of constant underlying growth rates for A and Ao is not applicable in a meaningful way in the current setting. To remove the variation in the trend components, I instead estimate the relevant parameters for three sub-periods with distinct average growth rates, 1970-1987, 1987-1993, and 1993-2011, and set the parameters ρz , ρzo , σ z and σ zo to their weighted averages of the estimates over the periods.22 This implies setting ρz = 0.6355, ρzo = 0.5110, σ z = 0.0157, and σ zo = 0.0325. The correlation between z and zo is set to zero in the model, which is close to the correlation of 0.1251 that is found in the data. The supply of ground oil can be high, η h , or low, η l . This seems realistic in that bad news signals a higher risk of a future shortfall in supply, but does not require the supply of ground oil to be substantially above average levels in some states following bad news as it would be with a mean-preserving spread. Hamilton (2003) estimates the exogenous shortfalls in world production for five specific events and finds them to be be22

See Section A.4 for a more detailed discussion about the estimation process.

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tween 7.2-10.1 percent.23 I set η l = η m − x and choose x and η m so that the unconditional expected value of η equals zero and that, conditional on bad news in period t, the expected short fall in supply in the subsequent period is equal to 10.1 percent. This is the upper bound of Hamilton’s estimates, but the interval is fairly small. Bad news is thought of as big events such as wars and political instability in the oil-supplying region and it signals a positive probability of a supply shortfall in the subsequent period. There have been roughly nine distinct episodes of net oil-price increases since 1949.24 Even though most of these episodes were associated with at least, some supply short falls, there are also a few cases where bad news did not translate into a drop in oil supply. Based on these facts, the two probabilities are set so that bad news occurs roughly every tenth year, whereas the probability that it actually materializes into a supply shortfall is ninety percent. This implies setting π ξ = 0.10 and π l = 0.90. The calibration is summarized in Table 1, and the details about the numerical approximation of the equilibrium, alongside the Euler equation errors, are discussed in Appendix A.5. Table 1: Calibration α 0.32

Production and preference parameters β γ δ μ ε ϕ 0.98 0.05 0.08 0.65 0.03 0.561

κ 0.0005

Shock parameters ρz o σz σ zo ηl ηh πξ πl ρz 0.6355 0.5110 0.0157 0.0325 0.8966 1.0109 0.10 0.90 The top panel of the table provides the values assigned to production and preference parameters, whereas the lower panel states the values for the parameters that govern the stochastic processes. 23

The events are the Suez crisis in 1956, the Arab-Israeli War in 1973, the Iranian Revolution in 1978/79, the Iran-Iraq War in 1980, and the Persian Gulf War in 1990/91. Kilian (2008a) considers an alternative measure of exogenous shortfalls in oil supply. 24 Kilian and Vigfusson (2017) argues that there have been eight episodes since 1974.

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2

Data

This section describes the data to which the model is compared. The considered period is 1970-2014.25 I follow the tradition in the macroeconomic literature on oil and only allow for one energy input in the model.26 Since oil is not the only energy input in practice, however, a relevant question is to what extent such simplification is restrictive. This issue is analyzed in Appendix A.1, and the conclusion is that it is not restrictive to focus on oil as the sole energy input for the United States. Basically, the nonfossil energy sources have only been of minor importance in the U.S. over the period 1970-2014, and there is almost no short-run substitution taking place between these energy inputs and oil during this period. There is also limited short-run substitution going on between the different fossil fuels. Data on energy use is from the U.S. Energy Information Administration, and the data on oil prices is from the FRED database.27 The GDP data is denoted in chained (2009) dollars and is taken from the Bureau of Economic Analysis. Hours worked per person between the ages 15-64 are computed with data from the OECD database. Data on the ending stock of oil (i.e., oil inventories) is taken from the Energy Information Administration. Specifically, the ending stock consists of the “primary stocks of crude oil and petroleum products held in storage as of midnight on the last day of the month. Primary stocks include crude oil or petroleum products held in storage at (or in) leases, refineries, natural gas processing plants, pipelines, tank farms, and bulk terminals that can store at least 50,000 barrels of petroleum products or that can receive petroleum products by tanker, barge, or pipeline. Crude oil that is...in the Strategic Petroleum Reserve [SPR] is included.” The SPR is maintained by the United States Department of Energy and is the world’s largest supply of emergency crude oil. Its build-up has 25 A previous version of the paper considered the period 1949-2014. Until the early 1970s, however, U.S. regulatory agencies such as the Texas Railroad Commission sought to keep oil prices stable by setting production targets. For this reason, I instead focus on the period 1970-2014. 26 See, for example, Kim and Loungani (1992), Rotemberg and Woodford (1996), Backus and Crucini (2000), and Bodenstein, Erceg and Guerrieri (2011a). 27 The oil price is the West Texas Intermediate spot price, deflated using the Consumer Price Index for the United States.

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mainly been politically motivated; it acts as a significant deterrent to oil import cut-offs and is an important tool of foreign policy. For this reason, it has only been used 6-8 times since its build-up, depending on exactly what counts as sales.28

3

Results

The results from the model simulations are now presented and compared to the data. Section 3.1 first evaluates the ability of the model to replicate observed business cycle properties. Section 3.2 then focuses specifically on the distribution of oil-price changes in the model and the data, whereas Section 4 provides impulse response functions.

3.1

Business cycle statistics

Table 2 presents outputs from the simulations of three different models along with the data. First, output is reported for the benchmark model that, in the table, is labelled “With oil”. The second model is labelled “With oil and no storing” and is identical to the benchmark, except that storing of oil is disallowed. For comparison, finally, results are also presented for a standard real business cycle “RBC” model that does not take oil as an input. The RBC model is the same as the benchmark model, but with γ in equation (2) set to zero. This completely eliminates the importance of oil. It is also important to point out that none of the ten moments presented in Table 2 were targeted in the calibration. Even though the benchmark model does not match any of the considered moments exactly, most model moments are relatively close to the data. The ordering of the volatilities of inputs and output in the model coincides with that in the data: oil use is more volatile than both output and hours worked, with the latter being the least volatile of the three. As in the RBC model, the standard deviation for hours worked relative to the standard deviation for output is too small in the model.29 28 The SPR also provides loans that are made on a case-by-case basis to alleviate supply disruptions. Such loans have been issued about ten times. 29 See, for instance, King and Rebelo (1999) for a discussion about this general feature.

16

Table 2: Business cycle statistics in the data and the model Data Models With oil With oil and no storing Standard RBC

std (y) 1.46

std (o) 2.38

std (l) 1.28

std (po ) 17.54

std (R) 1.77

1.54

2.27

1.20

19.21

1.45

2.18

2.97

2.89

74.89

0.00

1.63

-

0.89

-

-

corr (y, l) corr (y, o) corr (y, ΔR) corr (y, po ) AR (1) for po Data 0.88 0.86 -0.05 -0.01 0.95 Models With oil 0.77 0.46 -0.19 0.11 0.83 With oil and 0.88 0.72 0.44 no storing Standard 0.99 RBC The upper half of the table provides standard deviations and the lower half presents correlations. ΔR denotes the net change in the stock of stored oil. All variables are in logarithms and have been detrended with the HP filter using a smoothing parameter of 6.25 except in the last column in the bottom part of the table that reports the autocorrelation coefficient for the log-level of the oil price.

It is interesting to note that the oil price is so volatile even though it is possible to store oil between periods.30 In fact, the volatility of the oil price is more than one order of magnitude larger than the volatility of output in both the model and the data. The volatility that matches the data the least is that for oil inventories, which is too low in the model. The model without storing and the RBC model both fail to match the data. Specifically, the former model produces excessive volatility for all the variables, whereas output is too volatile and labor is not enough volatile in the latter model. Turning to the correlations, the benchmark model predicts a correlation between output and hours worked of about 0.77, which is somewhat lower than the actual correlation of 0.88. Standard real-business-cycle models typically produce substantially higher values for this correlation as can be seen in the last row of the table. The correlation between changes in inventories and output is close to the data, but the correlation between oil use and output is somewhat off. The last column in the lower half of the table presents the autocorre30

It is not reported, but this is true also if there are no physical costs to storing oil.

17

lation for the log-level of the oil price (as in Deaton and Laroque, 1992, 1996). It shows that the oil price is highly autocorrelated both in the data and the model even though the supply shocks are iid. Note also that the autocorrelation coefficient is significantly lower without storing, thus implying that storing is an important explanation for the high level of persistence in the oil price. This point was first made in Deaton and Laroque (1992, 1996) in a partial equilibrium setting. The intuition is that the incentives associated with storing link the current oil price with the expected future price. Deaton and Laroque, however, concluded that a standard partial equilibrium competitive storage model fails to generate the persistence that is observed in the data. In the general equilibrium model here, the oil price is still somewhat less persistent than in the data, but the difference is smaller.31 Overall, storing is necessary for the model to match the data; except for two correlations; the model without storing substantially over- or undershoots all empirical observations.

3.2

The distribution of oil prices in the model and the data

To what extent can the model account for the distribution of oil prices observed in the data? The top graphs in Figure 1 answer that question by plotting the distributions of annual oil-price changes in the data as well as in the model. The graphs show that the two distributions are similar, thus implying that the model economy experiences fluctuations in the oil price that are similar to those in the data. The main difference is that the model distribution has slightly more mass for large, negative oil-price changes. In addition, the model has almost zero mass for price changes of more than 200 percent. The left bottom graph plots the cumulative distribution of oil-price changes in the model and the data and verifies that the model has more mass for large, negative price changes and somewhat less mass for really large price changes. Recall that the oil-price distribution was not 31

See Arseneau and Leduc (2012) for a similar conclusion in a model of commodity prices.

18

Figure 1: Top graphs: the distribution of annual real oil-price changes in the data and the model. Bottom left graph: the cumulative distribution of oil-price changes in the model and the data. Bottom right graph: the distribution of oil prices, conditional on starting out at the stochastic steady state. specifically targeted in the calibration. The conclusion is that the model distribution captures the empirical pattern of relatively few but huge price increases and relatively many but small price decreases. 3.2.1

Hotelling pricing?

Hotelling (1931) shows that the net price received after paying the cost of extraction of a resource in finite supply, such as oil, should grow at the rate of the interest rate. This is a strong theoretical prediction that seems to have weak empirical support for many natural resources.32 Several explanations for why the theory fails to explain the data has been offered, but it is probably safe to say that this discrepancy is still not fully understood.33 32

See, for example, Hart and Spiros (2011). Anderson et al. (2018), for instance, shows that the Hotelling prediction breaks down in a setting where the resource owners have two margins, well-level oil production 33

19

Even though oil is not exhaustible in the model, the presence of storing gives rise to a stochastic Hotelling equation that says that expected oilprice growth times the marginal utility of consumption should equal the interest rate times the marginal utility of consumption.34 This Hotelling equation, however, breaks down whenever the non-negative constraint on stored oil is binding. Consequently, the expected oil-price growth will then be strictly less than the interest rate as is formally shown in Appendix A.3. Note also that even though the expected increase of the oil price between two periods is around two percent (which is the same as the interest rate), most periods will actually feature zero or negative changes in the oil price. This can be seen in the bottom right graph in Figure 1. Specifically, the figure plots the distribution of oil prices conditional on starting out at the stochastic steady state, and more than 50 percent of the density, in fact, supports price reductions.

4

The propagation of shocks

This section evaluates the contribution of each shock to the variations in output, the labor supply, the inventories of oil, and the oil price. Following Koop, Pesaran, and Potter (1996), impulse response functions can be computed as the difference between two forecasts, i.e., IR (s, dt ) = E (Yt+s |Vt = dt , History) − E (Yt+s |Vt = 0, History) ,

(15)

where Yt is an n × 1 random vector, Vt is the n × 1 vector of reducedform disturbances, and dt contains the relevant shocks. The impulse responses can also be allowed to depend on the state variables. Of particular interest is the level of oil inventories. To evaluate the role of inventories for the propagation of shocks, I also compute impulse response functions that condition on the level of oil inventories. These functions are straightforwardly computed by adding the restriction Rt ≤ R to the first term of the right hand side of (15) and where R is a chosen and the rate of drilling new wells, and where the first margin is characterized by a capacity constraint on oil extraction. 34 See equation (20) in Appendix A.2.

20

threshold level. Specifically, the impulse responses are then given by

IR (s, d) =   E Yt+s |Vt = dt , Rt ≤ R, History − E (Yt+s |Vt = 0, History) .

(16)

I set R = 0.05 ∗ E [o], which implies that the level of oil in storage is required to be less than or equal to five percent of the average annual oil consumption when the shocks hit the economy. This value is consistent with the actual amount kept in storage in 1973 when the oil price increased by more than 200 percent, after which the U.S. economy went into a recession. If the SPR is included in the empirical measure of oil in storage, then the amount of stored oil has consistently been above five percent since 1980. As mentioned above, however, the SPR has only been used a few times, which implies that the market may not gain access to that specific oil at all times. Excluding the SPR from the empirical measure of stored oil delivers an average value of about five percent of the average annual oil consumption for the period 1970-2011. Hence, a threshold of five percent does not seem inconsistent with the data also after 1973.

4.1

Impulse responses without conditioning on the level of oil inventories

Figure 2 plots the impulse responses without conditioning on the level of oil inventories. As can be seen, the shock to the capital/labor-efficiency accounts for the bulk of the variation in output, but the three oil-related shocks all have non-negligible effects on this variable. All oil-related shocks also have a somewhat larger influence on the labor supply than the capital/laborefficiency shock. The largest influence on oil inventories comes from the shock to the oil supply, and, as expected, news and oil-supply shocks have opposite effects on the change in inventories of oil on impact. The last row in Figure 2 shows that, of the considered shocks, the news shock has the largest effect on the oil price. In fact, the effect on impact of the news shock is more than eight times as large as that of the supply shock. This illuminates the problem of exclusively focusing on shocks to flow demand and flow supply when trying to understand changes in the oil 21

Figure 2: Impulse response functions without conditioning on the level of oil inventories. a and ao respectively denote the shocks to the capital/labor and the oil efficiency, whereas ξ and η respectively denote the news and oil-supply shocks. price. The above results can be compared to the empirical findings in Kilian and Murphy (2014). Specifically, Kilian and Murphy also consider shocks to the flow demand for oil, the flow supply of oil, and the speculative demand for oil, thus implying a relatively close correspondence to a, η, and ξ in this paper. The main difference is that Kilian and Murphy’s speculative shock is associated with future oil-supply conditions relative to future oil demand, whereas ξ only contains information about future oil-supply levels. The impulse response functions in Kilian and Murphy (2014) first show that ξ has a larger effect on the oil price than η.35 Second, demand shocks have a larger impact on GDP than news and oil-supply shocks. Third, a news shock has a positive effect on inventories on impact, whereas the 35

See Figure 1 in Kilian and Murphy (2014).

22

opposite is true for an oil-supply shock. As can be seen in Figure 2, all these results are also true in the model in this paper. Note finally that, as in Kilian and Murphy (2014), the effect of bad news on the real price of oil would be substantially reduced if the global real activity would be low, i.e., if a negative capital/labor-efficiency shock would be realized simultaneously as a negative news shock. Appendix A.6.2 removes news shocks from the model so that the social planner no longer gets any signals about the future oil supply. The results from that analysis show that news shocks do not affect the unconditional volatilities of inputs and output much.36 Without the news shock, however, the importance of the oil-supply shock, in particular, increases dramatically for the oil price.37 This shock then also has larger effects on output and labor supply relative to with the news shock. This is not very surprising given that there then is no information about the oil supply to which precautionary demand can respond to.

4.2

Impulse responses when oil inventories are low

Figure 3 plots the impulse responses when oil inventories are low. As can be seen, the effects of all shocks are fundamentally different when oil stocks are low. The most striking result is that the importance of the capital/laborefficiency shock is reduced in both relative and absolute terms, whereas the importance of the oil-related shocks increased. The impact of the capital/labor-efficiency shock on output is redced by roughly a factor of two. This reduction comes from the fact that this shock now generates a negative response in labor supply (instead of a positive one as when oil is not scarce). Intuitively, a shock to the capital/labor efficiency increases labor productivity, which incentivizes an increase in the labor supply. Due to complementarity between capital/labor and oil, however, this increase needs to be accompanied by an increase in oil use. When oil stocks are low, this is not possible. Oil is then, in fact, so scarce that labor supply is reduced, and this is what offsets a large part of the positive effect that the shock has on output. The effect on the change in 36 37

See Table 2. The same is true if storing is not allowed.

23

Figure 3: Impulse response functions when oil stocks are low. Specifically, the level of oil in storage is required to be less than or equal to five percent of the average annual oil consumption when the shocks hit. a and ao respectively denote the shocks to the capital/labor and the oil efficiency, whereas ξ and η respectively denote the news and oil-supply shocks. the oil price is also dampened, as can be seen in the first graph in the bottom row of Figure 3. The immediate effect of the oil efficiency shock on output is almost twice as large when oil inventories are low. This shock then relieves the economy from the restraint that oil scarcity imposes. As a result, the oil price falls by 40% in response to the shock (compared to less than 20 percent when oil is not scarce). Maybe most interestingly, news and oil-supply shocks both have substantial effects on output and labor supply when oil is scarce. Indeed, if any of these shocks hit the economy when oil inventories are low, they each generate a four percent contraction in output and a six percent reduction in

24

labor supply. Intuitively, oil scarcity lowers the marginal product of labor (again, because of complementarity between labor and oil), and this leads to a reduction in labor supply. A low elasticity of substitution between capital/labor and oil is crucial for these results. If the elasticity of substitution were high, oil would never impose a constraint on the economy since it would always be possible to use capital and/or labor instead in times of oil scarcity. Oil would then not be important for the business cycle. As stated in Section 1.3, an alternative approach would be to allow the long-run elasticity of substitution to be higher than that for the short run as in Hassler, Krusell, and Olovsson (2017) and Atkeson and Kehoe (1999). This would affect the dynamics in such a way that variables would return faster to their steady state values. It would not, however, affect the effects on impact since these are fully determined by the short-run elasticity of substitution. The largest effect on the change in the oil price induced by the news shock is also when inventories are low, even though the supply shock now also generates dramatic swings in this price. Note though, that the relative changes in output, labor supply, and the oil price are nonlinear. The responses of labor supply and output to a news shock are more than four times larger when oil is scarce, relative to no scarcity, but for the change in the oil price the corresponding difference is less than two times larger when oil is scarce. The results from this and the previous section suggest that, for the most part, oil-related shocks are not very important for understanding the business cycle. Even though these shocks have non-negligible effects on output and labor supply, their largest influence is on the oil price. In these “normal” times, oil is not scarce because additional oil can easily be drawn from the stock of stored oil. About fifteen percent of the time, however, the economy is either at the zero lower bound on stored oil or close to this constraint. In this state, the availability of oil can substantially influence the business cycle. Bad news about the future oil supply and/or an oilsupply shock that hits the economy can then drive the economy into a deep recession that is triggered by oil scarcity.

25

4.3

Do variables respond asymmetrically to positive and negative shocks?

Several empirical papers have suggested an asymmetric relationship between oil prices and economic variables, where positive oil-price shocks have larger effects on GDP growth and labor supply than negative oil-price shocks.38 This view was initially formulated after observing that the recessions of 1973-1975, 1980-1982, and 1990-1991 were all preceded by increases in the price of oil, but the sharp decline in the oil price of 1985-1986 did not lead to an economic boom in oil-importing countries. The view that the relationships between oil prices and other economic variables are asymmetric, however, has not been fully accepted. As shown by Kilian and Vigfusson (2011, 2016), the estimation methods used in the mentioned studies produce inconsistent estimates. Consequently, compelling evidence in support of asymmetric relationships does not seem to exist. This section evaluates to what extent model responses to positive and negative shocks are asymmetric. Since news and oil-supply shocks both are asymmetric by assumption, I focus on the effects of the (symmetric) factor-specific shocks. The response functions are again allowed to depend on the level of oil inventories, and to improve comparability the impulse responses to the negative shocks in Figures 4 and 5 below are multiplied by minus one. Full symmetry is then characterized by the positive and the negative impulse responses being plotted right on top of each other. Figure 4 does not condition on oil inventories and presents results for both positive and negative shocks.As can be seen, the impulse responses are slightly asymmetric, but the effects are small. In particular, output responds slightly stronger to a negative than a positive oil-efficiency shock. Labor supply also responds relatively more to a negative shock, and this is true for both types of shocks. For oil inventories, the asymmetric effects persist for several periods for both types of shocks. The change in the oil price, finally, is slightly larger immediately after a positive shock to 38

See, for instance, Mork (1989), Bernanke, Gertler, and Watson (1997), Hamilton (1996, 2003). Papers that build on an asymmetric relationship include Davis and Haltiwanger (2001), Lee and Ni (2002), Jones, Leiby, and Paik (2004), and Ramey and Vine (2010).

26

Figure 4: Impulse response functions in the model after positive and negative shocks without conditioning on the level of oil inventories. The responses to the negative shocks have been multiplied by minus one. Full symmetry is then characterized by the positive and the negative impulse responses being plotted right on top of each other. a and ao respectively denote the shocks to the capital/labor and the oil efficiency. the capital/labor-efficiency shock than after a negative shock, whereas the opposite is true for the oil-efficiency shock. There are, thus, some asymmetric effects in “normal” times, but these are too small to be economically significant. Figure 5 plots responses when the economy is closer to the zero lower bound on stored oil, and it reveals strong and pronounced asymmetric responses. In this case, both output and labor supply respond substantially more to a negative shock to the capital/labor efficiency than to a positive shock. In fact, the negative shock induces a drop in output of almost five percent and an increase of the oil price by 30 percent. A positive shock, in contrast, only generates an increase in output of two percent, and the oil 27

Figure 5: Impulse response functions in the model after positive and negative shocks when oil stocks are low. Specifically, the level of oil in storage is required to be less than or equal to five percent of the average annual oil consumption when the shocks hit. The responses to the negative shocks have been multiplied by minus one. Full symmetry is then characterized by the positive and the negative impulse responses being plotted right on top of each other. a and ao respectively denote the shocks to the capital/labor and the oil efficiency. price increases by 10 percent. The effect of the oil-efficiency shock on labor supply is almost four times larger for a negative shock than for a positive shock. These asymmetries originate from the constraint that the zero lower bound on stored oil imposes. Note that the positive shock to the capital/labor efficiency induces a complete run-down of inventories. This means that the social planner would like to input more oil into production, but this is not possible due to the binding constraint on stored oil. Again, oil is so scarce that labor supply responds negatively to the positive productivity shock, which severely dampens output. The effect is not symmetric 28

for a negative shock because the constraint does not bind then.39 A similar logic applies for the oil-efficiency shock. In this case, inventories are instead completely run down in response to the negative shock, and this is what causes the reduction in output and labor supply to be larger than the expansion occurring after a positive shock. In both cases, the constraint contributes to making recessions deeper than expansions. For the capital/labor-efficiency shock, the constraint hinders output from expanding enough in response to the positive shock, and for the oil-efficiency shock the constraint makes the contraction more severe than what it would have been without the binding constraint. The constraint is also what causes the small asymmetries in “normal” times that are displayed in Figure 4. Specifically, the economy moves stochastically through the state space, and when it approaches the constraint, the asymmetric effects become increasingly pronounced. Similar to in Section 4.2, the analysis thus reveals that the extent to which economic variables respond asymmetrically to positive and negative shocks depends crucially on the state of the economy. These results indicate that it is potentially important to condition on the state of the economy prior to when a shock that induces a large increase in the oil price hits in order to asses the importance of that specific shock on output, labor supply, and the oil price. In addition, since the model economy spends about fifteen percent of the time being close to the zero lower bound on stored oil, this suggests that models that are linearized around a steady state might miss important nonlinear and asymmetric effects.

4.4

Are oil-price increases followed by economic contractions?

A long-standing question in the literature concerns the relationship between oil prices and recessions. Hamilton (1983, 2011) show that all but one of the U.S. recessions between World War II and 2011 was preceded by a dramatic increase in the price of crude petroleum. Kilian and Vigfusson (2017), however, points out that only statements about how many times 39

Recall that a symmetric response would have the dashed and the solid lines plotted right on top of each other.

29

oil-price increases are followed by recessions speak to the predictive power of oil prices. The authors argue that there have been eight distinct episodes of net oil-price increases during the observed period and only five of them were followed by recessions. The model in this paper features both business cycles and substantial oil-price fluctuations, which makes it ideal for analyzing the relationship between oil-prices and economic activity. I therefore focus on unfiltered data and analyze to what extent substantial oil price increases are followed by contractions in economic activity. NBER defines a recession as “a significant decline in economic activity spread across the economy, lasting more than a few months, normally visible in real GDP, real income, employment, industrial production, and wholesale-retail sales.” I consider a slightly simpler measure and define a recession as when GDP falls below its trend. 40 Table 3 presents the share of substantial oil-price increases that are succeeded by contractions in economic activity. Table 3: Oil-price increases and economic contractions in the model Storing Oil-price increase in t Share of contractions in t + 1 40% 0.52 50% 0.57 60% 0.63 No storing Oil-price increase in t Share of contractions in t + 1 40% 0.44 50% 0.44 60% 0.44 The first column gives oil-price increases by size, and the second column presents the share of these increases that are followed by a contraction in economic activity.

The upper half of the table shows that, when storing is allowed, large oil-price hikes tend to be followed by contractions in economic activity. It also shows that far from all price increases are followed by a contraction and the probability of a recession increases as the oil price increases. The numbers presented in Table 3 are, in fact, not that far from the share in the data of 62.5% as reported in Kilian and Vigfusson (2017). When storing is allowed, the oil price jumps when the news shock hits the economy, i.e., one period before the supply has actually been affected. 40

Kilian and Vigfusson (2017) analyses the recessions defined by the NBER.

30

The reason for the jump in the oil price is that the news shock induces the social planner to move oil from current production to storage to increase the oil buffer against the future shortfall.41 This raises the marginal product (and price) of oil. If the oil supply then falls in the subsequent period, the implied oil scarcity lowers the marginal product of labor. The result is lower levels of oil use, labor supply and output. Oil then remains scarce for a number of periods because the social planner needs to rebuild inventories of oil again after the initial rundown as can be seen in the the third row of Figure 3. Hence, labor supply and output also remain low for a number of periods. The lower half of Table 3 reveals that the model without storing is unable to match the empirical relationship between oil-price changes and economic contractions. Only 44 percent of the times is a large oil-price increase followed by a contraction in economic activity. The intuition is that, without storing, it is not possible to move oil from current to future production. The oil price will therefore spike simultaneously with the reductions in inputs and output. In the subsequent period, oil supply is again high 90 percent of the time.42 Due to complementarity between oil and labor supply, labor supply must also be high, which implies a high level of output.

4.5

Oil-price changes and inventories

Sections 4.1 and 4.2 showed that the magnitude of oil-price changes is negatively related to the level of oil stocks. The question is if the data support such a relationship. To analyze whether the negative correlation between inventories and oil-price changes is present in the data, I regress annual oil-price changes on the stock of oil inventories.43 Specifically, I run the following regression Δpo,t = a + b ∗ Effective_inventories t−1 + ut , where Δpo,t ≡ po,t /po,t−1 is the measure of annual oil-price changes, Ef41 This can be seen in Figures 2-3, where the changes in the oil stock (ΔR) are positive on impact. 42 The unconditional probability that news is good is 0.90. 43 See also Kilian and Murphy (2017), which takes inventories of oil into account.

31

fective_inventories is a measure of the stock of oil in inventories and ut is an error term. It is important to point out that I am only looking here for a correlation between two variables. Hence, I do not take a stand on whether one variable could be considered exogenous. As explained in Section 1.3, annual oil consumption has been growing over time during the considered period, which implies that the measure of inventories must be scaled to control for the fact that an inventory of 100 million barrels in 2015 was a relatively small buffer compared to in 1970. For this reason, Effective_inventories is Actual_inventories t defined as follows: Effective_inventories t = . 1 t o x+1

j=t−x

j

The definition of effective inventories relates actual inventories (in quadrillion Btus) in year t to average oil consumption (in quadrillion Btus) between year t − x and t. I set x = 2, which implies averaging over three years, but the results are similar for alternative values for x. Actual inventories are measured in January each year. Results are only reported for an inventory measure that excludes the SPR. The main reason for this is that an SPR-inclusive Effective_inventories variable is not stationary, thus resulting in an unbalanced regression. Excluding the SPR from Effective_inventories, however, results in a stationary measure and, thus, a balanced regression. As explained in Section 2, the SPR is mainly a political tool that only has been used a few times over a 40-year period. It therefore seems reasonable to assume that the market does not fully rely on the SPR when deciding how much precautionary oil to hold since it is unlikely that these stocks will be used should there be supply short fall. The regression results are displayed in Table 4. As can be seen, the Table 4: Regression results 1972-2014 -88.89∗∗ (38.92) Constant 97.58∗∗ (38.70) N 41 0.0966 R2 (Adjusted) The standard errors are provided in parentheses; ∗ significant at 10%; 5%; ∗∗∗ significant at 1%. Effective_inventories

∗∗

significant at

point estimate for the effect of the level of effective inventories on oil-price 32

changes is negative and statistically significant. The interpretation is that a reduction of the stock of stored oil by 50 percent is associated with a five-time increase in the oil price. I conclude that the negative correlation between oil-price changes and inventories identified in Sections 4.1 and 4.2 is also present in the data.

5

Discussion about the assumptions and sensitivity analysis

In the model, supply shocks are preceded by news shocks that signal potential short falls. Naturally, this assumption matters for the relative importance of supply versus news shocks. If variations in oil supply cannot be anticipated, there is no room for large jumps in the oil price to originate from increasing precautionary demand for oil. The assumption that changes in the oil supply are, at least, somewhat predictable seems reasonable as a first approximation. Kilian (2008a) computes the exogenous short falls associated with the Iranian Revolution of 1978/79, the Iran-Iraq War of 1980-1988, the Gulf War of 1990/91, the Iraq War of 2002/03 and the civil unrest in Venezuela in 2002/03. In all these cases, noisy information was available prior to the specific events. One way to evaluate whether the benchmark specification where supply shocks are preceded by news shocks imposes too little risk in the model is to compare future prices for oil in the model and in the data. Oil futures that were traded on the New York Merchantile Exchange (NYMEX) over the period 1983-2015 are available from the U.S. Energy Information Administration.44 The standard deviation of these prices is 14.29 percent, which is basically the same as the standard deviation for the spot price over the same period: 14.48. In the model, the standard deviation of the 12-month future price is 19.19, i.e., roughly the same as for the spot price.45 The fact 44

The fact that the longest maturity is four months (compared to 12 in the model) should only be a minor concern. See Alquist and Kilian (2010) for a related study on oil futures. 45 The futures price is commonly used by policy institutions, such as central banks, as a proxy for the market’s expectation of the spot price. Their accuracy for this purpose is questioned by Alquist and Kilian (2010). Baumeister and Kilian (2015) provides a measure of oil-price expectations, and this measure is less volatile. The measure is only

33

that the volatility of future prices is not significantly lower than spot prices in the model suggests that supply shocks do not impose too little risk in the model relative to the data. Appendix A.6.1 presents results for higher values for the elasticity of substitution between capital/labor and oil. The results show that a high elasticity fails to generate enough volatility for the oil price. The oil price is also substantially less persistent with a high elasticity.

6

Conclusions

This paper analyzes the interaction between oil prices and macroeconomic outcomes by setting up a general equilibrium model where output is produced with a capital-labor composite and oil, all factor prices are endogenous, and it is possible to store oil above ground between periods. In contrast to most models in the literature, the model provides an explicit role for changes in precautionary demand to affect the oil price. The driving forces are factor-specific technology shocks, oil supply shocks, and news shocks about future oil supply. The results show that the model roughly matches a large number of observed business-cycle properties. The distribution of oil prices is similar in the model and the data, implying that the model economy endogenously goes through episodes with dramatic swings in the oil price. The most important reason for large increases in the oil price comes from increasing demand to hold oil for precautionary/smoothing reasons. Most of the time, oil-related shocks are not particularly important for understanding the business cycle. When the economy is close to or at the zero lower bound on stored oil, however, the oil-related shocks may have substantial impact on the business cycles. Negative news about the future oil supply and/or oil-supply shock can then drive the economy into a deep recession that is triggered by oil scarcity. The analysis, thus, reveals highly state-dependent and nonlinear effects of the shocks. available from 1992, however, and the lower volatility comes exclusively from the Great Recession, where the market failed to predict the large swings in the oil price. These swings seem to have been driven by demand shocks rather than supply shocks.

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