Preliminary: please do not quote
The Effects of Oil Shocks on the Global Economy
Luca Guerrieri∗
June 2005
Abstract
One of the limitations that has prevented the more widespread use of SDGE models for policy
analysis is the relative paucity of shocks that these models have typically incorporated. In this paper,
I expand a model for policy analysis developed at the Federal Reserve Board (SIGMA) to incorporate
an oil sector. The expanded model is innovative in its ability to assess the differential effects of oil
shocks for oil importing and exporting countries in a unified framework. Under a Taylor rule for
monetary policy, I find that the GDP impact of oil shocks is negative in oil exporting countries, and
even larger than for oil importing countries, despite an observed increase in private consumption. The
terms of trade for oil exporting countries improve and their non-oil trade balance deteriorates. By
contrast, countries that import most of the oil they consume experience terms of trade deteriorations
and improvements in the non-oil trade balance. Monetary policy, the GDP share of oil demand, and
the local level of oil production are found to be key determinants of the impact of oil shocks.
Keywords: open economy macroeconomics, oil-price shocks, oil-demand shocks, SDGE models.
∗
Board of Governors of the Federal Reserve System, Washington D.C. 20551-0001. Telephone (202) 452 2550.
E-mail Luca.Guerrieri@frb.gov.
∗∗
I thank David Bowman, Brett Berger, Joe Gagnon, Stephen Kamin, Trevor Reeve, Ralph Tryon for many
useful conversations. I am particularly indebted to Chris Erceg and Chris Gust. Remaining errors are mine only.
The views expressed in this paper are solely the responsibility of the authors and should not be interpreted as
reflecting the views of the Board of Governors of the Federal Reserve System or of any other person associated
with the Federal Reserve System.
1
Introduction
One of the limitations that has prevented the more widespread use of SDGE models for policy
analysis is the relative paucity of shocks that these models have typically incorporated. The
introduction of an oil sector in a SDGE framework contributes to obviating these concerns by
allowing additional simulations of great interest to policy-makers.
In this paper, I expand a model for policy analysis developed at the Federal Reserve
Board to incorporate an oil sector. A two-country version of the model (named SIGMA) is
described by Erceg, Guerrieri, and Gust (2005b). Here, I detail the addition to SIGMA of an
oil input into local production and consumption and the inclusion of oil-producing sectors, as
well as of international oil trade. The model comprises a total of seven country blocks. Each
country block uses oil in the production of intermediate goods and directly in the consumption
basket. I allow for local production of oil as well as for international trade of oil to reflect the
trade flows observed on average in recent data. For instance, the United States block produces
part of the oil it consumes, but also imports oil from Canada, Mexico as well as the ROW
block. Conversely, Canada and Mexico produce enough oil to satisfy their domestic demand
and to export to the United States block.1
The incorporation of oil production in a SDGE model is a relatively recent endeavor.2 .
This paper is innovative in its ability to assess the differential effects of oil shocks for oil
importing and exporting countries in a unified framework and in its ability to differentiate
between oil demand and supply shocks. The multicountry nature of the model allows the trade
links to reinforce or attenuate the direct effects of oil shocks, that a simple two-country model
would miss. The version of SIGMA described here also incorporates distortions not present in
previous modelling work that are important determinants of the macroeconomic impact of oil
1
2
In the data, Canada and Mexico’s oil exports to third countries are a negligible fraction of their oil trade.
Jones, Leiby, and Paik (2004) provide a helpful overview of both empirical and modeling exercises on the
effects of oil shocks. Among the more recent studies Wei (2003) provides an assessment of the effects of oil price
shocks on the stock market in a putty-clay investment model; Leduc and Sill (2004) attempts to disentangle the
effects of oil shocks from the reaction of monetary policy.
2
shocks. These include the extent of local oil production as well as distortionary ad valorem and
specific taxes on oil.
The empirical literature on the macroeconomic effects of oil shocks has focused mostly
on oil-price shocks in the United States.3 One of the difficulties that has plagued the empirical
literature concerns disentangling the effects of oil shocks from the response of monetary policy.
As stressed by Leduc and Sill (2004), the modelling approach has some distinct advantages in
this respect as within a structural setting the effects of oil shocks under alternative monetary
policies can easily be compared.
Another advantage of a model exercise is that it allows a clear assessment of how particular
features of the underlying economy affect the macroeconomic impact of oil shocks. For instance,
I explore how the GDP share of oil demand affects the impact of oil shocks on the macroeconomy.
Finally, this kind of modelling exercise can provide guidance to empirical studies on
the factors whose variation over the estimation sample ought to be controlled. For instance,
expenditures on oil as a fraction of GDP varied widely in the United States over the sample
typically used for estimation. As we show, the oil share is an important determinant of the
impact on GDP of oil shocks. To the extent that oil shocks of the 1970s coincided with much
higher oil shares than in the 1990s, the oil-GDP multiplier would be biased upwards in studies
not directly controlling for variation in the oil share.
In the simulations presented, under a Taylor rule for monetary policy, I find that the
GDP impact of oil shocks is negative in oil exporting countries, and even larger than for oil
importing countries, despite an observed increase in private consumption. The terms of trade
for oil exporting countries improve and their non-oil trade balance deteriorates. By contrast,
countries that import most of the oil they consume experience terms of trade deteriorations and
improvements in the non-oil trade balance. Monetary policy, the GDP share of oil demand, and
the local level of oil production are found to be key determinants of the impact of oil shocks. In
3
Hamilton (1983) and Hamilton (2003) document the non-linear relationship between oil prices and U.S. GDP.
Bernanke, Gertler, and Watson (1997) stress the importance of controlling for the monetary policy response in
assessing the impact of oil-price shocks on GDP.
3
the popular press, the recent surge in the price of oil has been linked to spikes in demand rather
than to a deliberate desire of OPEC to drive up the price. I assess the differential impacts on
the United States block of supply shocks originating in the ROW block and of demand shocks
arising in the China block.
The remainder of the paper is organized as follows. In Section 2, I describe the additions
to the SIGMA model to allow for the analysis of oil shocks. In Section 3, I give the calibration
details. Section 4 describes some simulation results. Section 5 concludes.
2
2.1
Model Description
Model Overview
The SIGMA model is related to the open-economy framework of Obstfeld and Rogoff (1995).
However, the model also includes many of the nominal and real frictions that have been identified as empirically important in the work of Christiano, Eichenbaum, and Evans (2005) and
Smets and Wouters (2003), such as habit persistence in consumption and adjustment costs
in investment as well as analogous rigidities that enhance the empirical relevance of the openeconomy aspects, such as costs of adjustment for goods imports. Here, I detail the modifications
to our framework that allows me to analyze oil price shocks in a multicountry setting.
Erceg, Guerrieri, and Gust (2005b) give a full description of the a two-country version
of the SIGMA model that excludes the oil sector. In this paper, I abstract from some of the
features of SIGMA, such as rule-of-thumb behavior in consumption, that are less central to the
analysis of oil shocks (and are excluded from the model used for the simulations presented),
but detail the multicountry extension of the model that is germane to the analysis of oil shocks.
The version of SIGMA used here comprises seven country blocks calibrated to match features
of the economies of the United States, Canada, Mexico, the euro area, Japan, China and the
rest-of-the-world block (ROW).
In the model, all country blocks have an analogous structure. Each country, in effect,
specializes in the production of one final good that is an imperfect substitute for the goods pro4
duced in other countries, although we adopt a standard monopolistically competitive framework
to rationalize stickiness in the aggregate price level. While household utility depends on consumption of both the domestic output good and imported goods, as well as oil, it is convenient
to assume that a competitive distribution sector purchases inputs from all countries and oil, and
simply resells a final consumption good to households. Similarly, we assume that competitive
distributors combine the domestic output good with imports of goods and oil to produce a final
investment good.
Production of the domestic good requires labor, capital and oil inputs. With the exception
of the ROW block, each country has an oil endowment that allows a constant level of oil
extraction, but this endowment varies across countries. For some countries in the model (e.g.,
the United States), the oil production is not sufficient to meet the domestic demand and they
resort to importing oil. For other countries (e.g., Canada), the local oil production is more than
enough to meet the domestic demand and they export the excess production. Rather than just
having an oil endowment, the ROW block has two distinct production sectors. Just like for
any other country block, one sector produces a final good that is an imperfect substitute of
the goods produced abroad. The other sector produces oil and the level of production is set to
maximize profits. Unlike in the other country blocks, each sector has its own distinct capital
stock.
2.2
Firms and Production
In each country, there is a continuum of differentiated intermediate goods (indexed by i ∈ [0, 1])
produced by a single monopolistically competitive firm. To simplify notation, I have dropped
the country-specific labels as the model setup is replicated with just a few exceptions that are
highlighted below. I focus on the description of one of the country blocks that I denote as
“home country.” In the home market, firm i faces a demand function that varies inversely with
its output price PDt (i) and directly with aggregate demand at home YDt .
·
PDt (i)
YDt (i) =
PDt
p)
¸ −(1+θ
θ
p
YDt ,
(1)
5
where θp > 0, and PDt is an aggregate price index defined below. Similarly, in the foreign
market, firm i faces the demand function:
·
Xtk (i)
PDt (i)
=
PDt
p)
¸ −(1+θ
θ
p
Mtk ,
(2)
where Xt (i) denotes the quantity demanded of home good i in country k and Mtk is the aggregate
demand from the foreign country k for home goods.
Each producer utilizes capital services Kt (i), a labor index Lt (i) (defined below) and oil
inputs OtA (also defined below) to produce its respective output good. The production function
is assumed to have a constant-elasticity of substitution (CES) form over capital and labor. The
the capital-labor inputs are then combined with the oil input via a Cobb-Douglas production
function.
·³
Yt (i) =
ρ
1+ρ
ωK Kt (i)
1
1+ρ
+ ωL
ρ
1+ρ
(Zt Lt (i))
1
1+ρ
´1+ρ ¸γy
OtA
1−γy
.
(3)
Technological progress Zt is labor-augmenting and governed by an exogenous autoregressive
process.4 At the firm-level, there are perfectly competitive factor markets for hiring capital
and labor and purchasing oil inputs. Thus, each firm chooses Kt (i), Lt (i) and OtA (i), taking
as given the rental price of capital RKt , the aggregate wage index Wt (defined below), and
A
the price of the oil input POt
(defined below). As all firms can costlessly adjust the factors
of production, the standard static first-order conditions for cost minimization imply identical
marginal cost per unit of output, M Ct .
At the aggregate level, however, it is costly to adjust the energy input. The costs are
born by a perfectly competitive energy distribution sector and are passed on to households in
the form of diminished profits. The cost minimization problem of a representative firm i in the
oil distribution sector which produces the oil “adjusted” output OtA (i) is the following:
½
∞
X
ψt,t+j (1 + τP O,t+j )POt Ot+j (i) + τQO,t+j PDt+j Ot+j (i)
min Et
Ot (i)
4
j=0
In Erceg, Guerrieri, and Gust (2005a) we allow for trend technology and population growth. Here, I simplify
the exposition by abstracting from trend growth.
6


A
A
Ot+j
+POt+j
(i) − Ot+j (i) 1 −

ϕO,i 
2
Ot+j (i)
YDt+j
Ot+j−1 (i)
YDt+j−1
2 

− 1  

(4)
where the operator Et represents expectations conditional at time t; Ot+j (i) is the oil input and
POt is its price; the term τP O,t+j stands in for ad-valorem oil taxes, and τQO,t+j for specific oil
taxes (these taxes are not linked directly to the price of oil); ϕO,i is a parameter regulating the
quadratic costs of adjustment and YDt+j is the aggregate output of the domestic good (defined
below).
We assume that the prices of the intermediate goods are determined by Calvo-style staggered contracts (see Calvo (1983)). In each period, a firm faces a constant probability, 1 − ξp , of
being able to reoptimize its price (PDt (i)). These probabilities are assumed to be independent
across firms and time. If a firm is not allowed to optimize its prices, we follow Christiano,
Eichenbaum, and Evans (2001) and assume the firm must reset its price based on lagged aggregate inflation. Prices are updated according to PDt (i) = πt−1 PDt−1 (i) where πt = PDt /PDt−1 .5
This form of lagged indexation is a mechanism for introducing inflation inertia into the key
price-setting equations.
When firm i is allowed to reoptimize its price in period t, the firm maximizes
!#
"
Ã
∞
X
X
Xtk (i)
.
Et
ξpj ψt,t+j (VDt+j PDt (i) − M Ct+j (i)) YDt+j (i) +
j=0
(5)
∀k
The firm discounts profits received at date t + j by the state-contingent discount factor ψt,t+j ;
for notational simplicity, we have suppressed all of the state indices.6 Also, VDt+j is defined by:
VDt+j =
j
Y
πt+h−1 .
(6)
h=1
5
In alternative calibrations of SIGMA, we also consider the specification used by Yun (1996) and Erceg,
Henderson, and Levin (2000) where PDt (i) = πPDt−1 (i) so that VDt+j = π j in the profit functional defined
below. For this alternative calibration, prices are updated according to PM t (i) = π k PM t−1 (i) in foreign markets.
6
We define ξt,t+j to be the price in period t of a claim that pays one dollar if the specified state occurs in
period t + j (see the household problem below); then the corresponding element of ψt,t+j equals ξt,t+j divided
by the probability that the specified state will occur.
7
Production of the Domestic Output Index
Because households have identical Dixit-Stiglitz preferences, it is convenient to assume that a
representative aggregator combines the differentiated intermediate products into an aggregate
for the domestic demand for home-produced goods YDt :
·Z
1
YDt =
YDt (i)
1
1+θp
¸1+θp
di
.
(7)
0
The aggregator chooses the bundle of goods that minimizes the cost of producing YDt , taking
the price PDt (i) of each intermediate good YDt (i) as given. The aggregator sells units of each
sectoral output index at its unit cost PDt :
·Z 1
¸−θp
−1
θp
PDt =
PDt (i) di
.
(8)
0
We also assume a representative aggregator in each of the foreign economy who combines the
differentiated home products Xt (i) into a single index for foreign imports:
·Z 1
¸1+θp
1
k
1+θp
Xt (i)
Mt =
di
,
(9)
0
and sells Mtk at price PDt :
Production of Consumption and Investment Goods
Final consumption goods are produced by a representative consumption good distributor. This
firm combines purchases of domestically-produced goods with imported goods and oil inputs
to produce a final consumption good (Ct ) according to the following production function:
Ã
1+ρc γct
ρc
! 1+ρ
c
ρc
1
X
X
1
1+ρc
1+ρc
 [ϕOt OCt ]1−γct (10)
Ct = Ac  1 −
ωCk
CDt+k
+
ϕCkt ωCk
MCkt 1+ρc 
∀k
∀k
where CDt denotes the consumption good distributor’s demand for the index of domesticallyproduced goods, MCkt denotes the distributor’s demand for the index of goods produced in
the foreign country k and OCt represents the distributor’s oil demand; finally, ϕCkt and ϕOt
represent costs of adjusting consumption imports and oil inputs, respectively. The form of the
8
production function mirrors the preferences of households over consumption of domesticallyproduced goods, imports, and oil inputs. Accordingly, the quasi-share parameters ωCk may
be interpreted as determining household preferences for home relative to foreign goods, or
equivalently, the degree of home bias in household consumption expenditure. Similarly γct
is a share parameter determining the importance of oil expenditures in households’ overall
expenditures. This parameter is time varying to incorporate a preference shock that allows the
analysis of exogenous demand shocks.
The adjustment cost term, ϕCt , is assumed to take the quadratic form:

à M
!2 
Ct
ϕMC
CDt
ϕCt = 1 −
− 1 .
MCt−1
2
C
(11)
Dt−1
This specification implies that it is costly to change the share of the imported good in total
consumption and has the attractive feature that import demand in the short run will be relatively unresponsive to changes in the real exchange rate while remaining relatively responsive
to changes in overall consumption demand.
Similarly, the adjustment cost for the oil input in consumption, ϕOt , takes the form:

à O
!2 
Ct
ϕO
CDt
ϕOt = 1 −
− 1 .
(12)
OCt−1
2
C
Dt−1
These adjustment costs on oil mirror the ones on the firms’ side. They allow the flexibility
to dampen the responsiveness of oil demand to price fluctuations, as in the time series data.
However, they still allow oil demand to adjust quickly in response to income changes, insofar
as those changes will also lead to an increase in the non-oil consumption demand.7
Given the presence of adjustment costs, the representative consumption goods distributor
chooses (a contingency plan for) CDt , MCkt ∀k, and OCt to minimize its discounted expected
costs of producing the aggregate consumption good. The distributor sells the final consumption
good to households at a price PCt , which may be interpreted as the consumption price index
(or equivalently, as the shadow cost of producing an additional unit of the consumption good).
7
Gately and Huntington (2002) document the differential speeds of oil demand adjustment to changes in
price and changes in incom, concluding that demand adjusts faster to income changes than to price changes.
9
We model the production of final investment goods in an analogous manner. Thus, the
representative “investment goods distributor” produces a final investment good by combining
its purchases of domestically-produced goods with purchases of foreign-produced goods from all
foreign countries, and with purchases of the oil inputs, subject to quadratic adjustment costs.
Investment goods distributors solve an intertemporal cost minimization problem isomorphic
to that of consumption goods distributors. The distributor sells the final investment good
to households at a price PIt , which may be interpreted as the investment price index. This
price may differ from the price index of the consumption good PCt , even in the absence of
the adjustment costs for consumption and investment imports because of differences in import
composition, governed by distinct quasi share parameters from the ones for consumption.8
Oil Production
With the exception of the ROW block, each country block in the model is endowed with oil
reserves that allow a certain level of production each period. Local oil production in country
k, YOk , is assumed to remain at a constant level. However, this level of production varies by
country and does not require capital or labor services.
In the ROW block, oil production requires the use of capital according to the production
schedule:
ROW
YOt
= ZOt KOt
(13)
where ZOt is oil-specific technology determined by an exogenous process. Given perfectly competitive factor markets, the first order condition for cost minimization in the oil sector implies
that the relative price of oil φOt ≡ POt /PDt will be equated with the real rental rate of oil capital
RKOt . At the production stage, capital for the final good sector and capital for the oil sector
are fully fungible; however, once installed, the two kinds of capital become sector specific. In
the oil sector, a single firm rents oil capital from competitive markets to maximize profits given
domestic and foreign demand for oil.
8
The problem of the investment distributor is described in more detail in Erceg, Guerrieri, and Gust (2005a).
10
2.3
Households and Wage Setting
We assume a continuum of monopolistically competitive households (indexed on the unit interval), each of which supplies a differentiated labor service to the intermediate goods-producing
sector (the only producers demanding labor services in our framework). It is convenient to
assume that a representative labor aggregator (or “employment agency”) combines households’
labor hours in the same proportions as firms would choose.
Thus, the aggregator’s demand
for each household’s labor is equal to the sum of firms’ demands. The aggregate labor index
Lt has the Dixit-Stiglitz form:
·Z 1
¸1+θw
1
1+θ
Lt =
(Nt (h)) w dh
,
(14)
0
where θw > 0 and Nt (h) is hours worked by a typical member of household h. The aggregator
minimizes the cost of producing a given amount of the aggregate labor index, taking each
household’s wage rate Wt (h) as given, and then sells units of the labor index to the production
sector at their unit cost Wt :
·Z 1
¸−θw
−1
Wt (h) θw dh
Wt =
.
(15)
0
It is natural to interpret Wt as the aggregate wage index. The aggregator’s demand for the
labor services of a typical member of household h is given by
·
Wt (h)
Nt (h) =
Wt
¸− 1+θ
w
θ
w
Lt /ζt .
(16)
The utility functional of a typical member of household h is
(
µ
¶1−σ
∞
X
Ct+j−1
1
j
β
Ct+j (h) − κ
+
Et
1
−
σ
ζ
t+j−1
j=0
¶1−µ )
µ
1−σ
χ0 Zt+j
µ
M
B
(h)
0
t+j+1
,
(1 − Nt+j (h))1−χ +
1−χ
1−µ
PCt+j
(17)
where the discount factor β satisfies 0 < β < 1. As in Smets and Wouters (2003), we allow
for the possibility of external habits, where an individual in the household cares about their
consumption relative to lagged aggregate consumption per capita. The period utility function
11
depends on an individual’s current leisure 1 − Nt (h), his end-of-period real money balances,
M Bt+1 (h)
.
PCt
Each member of household h faces a flow budget constraint in period t which states that
his combined expenditure on goods and on the net accumulation of financial assets must equal
his disposable income:
PCt Ct (h) + PIt It (h) + M Bt+1 (h) − M Bt (h) +
−BDt (h) + PBt BGt+1 − BGt +
∗ B
et PBt
F t+1 (h)
φbt
R
ξ
B
(h)
s t,t+1 Dt+1
− et BF t (h)
(18)
= (1 − τN t )Wt (h) Nt (h) + Γt (h) + T Rt (h) − Tt (h) + (1 − τKt )RKt Kt (h)+
PIt τKt δKt (h) − PDt φKt (h) − PDt φIt (h).
Final consumption goods are purchased at a price PCt , and final investment goods at a price
PIt . Investment in physical capital augments the per capita capital stock Kt+1 (h) according to
a linear transition law of the form:
Kt+1 (h) = (1 − δ)Kt (h) + It (h),
(19)
where δ is the depreciation rate of capital.9
Financial asset accumulation of a typical member of FL household h consists of increases
in nominal money holdings (M Bt+1 (h)−M Bt (h)) and the net acquisition of bonds. We assume
that agents within a country can engage in frictionless trading of a complete set of contingent
claims, while trade in international assets is restricted to a non-state contingent nominal bond.
9
In the ROW block, the household problem is modified to reflect capital accumulation in the oil sector.
Thus, the budget constraint has the following additional terms on the right hand side: (1 − τKOt )RKOt Kt (h) +
PIt τKt δKO t(h) − PDt φKOt (h) − PDt φIOt (h). The first terms gives the revenue net of taxes from renting the
oil capital to firms; the second term reflects the depreciation allowance on oil capital; The last two terms
summarize costs of adjustment for oil capital and oil investment, respectively (described in more detail below
for the analogous goods sector costs). Finally the transition law for oil capital is analogous to the one for goods
capital.
12
The term PBt BGt+1 − BGt represents an individual’s net purchases of domestic government
R
bonds, while s ξt,t+1 BDt+1 (h) − BDt (h) are net purchases of state-contingent domestic bonds.
We denote ξt,t+1 as the price of an asset that will pay one unit of domestic currency in a
particular state of nature at date t + 1, while BDt+1 (h) represents the quantity of such claims
purchased by a member of household h at time t. Thus, the gross outlay on new state-contingent
domestic claims is given by integrating over all states at time t + 1, while BDt (h) indicates an
individual’s value of existing claims given the realized state of nature.
Only one of the foreign countries (the numeraire country) issues a bond that is traded
across countries. In equation (18), BF t+1 (h) represents the quantity of a non-state contingent
bond purchased by a typical member of household h at time t that pays one unit of currency
∗
of the foreign numeraire country in the subsequent period, PBt
is the foreign currency price of
the bond, and et is the exchange rate for the numeraire country expressed in units of home
currency per unit of foreign currency. We follow Turnovsky (1985) (and many thereafter)
and assume there is an intermediation cost φbt paid by households in the home country for
purchases of foreign bonds, which ensures that net foreign assets are stationary in the model.10
More specifically, the intermediation costs depend on the ratio of economy-wide holdings of net
foreign assets to nominal output and are given by:
µ
µ
¶
¶
et BF t+1
φbt = exp −φb
+ νbt .
PDt Yt
(20)
In the above, νbt is a mean-zero stochastic process, which we interpret as a risk-premium shock
or shock to the uncovered interest-rate parity condition. Abstracting from this shock, if the
home economy has an overall net lender position internationally, then a household will earn a
lower return on any holdings of foreign bonds. By contrast, if the economy has a net debtor
position, a household will pay a higher return on any foreign debt.
Each member of household h earns after-tax labor income, (1 − τN t )Wt (h) Nt (h), where
τN t is a stochastic tax on labor income. The household leases capital to firms at the after-tax
rental rate (1−τKt )RKt , where τKt is a stochastic tax on capital income. The household receives
10
This intermediation cost is asymmetric, as foreign households do not face these costs. Rather, they collect
profits on the monopoly rents associated with these intermediation costs.
13
a depreciation writeoff of PIt τKt δ per unit of capital. Each member also receives an aliquot
share Γt (h) of the profits of all firms and a lump-sum government transfer, T Rt (h) and pays a
lump-sum tax Tt (h).
We allow for two types of costs associated with adjusting the capital stock. First, there
is a cost associated with changing the net stock of physical capital, as in the standard q-theory
literature; specifically, these costs (in per capita terms) are given by
µ
¶2
1
It (h)
φKt (h) = φK Kt (h)
−δ ,
(21)
2
Kt (h)
and penalize the adjustment of the deviation of the investment-to-capital ratio from its steady
state level, δ, Second, as in Christiano, Eichenbaum, and Evans (2005), it is also costly to
change the level of gross investment from the previous period, so that the acceleration in the
capital stock is penalized:
1 (It (h) − It−1 (h))2
φIt (h) = φI
.
(22)
2
It−1 (h)
In every period t, household h maximizes the utility functional (17) with respect to its
consumption, investment, (end-of-period) capital stock, money balances, holdings of contingent
claims, and holdings of foreign bonds, subject to its labor demand function (16), budget constraint (18), and transition equation for capital (19).11 In doing so, a household takes as given
prices, taxes and transfers, and aggregate quantities such as lagged aggregate consumption and
the aggregate net foreign asset position.
Forward-looking households set nominal wages in staggered contracts that are analogous
to the price contracts described above. In particular, with probability 1 − ξw , each member of a
household is allowed to reoptimize its wage contract. If a household is not allowed to optimize
its wage rate, we assume each household member resets its wage according to:
Wt (h) = ωt−1 Wt−1 (h),
(23)
where ωt = Wt /Wt−1 and in steady state ω = πgz .12 Each member of household h chooses the
value of Wt (h) to maximize its utility functional (17).
11
In the ROW block households also choose capital and investment for the oil sector subject to the law of
motion for oil capital.
12
In alternative specifications, we also consider Wt (h) = ωWt−1 (h).
14
2.4
Monetary Policy
We assume that the central bank follows an interest rate reaction function similar in form to
the historical rule estimated by Orphanides and Wieland (1998) over the Volcker-Greenspan
period. Thus, the short-term nominal interest rate is adjusted so that the ex post real interest
rate rises when inflation exceeds its constant target value, or when aggregate output growth
rises above some target value.13 With some allowance for interest rate smoothing, monetary
policy is described by the following interest rate reaction function:
(4)
it = γi it−1 + r + π t + γπ (πt − π t ) + γy (yt − yt−1 ) + ²it .
(24)
(4)
In the above, it is the annualized nominal interest rate, πt is the four-quarter inflation rate of
P
(4)
the aggregate output deflator (i.e., πt = 3j=0 πt−j ), r̄ and π̄ are the steady-state real interest
rate and the central bank’s constant inflation target (both expressed at annual rate). Also,
yt − yt−1 is the (annualized) quarterly growth rate of aggregate output.
2.5
Fiscal Policy
Some of the domestically-produced good is purchased by the government. Government purchases (Gt ) are assumed to have no direct effect on the utility of a household.14 We also assume
that government purchases as a fraction of output, gt = Gt /Yt , follow an exogenous stochastic
process.
The government can issue debt BGt+1 to finance a deficit so that its budget constraint is
given by:
PBt BGt+1 − BGt = PDt Gt + T Rt
−Tt − τN t Wt Lt − (τKt RKt − δPIt )Kt − τP O,t+j POt Ot+j − τQO,t+j PDt+j Ot+j
−(M Bt+1 − M Bt ).
13
14
(25)
Aggregate output from the oil and the goods sectors is obtained by using the Fisher ideal index.
We could have assumed instead that government purchases enter separably in the utility function. This
would not alter the model’s dynamics but would have different welfare consequences.
15
In equation (25), we have aggregated the capital stock, money and bond holdings, and transfers
R1
and taxes over all households so that, for example, Tt = 0 Tt (h)dh. We have also aggregated
oil demand, Ot+j , over all households and firms. As noted above, labor and capital taxes are
determined exogenously, while we assume that real transfers as a fraction of domestic output,
trt =
T Rt
,
PDt Yt
evolve according to a exogenous stochastic process. Given that the central bank
uses the nominal interest rate as its policy instrument, the level of seignorage revenues are
determined by nominal money demand.
Lump-sum taxes are adjusted in a manner that the government satisfies an intertemporal
solvency constraint, requiring that the present discounted value of the government debt stock
tends toward zero in the long run. In particular, we assume that the real lump-sum tax rate,
τt =
Tt
,
PDt Yt
is determined according to the following reaction function:
τt = ν0 τt−1 + ν1 (bGt+1 − bG ) + ν2 (bGt+1 − bGt ),
where bGt+1 =
BGt+1
PDt Yt
(26)
and bG is the government’s target value for the ratio of government debt
to nominal output.
2.6
Resource Constraints Oil Trade and Net Foreign Assets
The resource constrain for the goods sector of the home economy can be written as:
Yt = CDt + IDt + Gt +
X
Mtk + φKt + φIt ,
(27)
∀k
k
k
where Mtk = MCt
+ MIt
and φKt and φIt are the adjustment costs on capital and investment
aggregated across all households, and Gt is government consumption.15
The resource constraint for the oil sector across countries is such that:
YOt +
X
∀k
k
= Ot +
YOt
X
Otk
(28)
∀k
which states that the sum of the home and foreign oil production needs to equal the sum of
home and foreign consumption.
15
In the case of the ROW, the term IDt reflects investment in both the goods and the oil sectors
16
The oil trade has features that we believe bolster the empirical relevance of the model.
The oil production of Canada and Mexico exceeds the domestic demand. The excess production
is exported to the United States. In the face of higher prices and lower demand, the US keeps
imports from Canada and Mexico constant and reduces imports from the ROW block only. The
ROW block, acts as the residual oil supplier for the United States, and the only oil supplier for
the remaining country blocks in the model.
The evolution of net foreign assets can be expressed as:
∗
X
et PB,t
BF,t+1
k
Mtk − PDt Mt + POt (Ot − YOt ) .
= et BF,t +
ekt PDt
φbt
∀k
(29)
This expression can be derived from the budget constraint of the FL households after imposing
the government budget constraint, the consumption rule of the RT households, the definition
of firm profits, and the condition that domestic bonds (BDt+1 ) are in zero net supply.
3
Solution Method and Calibration
We solve the model by log-linearizing the equations around the steady state. To obtain the
reduced-form solution of the model, we use the numerical algorithm of Anderson and Moore
(1985), which provides an efficient implementation of the method proposed by Blanchard and
Kahn (1980) (see also Anderson (1997)).16
3.1
Calibration of Parameters
The model is calibrated at a quarterly frequency. Structural parameters are set at identical
values for all country blocks, except for the parameters determining the consumption, investment, government spending, foreign imports and oil shares of GDP in steady state, as well as
16
The steady state around which we linearize depends on the relative level of technology in each country,
which we initialize to unity (so that per capita income in each chountry is identical in the steady state, though
GDP may differ across countries due to population differences). We evaluated the robustness of our solution
procedure by using a nonlinear Newton-Raphson algorithm that does not rely on linearization around an initial
steady state, and found that the results were nearly identical to those reported.
17
distortionary tax rates. I will first discuss the country-specific parameters, then the parameters
common across country blocks.
The steady-state technology levels are set so that the steady state GDP ratios reproduce
the 1997-2002 average ratios calculated using World Bank data and reported in Table 1. Accordingly, the U.S. is calibrated to have a GDP 14 times the size of Canada’s and 16 times
Mexico’s.
The ratio of private consumption to output, the ratio of private investment to output
and the ratio of government spending to output in steady state are reported in Table 2. These
steady-state ratios are matched by adjusting quasi-capital share parameter ωK in conjunction
with setting the steady-state share of government spending ḡ and the assumption that trade of
goods and oil is balanced.
Oil demand as a share of output in steady state, together with the share of oil demand
that is locally produced and the tax rates on oil are reported in Table 3, calculated using OPEC
and IEA data for 2002.
The quasi-share parameters ωC and ωI are set so that imported goods as a share of GDP
replicate the aggregate import shares reported in Table 4 the bilateral import shares reported
in Table 5. These shares were calculated using IMF data averaged over the period 1997-2002.
Moreover, based on U.S. NIPA data, we impose that two thirds of imports are used for private
consumption and the remainder for private investment. Given that investment accounts in
all countries for a smaller share of GDP than consumption, this assumption also implies that
investment is more import-intensive than consumption.17
We assume that the discount factor β = .98. These values are consistent with a steadystate annualized real interest rate r of about 3 percent. The utility functional parameter σ is
set equal to 2, while the parameter determining the degree of habit persistence in consumption
κ = 0.8. We set χ = 10, implying a Frisch elasticity of labor supply of 1/5, which is considerably
lower than if preferences were logarithmic in leisure, but well within the range of most empirical
estimates. The utility parameter χ0 is set so that employment comprises one-third of the
17
Data analogous to the NIPA on the use of imports is not available for the other countries modelled here.
18
household’s time endowment, while the parameter µ0 on the subutility function for real balances
is set an arbitrarily low value (so that variation in real balances has a negligible impact on other
variables).
The depreciation rate of capital δ = .025 (consistent with an annual depreciation rate of
10 percent). The price and wage markup parameters θp = θw = 0.20, similar to the estimated
values obtained by Rotemberg and Woodford (1997) and Amato and Laubach (1999).18 We
set ξp and ξw to be consistent with four-quarter contracts (subject to full indexation). The
parameter ξp,x is chosen to be consistent with two-quarter contracts. We set the steady state
inflation rate π to yield an annual inflation rate of four percent.
The parameter ρ in the CES production function of the intermediate goods producers is
set to -2, implying an elasticity of substitution between capital and labor of 1/2. Thus, capital
and labor are less substitutable than the unitary elasticity case implied by the Cobb-Douglas
specification. We set the cost of adjusting investment parameter φI = 4, close to value used by
Christiano, Eichenbaum, and Evans (2001) (φK = 0 so that there is only type of adjustment
cost for investment in our baseline calibration).
We assume that ρC = ρI = 1, consistent with a long-run price elasticity of demand for
imported consumption and investment goods of 2. While this is higher than most empirical
estimates using macro data, we emphasize that the presence of adjustment costs translates into
a much lower relative price sensitivity in the short to medium-term. In particular, we set the
adjustment cost parameters ϕMC = ϕMI = 10, implying a price-elasticity near unity after four
quarters. We choose a small value (0.001) for the financial intermediation cost φb , which is
necessary to ensure the model has a unique steady state.
We estimated the parameters of the monetary policy rule using U.S. data from 1983:12003:4.19 Our estimates implied γπ = 0.4, γy = 0.28, and γi = 0.8. For the tax rate reaction
18
Rotemberg and Woodford (1997) found θp = 0.15, while Amato and Laubach (1999) obtained θp = 0.19
and θw = 0.13. Given our assumption that there is perfect capital mobility across firms within a country, the
parameter θp only affects the steady state capital-output ratio, and does not otherwise appear in the dynamic
equations of the log-linearized model.
19
We estimated the rule using instrumental variables using lags of inflation and output growth as instruments.
19
function, we choose ν0 = 1, ν1 = 0.1, ν2 = 0.001, and bG = 0.6.20
4
Simulation Results
First, I will consider the effect of oil price shocks. I will focus on the effects of a permanent
increase in the price of oil in the U.S. and foreign economies under the baseline calibration.
One summary statistic that the literature on the effects of oil price shocks has focused on is
the oil price/GDP elasticity. I will consider alternative parameterizations to highlight some key
structural determinants of this elasticity. Second, I will take up the comparison of oil demand
and supply shocks.
4.1
Price Shocks
In order to simulate a permanent increase in the price of oil I endogenized the technology for
oil production in the ROW block, ZOt in equation (13) by adding an oil target price equation.21
Figure 1 shows the effect on the U.S., Euro Area and Canadian Economies of a 50% permanent
increase in the U.S. dollar price of oil starting in the first quarter of 2004.
In the United States, within a year from the shock, output declines by about 0.4% below
steady state. This decline is attributable to several sources. First, the oil-price increase leads
to a permanent reduction in the use of oil as a factor of production, which lowers domestic
output. Given the unitary long-run elasticity of substitution between oil and the other factors
of production, the long-run effect of the shock is to reduce oil demand by 50% so as to keep
expenditure on oil at a roughly constant fraction of GDP. The half life of the response is ten
years, but some initial adjustment is enough to reduce the productivity of labor and capital
and to bring up the real marginal cost. Second, higher oil prices reduce household wealth,
20
TO DO: Add table with labor and capital tax rates and details on calibration of investment
share for oil sector in ROW.
21
An alternative mechanism would be to build in variable capacity utilization and introduce a series of supply
shocks in the ROW block calibrated to stabilize the oil price at a new target level. This alternative modelling
approach produced quantitatively indistinguishable results from the one presented in this simpler framework.
20
and hence consumption demand. Third, some of the crowding out of the private absorption
components is linked to the monetary policy response. Under the baseline rule, real rates rise,
which contributes to curb private consumption and investment.
Under a Taylor rule, core inflation increases initially, reaching a peak of about 0.2 percentage point above steady state after two years. This rise in inflation primarily reflects the
direct effect of higher oil prices on marginal costs. Later, as real wages adjust downwards in
response to slack demand, prices ease back a bit. By contrast, consumption price inflation (not
shown) jumps in reaction to the increase in oil prices, reflecting that the consumption basket
includes oil directly.
As private consumption and investment display a large degree of home bias, their contraction makes the U.S. good more abundant relative to the goods produced abroad. This
leads to a slight deterioration of the terms of trade (as shown by a rise in the lower left panel of
Figure 1). The net foreign assets, show a protracted decline, reflecting that the deterioration
of the terms of trade is not enough to boost exports by a degree that can compensate for the
higher-priced oil imports. However, as the oil demand declines, eventually the trade balance
swings into surplus (not shown).
It is interesting to contrast the effects of an oil price shock in the U.S. with those in Canada
(an oil exporter) and with those in the Euro Area (a block with no local oil production).22 In
Canada, the wealth effect of the shock is positive, as import revenues increase more than enough
to offset the long-run decline in local production due to the higher cost of oil. Initially GDP
rises. The higher consumption demand more than offsets the decline in investment. As imports
are costly to adjust, the higher consumption demand initially falls mainly on domestically
produced goods. GDP can rise because sticky wages allow labor supply to meet the higher
short-run labor demand. However, as wage contracts expire, the real wages are pushed up in
an attempt by households to decrease their labor supply (in reaction to the wealth effect of the
shock). Moreover, as imports adjust, expenditures switch away from the domestic good into
22
Empirical work has concentrated mostly on the United States. A notable exception is a recent paper that
looks a at group of OECD countries by Jiménez-Rodrı́guez and Sánchez (2004).
21
the cheaper foreign goods.
By contrast, in the euro area, the negative wealth effect of the shock is even larger than in
the U.S. This is easily attributed to the fact that there is no local oil production to mitigate the
higher cost of oil imports. As private consumption drops even further than in the U.S., the terms
of trade deteriorate further. In turn this deterioration boosts exports and leads to expenditures
switching away from the higher priced imports. This accounts for why investment declines only
modestly (especially relative to investment in Canada) and for the smaller contraction in GDP
relative to the U.S. or Canada. Another reason for the smaller contraction in euro area output
is the lower GDP share of oil, whose role I examine more fully below.
Table 6 allows comparisons of the effects of oil-price shocks on all the country blocks in
the model. The ROW block stands out among the oil exporting countries. While expenditures
on oil do not decrease overall because of the unitary long-run elasticity of substitution, by
assumption Canada and Mexico capture a higher share of U.S. oil imports at the expense of
the ROW block.23 Accordingly, the effect of the shock on ROW wealth is negative. ROW
consumption declines and the ROW non-oil terms of trade deteriorate.
SIGMA’s predictions for the effects of an oil shock are not greatly different from those
produced by large-scale econometric models, which tend to show only modest output effects.24
However, some of the simulation results seem at odds with the finding of empirical studies
summarized in Figure 2, and in particular with the large declines found by Hamilton (2003).
There are several reasons why the model-based estimates, such as those produced by
SIGMA, may be lower than those found in the empirical studies. Recent studies have stressed
the importance of the asymmetric effects of oil price increases and declines, which we cannot
capture in a linearized framework. There may be large reallocation costs in multisector settings
where sectors have different oil intensities. However, one important factor is that oil consumption in the United States is much lower relative to GDP at present than it was during most
of the historical period analyzed by the empirical studies. Figure 3, shows that the U.S. oil
consumption as a fraction of nominal GDP varied over the past two decades from a peak of
23
24
It seems plausible that the U.S. would meet its oil demand from nearby supplier first.
For a review see Jones, Leiby, and Paik (2004).
22
roughly 8% in 1980 to as low as 1% in 1998. Time-series studies such as Hamilton (2003) implicitly put greater weight on periods characterized by higher oil shares, such as the late 1970s,
given that those periods are also the ones that saw the largest oil-price increases.
Figure 4 shows that the oil price/gdp multiplier is basically a linear function of the oil
share. As shown in the figure, doubling the U.S. oil share also doubles the gdp impact of a
permanent shock.
Finally, Figure 5 compares the effects of an oil shock on the U.S. block of the model
under an alternative monetary policy with the baseline Taylor rule. In contrast with the
baseline, the alternative policy puts no weight on output and targets only the four-quarter
change in core prices. As a result, core prices remain essentially flat, but the higher real rates
needed to implement the policy lead to a greater contraction of private absorption and of GDP.
This simulation underscores the importance of controlling for the monetary policy response in
empirical work.
4.2
Oil supply and Demand Shocks
In the simulations so far, I have assumed an exogenous path for the price of oil. I now consider
an alternative framework where oil supply is endogenous and responds gradually to changes in
oil prices. However, the costs of adjustment on oil capital in the ROW block are high enough
as to make the supply relatively unresponsive to price changes in the medium run.
Figure 6 compares the effects on the United States of a preference shock that raises
oil consumption in China (the solid lines, denoted “oil-taste shock”) with the effects of an
exogenous price shock (the dashed lines, denoted “oil-supply shock”). The exogenous shock
was phased in so as to result in the same oil-price path in U.S. dollars as the demand shock.
It is evident from Figure 6 that the effects of this taste shock on U.S. output and prices are
virtually identical to the effects of an exogenous oil-price shock. Insofar as the exogenous price
path may be interpreted as induced by supply shocks, our results indicate that a rise in oil
prices due to an oil-taste shock in China would have similar effects on the United States as if
the same price path were induced by a foreign supply disturbance. I find this result to hold
23
even if the oil-taste shocks originate in countries with much close trading ties to the United
States.25
I next consider the effects of an oil-price rise that is induced by a rise in foreign activity.
I illustrate this by considering the effects on the United States of a 10% rise in the level of
technology in China. This shock raises output in China and hence stimulates oil demand in
that country. The increase in oil demand accounts for the modest oil price rise (that peaks at
around 15% above baseline) as shown by the solid line in the the upper left panel of Figure
7. The dashed lines show the effects of an exogenous supply shock that generates the same
oil-price path.
The effects on the United States are insensitive to weather the oil-price increase is generated by a rise in activity in China, or by an exogenous fall in oil supply. In either case, U.S.
output contracts and the price level rises. Given that U.S. exports to China are a small fraction
of U.S. export, the stimulative effect of higher Chinese domestic demand on U.S. GDP is small
compared with the contractionary effects of higher oil prices.
Finally, I consider the importance of trade linkages by assuming that the rise in activity
occurs in Canada, rather than in China. The results are shown in Figure 8. For expositional
simplicity, I have calibrated the rise in Canadian productivity to yield the same oil price path
as shown in figure 7, and again compare its effects with that of the exogenous supply shock
that generates the same oil-price response.
In contrast with the effects of the oil supply shock, the activity-driven oil price increase
actually induces a rise in U.S. GDP in the first couple of years. The expansion of Canadian
domestic demand associated with the technology improvement provides a substantial boost to
25
One might expect that an oil-taste shock that occurred in a country with closer trading ties (e.g. Canada)
would exert somewhat different effects on the United States than if the oil-price rise occurred because of a supply
disruption. However, these two shocks have very similar effects on Canada. The only noteworthy difference is
that Canada must finance its additional thirst for oil in the case of an oil-taste shock, so that it must reduce
its non-oil consumption relative to the exogenous supply-shock case. However, given the small share of oil in
consumption, the difference is very small quantitatively. Accordingly, Canadian aggregate consumption responds
similarly in the two cases, and the effects on the United States are nearly the same.
24
U.S. exports. This increase in U.S. exports more than offsets the contractionary impact of the
higher oil prices, so that U.S. GDP rises about 0.1 percent above baseline. Moreover, given
the stronger external demand, U.S. core prices rise by more than in the case of the exogenous
oil-price rice.
5
Conclusion
The model analysis presented here can serve as guidepost in setting up time-series estimation
exercises. For oil-price shocks, the results highlight the importance of controlling for the oil share
of GDP and for the response of monetary policy. For oil supply shocks, the analysis stresses
the importance of trade links in determining the impact on the macroeconomy. Demand shocks
originating in countries with small trade ties with the United States will have the same impact
as exogenous price shocks. In contrast, when oil prices rise because of a rise in activity in a
country with close trade ties with the United States, the goods trade effects can dominate the
adverse effects of the oil price hike and even lead to increases in GDP.
This kind of exercise also sheds light on cross-country differences for the impact of oil
shocks and can serve as a reading guide for time-series results as attention shifts away from the
United States.
While the simulation presented here are based on calibrated parameters, in future work
I intend to pursue the estimation of key parameters governing the transmission of oil shocks by
using full information estimation methods.
25
References
Bernanke, B., M. Gertler, and M. Watson (1997). Systematic Monetary Policy and the Effects
of Oil Price Shocks. Brookings Papers on Economics Activity, 91–157.
Calvo, G. A. (1983, September). Staggered Prices in a Utility-Maximizing Framework. Journal of Monetary Economics 12, 383–398.
Christiano, L. J., M. Eichenbaum, and C. L. Evans (2005). Nominal Rigidities and the
Dynamic Effects of a Shock to Monetary Policy. Journal of Political Economy 113 (1),
1–45.
Erceg, C., L. Guerrieri, and C. Gust (2005a). Expansionary Fiscal Shocs and the Trade
Deficit. International Finance Discussion Paper 825.
Erceg, C., L. Guerrieri, and C. Gust (2005b). SIGMA: A New Open Economy Model for
Policy Analysis. Mimeo, Board of Governors of the Federal Reserve System.
Erceg, C. J., D. W. Henderson, and A. T. Levin (2000). Optimal Monetary Policy with
Staggered Wage and Price Contracts. Journal of Monetary Economics 46, 281–313.
Gately, D. and H. G. Huntington (2002). The Asymmetric Effects of Changes in Price and
Income on Energy and Oil Demand. Energy Journal 23 (1), 19–37.
Hamilton, J. (1983). Oil and the Macroeconomy since World War II. Journal of Political
Economy 91 (2), 228–48.
Hamilton, J. (2003). What Is an Oil Shock. Journal of Econometrics 113, 363–98.
Jiménez-Rodrı́guez, R. and M. Sánchez (2004). Oil Price Shocks and Real GDP Growth:
Empirical Evidence for Some OECD Countries. European Central Bank: Working Paper
No. 362.
Jones, D. W., P. Leiby, and I. K. Paik (2004). Oil Price Shocks and the Macroeconomy:
What Has Been Learned Since 1996. Energy Journal 25 (2), page 1–32.
Leduc, S. and K. Sill (2004). A Quantitative Analysis of Oil-Price Shocks, Systematic Monetary Policy, and Economic Downturns. Journal of Monetary Economics 51, 781–808.
26
Obstfeld, M. and K. Rogoff (1995). Exchange Rate Dynamics Redux. Journal of Political
Economy 103, 624–60.
Orphanides, A. and V. Wieland (1998). Price Stability and Monetary Policy Ineffectiveness
when Nominal Interest Rates are Bounded at Zero. Finance and Economics Discussion
Paper No. 98-35, Washington DC: Board of Governors of the Federal Reserve System.
Smets, F. and R. Wouters (2003). An Estimated Dynamic Stochastic General Equilibrium
Model of the Euro Area. Journal of the European Economic Association 1 (5), 1124–1175.
Turnovsky, S. J. (1985). Domestic and Foreign Disturbances in an Optimizing Model of
Exchange-Rate Determination. Journal of International Money and Finance 4 (1), 151–
71.
Wei, C. (2003). Energy, the Stock Market, and the Putty-Clay Investment Models. American
Economic Review 93 (1), 311–23.
Yun, T. (1996). Nominal price rigidity, money supply endogeneity, and business cycles. Journal of Monetary Economics 37, 345–370.
27
Table 1: Relative GDP Size
ROW
Canada
Japan
Euro Area
Mexico
China
U.S.
1.0
14
2.3
1.6
16
8.9
0.98
Canada
0.071
1.0
0.16
0.12
1.2
0.64
0.069
Japan
0.44
6.1
1.0
0.71
7.0
3.9
0.43
Euro Area
0.62
8.7
1.4
1.0
9.9
5.5
0.61
Mexico
0.062
0.87
0.14
0.10
1.0
0.56
0.061
China
0.11
1.57
0.26
0.18
1.8
1.0
0.11
U.S.
1.0
14
2.3
1.7
16
9.1
1.0
ROW
Source: World Bank data averaged over the 1997-2002 period. The numerator is indicated as the row label,
the denominator as the column label. The U.S. is calibrated to have a GDP 14 times the size of Canada’s and
16 times Mexico’s.
Table 2: Consumption, Investment and Government Spending as a Share of Output
Consumption
Investment
Government
ROW
0.56
0.09
0.29
Canada
0.57
0.17
0.31
Japan
0.56
0.17
0.26
Euro Area
0.57
0.17
0.25
Mexico
0.68
0.19
0.17
China
0.47
0.36
0.18
U.S.
0.70
0.12
0.18
Source: IMF data averaged over the period 1997-2002.
28
Table 3: Total oil use as a share of output, share of oil used produced locally, and ad-valorem
and specific tax rates on oil
Oil Share
Local Production
Ad-Valorem Tax
Specific Tax
ROW
0.020
1
0.10
0.20
Canada
0.021
1
0.07
0.25
Japan
0.011
0
0.05
0.33
Euro Area
0.014
0
0.20
0.4
Mexico
0.024
1
0.15
0.40
China
0.036
0.7
0.17
0.35
U.S.
0.020
0.4
0.10
0.17
Source: OPEC and IEA. For ROW average over some representative countries included in the ROW block.
Table 4: Goods Imports, Oil Imports, and Total Imports Shares of Output
Goods
Oil
ROW
0.17
0
0.17
Canada
0.40
0
0.40
Japan
0.08
0.01
0.09
Euro Area
0.14
0.01
0.16
Mexico
0.31
0
0.31
China
0.22
0.010
0.23
United States
0.09
0.01
0.11
Source: IMF and IEA data and author’s calculations. Averages for the 1997-2002 period.
29
Table 5: Imports of Goods and Services as a Share of Output
ROW
Canada
Japan
Euro Area
Mexico
China
U.S.
ROW
NA
0.004
0.017
0.073
0.001
0.009
0.041
Canada
0.058
NA
0.013
0.018
0.009
0.009
0.272
Japan
0.029
0.002
NA
0.009
0.001
0.009
0.023
Euro Area
0.104
0.002
0.007
NA
0.001
0.004
0.023
Mexico
0.027
0.010
0.008
0.015
NA
0.003
0.220
China
0.074
0.005
0.036
0.026
0.002
NA
0.048
U.S.
0.032
0.016
0.010
0.014
0.011
0.005
NA
Source: IMF data averaged over the 1997-2002 period. Each row shows imports of a country from all others
listed along the columns as a share of the GDP of the importing country.
30
*
Table 6: A 50% Permanent Increase in the Price of Oil
Absolute and Relative Deviation from Baseline
04:1
04:2
04:3
04:4
05:1
05:2
05:3
05:4
06:1
06:2
06:3
06:4
07:1
-0.06
0.04
0.03
-0.07
-0.05
-0.09
-0.03
-0.13
0.02
0.01
-0.13
-0.09
-0.18
-0.14
-0.18
-0.03
-0.05
-0.18
-0.12
-0.27
-0.24
-0.23
-0.10
-0.12
-0.21
-0.14
-0.35
-0.33
-0.28
-0.19
-0.21
-0.24
-0.15
-0.42
-0.42
-0.31
-0.28
-0.30
-0.25
-0.16
-0.47
-0.49
-0.34
-0.37
-0.39
-0.25
-0.16
-0.52
-0.56
-0.35
-0.45
-0.47
-0.25
-0.16
-0.56
-0.61
-0.36
-0.53
-0.54
-0.24
-0.15
-0.59
-0.65
-0.36
-0.59
-0.60
-0.23
-0.14
-0.61
-0.69
-0.36
-0.65
-0.65
-0.21
-0.13
-0.63
-0.72
-0.35
-0.69
-0.69
-0.19
-0.11
-0.65
-0.74
-0.34
-0.73
-0.72
-0.18
-0.10
-0.66
-0.76
Core Prices (4-qtr. change) (+/-)
United_States
0.02 0.06
Canada
0.05 0.16
Mexico
0.05 0.14
EMU11_Block 0.01 0.02
Japan
0.01 0.02
China
0.03 0.08
ROW
0.03 0.07
0.11
0.30
0.26
0.04
0.03
0.15
0.13
0.16
0.48
0.42
0.06
0.04
0.22
0.20
0.20
0.63
0.55
0.06
0.04
0.25
0.25
0.21
0.76
0.65
0.05
0.03
0.26
0.28
0.22
0.86
0.74
0.03
0.02
0.26
0.29
0.21
0.95
0.81
0.01
0.01
0.24
0.29
0.20
1.02
0.86
-0.01
-0.01
0.22
0.29
0.18
1.07
0.90
-0.04
-0.03
0.20
0.27
0.15
1.10
0.92
-0.06
-0.04
0.18
0.25
0.13
1.11
0.94
-0.09
-0.06
0.16
0.22
0.11
1.12
0.94
-0.11
-0.08
0.15
0.20
0.21
0.73
0.64
0.05
0.04
0.22
0.28
0.22
0.86
0.73
0.03
0.03
0.22
0.30
0.21
0.97
0.81
0.00
0.01
0.20
0.30
0.19
1.05
0.87
-0.02
-0.01
0.17
0.30
0.17
1.12
0.91
-0.05
-0.03
0.15
0.28
0.15
1.17
0.95
-0.08
-0.05
0.12
0.26
0.13
1.21
0.97
-0.10
-0.06
0.10
0.24
0.10
1.23
0.98
-0.12
-0.08
0.09
0.21
-0.34
2.38
1.76
-0.70
-0.44
-0.35
-0.18
-0.38
2.53
1.86
-0.76
-0.48
-0.40
-0.21
-0.41
2.66
1.95
-0.81
-0.51
-0.45
-0.23
-0.44
2.76
2.02
-0.86
-0.54
-0.49
-0.24
-0.47
2.84
2.07
-0.89
-0.57
-0.53
-0.26
-0.49
2.91
2.12
-0.93
-0.59
-0.57
-0.27
-0.51
2.97
2.16
-0.96
-0.61
-0.62
-0.27
-0.52
3.02
2.20
-0.99
-0.63
-0.66
-0.28
0.35
-2.82
-3.38
1.34
1.50
-0.01
-0.65
0.34
-2.81
-3.38
1.33
1.50
-0.05
-0.63
0.32
-2.79
-3.37
1.31
1.49
-0.10
-0.62
0.31
-2.76
-3.36
1.29
1.48
-0.14
-0.60
0.29
-2.72
-3.34
1.26
1.48
-0.19
-0.57
0.27
-2.67
-3.32
1.24
1.47
-0.24
-0.55
0.25
-2.61
-3.29
1.21
1.46
-0.29
-0.53
0.23
-2.55
-3.26
1.18
1.45
-0.35
-0.50
-0.16
-1.82
-2.12
0.38
0.45
-0.24
-0.57
-0.18
-2.06
-2.39
0.46
0.55
-0.26
-0.62
-0.18
-2.27
-2.65
0.54
0.65
-0.28
-0.66
-0.17
-2.46
-2.88
0.63
0.75
-0.29
-0.69
-0.15
-2.63
-3.09
0.73
0.86
-0.29
-0.72
-0.12
-2.78
-3.28
0.82
0.97
-0.30
-0.73
-0.08
-2.91
-3.46
0.92
1.08
-0.30
-0.74
-0.04
-3.03
-3.62
1.01
1.19
-0.31
-0.75
GDP (%)
United_States
Canada
Mexico
EMU11_Block
Japan
China
ROW
Consumer Prices (4-qtr. change) (+/-)
United_States
0.53 0.57 0.62 0.67 0.20
Canada
-0.59 -0.50 -0.38 -0.21 0.58
Mexico
-0.37 -0.29 -0.18 -0.03 0.52
EMU11_Block 0.69 0.70 0.72 0.74 0.06
Japan
0.45 0.47 0.48 0.49 0.05
China
1.46 1.50 1.56 1.62 0.21
ROW
0.37 0.42 0.48 0.55 0.25
Consumption (%)
United_States
-0.07 -0.13 -0.19 -0.25 -0.30
Canada
0.68 1.21 1.62 1.94 2.19
Mexico
0.51 0.90 1.21 1.44 1.62
EMU11_Block -0.17 -0.31 -0.44 -0.54 -0.62
Japan
-0.11 -0.20 -0.27 -0.34 -0.39
China
-0.06 -0.12 -0.18 -0.24 -0.30
ROW
-0.03 -0.06 -0.09 -0.12 -0.16
Terms of Trade (excluding oil, import weighted) (%)
United_States
0.37 0.36 0.36 0.36 0.36
Canada
-2.70 -2.74 -2.78 -2.81 -2.82
Mexico
-3.27 -3.30 -3.33 -3.36 -3.37
EMU11_Block 1.32 1.33 1.35 1.35 1.35
Japan
1.42 1.44 1.46 1.48 1.49
China
0.15 0.13 0.09 0.06 0.02
ROW
-0.64 -0.65 -0.65 -0.66 -0.66
Real Non-Oil Exports (share of GDP) (%)
United_States
-0.01 -0.04 -0.08 -0.11 -0.14
Canada
-0.34 -0.67 -0.98 -1.28 -1.57
Mexico
-0.39 -0.77 -1.14 -1.49 -1.81
EMU11_Block 0.06 0.12 0.17 0.24 0.30
Japan
0.07 0.14 0.21 0.28 0.36
China
-0.05 -0.09 -0.14 -0.18 -0.21
ROW
-0.12 -0.23 -0.33 -0.42 -0.50
Figure 1: A 50% Permanent Increase in the U.S. Dollar Price of Oil
Absolute and Relative Deviation from Baseline
GDP (chain weighted) (%)
0.2
Core Inflation (year on year) (+/-)
1.2
1.0
0.0
0.8
-0.2
0.6
-0.4
0.4
-0.6
0.2
-0.8
0.0
-1.0
-0.2
2004
2005
2006
2007
2008
Private Consumption (%)
4
2004
2005
2007
2008
2007
2008
Private Investment (%)
0
3
2006
-1
2
-2
1
-3
0
-4
-1
-2
2004
2005
2006
2007
2008
Terms of Trade (excluding oil, import weighted) (%)
2
-5
2004
2005
2006
Net Foreign Assets (as a share of GDP) (+/-)
8
6
1
4
0
2
-1
0
-2
-3
-2
2004
2005
2006
2007
2008
-4
Solid: United_States
Dotted: EMU11_Block
Dashed: Canada
2004
2005
2006
2007
2008
Figure 2: Estimated Contraction in GDP From 100% Increase in Oil Prices
Percent
Source
Range
Department of Energy
2.5
-
5.5
Hamilton and Herrera (2001)
2.7
-
5.5
Hamilton (2003)
5.4
-
12.0
SIGMA
0.7
Figure 3: U.S. Oil Consumption as a Share of Nominal GDP
Percent
8
7
6
5
4
3
2
1
1970
1972
1974
1976
1978
1980
1982
1984
1986
1988
1990
Figure 4: A Permanent 100% Increase
in the Price of Oil: Varying Oil Shares
GDP
Percent
1
0
1.8% Oil Share
-1
4% Oil Share
-2
8% Oil Share
-3
0
1
2
3
Years from shock
4
5
-4
\\
1992
1994
1996
1998
2000
2002
0
Figure 5: A 50% Permanent Increase in the U.S. Dollar Price of Oil: Alternative Monetary Policies
Absolute and Relative Deviation from Baseline
GDP (chain weighted) (%)
0.0
Core Inflation (year on year) (+/-)
0.25
0.20
-0.2
0.15
-0.4
0.10
-0.6
0.05
-0.8
-1.0
0.00
2004
2005
2006
2007
2008
Private Consumption (%)
0.0
-0.05
2004
2005
2006
2007
2008
2007
2008
Private Investment (%)
0.0
-0.5
-0.2
-1.0
-0.4
-1.5
-0.6
-2.0
-0.8
-1.0
-2.5
2004
2005
2006
2007
2008
Terms of Trade (excluding oil, import weighted) (%)
0.4
-3.0
2004
2005
2006
Net Foreign Assets (as a share of GDP) (+/-)
0.0
-0.5
0.3
-1.0
-1.5
0.2
-2.0
0.1
-2.5
0.0
2004
2005
2006
2007
2008
-3.0
2004
Solid: Baseline: Taylor Rule
Dotted: Inflation Targeting
2005
2006
2007
2008
Figure 6:Effects on the United States of an Oil-Taste Shock in China
Deviation from Baseline
Oil Price
Percent
60
GDP
Percent
0.05
55
-0.00
50
Oil-Taste Shock
Oil Supply Shock
45
-0.05
40
35
-0.10
30
-0.15
25
20
-0.20
15
10
-0.25
5
0
0
1
Core Inflation (+/-)
2
3
Years after shock
-0.30
0
4
Percentage Points
Four-quarter change 0.25
1
PCE Inflation
2
3
Years after shock
4
Percentage Points
Four-quarter change
0.8
0.20
0.6
0.15
0.4
0.10
0.05
0.2
0.00
0.0
-0.05
-0.2
-0.10
0
1
2
3
Years after shock
4
0
1
2
3
Years after shock
4
Figure 7: Effects on the United States of a Rise in Activity in China
Deviation from Baseline
Oil Price
Percent
20
GDP
Percent
0.10
0.05
15
Activity Shock
-0.00
Oil Supply Shock
10
-0.05
-0.10
5
-0.15
0
0
1
Core Inflation (+/-)
2
3
Years after shock
-0.20
0
4
Percentage Points
Four-quarter change 0.25
1
PCE Inflation
2
3
Years after shock
4
Percentage Points
Four-quarter change
0.8
0.20
0.6
0.15
0.4
0.10
0.05
0.2
0.00
0.0
-0.05
-0.2
-0.10
0
1
2
3
Years after shock
4
0
1
2
3
Years after shock
4
Figure 8: Effects on the United States of a Rise in Activity in Canada
Deviation from Baseline
Oil Price
Percent
20
GDP
Percent
0.10
0.05
15
Activity Shock
-0.00
10
-0.05
-0.10
Oil Supply Shock
5
-0.15
0
0
1
Core Inflation (+/-)
2
3
Years after shock
-0.20
0
4
Percentage Points
Four-quarter change 0.25
1
PCE Inflation
2
3
Years after shock
4
Percentage Points
Four-quarter change
0.8
0.20
0.6
0.15
0.4
0.10
0.05
0.2
0.00
0.0
-0.05
-0.2
-0.10
0
1
2
3
Years after shock
4
0
1
2
3
Years after shock
4