oil price shocks: causes and...
TRANSCRIPT
*Southern Methodist University and Federal Reserve Bank of Dallas **University of Nevada, Las Vegas and Resources for the Future ***Federal Reserve Bank of Dallas The authors thank Roger Cooke, Mario Crucini, Fred Joutz, Luca Guerrieri, William Helkie, Lutz Kilian, Prakash Loungani, Enrique Martinez-Garcia, Erwan Quintin, Tara Sinclair, Mark Wynne and Carlos Zarazaga for helpful comments and discussions and Stefan Avdjiev, Xin Jin and Zheng Zeng for capable research assistance. The authors retain all responsibility for omissions and errors. The views expressed are those of the authors and should not be attributed to the Federal Reserve Bank of Dallas, the Federal Reserve System, Resources for the Future, Southern Methodist University, or the University of Nevada, Las Vegas.
Oil Price Shocks: Causes and Consequences
Nathan S. Balke*, Stephen P. A. Brown** and Mine K. Yücel***
Revised June 15, 2011 Abstract: Research remains divided about the role that oil price shocks have played in U.S. economic volatility—in part because the source of those price shocks may vary. In this paper, we employ Bayesian methods with a dynamic stochastic general equilibrium model of world economic activity to identify the sources of world oil price shocks and to assess the effects of those shocks on U.S. economic activity. We find that changes in oil prices are best understood as endogenous because oil supply shocks, domestic shocks and foreign non-oil shocks all differ in their effects on oil prices and U.S. economic activity. In addition, we find that the oil price movements in the 1970s and early 1980s reflect a different mix of demand and supply shocks than those in the 2000s—oil prices in the 2000s being driven primarily by foreign demand shocks. Fluctuations in U.S. output owe mostly to domestic shocks, but oil supply shocks played little role, especially in the 2000s. JEL Codes: C3, E3, Q43 Keywords: oil price; international business cycles; general equilibrium; Bayesian estimation
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1. Introduction
Economic research has long focused on the economic effects of what have been regarded
as unfavorable oil supply shocks—the consequences being rising oil prices, slower GDP growth
and possible recession, higher unemployment rates, and higher price levels, as documented by
Brown and Yücel (2002), Jones et al, (2004), and Kilian (2008c). Some of the earlier studies
examining oil price shocks include Rasche and Tatom (1977), Mork and Hall (1980), Hamilton
(1983), and the Energy Modeling Forum 7 study documented by Hickman et al. (1987).
As oil prices rose sharply in the 2000s, however, the gains in oil prices seemed to be
positively related to economic growth. The apparent weakening or reversal of the past economic
effects of oil price shocks stimulated a new literature about why the U.S. economy might
respond differently to rising oil prices in the 2000s than it did in the 1970s and early 80s. The
explanations included increased global financial integration, greater flexibility of the U.S.
economy (including labor and financial markets), the reduced energy intensity of the U.S.
economy, increased experience with energy price shocks, better monetary policy and good
luck—the latter meaning smaller and less frequent shocks. Contributions include Huntington
(2003), Stock and Watson (2003), CBO (2006), Nakov and Pescatori (2007a), Blanchard and
Gali (2007), Edelstein and Kilian (2007), Segal (2007), and Herrera and Pesavento (2009), who
(except for Nakov and Pescatori) mostly treat oil price shocks as exogenous.
In contrast, a growing literature explores the implications of treating oil price shocks as
endogenous with sources that could include demand as well as supply, including Barsky and
Kilian (2002, 2004), Bodenstein, Erceg and Guerrieri (2007), Nakov and Pescatori (2007a,b) and
Kilian (2008 a,b; 2009). The differing sources of oil price shocks can explain the apparent
instability of the oil price-macroeconomy relationship. Kilian (2008b) maintains that most of the
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oil price gains after 1970 were the result of demand shocks; only the recession of 1980-82 was
the result of exogenous oil supply shocks; and that exogenous supply shocks explain only a small
fraction of the oil price increases during the 1973-74, 1990-91 and 2002-03 episodes. Kilian
(2009) identifies oil price shocks as variously arising from shocks to crude oil supply, global
demand and precautionary demand and then uses a vector autoregressive model to show that
these different sources of shocks have substantially different effects on U.S. GDP.
In the present analysis, we expand the inquiry by differentiating between the supply,
domestic demand and foreign demand shocks driving oil price fluctuations and by mapping those
shocks to fluctuations in U.S. economic activity. Our principal tool is a dynamic stochastic
general equilibrium (DSGE) model of world economic activity. The model provides a mapping
from “structural shocks” in technology and preferences to observables such as oil prices, oil
output, and other measures of economic activity. Our model is similar to that of Backus and
Crucini (2000) in that the world economy is represented as two manufacturing countries and an
oil-producing country. The model includes many of the features in the recent DSGE literature,
such as the inclusion of oil in consumption (Bodenstein, Erceg and Guerrieri 2007).
Our model departs from the previous literature by treating oil supply decisions in an
optimizing framework. Oil producers face an intertemporal tradeoff when deciding how much
oil to produce: higher production today reduces the oil reserves available in the future. Oil
producers also can invest to expand oil reserves, which increases future oil production capacity.
Thus, the evolution of reserves and production are choice variables for producers.
Rather than calibrate the parameters of the model and use it for a simulation exercise, we
use Bayesian methods to estimate the parameters of technology and preferences as well as the
parameters for the stochastic process generating the exogenous shocks. In the process of
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estimating the parameters, we also estimate realizations for the unobserved shock processes. The
latter allows us to identify and differentiate oil supply and demand shocks. In particular, the
model allows us to estimate the effects of various types of shocks on oil markets and aggregate
economic activity. These shocks include those to oil production and oil reserves in the oil-
producing countries; total factor productivity, preferences between goods and leisure, investment
efficiency, and oil efficiency in the manufacturing countries.
We find that domestic demand shocks, foreign demand shocks and oil supply shocks
differ substantially in their effects on U.S. GDP. That finding underscores the view that oil price
fluctuations are best understood as endogenous and that treating oil price shocks as exogenous
may seriously limit our understanding of the effects of oil price shocks on economic activity.
We also find oil supply shocks have had only mild effects on U.S. economic activity.
The episodes of poor U.S. economic performance during our 1970-2009 estimation period
appear to be mostly the result of domestic shocks. In the 2000s, oil prices were driven upward
by a combination of supply, foreign demand and domestic demand shocks, which combined had
little effect on U.S. economic activity.
The rest of the paper is organized as follows. In section 2, we present a three country
neoclassical model of the world economy, in which oil is used as a factor input and for
consumption services. One of the countries is an oil producing country which determines oil
production and oil reserves (capital). In section 3, we discuss the empirical estimation of this
model and the posterior distribution of some of the key parameters in the model. To understand
the dynamic implication of various shocks in the estimated model, we present impulse response
analysis in section 4. Section 5 contains our analysis of historical fluctuations in oil prices and in
economic activity as implied by our estimated DSGE model. Section 6 concludes.
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2. The Model
We approach identification of the source of oil price fluctuations through the lens of a
multi-country dynamic stochastic general equilibrium model. The model combines elements
from the open economy model of Backus and Crucini (2000) with oil market features in
Bodenstein, Erceg, and Guerrieri (2007). In a three-country model, two of the countries each
produce a manufactured good that is used to produce consumption and investment. The third
country produces oil, which is an intermediate good used in consumption and the production of
manufactured goods. Departing from Backus and Crucini, we treat oil production and the
evolution of oil reserves in the oil-producing country as completely endogenous.1
2.1 Consumers
This treatment
of oil-production and pricing as endogenous allows us to consider the role that shocks originating
in the two manufacturing countries can have in generating oil price fluctuations. By modeling
the evolution of oil reserves, we introduce an intertemporal channel through which oil markets
can be affected; expectations about future oil prices can have a direct effect on current oil prices.
Consumers in each country j maximize lifetime utility:
β tU(C j,t ,N j,t )t= 0
∞
∑ for j = a, b, o (1)
where β is a discount factor, t,jC is the consumption of the representative agent in country j and
t,jN is hours worked. We adopt the standard preference specification:
σχ ση
−
−−=
−
111 1))ZN(C(
)N,C(UU
t,jt,jt,jt,jt,j , for j = a, b, o (2)
1 Backus and Crucini represent oil production as having an exogenous component (OPEC) and an endogenous supply component via a labor-only technology.
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where Ut,jZ is a exogenous preference shock, σ/1 is the intertemporal elasticity of substitution,
and η and χ are parameters that govern the elasticity of labor supply and the ratio of work to
leisure, respectively.
Consumption is a CES aggregate of manufactured goods and oil usage as in Bodenstein,
Erceg and Guerrieri.
)/(ct,jt,j
cG
ct,j
cGt,j
ccc ])OE)((G[C µµµωω −−−
−+= 1111 1 for j = a, b, o (3)
where ct,jG is country j’s use of manufactured goods and c
t,jO is the country j’s use of oil for
consumption; cgω captures the weight households place on the consumption of goods relative to
oil; cµ is the elasticity of substitution between goods and oil in consumption; and t,jE reflects
the relative efficiency of oil usage and is common to both production and consumption.2
)OE( ct,jt,j
One
can think of as effective energy input. This specification captures the reality that oil
is used in the consumer sector and is in line with Edelstein and Kilian (2007) who show that
consumer spending on energy can be a major transmission mechanism of oil price shocks.
Manufactured goods are themselves a composite of domestic and foreign produced
goods:
)/(ct,j
c,gj,A
ct,j
c,gj,A
ct,j
ggg ]B)(A[G µµµ ωω −−−−+= 1111 1 for j = a, b, o (4)
where
ωA , jg,c
is the weight that good A (produced by country a) receives in country j’s composite
consumption good ( ct,jA ). For countries a and b, we assume home bias,
ωA ,ag,c >1−ωA ,a
g,c and
2 For the oil producing country, we drop
Z j,tU , t,jE because we lack the detailed data with which to separately
identify such shocks.
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1−ωA ,bg,c > ωA ,b
g,c and symmetry,
ωA ,ag,c = (1−ωA ,b
g,c ). For the oil producing country, )1( c,go,A
c,go,A ω−=ω
=0.5.
2.2 Manufacturing, Production and Investment
In each of the manufacturing countries, output is a function of capital, labor, oil use and
the technology available in each time period:
υα
υυα ωω −−
−− −+= 11
11 1 ))OE)((K(NZY Yt,jt,j
yKt,j
yKt,j
Yt,jt,j for j = a, b (5)
where Yj,t is country j output at time t, Kj,t is capital, Nj,t is labor, Yt,jO is oil use in production,
Yt,jZ is total factor productivity, and t,jE is oil efficiency and Y
t,jt,j OE is effective oil input.3
1/ν
With
this function oil and capital are used to produce capital services, which are combined with labor
to produce goods. The elasticity of substitution between capital and oil in the production of
capital services is given by and is different than that between capital services and labor
(which is unitary).
Similar to that for consumption, the CES investment aggregate for each manufacturing
country is as follows:
)/(It,j
gj,A
It,j
gj,A
It,j
Kt,j
ggg ]B)(A[ZI µµµωω −−−
−+= 1111 1 for j = a, b (6)
where It,jA is country j’s use of good A for investment, I
t,jB is the country j’s use of good B for
investment, and It,jZ an investment technology shock. Capital accumulation in each of the
manufacturing countries takes into account depreciation and investment as follows:
t,jt,jK
t,jt,jt,j K)K/I(K)(K Φ+−=+ δ11 for j = a, b (7)
3 As in Backus and Crucini (2000), we allow total factor productivity to be correlated across manufacturing countries, both contemporaneously and with a lagged spillover, but the stochastic processes are not the same across the two countries. We assume that the (logs) of the other exogenous driving forces follow independent first-order autoregressive processes.
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where δ is the depreciation rate and Kt,jI is investment and )K/I( t,j
Kt,jΦ is the rate at which
investment goods become capital. The latter expression reflects adjustment costs in changing the
stock of capital with
′ Φ (.) > 0 and
′ ′ Φ (.) < 0.
2.3 Energy efficiency
We let energy efficiency, t,jE , evolve over time according to:
𝐸𝑗,𝑡+1 = 𝑍𝑗,𝑡𝐸 �𝐸𝑗,𝑡�
𝛾𝐸�𝐼𝑗,𝑡𝐸 �
1−𝛾𝐸 for j = a, b (8)
where 𝐼𝑗,𝑡𝐸 is investment in energy efficiency and 𝑍𝑗,𝑡
𝐸 is an exogenous energy efficiency shock.
We assume that investment in capital and in energy efficiency are tied together. The total
resources devoted to investment in capital and energy efficiency are:
𝑃𝑗,𝑡𝐼 𝐼𝑗,𝑡
𝐾 �1 + Δ�𝐼𝑗,𝑡𝐸 �� for j = a, b (9)
where 𝑃𝑗,𝑡𝐼 𝐼𝑗,𝑡
𝐾 = 𝑃𝐴,𝑡𝐴𝑗,𝑡𝐼 + 𝑃𝐵,𝑡𝐵𝑗,𝑡
𝐼 is the expenditures on investment in physical capital and
Δ�𝐼𝑗,𝑡𝐸 � represents the relative contribution of energy efficiency investment to total investment
expenditures. We assume Δ′(. ) > 0 and Δ′′(. ) > 0 and normalize energy efficiency and its
costs so that in the steady state: 𝐸𝑗,. = 𝐼𝑗,.𝐸 = 𝑍𝑗,.
𝐸 = 1 and ∆(1) = 0.
2.4 Oil Production and Reserves
For the oil producing country, the production of oil is a function of oil reserves, labor,
and the technology available in each time period:
Yo,t = Zo,ty (ωX
y Xt1−ρo + (1−ωX
y )No,t1−ρo )
11−ρo (10)
where Yo,t is oil production at time t, Xt is oil reserves, No,t is the labor used in oil production, and
Zo,ty is the oil production technology. The term 1 𝜌𝑜� is the elasticity of substitution between
reserves and labor in oil production. This elasticity is important in that it affects the short-run
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elasticity of oil supply. Note that in time period t, Xt is predetermined. We want to interpret oil
reserves broadly in that it reflects not only oil in the ground but oil producing capital (refineries,
pipelines, etc).
The evolution of oil reserves depends on both additions to reserves and the depletion due
to production:
t,ottX
t,ot YGXZX −+=+1 (11)
where Gt is gross addition to reserves and t,ot YG − is net additions to reserves. Xt,oZ is a shock
to existing reserves and reflects oil market disturbances which lower/increase the stock of
reserves. Gross additions to reserves determined by:
Gt = Φg (Ix,t / Xt )Xt (12)
where Ix,t is the investment in the production of reserves.
)/(It,j
go,A
It,j
go,At,x
ggg )B)(A(I µµµ ωω −−−−+= 1111 1 (13)
Here we assume symmetry with respect to the weight the oil producing country places on goods
A and B,
ωA ,og = (1−ωA ,o
g ) = 0.5. Additions to reserves reflect an adjustment cost mechanism
similar to that employed by capital in manufacturing countries, where
Φg '(.) > 0 and
Φg"(.) < 0.
Note that in the steady state: 1=XoZ , X/Y)X/I( oxg =Φ , and 1=Φ )X/I(' xg . We think of
reserves in our model as representing total capital in the oil-producing sector, which includes oil-
production infrastructure (capital) as well as oil in the ground. The depletion of reserves (i.e., the
depreciation of oil-producing capital) depends on how much oil is produced.
2.5 Optimal Oil Production
Maximizing the representative agent’s utility in the oil-producing country and taking
prices as given yields the decisions rules for the production of oil and reserves. Oil production is
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determined so that:
po,t = px,t + mco,t , (14)
where
po,t is the price of oil
px,t is the price of reserves (user cost of oil), and
mco,t is the
marginal cost of producing oil in time period t.4
mco,t = wo,t /mpl ,to
Given that the stock of reserves is fixed in time
t, where
wo,t is the wage in the oil-producing country and
mpl,to is the marginal
product of labor in the oil-producing country.5
The presence of reserves introduces an intertemporal element to the oil producers supply
decision. The first order condition for the production of reserves is given by:
px,t = Et[Mt +1{(po,t +1 − px,t +1)mpx,t +1
o + px,t +1(1+ Φg,t +1 − ′ Φ g,t +1Ix,t +1
Xt +1
)}], (15)
where
Mt +1 is the stochastic discount factor and
)}XI
(pmp)pp{(t
t,xt,gt,gt,x
ot,xt,xt,o
1
1111111 1
+
+++++++ Φ′−Φ++− is the payoff of having more reserves
next period.6
For a given level of inputs, a negative technology shock to oil production,
Thus, expectations of future oil market conditions have a direct effect on current
oil production decision through the interplay of equations (14) and (15).
Zo,tY , will lower
the production of oil and increase marginal costs—lowering output and raising the price. To the
extent that the shock is persistent, it will result in higher prices for reserves both currently and in
the future, stimulating the development of reserves in the future. These reserve additions enable
higher oil production in the future.
4 Modeling the oil-producing country as a price-taker is contrary to the view that OPEC restricts production or sets oil prices. As long as price is a constant mark up over costs, however, such an assumption will not have an appreciable effect on our analysis. Fluctuations in the price of reserves will reflect any fluctuations in the mark-up of oil prices over marginal costs. Thus, changes in OPEC’s price setting stance will in part be captured by our measures of technology shocks to oil production and reserves. 5 The wage in the oil producing country, in turn, depends on the marginal utility of leisure and of income. 6 The stochastic discount factor is the marginal rate of substitution between consumption in the future and consumption today.
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Although a shock to reserves, Xt,oZ , has no direct effect on contemporaneous oil supply
(recall that
Xt is predetermined in time period t), it can affect current oil prices and oil output.
For instance, a negative shock to reserves will mean fewer reserves in the future, which will
reduce future oil production and raise future oil prices. Taken alone, this shock would boost the
price of reserves (user cost of oil, 1+t,xp ) and, hence, result in a reduction of current oil output
and an increase in current oil prices.
2.6 International Market Clearing Constraints
In each time period, market clearing for each of the three goods implies:
)AA()A))I((A()A))I((A(Y It,o
Ct,oo
It,b
Et,b
Ct,bb
It,a
Et,a
Ct,aat,aa ++∆+++∆++= ψψψψ 11 (16)
)BB()B))I((B()B))I((B(Y It,o
Ct,oo
It,b
Et,b
Ct,bb
It,a
Et,a
Ct,aat,bb ++∆+++∆++= ψψψψ 11 (17)
)O()OO()OO(Y Ct,oo
Yt,b
Ct,bb
Yt,a
Ct,aat,oo ψψψψ ++++= (18)
Where
ψa ,
ψb , and
ψo reflect the relative sizes of three countries. We also assume complete
asset markets internationally, which allows for perfect risk sharing across countries.
We take the United States to be one of the manufacturing countries in the model. The
other manufacturing country, denoted below by ROW, we take to be the OECD countries (less
Mexico and the United States) plus Brazil, China, and India. We set the relative size of the
United States at
ψa =.25 while for the ROW,
ψb =.65.
3. Model Estimation
To solve the model for a given set of parameters, we log-linearize the first order
conditions of the social planner’s problem around the deterministic steady state and solve the
resulting linear rational expectations model as in Blanchard and Kahn (1980). Rather than
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calibrate the parameters, we use Bayesian methods to estimate the parameters of technology,
preferences, and the stochastic processes generating the exogenous shocks.
In our empirical analysis, we examine a total of eleven observable variables. As the
estimation procedure readily handles the use of mixed frequency data and missing observations,
the observation variables are a mixture of quarterly and annual data, U.S. and ROW data, and oil
market data. Five U.S. quarterly time series are included in the analysis: U.S. real GDP, U.S.
real consumption, U.S. real investment, U.S. hours worked, and U.S. oil consumption. Quarterly
real oil prices (deflated by the U.S. GDP deflator) and world oil production are also included. In
addition to these oil market variables, we include a quarterly series that reflects capacity
utilization in oil production (see appendix C for more details) in order to obtain some
information about the short-run oil supply. As the model assumes oil reserves are fixed in the
current period, the only way to endogenously increase oil production with in a period is to
increase labor input in the oil producing country; that is, the short-term elasticity of oil supply
depends in part on the labor supply and labor demand elasticities in the oil producing country.
Unfortunately, employment data for oil producing countries is generally not available. However,
the inclusion of the oil capacity utilization series helps to identify endogenous short-run changes
in oil production not due to changes in reserves as oil production capacity is also fixed in the
short-run. Finally, we include three series that reflect ROW economic activity: annual ROW
real GDP, annual ROW real investment, and a quarterly series on ROW industrial production.
In the empirical model, we assume that the five U.S. series, real oil prices, and oil output
are measured without error. However, we assume that the oil capacity utilization and ROW
observations include a white noise measurement error. This reflects the fact that we are less
confident these observables series correspond to the variables implied by the model. For ROW
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industrial production, we allow its factor loadings to be scaled up over those implied by the
model’s country b (ROW) output (see appendix A). Our sample period runs from 1970:Q1
through 2010Q2 for quarterly data and 1970 through 2009 for annual data. As the quarterly
capacity utilization data starts in 1990, we treat the pre-1990 as missing observations for capacity
utilization in the empirical analysis.
The linearized DSGE model links the observed time series and the underlying driving
processes that result in deviations from the steady state.7 Markov Chain Monte Carlo methods
similar to those of Lubik and Schorfheide (2004) and Smets and Wouters (2007) are employed to
estimate the posterior distribution of the parameters.8
3.1 Prior and posterior distributions of the structural parameters.
In the process of estimating the posterior
distribution of the parameters, we also estimate a posterior distribution for the unobserved shock
processes. These estimates allow us to decompose movements in actual observables into
contributions due to various exogenous shocks.
In implementing the Bayesian estimation strategy, we specify prior distributions for the
structural parameters and the parameters of the stochastic processes of the ten exogenous driving
forces. For the elasticities of substitution between home and foreign produced manufacturing,
elasticities of substitution between oil and manufacturing goods (or capital), and the shares of oil,
domestic goods, and foreign goods, we set the mode of prior distribution equal to values in
Backus and Crucini or Bodenstein, Erceg, and Guerierri. For the oil-producing country, we use
7 The natural logs of U.S. real GDP, consumption, investment, hours, oil consumption; relative price of imports to the United States; rest of world output , investment, and industrial production; and world oil production are linearly detrended. The logs of real oil price and the logit of capacity utilization are demeaned. 8 See Appendix B for the details of the Markov Chain Monte Carlo approach taken in the current paper.
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information on the ratio of reserves to oil production, 0Y
X, and the ratio of oil price to reserve
price,
po
px
=po
p0 − mc0
, to help set the prior distributions of the parameters.
As for how much weight to place on the prior distribution versus the data when
estimating the posterior distributions, we divide the parameters into four groups. Parameters
such as the discount factor, steady state depreciation rate on physical capital, and steady-state oil
capacity utilization are set a priori.9
Because the DSGE models are highly nonlinear in parameters, the likelihood function is
typically multi-modal. Preliminary evaluation of the posterior distribution did reveal multi-
modality. Our approach was to impose prior beliefs about a few key features of the model.
Specifically, the parameter space was restricted so that the linearized model had a unique,
stationary solution. Second, the signs of a few key impulse responses to structural shocks were
restricted: oil price falls and output rises on impact for a positive oil production shock; reserves
rise after four quarters after a positive oil reserve shock; oil prices rise on impact in response to
U.S. and ROW demand (preference, TFP, and investment) shocks.
Parameters that reflect shares of steady state values (such
as, output elasticity of labor equals labor’s share in GDP) have relatively tight priors. Parameters
that reflect elasticities of substitution or adjustment costs for capital and reserves have more
diffuse priors. Finally, a third group of parameters, namely the parameters of the stochastic
processes governing the driving forces have relatively uninformed priors—as we have very little
direct prior information concerning these stochastic processes.
Table 1 displays the prior and estimated posterior distributions of the structural
parameters. For many parameters, using the information in the data results in a substantial shift
9 We set β = .98 and δ = .025 while the steady state capacity utilization rate is set equal to its sample average.
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in the posterior distribution relative to the prior distribution; for most parameters the posterior
distribution is substantially tighter than the prior distribution. Not surprisingly given the tight
priors for these parameters, the posterior distributions for labor’s share in manufacturing country
GDP, the share of home and foreign goods, and oil’s shares in production and consumption are
similar to the prior distributions of those parameters.
Our posterior distribution suggests an estimate of the intertemporal elasticity of
substitution that is a little higher that than typically assumed in the macroeconomics literature.
The posterior distribution of the elasticity of substitution between capital and oil is lower than
the prior while the elasticity of substitution between oil and consumption is higher. Note that the
posterior distributions these elasticities are substantially “tighter” than their prior distributions.
The exception is the posterior distribution of the elasticity of substitution between domestic and
foreign goods which is substantially more dispersed than its prior. The adjustment costs for
capital are estimated to be substantially higher than those for oil reserves suggesting that it is
easier to add to reserves than it is to add to capital in the manufacturing country. Finally, for
ROW industrial production the factor loading scaler is nearly 1.5, which suggests that actual
ROW industrial production is about 50 percent more volatile than ROW aggregate output
implied by the model.
Table 2 presents the prior and posterior distributions for the stochastic processes
governing the exogenous variables in the model. Given that prior distributions were relatively
uninformative, the data have a lot to say about these parameters. The autoregressive parameters
for most of the exogenous shocks are quite high suggesting that these shocks are very persistent.
The exceptions are the shocks to oil efficiency and oil reserves. As oil efficiency and reserves
have persistent endogenous dynamics, the model does not need the exogenous shocks to these
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variables to be persistent also. The standard deviation of shocks to oil production and oil
reserves are relatively large compared to shocks in total factor productivity (TFP) in the
manufacturing countries. On the other hand, the standard deviation of the investment shocks in
the two manufacturing countries are large relative to the other shocks.
Table 3 presents the prior and posterior distributions for the measurement error variances
in the ROW real GDP, ROW investment, ROW industrial production, and oil capacity utilization
observation equations. The posterior distribution suggest a substantial increase in the
measurement error variance for ROW real GDP over that implied by the prior. Relative to ROW
industrial production or ROW investment, the model does not capture very well the movements
in our estimate of ROW real GDP and, as a result, requires a relatively large measurement error
variance.
4. Estimated Impulse Responses
To obtain a better perspective of how the source of an oil price shock affects economic
activity as represented in the model, we examine the impulse responses that show how oil
markets and economic activity respond to a variety of shocks, including an oil production shock,
an oil reserve shock, U.S. and ROW total factor productivity shocks, U.S. and ROW preference
shocks, U.S. and ROW oil efficiency shocks, and U.S. and ROW investment shocks. We also
examine in some detail how various aspects of U.S. activity respond to oil production and oil
reserve shocks. For each series, we report the mean, 5th and 95th percentile of the posterior
distribution of the impulse responses.
4.1 Responses of the oil market to structural shocks
Figure 1 displays the response of oil prices and oil output to the various structural shocks
in our model. Oil production and reserve shocks yield oil-market dynamics that are similar to
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the classic supply shock. A positive oil production shock lowers the price of oil and boosts oil
output. As the shock dissipates, the oil price and output return toward their steady state values.
Similarly, a positive shock to reserves leads to higher oil output and lower oil prices, but these
shocks take longer to have a substantial effect and have a longer-lived effect on oil prices and oil
output.
The other eight shocks look similar to demand shocks for oil. A positive total factor
productivity (TFP) shock, both in the United States and the ROW, raises oil prices and oil. The
initial increase in oil prices is higher with a U.S. TFP shock than with a ROW TFP shock, but the
price does not rise as much over time. In both cases, oil output increases for about 8 quarters,
and then begins to decline. U.S. or ROW investment shocks yield qualitatively similar results,
leading to a rise in both real oil prices and oil output. An increase in investment increases the
productivity of investment in creating capital goods, which gradually increases GDP in the
country where such a shock occurs. The shock to ROW investment leads to a higher oil price and
about one and one-half times the increase in output than a shock to investment in the US. A
higher response is consistent with the ROW accounting for about 65 percent of world economic
activity in the model.
A positive shock to preferences or to oil efficiency are akin to a negative demand shock
and have negative effects on oil prices and oil production. A shock to U.S. or ROW labor-leisure
preferences reduces hours worked and GDP in the country in which the shock occurs. With a
U.S. preference shock, for example, weaker domestic economic activity reduces oil
consumption, and lowers oil price and output. The oil market response to a ROW shock to
labor-leisure preferences is very similar. Again, the magnitudes of the oil market response are
somewhat larger with a ROW shock than a U.S. shock.
17
An oil efficiency shock increases the productivity of oil, both in production and
consumption, and has a direct effect on oil demand lowering the oil prices and output. The effect
of ROW oil efficiency shocks are more than twice as large as U.S. oil efficiency shocks. Again,
this finding is generally consistent with the ROW accounting for 65 percent of world economic
activity in the model.
4.2 Oil Supply Shocks and U.S. Economic Activity
As modeled here, there are two types of oil supply shocks: one whose effect is primarily
on current oil production and another whose effect is primarily on future oil production. Figure
2 displays the responses of the U.S. variables used in estimating the model to these two oil
supply shocks. The effects of these two shocks on the U.S. economy are fairly similar. As
expected, a favorable oil production shock increases U.S. GDP. Positive oil production shocks
reduce the price of oil, and increase the amount of oil used in consumption and production. The
increase in oil use increases the demand for labor, leading to higher hours worked and higher
consumption.
The effects of a reserve shock are similar to a production shock, but longer lasting. While
the effects on GDP, consumption, hours and investment are all positive with a production shock,
they dissipate with time. With a reserve shock however, the effects are fairly persistent since
reserve shocks effect not only current, but also future production.
Historically, one might consider oil supply shocks to be instances in which oil production
and oil reserve shocks occurred at the same time. Taken together, the oil production and oil
reserve shocks generate a negative relationship between oil prices and U.S. economic activity.
The combination of these two supply shocks implies an estimated posterior distribution for the
oil price elasticity of U.S. real GDP with a mean of −0.010 in the short-run and -0.020 in the
18
long run.10 These estimates are at the lower end of the range, −0.012 to −0.12, found in earlier
empirical research, but more in line with newer studies, which find a range of −0.012 to −0.029
for the United States.11
4.3 Domestic and foreign shocks and U.S. economic activity
To better assess the mechanisms through which shocks affect oil prices, we consider the
responses of U.S. economic activity to domestic (Figure 3) and ROW shocks (Figure 4). Shocks
to U.S. TFP and investment both have an expansionary effect on the U.S. economy. A positive
shock to U.S. TFP expands U.S. output, consumption, investment and hours worked and
increases the U.S. consumption of oil (both for consumption and production purposes). For
investment shocks, the effects are larger at longer horizons than at shorter horizons. The
expansion of economic activity occasioned by these shocks, in turn, drives up the demand for oil
as we saw in Figure 1. A positive shock to preferences represents a decline in the willingness of
households to work. This results in a decline in U.S. output, consumption, investment, hours,
and U.S. oil consumption and a corresponding decrease in oil demand. An exogenous oil
efficiency shock is reminiscent of a U.S. investment shock with the exception that U.S. oil
consumption falls in response to an oil efficiency shock. In this case, the effect of an expansion
in economic activity on oil demand is not large enough to offset the decrease in oil demand due
to the direct effect of an increase in oil efficiency.
Turning to the effects on U.S. economic activity of shocks originating in the ROW
(Figure 4), ROW TFP results in slightly lower U.S. GDP, a substantial reduction in investment ,
and gradual declines in hours and oil consumption in the U.S. The desire to move productive
resource to their most productive location (here ROW) is somewhat offset by the spillover of
10 The estimated elasticity is the percentage change in U.S. GDP divided by the percentage change in the oil price. 11 See Jones, Leiby, and Paik (2004) and Brown and Huntington (2010).
19
technology to the U.S. Note that if an oil price increase is the result of a ROW TFP shock (see
Figure 1) the effect on U.S. real GDP of this same shock is relatively modest—there is an
increase in oil prices but not much change in U.S. real GDP. U.S. consumption, in fact,
increases in response to the positive income effect that an increase in ROW TFP brings. ROW
investment shocks work in a similar way, except that U.S. consumption falls (in response to
higher world interest rates such a shock would bring). A shock to ROW preferences leads to
higher U.S. GDP, consumption, investment, hours worked and oil consumption. The decline in
oil prices brought about by ROW preference shock, stimulates economic activity in the U.S.
Finally, a ROW oil efficiency shock yields the same qualitative results for U.S. GDP,
consumption, investment and hours worked as with a domestic oil efficiency shock. The only
difference is in that U.S. oil consumption increases as the expansion in U.S. activity in not offset
by an increase in U.S. oil efficiency.
5. Historical Decompositions
Historical decompositions provide the means for showing how various shocks affected
the evolution of oil prices, oil production and U.S. real GDP. In each figure, we represent the
history of the demeaned log of the oil price, the detrended log of oil output, or the detrended log
of U.S. real GDP or the detrended log of ROW industrial production over the 40-year period
from 1970 through 2009. For each series, we also represent the mean, 5th percentile and 95th
percentile of the posterior distribution. The extent to which the posterior distribution moves with
the historical series shows the extent to which the given variable explains the historical
movement.
The impulse response analysis provides a window into understanding the historical
decompositions. The identification of unfavorable oil supply shocks requires finding periods in
20
which oil prices rise, oil output falls and U.S. GDP falls. On the other hand, the identification of
oil demand shocks requires oil prices and oil output to move in the same direction. Depending
on the source of the shock creating the change in oil demand, U.S. GDP can rise or fall.
5.1 Real Oil Price and Oil Output
As shown in Figure 5, the historical decompositions suggest that both oil supply and oil
demand shocks have contributed to the historical movements of oil prices. Supply shocks (the
combination of oil production and reserve shocks) are characterized by somewhat longer swings
than oil output with supply falling from the mid-1970s to mid-1980s in the late 1970s and early
1980s, rising from mid-1980s to about 1990, and remaining relatively constant thereafter.
The historical decompositions show that a supply shock contributed to oil price spike in
1973 -74, and supply restraint contributed to the rise in oil prices from 1979 through 1982.
Abundant supply also contributed somewhat to the weakness of oil prices from the mid-1980s to
2000. A look at oil output suggests that supply shocks contributed to a decline in oil output and
increase in oil prices from about 2000 onward. Nonetheless, most of the recent increases in oil
prices were due to demand shocks.
In fact, world oil demand shocks contributed to much of the volatility in oil prices and oil
output seen from 1970 through 2009, especially after the early 1980s. Weak demand had a
prominent role in weak oil prices from the mid-1980s through 2000, and growing demand had a
prominent role in the rise in oil prices thereafter.
ROW shocks played a strong role in driving oil demand.12
12 For ROW, TFP and investment shocks contributed to long swings in oil demand, oil efficiency shocks contributed to short-term volatility, and labor-leisure preferences had relatively little role. The strong growth in ROW investment in the 2000s also slowed investment in oil development.
In contrast, U.S. demand
shocks are characterized by relatively long swings that contributed to the general direction of
21
world oil prices and output but not so much to the absolute magnitudes.13
5.2 U.S. Economic Activity
In that sense, our
findings are generally consistent with Hamilton’s (2009a, 2009b, 2009c) view that much of the
observed world oil price volatility is driven by market developments outside the United States.
They are also consistent with Kilian’s (2009) finding that world oil price movements have been
driven by both demand and supply. Sharp reductions in supply help create the sharp oil price
increases in the 1970s and early 1980s, and the failure of oil output to keep pace with the growth
of demand contributed to rising oil prices after 2000.
As shown in Figure 6, the historical decompositions show that oil supply shocks had a
relatively small effect on U.S. economic activity. Oil supply shocks contributed slightly to U.S.
downturns in the 1970s and early 1980s, but the contributions were even smaller thereafter.
Although oil supply shocks have contributed to oil price movements, we find the effect of such
shocks on U.S. GDP has been small.14
The historical decompositions also show that earlier ROW shocks are similarly moderate
in their effects—even in those cases where ROW shocks have contributed to rising oil prices. In
looking at the period after 2000, however, we see that ROW shocks contribute to a slowing of
U.S. economic activity—in part by pushing up world oil prices, and in part by drawing
investment capital. These effects are moderated in part by small income gains and productivity
spillovers to the United States.
In that sense, our findings differ from Kilian (2009), who
finds that oil supply shocks had a limited effect on world oil prices, but are consistent with Kilian
in finding that oil supply shocks have relatively little impact on U.S. economic activity.
13 For the United States, TFP and oil efficiency shocks contributed to long swings in oil demand. Labor-leisure preferences and investment had little roles. 14 We note that the assumed symmetry in our model limits its ability to reflect differential effects of rising and falling oil supply on U.S. economic activity.
22
The historical decompositions identify U.S. shocks as having the greatest effect on the
evolution of U.S. GDP. With oil efficiency playing only a general role, U.S. labor-leisure
preference, total factor productivity and investment shocks show the greatest effects. Total
factor productivity played the biggest role from the 1970s to the early 1980s. Investment
contributed long-term swings, generally benefitting the economy in the 1990s and doing less in
the 2000s. Labor-leisure preferences are seen as an important contributor from the early 1980s
onward. The preference shock reflects the so-called labor wedge that has featured prominently
in research on U.S. business cycle fluctuations (Hall 2007, Chari, Kehoe, McGrattan (2007)).
5.3 Sources of ROW Fluctuations
Although our focus is primarily on oil price movements and U.S. economic activity, our
model does have something to say about fluctuations in the rest of the world. As our estimates
suggests that measurement error component of ROW of real GDP is large in our empirical
model, Figure 7 presents instead the historical of ROW industrial production. Oil supply and
U.S. shocks explain relatively little of the fluctuations in ROW economic activity. Fluctuations
in ROW output fluctuations are driven primarily by ROW shocks, with preferences and total
factor productivity being the most important. Note that total contribution of all shocks tracks
actual ROW industrial production pretty well.
5.4 Discussion: Oil Prices and U.S. Economic Activity From 1970s to the 2000s
We find the relatively poor U.S. economic performance in the mid-1970s through the
early 1980s appears largely to have to have been the result of shocks to total factor productivity.
Oil supply shocks contributed only moderately to the poor economic performance in these years.
These findings differ sharply from earlier studies, such as Hamilton (1983) and Balke et al.
(2002), that found that oil price shocks had a substantial effect on economic activity but neither
23
distinguished between sources of oil price shocks nor identified the effect of other shocks on
U.S. economic activity. In failing to consider these other factors, these earlier studies likely
attributed too much of the economic loss to oil price shocks.
Our findings for the 1970s and early 1980s are consistent with Kilian (2009), Blanchard
and Gali (2007), as well as Greenwood and Yorukoglu (1997), and Samaniego (2006). Kilian
finds that oil supply shocks are of lesser importance to U.S. GDP than other sources of economic
fluctuations. In contrast, Blanchard and Gali find the poor U.S. economic performance of the
1970s owes to a combination of adverse oil price shocks and other negative factors. Greenwood
and Yorukoglu and Samaniego attribute some of the negative productivity shocks of that era to
significant learning costs associated with the adoption of new technologies and the necessity of
plant-level reorganization.15
For the 1990s and 2000s, we find the strong growth in U.S. real GDP (and the subsequent
recession) mostly reflects domestic sources, particularly TFP and preference shocks. In the late
2000s, shocks to labor-leisure preferences were the main contributors to the decline in U.S. GDP.
Investment also played a minor role.
16
In the 2000s, ROW and U.S. oil demand shocks had a more important role in shaping oil
prices than supply shocks, and those oil prices had only a moderate effect on U.S. economic
activity. These findings are similar to Blanchard and Gali (2007) who find that rising world oil
prices had small negative effects on U.S. output, which were generally dwarfed by other positive
shocks. But the findings are also in the same spirit as Kilian (2009) and Kilian and Hicks (2010)
15 Some of the negative productivity shocks of the 1970s may have been the result of the new and relatively inefficient environmental regulation introduced during that era. 16 The lack of a financial sector in the model forces the model to attribute the decline in U.S. GDP in 2008-2009 to investment and preference shocks.
24
who find that growing world demand pushed oil prices upward with little effect on U.S.
economic activity.
In considering our findings, we recognize that neoclassical models, such as the one used
in our analysis, tend to ascribe only a small role to oil supply shocks in generating economic
fluctuations. Oil’s role is limited by its relatively small shares in production and consumption,
as explained by Barsky and Kilian (2002) and Hamilton (2009). Models that allow for sectoral
adjustment, such as Hamilton (1988), or irreversible capital, such as Atkeson and Kehoe (1999)
can generate stronger economic responses to oil price shocks. Because our focus is on using a
linearized, multi-country DSGE model to identify the sources of endogenous changes in oil
prices and to estimate their effects, we leave such extensions to future research.
6. Conclusions
Economic history has provided seemingly contradictory evidence about the relationship
between oil price movements and aggregate U.S. economic activity. Oil prices rose sharply in
the 1970s and early 1980s, and U.S. economic activity contracted sharply. Oil prices rose
strongly throughout much of the 2000s, but U.S. economic activity continued to expand until
recession hit in early 2008.
Previous research has offered a number of different reasons for these contradictory
historical experiences. One explanation is that the 2000s were characterized by oil demand
shocks that yielded a positive relationship between oil prices and economic activity, while the
1970s and early 1980s were characterized by oil supply shocks that yielded an inverse
relationship between oil prices and economic activity. Perhaps a better explanation is that oil
price fluctuations originate from many different sources and the differences in those sources
greatly influence how U.S. GDP responds to oil prices shocks.
25
As we demonstrate above, the differences between demand shocks as well as those
between supply and demand shocks are important to understanding the response of U.S.
economic activity to higher oil prices. Higher oil prices that result from increased U.S. oil
demand are consistent with increased U.S. GDP. Higher oil prices that arise from increased
foreign oil demand lead to moderate reductions in U.S. GDP. As China and other emerging
markets have become bigger players in the world economy, demand shocks arising in these
countries that increase oil prices have moderately negative effects on U.S. economic activity.
Higher oil prices that arise from oil supply shocks lead to the largest reductions in U.S. GDP.
These differences in the response of U.S. economic activity to the various sources of oil
price shocks provide considerable insight into the processes that have driven oil prices and U.S.
economic activity over the past four decades. Overall, we find that oil supply shocks had a
relatively minor effect on U.S. economic activity during the 1970-2009 estimation period. The
strongest effects are found in the 1970s and early 1980s, but negative U.S. productivity shocks
also contributed to the economic weakness that characterized that period. By not taking into
account the possibility of domestic shocks, some of the earlier literature likely overestimated the
effects that oil supply shocks had on economic activity. In the 2000s, oil prices were driven
upward by a combination of supply, foreign demand and domestic demand shocks. Combined
these shocks appear to have had little net effect on U.S. economic activity.
26
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Table 1. Prior and posterior distributions of structural parameters
Prior distribution Posterior distribution
Parameter type mode 5th percentile
95th percentile mode Mean 5th
percentile 95th
percentile Labor’s share in time Beta 0.2 0.175 0.228 0.200 0.200 0.174 0.228 Labor’s share in GDP Beta 0.64 0.619 0.661 0.627 0.630 0.611 0.648
Share of foreign goods in investment Beta 0.40 0.372 0.428 0.390 0.399 0.369 0.428 Share of foreign goods in consumption Beta 0.06 0.051 0.070 0.059 0.060 0.051 0.070
Oil’s share in production Beta 0.06 0.051 0.070 0.059 0.058 0.051 0.066 Oil’s share in consumption Beta 0.04 0.035 0.046 0.031 0.032 0.028 0.036
labor supply parameter,𝜂, (US,ROW) Gamma* 2.5 1.528 12.722 2.613 2.711 2.294 3.209 Intertemporal elasticity of substitution Gamma 0.5 0.159 1.223 0.847 0.796 0.582 1.060
Elast. of subst., home and foreign Gamma 1.5 0.239 4.336 5.537 58.360 5.072 281.793 Elast. of subst., goods and oil in cons. Gamma 0.09 0.036 0.300 0.221 0.228 0.149 0.305 Elast. of subst., capital and oil in prod. Gamma 0.09 0.036 0.300 0.014 0.015 0.002 0.037
Capital adjustment cost Gamma 0.05 0.025 0.993 2.386 2.318 1.810 2.919 Oil efficiency cost elasticity, (.)/(.) ∆′∆ ′′ Gamma 5 1.91 54.21 10.04 23.31 7.09 53.35
Oil efficiency adjustment, Eγ Beta .9 0.311 0.968 0.999 0.996 0.998 0.999
Elast. of subst., labor and reserves Gamma 0.10 0.041 0.315 0.131 0.140 0.084 0.215 labor supply parameter,𝜂, (Oil producer) Gamma† 2.5 1.528 12.722 2.154 2.291 1.017 5.569
po / px Gamma‡ 4 1.366 8.754 4.547 4.718 3.874 5.749 Reserves to oil production ratio Gamma§ 153.84 127.24 196.12 180.11 192.37 159.68 230.28
Reserve adjustment cost Gamma 0.05 0.026 0.993 0.770 0.696 0.503 0.930
Oil capacity utilization adjustment Beta .5 0.070 0.930 0.249 0.204 0.043 0.329 ROW Ind. Prod. factor loading Gamma 1 0.617 1.697 1.487 1.476 1.329 1.631
* The prior distribution of -1 is a Gamma distribution. † The prior distribution of -1 is a Gamma distribution. ‡ The prior distribution for
po / px - 1 is a Gamma distribution. § The prior distribution of 70 is a Gamma distribution.
29
Table 2. Prior and posterior distributions of parameters of exogenous driving forces
Prior distribution Posterior distribution
AR(1) coefficient type mode 5th percentile
95th percentile mode Mean 5th
percentile 95th
percentile US total factor productivity Beta 0.70 0.112 0.942 0.937 0.936 0.934 0.938
ROW total factor productivity Beta 0.70 0.112 0.942 0.947 0.947 0.944 0.949 Spillover in total factor productivity Normal 0.088 0.006 0.170 0.007 0.008 0.006 0.010
Oil production shock Beta 0.70 0.112 0.942 0.913 0.910 0.898 0.920 US preference shock Beta 0.70 0.112 0.942 0.933 0.933 0.931 0.934
ROW preference shock Beta 0.70 0.112 0.942 0.925 0.925 0.921 0.929 US investment shock Beta 0.70 0.112 0.942 0.796 0.802 0.758 0.837
ROW investment shock Beta 0.70 0.112 0.942 0.821 0.816 0.781 0.842 Oil reserve shock Beta 0.50 0.070 0.930 0.041 0.048 0.001 0.184
US oil efficiency shock Beta 0.50 0.070 0.930 0.021 0.029 0.001 0.104 ROW oil efficiency shock Beta 0.50 0.070 0.930 0.004 0.010 0.001 0.033
Standard deviation of innovations US total factor productivity Gamma 0.50 0.178 2.372 0.767 0.774 0.705 0.852
ROW total factor productivity Gamma 0.50 0.178 2.372 0.449 0.446 0.388 0.510 Corr(US TFP, ROW TFP) Beta* 0.258 -0.240 0.630 0.268 0.279 0.136 0.415
Oil production shock Gamma 0.50 0.178 2.372 1.640 1.620 1.325 1.947 US preference shock Gamma 0.50 0.178 2.372 0.981 1.030 0.829 1.276
ROW preference shock Gamma 0.50 0.178 2.372 1.252 1.324 1.048 1.661 US investment shock Gamma 0.50 0.178 2.372 9.322 9.301 7.506 11.322
ROW investment shock Gamma 0.50 0.178 2.372 6.357 6.216 4.706 7.959 Oil reserve shock Gamma 0.50 0.178 2.372 1.667 1.636 1.278 2.010
US oil efficiency shock Gamma 0.50 0.178 2.372 1.890 1.921 1.735 2.135 ROW oil efficiency shock Gamma 0.50 0.178 2.372 2.167 2.213 1.965 2.493
* The prior distribution for (Corr(US TFP,ROW TFP)+1)/2 is a beta distribution.
30
Table 3. Prior and posterior distributions of measure error standard deviations
Prior distribution Posterior distribution
Measurement error standard Devation for: type mode 5th
percentile 95th
percentile mode Mean 5th percentile
95th percentile
ROW real GDP (Annual) Gamma 0.10 0.041 0.315 1.965 1.999 1.735 2.290 ROW Investment (Annual) Gamma 0.20 0.099 0.458 0.200 0.200 0.068 0.395
ROW Indust. Prod. (Quarterly) Gamma 0.20 0.099 0.458 0.125 0.120 0.049 0.213 Oil production capacity utilization Gamma 1.00 0.493 2.288 0.984 0.988 0.362 1.877
0 20 40 60-10
-5
0
5Real oil price: Oil production shock
0 20 40 60-1
0
1
2Oil output: Oil production shock
0 20 40 60-10
-5
0Real oil price: Oil reserve shock
0 20 40 600
0.5
1
1.5Oil output: Oil reserve shock
0 20 40 60-5
0
5Real oil price: US TFP shock
0 20 40 60-0.5
0
0.5Oil output: US TFP shock
0 20 40 600
2
4
6Real oil price: ROW TFP shock
0 20 40 60-0.5
0
0.5Oil output: ROW TFP shock
0 20 40 60-2
-1
0
1Real oil price: US pref. shock
0 20 40 60-0.1
-0.05
0Oil output: US pref. shock
0 20 40 60-2
-1
0Real oil price: ROW pref. shock
0 20 40 60-0.2
-0.1
0Oil output: ROW pref. shock
0 20 40 60-6
-4
-2
0Real oil price: US oil eff. shock
0 20 40 60-0.5
0
0.5Oil output: US oil eff.shock
0 20 40 60-15
-10
-5
0Real oil price: ROW oil eff. shock
0 20 40 60-2
-1
0
1Oil output: ROW oil eff. shock
0 20 40 60-2
0
2
4Real oil price: US invest. shock
0 20 40 60-0.5
0
0.5Oil output: US invest. shock
0 20 40 60-5
0
5Real oil price: ROW invest. shock
0 20 40 60-0.5
0
0.5
1Oil output: ROW invest. shock
Figure 1. Posterior distribution of impulse response of real oil price and oil output to various shocks;mean, 5th and 95th percentiles
0 20 40 600
0.05
0.1
0.15
0.2US GDP: Oil production shock
0 20 40 600
0.05
0.1
0.15
0.2US GDP: Oil reserve shock
0 20 40 600
0.05
0.1
0.15
0.2US Consumption: Oil production shock
0 20 40 60-0.1
0
0.1
0.2
0.3US Consumption: Oil reserve shock
0 20 40 600
0.5
1US Investment: Oil production shock
0 20 40 600
0.1
0.2
0.3
0.4US Investment: Oil reserve shock
0 20 40 60-0.1
0
0.1
0.2
0.3US hours: Oil production shock
0 20 40 600
0.05
0.1
0.15
0.2US hours: Oil reserve shock
0 20 40 60-0.5
0
0.5
1US Oil consumption: Oil production shock
0 20 40 600
0.2
0.4
0.6
0.8US Oil consumption: Oil reserve shock
Figure 2. Impulse response of US variables to oil production and oil reserve shocks.
0 10 20 30 40 50 60-1
-0.5
0US GDP: US preference shock
0 10 20 30 40 50 600
0.5
1
1.5US GDP: US TFP shock
0 10 20 30 40 50 600
0.2
0.4US GDP: US Oil eff. shock
0 10 20 30 40 50 600
0.5
1US GDP: US invest. shock
0 10 20 30 40 50 60-1.5
-1
-0.5
0US Cons.: US preference shock
0 10 20 30 40 50 600
0.5
1US Cons.: US TFP shock
0 10 20 30 40 50 60-0.5
0
0.5US Cons.: US Oil eff. shock
0 10 20 30 40 50 60-0.5
0
0.5US Cons.: US invest. shock
0 10 20 30 40 50 60-4
-2
0US Invest.: US preference shock
0 10 20 30 40 50 600
2
4
6US Invest.: US TFP shock
0 10 20 30 40 50 600
0.2
0.4US Invest.: US oil eff. shock
0 10 20 30 40 50 600
1
2
3US Invest.: US invest. shock
0 10 20 30 40 50 60-1.5
-1
-0.5
0US hours: US preference shock
0 10 20 30 40 50 600
0.5
1US hours: US TFP shock
0 10 20 30 40 50 600
0.1
0.2US hours: US Oil eff. shock
0 10 20 30 40 50 600
0.2
0.4US hours: US invest. shock
0 10 20 30 40 50 60-1
-0.5
0US Oil cons.: US preference shock
0 10 20 30 40 50 600
0.5
1US Oil cons.: US TFP shock
0 10 20 30 40 50 60-2
-1
0
1US Oil cons.: US oil eff. shock
0 10 20 30 40 50 60-1
0
1
2US Oil cons.: US invest. shock
Figure 3. Impulse response of US variables to US shocks
0 20 40 600
0.05
0.1US GDP: ROW preference shock
0 20 40 60-0.2
0
0.2US GDP: ROW TFP shock
0 20 40 600
0.1
0.2US GDP: ROW Oil eff. shock
0 20 40 60-0.2
0
0.2US GDP: ROW invest. shock
0 20 40 60-0.5
0
0.5
1US Consumption: ROW preference shock
0 20 40 60-0.5
0
0.5US Consumption: ROW TFP shock
0 20 40 60-0.5
0
0.5US Consumption: ROW Oil eff. shock
0 20 40 60-0.5
0
0.5US Consumption: ROW invest. shock
0 20 40 600
0.5
1US Investment: ROW preference shock
0 20 40 60-1
-0.5
0
0.5US Investment: ROW TFP shock
0 20 40 600.2
0.3
0.4
0.5US Investment: ROW oil eff. shock
0 20 40 60-1
-0.5
0
0.5US Investment: ROW invest. shock
0 20 40 600
0.02
0.04
0.06US hours: ROW preference shock
0 20 40 60-0.1
-0.05
0US hours: ROW TFP shock
0 20 40 600
0.2
0.4US hours: ROW Oil eff. shock
0 20 40 60-0.1
0
0.1US hours: ROW invest. shock
0 20 40 600
0.2
0.4US Oil cons.: ROW preference shock
0 20 40 60-0.5
0
0.5US Oil cons.: ROW TFP shock
0 20 40 600
0.5
1
1.5US Oil cons.: ROW oil eff. shock
0 20 40 60-1
-0.5
0US Oil cons.: ROW invest. shock
Figure 4. Impulse response of US variables to ROW shocks
1970 1980 1990 2000 2010-100
0
100
200Real oil price: Contribution of oil supply
1970 1980 1990 2000 2010
-10
0
10
20
Oil output: Contribution of oil supply.
1970 1980 1990 2000 2010-100
0
100
200Real oil price: oil demand shocks
1970 1980 1990 2000 2010
-10
0
10
20
Oil output: oil demand shocks
1970 1980 1990 2000 2010-100
0
100
200Real oil price: Contribution of US oil demand shocks
1970 1980 1990 2000 2010
-10
0
10
20
Oil output: Contribution of US oil demand shocks
1970 1980 1990 2000 2010-100
0
100
200Real oil price: Contribution of ROW demand shocks
1970 1980 1990 2000 2010
-10
0
10
20
Oil output: Contribution of ROW demand shocks
Figure 5. Historical decomposition of real oil price and oil output
1970 1980 1990 2000 2010-15
-10
-5
0
5
10US GDP: Contribution of oil supply shocks
1970 1980 1990 2000 2010-15
-10
-5
0
5
10US GDP: Contribution of ROW shocks
1970 1980 1990 2000 2010-15
-10
-5
0
5
10US GDP: Total contribution of US shocks
1970 1980 1990 2000 2010-15
-10
-5
0
5
10US GDP: Contribution of US preference shocks
1970 1980 1990 2000 2010-15
-10
-5
0
5
10US GDP: Contribution of US TFP shocks
1970 1980 1990 2000 2010-15
-10
-5
0
5
10US GDP: Contribution of US investment shocks
1970 1980 1990 2000 2010-15
-10
-5
0
5
10US GDP: Contribution of US oil efficiency shocks
Figure 6. Historical decomposition of U.S. real GDP
1970 1980 1990 2000 2010-20
-10
0
10
ROW IP: Contribution of oil supply
1970 1980 1990 2000 2010-20
-10
0
10
ROW IP: Contribution of US shocks
1970 1980 1990 2000 2010-20
-10
0
10
ROW IP: Total contribution of ROW shocks
1970 1980 1990 2000 2010-20
-10
0
10
ROW IP: Total contribution of all shocks
1970 1980 1990 2000 2010-20
-10
0
10
ROW IP: Contribution of ROW TFP shocks
1970 1980 1990 2000 2010-20
-10
0
10
ROW IP: Contribution of ROW preference shocks
1970 1980 1990 2000 2010-20
-10
0
10
ROW IP: Contribution ROW oil efficiency shocks
1970 1980 1990 2000 2010-20
-10
0
10
ROW IP: Contribution of ROW invest shocks
Figure 7. Historical decompositon of ROW industrial production
Technical Appendix
A. Observation Equations in the State Space Model
Our data consists of quarterly observations on U.S. GDP, consumption, investment, and
hours, U.S. oil consumption (barrels), real oil price (deflated by U.S. GDP deflator), world oil
production (barrels), annual ROW real GDP (PPP, in dollars), annual ROW real investment
(PPP, in dollars), quarterly ROW industrial production, and oil capacity utilization. For several
variables the mapping between the model and the data are exact:
ˆ Y us,tcons = ˆ C a,t ,
ˆ Y us,tinv = ˆ I a,t ,
t,binv
t,row IY = ,
ˆ Y us,temp = ˆ N a,t ,
ˆ Y oil output,t = ˆ Y o,t , and
ˆ Y us,toil cons = ˆ O a,t where “^” represents deviations from
the deterministic steady state. However, several variables need to be transformed to correspond
to the data we employ. Output in the model corresponds to gross output rather than value added,
thus GDP is given by
ˆ Y row,tgdp = ( ˆ Y b,t −
PoOb
PbYa
ˆ O b,t ) /(1−PoOb
PbYb
) , and
ˆ Y us,tgdp = ( ˆ Y a,t −
PoOa
PaYa
ˆ O a,t ) /(1−PoOa
PaYa
).
Similarly, as the GDP (value added) deflator was used to deflate the oil price:
ˆ Y real oil price,t = ( ˆ P o,t − ˆ P a,t ) /(1−PoOa
PaYa
). For ROW industrial production, we allow the model to scale
up country b’s output so that t,bprodindt,row YY φ= where φ is the scaling parameter. This is to take into
account that measured industrial production is a narrower measure of output and possibly more
volatile than the aggregate output implied by the model.
For oil capacity utilization, 𝑢𝑜,𝑡 = 𝑌𝑜,𝑡𝑐𝑎𝑝𝑜,𝑡
where 𝑌𝑜,𝑡 is oil production and 𝑐𝑎𝑝𝑜,𝑡 is oil
production capacity. We use the logit of 𝑢𝑜,𝑡, 𝑙𝑛 �𝑢𝑜,𝑡
1−𝑢𝑜,𝑡�, as the actual observation variable.
Taking a linear approximation around the steady state:
39
𝑙𝑛 � 𝑢𝑜,𝑡1−𝑢𝑜,𝑡
� − 𝑙𝑛 � 𝑢𝑜1−𝑢𝑜
� ≈ 11−𝑢𝑜
�𝑌�𝑜,𝑡 − 𝑐𝑎𝑝� 𝑜,𝑡� (A.1)
As the model does not explicitly contain a capital utilization variable, we assume that oil
production capacity is a function of capital in the oil production sector (reserves). We allow the
relationship between capacity and reserves to evolve over time but that they are proportional in
steady state. In terms of deviations from the steady state, law of motion for capacity is given by:
𝑐𝑎𝑝� 𝑜,𝑡 = 𝜌𝑐𝑎𝑝𝑐𝑎𝑝� 𝑜,𝑡−1 + �1 − 𝜌𝑐𝑎𝑝�𝑥�𝑡 (A2)
Equations (A1) and (A2) link the variables in the model to the observed logit of capital
utilization in oil production, 𝑙𝑛 � 𝑢𝑜,𝑡1−𝑢𝑜,𝑡
�.
B. Bayesian Estimation of the DSGE Model
One can write the solution to the linearized, rational expectations DSGE model in terms
of a state space model:
modt
modt SY Π= (B1)
modt
modt
modt VMSS += −1 . (B2)
where modtY is a vector of endogenous variables in the model; mod
tS is the state vector which
includes the capital stocks of U.S. (country a) and ROW (country b), oil reserves and oil
capacity, and the level of energy efficiency in the U.S. and ROW, as well as the ten exogenous
shock variables: TFP, labor-leisure preferences, exogenous oil efficiency, investment (capital
accumulation) shocks for countries a and b and oil production and oil reserve shocks.
The model is written in terms of quarters while we have only annual data for ROW GDP
and ROW investment. Thus, we partition the observation equation of the state space model into
40
two sets of equations—one corresponding to quarterly observations, the other corresponding to
annual observations. The observation equation is given by:
t
modt
modt
modt
modt
annualt
quarterlytobs
t W
SSSS
....YY
Y +
ΠΠΠΠ
Π=
=
−
−
−
3
2
1
2222
1
25252525000
(B3)
The corresponding state equation is given by:
+
=
−
−
−
−
−
−
−
000
000000000000
4
3
2
1
3
2
1
modt
modt
modt
modt
modt
modt
modt
modt
modt V
SSSS
II
IM
SSSS
. (B4)
The empirical state space model implied by (B3) and (B4) can be rewritten as:
))(R,(MVN~W,WS)(HY tttobs
t θθ 0+= (B5)
))(Q,(MVN~V,VS)(FS tttt θθ 01 += − (B6)
where obstY is the vector of observable time series, tS is the vector of unobserved state variables,
and θ is the vector of structural parameters in the DSGE model. tW is a vector of measurement
errors. In our application, obstY contains detrended quarterly log per capita real U.S. GDP,
detrended quarterly per capita real U.S. consumption, detrended quarterly log per capita real U.S.
investment, detrended log per capita quarterly U.S. oil consumption, detrended quarterly log
world oil production, demeaned quarterly log real oil price, detrended quarterly log ROW
industrial product, detrended annual real GDP for ROW (PPP constant U.S. dollars), detrended
annual real investment expenditures for ROW (PPP constant U.S. dollars), and demeaned logit of
oil production capacity utilization. We scale up all the variables by 100. We set R to be a
diagonal matrix with variance of measurement errors along the diagonal. We estimated measure
41
error variances for the ROW series and for oil production capacity utilization. We treat
observations for the annual data as missing for all but the fourth quarter of the year.
Given the parameters,θ , we can estimate the unobserved states by the Kalman Filter.
The predictive log likelihood of the state space model is given by:
l(YT ,θ) = {−.5log(det(H(θ)'Pt | t−1H(θ) + R))t=1
T
∑
− .5(Yt − H(θ)St | t−1)'(H(θ)'Pt | t−1H(θ) + R)−1(Yt − H(θ)St | t−1)} (B7)
where 1−t|tS and 1−t|tP are the conditional mean and variance of tS from the Kalman filter.
Given a prior distribution over parameters,
h(θ) , the posterior distribution,
P(θ | YT ) , is
P(θ | YT ) ∝ exp( l(YT ,θ))h(θ) . (B8)
Because the log-likelihood is a highly nonlinear function of the structural parameter vector, it is
not possible to write an analytical expression for the posterior distribution. As a result, we use
Bayesian Markov Chain Monte Carlo methods to estimate the posterior distribution of the
parameter vector,
θ . In particular, we employ a Metropolis-Hasting sampler to generate draws
from the posterior distributions. The algorithm is as follows:
(i) Given a previous draw of the parameter vector,
θ (i−1), draw a candidate vector cθ
from the distribution
g(θ |θ (i−1)).
(ii) Determine the acceptance probability for the candidate draw,
α(θ c,θ ( i−1)) = min exp( l(YT ,θ (c )))h(θ (c ))exp( l(YT ,θ (i−1)))h(θ ( i−1))
g(θ (i−1) |θ c )g(θ c |θ (i−1))
, 1
.
(iii) Determine a new draw from the posterior distribution,
θ (i).
θ (i) = θ c with probability
α(θ c,θ ( i−1))
θ (i) = θ (i−1) with probability
1−α(θ c,θ ( i−1)) .
(iv) Return to (i).
42
Starting from an initial parameter vector and repeating enough times, the distribution parameters
draws,
θ (i), will converge to the true posterior distribution.
In our application,
θ c = θ (i−1) + v , where
v is drawn from a multivariate t-distribution with
50 degrees of freedom and a covariance matrix Σ . We set Σ to be a scaled value of the Hessian
matrix of
− l(YT ,θ)) − ln(h(θ))evaluated at the posterior mode. We choose the scaling so that
around 30 percent of the candidate draws are accepted. We run four separate Markov Chains
each with a different initial condition. For each chain, we set a burn-up period of 100,000 draws,
and then sample every tenth draw for a total of 10,000 draws. Thus, the posterior distribution of
parameters is based on a total of 50,000 draws. We also obtain the posterior distributions for the
unobserved states. Given a parameter draw, we draw from the conditional posterior distribution
for the unobserved states,
P(ST | Θ(i),YT ) . Here we use the “filter forward, sample backwards”
approach proposed by Carter and Kohn (1994) and discussed in Kim and Nelson (1999).
C. Data Sources
U.S. data on real GDP, consumption, investment, government expenditures and relative
price of imports are from the Bureau of Economic Analysis (BEA). Hours worked and
employment data are from the Bureau of Labor Statistics. Oil consumption and production data
are from the Energy Information Administration (EIA) of the U.S. Department of Energy. The
real oil price is from the Wall Street Journal database and the BEA. All U.S. data are quarterly.
In order to obtain an approximate estimate of the data for the rest of world oil-consuming
country, we aggregate data from 29 countries—Brazil, China, and India, plus 26 of the 30 OECD
countries. We exclude the United States, whose data is used for the Home Country in the model;
Mexico, which is a major oil-producing country, and the Czech Republic and Slovakia, neither
of which have reliable data prior to 1990. Because real GDP and investment are reported in U.S.
43
dollars, we aggregate these series across countries. We convert ROW GDP and investment to
per capita series by dividing with population aggregated across countries.
For the period 1970 to 2003, the data for population, real GDP, and real investment for
all 29 countries are taken from the Penn World Table. For the period 2004 through 2008, the
data for the 26 OECD countries are from the OECD; and the data for Brazil, India and China are
from Haver Analytics. The data from 2004 to 2008 were spliced to the earlier data in 2003,
country by country, and then aggregated to obtain per capita measures of ROW output and
investment.
Quarterly world industrial production is from the OECD. Oil capacity utilization is
constructed by taking annual OPEC oil capacity from the EIA and annual oil production from the
Oil and Gas Journal Database and adding to each non-OPEC production to get world oil
capacity and oil production. Capacity utilization is oil production divided by oil capacity.
References
Carter, C.K. and R. Kohn (1994). “On Gibbs Sampling for State Space Models,” Biometrika, 81 (3): 541-553.
Kim, Chang-Jin and Charles Nelson (1999). “Has the U.S. Economy Become More Stable? A Bayesian Approach Based on a Markov-Switching Model of the Business Cycle,” Review of Econ and Statistics, 81(4): 608-616.