Not All Oil Price Shocks Are Alike: A Neoclassical Perspective

Transcription

1 Not All Oil Price Shocks Are Alike: A Neoclassical Perspective Vipin Arora U.S. Energy Information Administration Junsang Lee SungKyunKwan University Pedro Gomis-Porqueras DeakinUniversity Abstract This paper studies the consequences of endogenizing oil prices and quantities when accounting for business cycles facts and crude oil dynamics. We first show that a model with endogenous crude oil can better account for business cycle data than models with exogenous oil prices or oil quantities. In particular, it can better account for the co-movements and first-order autocorrelations of crude oil observables. Our results also highlight the fact that a model which takes the real oil price as exogenous cannot capture the interactions between this price and macroeconomic aggregates in response to oil demand shocks. Similarly, a model that takes oil production as exogenous has difficulties when confronted with changes in oil supply. We also show that responses to oil shocks depend crucially on how oil is modeled. The divergence in impulse responses for consumption and hours across models lasts for more than twenty quarters implying distinct welfare implications after the economy is hit by oil supply shocks. JEL Classification: E37, F47, Q43. Keywords: Oil price, two regions, business cycle, endogenous. The analysis and conclusions expressed here are those of the authors and not necessarily those of the U.S. Energy Information Administration. We have benefitted greatly from the comments and suggestions of Dirk Krueger, Felix Klueber, Eric Leeper, Bruce Preston, Rod Tyers, Bob Gregory, Tim Kam, Timo Henckel, Peter Robertson, E. Juerg Weber, Justin Wang, Scott McCracken, and Yiyong Cai. We also received very helpful comments in seminars at Australian National University and University of Western Australia. Finally we would like to thank the participants at the 7 th WMD at University of Queensland as well as the Monash Macro Workshop for their valuable suggestions. U.S. Energy Information Administration, 1000 Independence Ave., S.W., Washington, D.C vipin.arora@eia.gov Deakin University, School of Accounting, Economics and Finance, 70 Elgar Road, Burwood, VIC 3125, Australia. Department of Economics,College of Economics, SungKyunKwan University, Seoul, Korea 1

2 1 Introduction There is a large body of work that explores the relationship between oil price changes and macroeconomic performance. 1 Much of the empirical literature has focused on the U.S. and assumed an exogenous oil price since the seminal contribution of [19]. A decade later, [30] incorporated an exogenously determined oil price in a real business cycle (RBC) framework. 2 Subsequent papers in the RBC literature have also assumed oil prices to be exogenous while including additional non-oil related features to better account for business cycle facts. 3 [6] and [7] challenge this exogenous assumption, and [25] traces major real oil price increases since the 1970 s to global aggregate demand or demand specific to the oil market. 4 In this view the real price of oil is ultimately determined by market forces and subject to demand and supply shocks like any other good. The empirical relevance of such supply and demand forces in shaping crude oil dynamics motivates our work. The objectives of this paper are to provide a framework for studying crude oil dynamics over the business cycle, and to determine the quantitative importance of endogenizing both the real oil price and its demand when accounting for business cycle facts. We begin with a standard real business cycle model where the real oil price is exogenous in the spirit of [30]. We then follow [4], [10], and [36] and assume that oil demand is exogenous while the oil price is endogenous. Our third framework contains both endogenous oil quantities and prices by including an oil exporting region. 5 This final environment allows for technology shocks in final goods production (which generate a stochastic demand for oil), and technology shocks in oil production (which generate a stochastic supply of oil). These shocks jointly determine the underlying dynamics of the economic environment. As a robustness check we also consider variable capacity utilization as in [18], or market power as in [41]. 6 Our paper is one of the few that explicitly models the crude oil market. Two other exceptions are [37] and [38], who endogenize both oil prices and quantities while studying their impact on macroeconomic aggregates. [37] show that oil played an important role in the Great Moderation, helping reduce the volatility of both inflation and GDP growth in the U.S. [38] study the monetary policy trade-offs when facing a dominant crude oil producer. Both of these papers report simulated oil price volatilities, but not other summary statistics such as the co-movement of oil demand with output, thus not fully exploring the business cycle properties of an endogenous crude oil market. Similarly, [5] use a multi-region model with endogenous oil production and prices. They find that changes in the oil price are best understood as endogenous, and that oil price shocks have different impacts depending on their source. The authors do not report oil statistics over the business cycle, which makes it difficult to asses whether this framework is well suited to analyze the propagation 1 See [12], [7], [22], [20], and [23] for overviews of this literature. 2 Their model can only account for a small portion of the variance of U.S. output growth. [41] introduce mark-up pricing into an otherwise standard real business cycle model to improve these predictions, and are able to replicate some of the observed movements in U.S. GDP and wages after an oil price shock. [18] obtains similar results using variable capacity utilization in lieu of mark-up pricing. 3 See [3], [33], [14], [1], [34], [13], [17], [8], [32], [9], and [39] among others for papers that take the oil price to be an exogenous process. 4 See also [24], [28], [29], and [21] for more on this issue. 5 We do not incorporate exhaustibility in the availability of oil or oil storage, as in the majority of papers in the literature. 6 These two extensions are often used in conjunction with an exogenous oil price or production. See for example [33], [14], [1], [34], [13], [44], [8], [32], and [9]. 2

3 of oil shocks in the economy, or how relevant it is in accounting for business cycle facts. What are the benefits of considering endogenous crude oil prices and quantities? Qualitatively, using such a framework accounts for the joint determination of oil prices and economic activity. There are quantitative benefits as well. Our model with an endogenous oil market is able to fit the data better than the environments with either exogenous oil prices or exogenous oil quantities. 7 The model with exogenous oil prices yields counterfactual co-movements between the real oil price and output. When oil production is exogenous, the magnitude of the correlation between non-u.s. oil production and output is vastly different from what is observed in the data. In contrast, when both the oil price and its quantity are endogenous the model better accounts for oil-related observables. The predicted co-movement between the real price of oil and output is comparable to the model with oil production exogenous, but there is an improvement in matching the co-movement between non-u.s. oil production and output. Moreover, the predictions for the first-order autocorrelation of the real price of oil also improve. The manner in which the oil market is modeled leads to differences in impulse responses to oil supply shocks. Consumption responds most to the shock when the oil price is exogenous, and it responds the least when both the price and the quantity of oil are endogenous. This is also true of hours worked, while investment has the opposite response. The divergence in impulse responses for consumption and hours across models lasts for more than twenty quarters. These differential patterns based on how oil is modeled imply distinct welfare implications after the economy is hit by oil supply shocks. They also highlight a point made by [25], that if oil prices are assumed to be exogenous over the business cycle then the implied macroeconomic responses to oil price changes predicted by a dynamic stochastic general equilibrium model may be misleading. 8 Discrepancies in the impulse responses of output, consumption, investment, and hours across models are also observed when the economy faces oil demand shocks. Finally, endogenizing oil is better able to reproduce the implied impulse responses generated by demand shocks when compared to what is observed in the data through the lens of a reduced form VAR. 9 A model with exogenous oil supply can be used to assess the impact of large, one-time shock, but is not suitable for studying the dynamics of sustained oil supply shocks. An advantage of using a framework where both the oil price and its demand are endogenous is that it is better equipped to deal with both supply and demand shocks affecting the oil market. The fact that endogenizing oil improves the predictions of business cycle models is not surprising, as such a model can capture important feedback mechanisms between oil prices, demand for oil, and macroeconomic observables. Our findings are consistent with the view put forth by [6], that allowing endogenous determination of oil observables within a general equilibrium framework is key in understanding how oil dynamics affect domestic macroeconomic aggregates. 7 The endogenous oil framework has the lowest sum of squared errors when comparing model results to sample data for the standard deviation, the relative standard deviation to GDP, the correlation with GDP, and the first-order autocorrelations. 8 The latter point has been elaborated and reaffirmed in a number of recent empirical and theoretical studies including [26], [38], [11], and [27]. 9 This is a difficult exercise since it requires taking a stand on how oil shocks are identified in a VAR framework, and there are many debates in the oil and macroeconomy literature on how best to do this. 3

4 2 The Model The basic building block is a real business cycle model that allows for variable capacity utilization and monopolistic competition. As a benchmark we first consider either the oil price or oil production to be exogenous. We then consider both of them to be endogenous. The economic environment has an oil producing and an oil consuming region, both with a representative consumer that owns the capital stock. The oil producing region has monopolistically competitive intermediate goods producers, and a final oil producer that exports oil to the consuming region, where it is used to produce intermediate goods. These intermediate goods producers are monopolistically competitive, and each can vary the rate at which they use capital in production. Each intermediate goods producer sells their output to a perfectly competitive final goods producer. Notice that all oil is purchased by the intermediate goods firms. This just reflects the fact that oil used in gasoline, plastics and energy must first be processed before households can consume these final goods. As in the standard real business cycle model, the dynamics in the economy are driven by supply shocks. In particular, we consider the standard real business cycle technology shock on final production in the consuming region, and a technology shock on oil production. These processes induce a stochastic event, s t, in each period t. The history of events up to and including t is denoted by s t = (s o, s 1,..., s t ). The initial realization, s o, is known. All equilibrium prices and allocations are a function of these histories, but the dependence will be suppressed throughout the paper for simplicity. Domestic and foreign agents have access to complete asset markets. Thus the household in each region has access to a contingent claims market where an array of Arrow securities, denoted by B t+1 (s t+1 s t ) for the oil consuming region and Bt+1 (s t+1 s t ) for the oil producing region, are traded. These claims pay one unit of final consumption goods at t + 1 if s t+1 is realized given the history at t is s t. The price of either security is denoted p b,t (s t+1 s t ). 2.1 Representative Consumers In the oil consuming region the representative household chooses consumption (C t ), labor (N t ), capital stock (K t+1 ), holdings of Arrow securities (one for each possible realisation of s t+1 ) and the capacity utilization rate (T t ) as to maximize expected utility: max {C t,n t,k t+1,{b t+1 (s t+1 s t )} st+1,t t} t=0 E t { t=0 } β t C1 σc t (1 N t ) 1 ξ + ξ 0 1 σ c 1 ξ subject to the budget constraint and the capital accumulation equation: C t + I t + p b,t (s t+1 s t )B t+1 (s t+1 s t ) = w t N t + r t T t K t + B t + π t s t+1 (2) I t = K t+1 (1 δ t )K t (3) where I t is investment, w t is the wage rate, r t is the return to capital, π t is firm s profits, β is the discount factor, δ t the depreciation rate of capital, σ c the coefficient of relative risk aversion (1) 4

5 (CRRA), ξ is a parameter which determines the labor supply elasticity, and ξ 0 is a parameter which determines labor supply. Because of variable capacity utilization, the depreciation rate is a function of the capital utilization rate so that: δ t = δt η t (4) with δ being a constant, and η (1 < η) a utilization parameter. Note that depreciation is convex in the utilization rate. Thus an increase in utilization raises depreciation, and successive increases raise depreciation by a larger and larger increment. Consumers in the oil producing region solve an identical problem, except they do not choose a capacity utilization rate. 2.2 Firms In the oil consuming region, there is a continuum of intermediate goods producing firms indexed by i [0, 1] that behave as imperfect competitors. The firms produce differentiated types of intermediate goods [Y t (i)] by choosing oil [Q t (i)], capital, and labor to maximize profits: max Q t(i),k t(i),n t(i) p y,t (i)y t (i) p q,t Q t (i) r t T t K t (i) w t N t (i) (5) where p y,t (i) is the price of a firm s good and p q,t denotes the price of oil. Capital services (J t ) are a constant elasticity of substitution (CES) composite of the capital stock and oil given by: J t (i) = [γq t (i) τ + (1 γ)[t t (i)k t (i)] τ ] 1 τ (6) where γ is an oil share parameter, and τ = (σ qk 1) σ qk, with σ qk the elasticity of substitution between oil and capital. 10 The production technology of intermediate goods is Cobb-Douglas with ψ denoting the oil share in production: Y t (i) = Z t J t (i) ψ N t (i) 1 ψ (7) where Z t is exogenous (aggregate) total factor productivity (TFP) that evolves as follows: ln Z t = ρ ln Z t 1 + ɛ t (8) and ρ captures the persistence of the shock. The innovation ɛ t i.i.d N(0,σ 2 v), where σ v denotes the standard deviation. The final goods producing firm behaves competitively and chooses these different intermediate input types as to maximize per period profits which are given by: max Yt(i)di Y t p y,t (i)y t (i)di (9) 10 The assumption taken here is that oil and capital are weak substitutes, and this is standard in the current framework as outlined in [30]. [2] provides some evidence in support of this assumption. 5

6 subject to: [ Y t = ] 1 Y t (i) θ θ di (10) where 1 θ is the markup. From now on, variables specific to the oil producing region are denoted with ( ). In the oil producing region, we assume there are a continuum of intermediate goods producing firms indexed by i [0, 1] that behave as imperfect competitors. The firms produce differentiated types of oil [Q t (i )] by choosing capital [Kt (i )] and labor [Nt (i )] to maximize profits: max K t (i ),N t (i ) p q,t (i )Q t (i ) r t K t (i ) w t N t (i ) (11) subject to a Cobb-Douglas production function with α denoting the capital share in production: Q t (i ) = Zt K (α) t (i )N (1 α) t (i ) (12) where α (0 < α < 1) is the capital share in production. Zt is exogenous (aggregate) total factor productivity (TFP) that follows the same process as Z t, but may have a different first-order autocorrelation coefficient and volatility. The final oil producing firm behaves competitively and chooses these different oil types as to maximize per period profits which are given by: subject to: max Qt(i )di Q t (i ) p q,t (i )Q t (i )di (13) [ Q t (i ) = Q t (i ) θ di ] 1 θ (14) where 1 θ is the markup. The optimality conditions and equilibrium concept are standard and outlined in Appendix Data and Calibration We consider quarterly U.S. data for the period 1974 to Our focus is on the U.S. to ease comparison with other papers in the literature. The observables that we use to calibrate and judge the model are real GDP (Y t ), real consumption (C t ), real investment (I t ), hours worked (N t ), the real oil price (p q,t ), and non-u.s. oil production (Q t ). The sample period begins in 1974 because the data series we use for the oil price is available from this point forward. The first four observables are taken from the Federal Reserve Economic Database (FRED), the real oil price is the deflated U.S. refiner acquisition cost of oil imports from the U.S. Energy Information Administration (EIA), and the non-u.s. production data comes from the EIA as well. Imported refiner acquisition costs are used because they are the costs paid by those who use oil as 6

7 an input to production, which is consistent with the model. Non-U.S. oil production is used instead of global oil production because there is no oil produced by the oil consuming region in the model. This simplification is unlikely to be important as the U.S. share of global oil production is roughly seven percent. Additional details regarding the data can be found in Appendix 2. Following [42], all time series except the real oil price are HP filtered with a smoothing parameter of This HP filtering procedure is standard for macroeconomic aggregates such as GDP, consumption, investment and hours. Non-U.S. oil production is also filtered because its correlogram shows evidence of a non-stationary process. Although there is ongoing debate in the literature about the order of integration of the real oil price, we filter the real oil price (p q,t ) in what follows. 11 The first four rows of Table 1 summarize standard business cycle statistics. 12 Consumption is less volatile than GDP over this time horizon, and the correlation between the two is almost 87%. Investment has a stronger correlation with GDP at over 91%, and is also 4.9 times more volatile than GDP. Hours worked are strongly procyclical at almost 89%, and are 1.25 times as volatile. Hours have a higher first-order autocorrelation than GDP, consumption, or investment. Variables Description Corr(X t, Y t ) SD SD X /SD Y Corr(X t, X t 1 ) Y t Real GDP C t Real Consumption I t Real Investment N t Hours p q,t Real Oil Price Q t Non-US Oil Production Table 1: Quarterly Real U.S. and Oil Market Summary Statistics The fifth row of Table 1 shows there has been a positive correlation, just over 15%, between the real oil price and U.S. GDP. Unsurprisingly, the oil price is very volatile relative to U.S. GDP with a relative standard deviation of roughly The real oil price series also has a first-order autocorrelation which is below the values for the macroeconomic aggregates. The final row shows that non-u.s. oil production has a positive correlation with U.S. GDP, at over 33%. It has been 2.5 times more volatile than U.S. GDP over the sample period, but is less autocorrelated than the other macroeconomic observables with a value of The model parameter values are calibrated to match stylized facts in the data; some are given standard values and others are obtained by the simulated method of moments. In particular, the CRRA parameters (σ c and σ c ), discount factors (β and β ), and capital shares (ψ and α) in both regions take standard values for a quarterly model of 2, 0.99, and 0.36, respectively. The depreciation parameter in the oil producing region (δ ) has also the standard value of The depreciation rate in the oil consuming region (δ) is chosen so that the steady-state capital to output ratio is 12, consistent with the calibration in [17]. When variable capacity utilization is added to the model, the steady state level of δ t is set to 0.025, and η is chosen so that the steady-state capital to output ratio is 12 in the oil consuming region. This capital to output ratio is consistent across all different versions considered in the paper. The oil share parameter in capital services (γ) is chosen so that the share of oil in final goods 11 See [16] for more on this debate. 12 SD stands for standard deviation. 7

8 output matches the average U.S. value of oil imports of 0.015, which is consistent with [1]. To allow for unbalanced trade, we choose the size of the oil consuming region relative to the oil producing region (µ) so that the ratio of U.S. imports from major oil producers to exports to major oil producers over the sample is 1.4. The parameters ξ and ξ, are set at 0.5, which imply a standard Frisch elasticity of 2. The other labor parameters, ξ 0 and ξ0 are chosen so that labor supply in either region is 0.33 of available time. In the extension with monopolistic competition, θ is chosen to be 0.9, as in [15]. We set θ =1, both because we lack a good estimate and changing this parameter does not substantially change our results. Each of the parameters outlined to this point are summarized in panel (a) of Table 7 in Appendix 2. The remainder of parameters in the model that describe the shock processes are determined by the simulated method of moments as in [10]. The exact values are summarized in panel (b) of Table 7 in Appendix 2. The parameter values are consistent across all variants used below and include the elasticity of substitution between oil and capital (σ qk ) in the consuming region, the first-order autocorrelations on each shock process (ρ, ρ, ρ q, ρ po ), and the volatilities of each shock process (σ v, σ v, σ v,q, σ v,po ). Each model is calibrated by minimizing the square of the distance between simulated model moments and those observed in the sample data. The relevant metric is calculated using the standard deviations and first-order autocorrelations of U.S. GDP, consumption, investment, hours, the real oil price, and non-u.s. oil production. Each of the simulated values are normalized by scaling by the size of the corresponding statistic in the data as in [10]. A key parameter in the model is the elasticity of substitution between oil and capital. The calibrated values for this parameter range from 0.21 in the exogenous production case to 0.31 in the endogenous case. All of these values fall in the range both estimated and summarized in [35]. The calibrated values of this parameter are below other estimates [0.4 as in [28]], but above others [0.09 as in [4]]. The calibrated first-order autocorrelations and volatilities on the oil consuming region TFP processes are similar to standard values in the real business cycle literature. The TFP process in the oil consuming region has a relatively low value for the first-order autocorrelation (0.412), as do the processes for the oil price (0.240) and oil production (0.240) in the other two models. The respective volatilities on each of these shocks (0.076, 0.176, 0.034) are substantially higher than that for consuming region TFP, mainly because the oil price is so volatile relative to GDP in the data. A solution to the model is approximated using standard techniques. We first find the values for each endogenous variable in the deterministic steady state. We then log-linearize the model equations around these steady state values. Finally, this system of log-linear equations is solved using the method of undetermined coefficients, as in [43]. The reported statistics from all the models considered in this paper are not HP filtered, as they are stationary by construction. 3 Quantitative Results We first consider a situation where either the price or quantity of oil is exogenous. We then analyze the case where both oil prices and quantities are endogenously determined. Given that introducing variable capacity utilization as in [18] or market power as in [41] delivers similar results relative to the competitive case, from now on we limit our reporting to the competitive case. 8

9 3.1 Exogenous Oil Prices In order to have exogenous oil prices, we assume that the oil price follows an AR(1) process and that oil production is exactly what the oil consuming region demands. This structure is standard in the literature [see e.g. [33]]. The specific calibration for this model is given in Table 7 of Appendix 2. Note that equation (28), which is in the appendix 1, can be rearranged as follows: ( pq,t J ρ t Q t = ψγy t ) 1 ρ 1. We can clearly see from the previous expression that a rise in the oil price leads to a fall in demand (Q t ). It follows that the demand for capital services (J t ) will decrease (capital and oil are only weak substitutes), so that output (Y t ) will fall. Of course this negative correlation between the oil price and final goods output may be off-set somewhat by general equilibrium effects. But these can only work through Y t because p q,t is exogenous and J t depends on oil, for which the price rises, and capital, which is fixed in the current period. This highlights one important feedback mechanism which is missing in a model without an endogenous oil price. The quantitative implications of having an exogenous oil price process are summarized in Table 2. C t I t N t p q,t Q t Data Model (a) Correlations with Y t Y t C t I t N t p q,t Q t Data Model 1.00 (0.016) 1.00 (0.020) (0.012) (0.011) 4.88 (0.078) 2.82 (0.055) 1.25 (0.020) (0.008) (0.185) 9.29 (0.181) 2.50 (0.040) 2.42 (0.047) (b) Standard Deviations Relative to Y t, Absolute Standard Deviations in Parentheses Y t C t I t N t p q,t Q t Data Model (c) First-Order Autocorrelation Table 2: U.S. Business Cycle Predictions with Exogenous Oil Prices The implied model co-movements of the standard real business cycle observables are similar to those observed in [30]. In particular, the correlations of consumption and investment with respect to final goods output are both close to those observed in the data. However, the co-movement of hours worked is counterfactual. The relative volatilities of consumption and investment are both lower than in the data. For hours worked, the model accounts for about 35% of the relative volatility. The first-order autocorrelations of the macroeconomic aggregates are slightly higher than the ones observed in the data with the exception of the real oil price, which is three times lower. In general, the business cycle properties of the exogenous oil price model with respect to macroeconomic observables are in line with standard real business cycle models [see [31]]. 9

10 The main benefit of having a model with an exogenous oil price is that the relative volatility of the oil price can account for around 80% of the data. Somewhat surprisingly, the model s predictions with respect to oil production/demand perform also relatively well, accounting for about 97% of the observed value. The major drawbacks of having an exogenous oil price are the implied correlations with output. The co-movement of the oil price and output and the co-movement of hours and output are both counterfactual. The negative correlation between the oil price and final goods output follows directly from the fact that the price is unable to adjust with the demand for oil as shown above. This lack of general equilibrium effects is also reflected in the implied firstorder autocorrelation, which is far lower that what is observed. We conclude from the implied co-movements that models with an exogenous oil price are not well suited to study the impact of oil price changes on economic performance. Moreover, such models are unable to analyze variations in oil demand which might be important to the economy. 3.2 Exogenous Oil Quantities In this new environment oil demand (or non-u.s. production) is assumed to follow an AR(1) process. The specific calibration for the model is given in Table 7 of appendix 2. The oil price is endogenous here, and adjusts to the appropriate level given by the exogenously specified supply. The quantitative implications of having an exogenous oil price process are summarized in Table 3. C t I t N t p q,t Q t Data Model (a) Correlations with Y t Y t C t I t N t p q,t Q t Data Model 1.00 (0.016) 1.00 (0.024) (0.012) (0.011) 4.88 (0.078) 3.27 (0.080) 1.25 (0.020) (0.012) (0.185) 7.72 (0.188) 2.50 (0.040) 1.44 (0.035) (b) Standard Deviations Relative to Y t, Absolute Standard Deviations in Parentheses Y t C t I t N t p q,t Q t Data Model (c) First-Order Autocorrelation Table 3: U.S. Business Cycle Predictions with Exogenous Oil Production The co-movements of macroeconomic aggregates are in line with the environment with exogenous oil prices, with the exception of the implied co-movement in hours and oil prices. Now the correlation between oil prices and output is no longer counterfactual. In fact, the implied comovement between oil prices and output is now 2.3 times larger than what is observed in the data, while the co-movement of crude oil quantities and output is ten times smaller. In terms of the relative volatilities of consumption and investment, having an exogenous quantity of oil is better able to account for the data than having an exogenous oil price. However, the model s ability to match the relative volatilities of the oil price and oil production is reduced. It can now account for only 67% of the relative volatility of the oil price (compared with 80%), and for 57% of the 10

11 relative volatility of oil supply (compared with 97%). In terms of first-order autocorrelations, both models perform similarly for non-oil related observables. With respect to the real oil price, the exogenous production model accounts for 61% of the autocorrelation, and it account for 81% of the autocorrelation in oil demand. In this model environment there is positive co-movement between final goods output and the oil price. What is driving this result? Consider a rise in oil production (Q t ). Equation (28), which can be found in Appendix 1, shows that, all else equal, the oil price must fall in order for the firm to increase demand in-line with this higher production. In particular, we have that: p q,t = ψγqρ 1 t But the higher demand for oil leads to an increase in capital services (J t ), which leads to higher production of final goods (Y t ). The equation above shows that both of these increases will create upward pressure on oil prices. There are offsetting effects on the oil price and the one which performs better will depend on the particular calibration of the model. Nevertheless, this model is an improvement relative to the exogenous oil price one because it allows the oil price to adjust so that the exogenous production can be matched to endogenous demand. Where the model fails is in capturing the feedback between oil production and other observables. In particular, the model s implied co-movement between oil production and final goods output is worse than those obtained when the oil price is exogenous. In this new environment the correlation only accounts for about 11% of the data, relative to almost 120% when the oil price is exogenous. J ρ t Y t. 3.3 All Crude Oil Observables Endogenous In this new environment the oil producing region is affected by the decisions of households and firms in the oil consuming region. The structure of both regions is described in Section 2. The specific calibration for this model is given in Table 7 of Appendix 2. The quantitative implications of an endogenous crude oil market are summarized in Table 4. The business cycle properties of macroeconomic aggregates in the endogenous model are no worse than those previously obtained when either the price or the quantity of oil are exogenous. In particular, the implied co-movements for consumption and investment are similar across all models. There are differences in hours, where the endogenous oil market model accounts for 25% of the data, which is less than the 51% accounted for by the exogenous quantity framework, but an improvement on the counterfactual results from the exogenous price model. The largest differences are observed in the oil-related observables. As in the case where oil production is exogenous, the correlation between the oil price and output is no longer counterfactual. The model s implied correlation accounts for over 47% of the data, and also nearly accounts for all of the co-movement between the quantity of oil and output. The implied relative volatilities for consumption are in line with the better of the two exogenous models, and similar results are obtained for the relative volatilities of investment and hours worked. The relative volatility of the oil price is lower than the other two models, accounting for 48% of data. This is not surprising, as the results in [4] indicate that it would be difficult for a model with only productivity shocks to generate sufficient volatility in the oil price. The relative volatility 11

12 C t I t N t p q,t Q t Data Model (a) Correlations with Y t Y t C t I t N t p q,t Q t Data Model 1.00 (0.016) 1.00 (0.022) (0.012) (0.012) 4.88 (0.078) 3.24 (0.072) 1.25 (0.020) (0.011) (0.185) 5.45 (0.120) 2.50 (0.040) 1.93 (0.043) (b) Standard Deviations Relative to Y t, Absolute Standard Deviations in Parentheses Y t C t I t N t p q,t Q t Data Model (c) First-Order Autocorrelation Table 4: U.S. Business Cycle Predictions with Endogenous Oil Price and Oil Production for the quantity of oil is improved, performing 20% better than the model with exogenous oil. Finally, regarding the first-order autocorrelations, the model with an endogenous crude oil market has similar predictions as the other two models. The major departure among the three models is the autocorrelation of the quantity of oil, where the prediction of the endogenous model is 13% closer to the data than the exogenous price model. We conclude from Table 4 that the endogenous model improves the implied correlation between oil production/demand and GDP and the real oil price and GDP over the other two models while predicting similar business cycle properties for non oil-related observables. 3.4 Overall Fit It is difficult to compare the overall goodness of fit across different models without specifying a metric. In this paper, we use the sum of squared differences between model moments and the sample data. The observables that we consider are the ones presented in previous sections: Y t, C t, I t, N t, p q,t and Q t. The four different moments considered are the standard deviation (SD), the standard deviation relative to output (SD X /SD Y ), the correlation with output [Corr(X t, Y t )], and the first-order autocorrelation [Corr(X t, X t 1 )]. When computing our goodness of fit measure, all observables and moments are weighted equally. Moreover, each model predicted moment is normalized by the corresponding data counterpart. Table 5 reports the value of the sum of squared differences between model moments and the sample data for each model. SD SD X /SD Y Corr(X t, Y t ) Corr(X t, X t 1 ) Total Error Exog Price Exog Prod All Endog Table 5: Value of the Sum of Squared Deviations 12

13 Table 5 shows that the model with both the oil price and oil production endogenous best fits the data when taking into account these four moments. The total error is about half the size of the other two exogenous models. While this is true of the total error, differences in goodness of fit vary across the different moments. The model with exogenous oil production outperforms the other models with respect to the first-order autocorrelations, while the model with exogenous oil prices fits the relative standard deviations the best. The largest difference observed among the different models is when accounting for co-movements. The endogenous model outperforms the other two by a factor of nearly three along this metric. 3.5 Variance Decomposition In this section we follow [30] and use our model to quantify the importance of oil supply shocks in accounting for the variance of U.S. GDP. Our model has two shocks that affect the underlying dynamics of the economy, an oil supply shock and an oil demand shock. Table 6 shows the percentage of the variance for each observable that can be attributed to just oil supply shocks. In this case we have turned off the demand shock, recorded the respective standard deviation of each observable, and then reported the ratio of this value with respect to the standard deviation when all shocks are turned on. The portion which is unexplained by oil supply shocks is then attributed to oil demand shocks. Y t C t I t N t p q,t Q t Exog Price Exog Prod All Endog Table 6: Percent of Explained Variance Due to Oil Supply Shocks It is clear from Table 6 that oil supply shocks are important in accounting for the variance of the real oil price and oil production in each model. These shocks are less important for investment or hours, but still account for up to 11.4% of the variance in hours and 31.06% of the variance in investment in different model variants. Oil supply shocks have a much smaller impact on output and consumption. In particular, the impact of the respective oil supply shocks on the variance of GDP is lower than found in [30], but in line with the results of [10]. In [30] energy price shocks accounts for 16% of output volatility in the CES case and this value is approximately 4% in [10] Impulse Responses To complement the analysis in Section 3, we analyze the impulse responses of an oil demand shock and an oil supply shock. We first consider the impact of both supply and demand shocks on model predictions regarding GDP, consumption, investment and hours. We then examine the impact of these shocks on oil observables and GDP while comparing the implied model impulse responses to those generated from two reduced form vector autoregression models. 13 For the oil shock we use an AR(1) process rather than the ARMA process used by [30]. This difference in the exogenous process makes comparison with the paper of [30] more difficult. 13

14 Figure 1 shows the impact (in percent changes) of a positive one standard deviation TFP shock in the oil consuming region on various macroeconomic observables corresponding to the three different models. Given that we study the TFP shock in the oil consuming region, we are then analyzing the impact to the economy when hit by stochastic demands for inputs. As we can see from Figure 1, the qualitative responses to this oil demand shock for GDP, consumption, investment, and hours are similar across the three different models. These impulse responses are in line with those reported in Figure 10 of [31] for the standard RBC model when the economy is hit by TFP shocks. In terms of the relative magnitudes after impact, differences across models are more significant. For instance, the top left panel of Figure 1 shows that GDP responds most to the shock when oil production is exogenous, and it responds least when the oil price is exogenous. This difference is not trivial, as it is approximately 0.35% of GDP, which is large compared to the size of the initial shock. Moreover, the implied time series for output after a demand shock exhibits a divergence across models that lasts approximately fifteen quarters. The difference between the instantaneous response of investment in these two models to an oil demand shock is around 1.5%. Similar patterns are observed for hours. In contrast, impulse responses for consumption are almost the same across models. 14 Given the differences in the evolution of hours and similar time series behavior for consumption after an oil demand shock, we find small welfare differences across models after the economy is hit by a TFP shock. The implications of an oil supply shock on the economy are shown in Figure 2. An oil supply shock in the model with exogenous oil prices is taken to be a positive one standard deviation shock to the oil price process. When oil production is exogenous, this supply shock is a negative one standard deviation shock to the oil production process. And when both prices and quantities of oil are endogenous, the oil supply shock is a negative one standard deviation shock to TFP in oil production. As we can see from Figure 2, the qualitative response to this oil supply shock for GDP, consumption and hours are similar across the different models. However, the endogenous crude oil market model has a rather different investment impulse response relative to the other models. While the exogenous models predict a smooth transition to the steady state investment level, the fully endogenous model predicts an overshooting of around 0.5% of the steady state level. In terms of the relative magnitudes after the impact of an oil supply shock, differences across the three models are more significant. For instance, the top right panel of Figure 1 shows that consumption responds most to the shock when oil price is exogenous, and it responds least when the price and the quantity of oil is endogenous. This difference is approximately 0.15% of consumption. Moreover, the implied time series for consumption and hours after a supply shock exhibits a divergence across models that lasts for more than twenty quarters. The different consumption and hours time series patterns imply rather different welfare predictions that critically depends on how oil is modeled. The different model implied impulse responses of macroeconomic aggregates show that the way in which oil is modeled changes the magnitude of their responses and the underlying dynamics. Differences are less pronounced when analyzing shocks to oil demand. In contrast, when oil supply shocks are analyzed the magnitude and dynamics across models show greater differences than those observed when the economy is hit by oil demand shocks. 14 This is likely the case because none of the models analyzed in this paper have oil in the consumption basket. 14

15 4.1 Impulses from VAR and RBCs Having analyzed the impulse responses to oil shocks across the different RBC models, we now compare impulse responses for the oil price, oil production, and GDP relative to those generated from two reduced form vector autoregression models (VARs). A general VAR process can be encapsulated by a mean-zero moving average representation (without a deterministic terms) given by: y t = B j Gɛ t j (15) j=0 where y t is an N 1 vector of observables, the B j are N N matrices of coefficients, and the orthogonal innovations are ɛ t = Gu t, so that E(ɛ t, ɛ t) = GE(u t, u t)g = I, and u are reduced form errors. In equation (15) the B j G summarize the impulse responses which we analyze below. We use two different VAR models when calculating the impulse responses, both identified using exclusion restrictions. The first matches our endogenous model exactly, in that it has an oil supply shock and a demand shock. The second VAR model more closely follows the literature and has three observables. In particular, we follow [25] and [28] who have shown the importance of separating out different demand shocks. The exclusion restrictions we use necessitate monthly data, and this ranges from 1974 to We first examine the two-variable VAR model. The first variable is the change in non-u.s. oil production ( pd), and the second is the change in the real oil price ( po). 15 Consistent with the previous notation, we decompose the errors and identify the shocks in the model as follows: u t ( u pd t u po t ) [ ] ( g11 0 ɛ oil supply shock = g 21 g 22 ɛdemand shock ). (16) The first shock is an innovation to non-u.s. oil supply. We assume that such unexpected changes can impact the real oil price in the current month. This ordering also implies that non-u.s. oil supply does not contemporaneously respond to the other shock. This reflects the costs and difficulties of quickly changing oil production. The second shock summarizes any remaining demand shocks which affect its price. These include changes both arising from demand due to economic activity and storage possibilities, an aspect not modeled in this paper. In the three-variable model we follow the variable selection and ordering in [25]. The variables include changes in non-u.s. oil production, changes in U.S. industrial production ( ip), and changes in the real oil price. This three-variable version can be decomposed as follows: u t u pd t u ip t u po t = g g 21 g 22 0 g 31 g 32 g 33 ɛ ɛ ɛoil supply shock aggregate demand shock precautionary demand shock. (17) 15 We use the natural logarithm of non-u.s. oil production and the real refiner acquisition cost of imported crude oil, both from the EIA. First differences are used to make the VAR more comparable with our RBC models, each of which uses stationary data. 15

16 Figure 3 shows the impulse responses to an aggregate demand shock for GDP, the real oil price, and non-u.s. oil production for each of the crude oil models and the three-variable VAR model. Here we assume that the TFP shock on final goods production is similar to an aggregate demand shock in the VAR. In the two-variable VAR this shock is the demand shock. The graph in the top left panel of Figure 3 shows that the instantaneous responses of GDP to a demand shock in the three models are qualitatively similar to those implied by the three-variable VAR. However, in the VAR the impact of the shock quickly dissipates while the model responses are more persistent. In terms of magnitudes, the initial responses for GDP are on the lower end in the VAR, closer to those predicted by the endogenous model or the model with an exogenous oil price. In terms of oil observables, the top right panel of Figure 3 shows that the real oil price rises by almost 0.5% in the three-variable VAR as a response to an aggregate demand shock, and by nearly 6% in the two-variable VAR in response to a demand shock. The larger value in the two-variable case reflects the fact that all demand is included in this shock, not just aggregate demand. The instantaneous impulse responses of the oil price in the three crude oil models are smoother and more persistent. The endogenous model best fits the impulse response from the three-variable VAR in this case. The bottom panel of Figure 3 shows that non-u.s. oil production has a jagged response to the demand shocks in each VAR, which differ from the smooth responses of each model. Having analyzed a demand shock we now compare the impulse responses to an oil supply shock. Figure 4 shows the responses of U.S. GDP, the real oil price, and non-u.s. oil production for each of the three models and the VARs to an unexpected fall in oil production. The shape of each model s responses to this shock with respect to the GDP and oil production are similar to each of the VARs. One substantial difference is that all of the models imply a much larger instantaneous response in the oil price than shown by either VAR. The simulated impulse responses from each model are similar in magnitude to those generated from both two and three-variable VARs, but can have substantially different dynamics. In most cases the model responses are more persistent than those obtained from the VARs. It is difficult to distinguish between the models using these impulse responses, except to make the point that only the endogenous model is able to be used for comparison for each variable considered. An important advantage of endogenizing both the real oil price and oil demand is that such a framework can be used to analyze both oil supply and oil demand shocks. Historically, both of these shocks have contributed to oil price changes. Moreover, these oil price changes are believed to contribute to variations in U.S. GDP. 16 This is not the case when either the oil price or oil demand are exogenous. Having both prices and quantities of oil endogenous allows us to capture important feedback mechanisms between oil prices, oil production, and macroeconomic aggregates which are critical in determining how oil shocks propagate through the economy. 5 Conclusion This paper studies the consequences of endogenizing oil prices and quantities when accounting for business cycles facts and crude oil dynamics. We first consider a standard real business cycle model with either oil prices or oil quantities being exogenous. We then extend the benchmark real business cycle model to include an oil exporting region so that both the oil price and its quantity 16 See [25] and [29], among others, for more on this issue. 16

17 are endogenous. We show that when oil prices are exogenous, the model delivers counterfactual business cycle facts regarding the co-movement between the real oil price and U.S. GDP. Once both oil prices and quantities are endogenous, the model can account for most of the business cycle properties of oil while being consistent with the standard business cycle facts. To compare the overall goodness of fit across different models we use the sum of squared differences between model moments and the sample data. We find that endogenizing oil improves the model s fit to data relative to environments with exogenous oil prices or exogenous oil quantities. To complement the business cycle analysis, we analyze the impulse responses of an oil demand shock and an oil supply shock on oil and non-oil observables. The implied impulse responses of an endogenous crude oil market are more in line when compared to a reduced form VAR. Assuming crude oil to be exogenous in either prices or quantities is not innocuous as it may seem a priori as the implied time series for consumption and hours across models are quite different after oil shocks hit the economy. These different time series patterns imply distinct welfare which crucially depends how oil is modeled after oil shocks hit the economy. The findings of this paper suggest that any framework intended to study the impact of oil shocks on the macroeconomy should endogenize both its price and quantity. References [1] Luis Aguiar-Conraria and Yi Wen. Understanding the large negative impact of oil shocks. Journal of Money, Credit and Banking, 39(4): , [2] Bobby E. Apostolakis. Energy-capital substitutibility/complementarity. Energy Economics, 12(1):48 58, [3] Andrew Atkeson and Patrick Kehoe. Models of energy use: Putty-putty versus putty-clay. The American Economic Review, 89(4): , [4] David K. Backus and Mario J. Crucini. Oil prices and the terms of trade. Journal of International Economics, 50: , [5] Nathan S. Balke, Stephen P.A. Brown, and Mine K. Yucel. Oil price shocks and u.s. economic activity: An international perspective. Working Paper 1003, Federal Reserve Bank of Dallas, [6] Robert B. Barsky and Lutz Kilian. Do we know that oil caused the great stagflation? a monetary alternative. In B. Bernanke and K. Rogoff, editors, NBER Macroeconomics Annual 2001, pages [7] Robert B. Barsky and Lutz Kilian. Oil and the macroeconomy since the 1970s. Journal of Economic Perspectives, 18(4): , [8] Olivier J. Blanchard and Jordi Gali. The macroeconomic effects of oil price shocks: Why are the 2000s so different from the 1970s? In Jordi Gali and Mark J. Gertler, editors, International Dimensions of Monetary Policy, chapter 7, pages University of Chicago Press, 1st edition,