Oil Price Shocks, Macroeconomic Stability and Welfare in a Small Open Economy

Research and Monetary Policy Department
Working Paper No:08/02
Oil Price Shocks, Macroeconomic Stability
and Welfare in a Small Open Economy
Deren ÜNALMIŞ
İbrahim ÜNALMIŞ
Derya Filiz ÜNSAL
May 2008
The Central Bank of the Republic of Turkey

---

Oil Price Shocks, Macroeconomic Stability
and Welfare in a Small Open Economy
Deren Unalmis];y
Ibrahim Unalmis];y
Derya Filiz Unsaly;z
May 2008
Abstract
Since the beginning of 2000s the world economy has witnessed a sub-
stantial increase in oil prices, which is seen to be an important source
of economic ‡uctuations, causing high in‡ation, unemployment and low
or negative growth rates. Recent experience, however, has not validated
this view. Despite rising oil prices, world output growth has been strong,
and although in‡ation has recently been increasing, it is relatively much
lower compared with the 1970s. This paper focuses on the causes of oil
price increases and their macroeconomic e¤ects. Di¤erent from most of
the recent literature on the subject, which understands the price of oil to
be an exogenous process, we model the price of oil endogenously within
a dynamic stochastic general equilibrium (DSGE) framework. Speci…-
cally, using a new Keynesian small open economy model, we analyse the
e¤ects of an increase in the price of oil caused by an oil supply shock
and an oil demand shock. Our results indicate that the e¤ects of an oil
demand shock and an oil supply shock on the small open economy are
quite di¤erent. In addition, we investigate the sensitivity of the general
equilibrium outcomes to the degrees of oil dependence and openness, as
well as the strength of the response of monetary policy authority to the
in‡ation. Finally, we evaluate the welfare implications of alternative
monetary policy regimes.
Keywords: Oil price, small open economy, demand and supply shocks
JEL Classi…cation: C68, E12, F41, F42
] Central Bank of Turkey
y Department of Economics and Related Studies, University of York
z Department of Economics, Middle East Technical University
E-mail addresses: du100@york.ac.uk, iu500@york.ac.uk, dfu500@york.ac.uk. We thank
Mai Farid, Gulcin Ozkan, Fabrizio Iacone, Mike Wickens, Peter Sinclair, Peter Smith, the
participants at the RES Easter School and two anonymous referees for helpful comments
and suggestions. The usual disclaimer applies.

---

1
Introduction
Macroeconomic e¤ects of oil price shocks have been extensively investigated
since the 1970s. Among the earlier contributions, Hamilton (1983) argues that
exogenous oil price shocks were responsible for the post-war US recessions.
More recently, Bernanke, Gertler and Watson (1997) have pointed out that
macroeconomic e¤ects of oil price shocks were aggravated by the wrong mon-
etary policy decisions. On the other hand, starting with Hooker (1989), many
empirical studies have revealed that the link between oil price and the output
growth seems to break down after 1980. Recent developments in the world
economy have supported these …ndings. At the end of 2007, the real oil prices
have reached the level of the late 1970s, while the world output growth is still
strong and in‡ation is at historically low levels (Figure 1).
Blanchard and Gali (2007) propose explanations for the observed change
in the e¤ects of the oil price shocks. First, they argue that labour markets
are more ‡exible now than in the past, and hence some of the negative e¤ects
of the oil price shocks can be absorbed by the labour market. Second, more
credible and stronger anti-in‡ationary stance of monetary policies of the 2000s
may have kept in‡ation expectations relatively stable. In addition, they argue
that the share of oil in production in the major economies has declined since
1970s. Data supports the last argument, showing that the oil intensity in the
major economies has almost halved since the 1970s (Figure 2).
Woodford (2007) argues that the o¤ered explanations are not convincing
enough because they ignore the endogenous responses of the real price of oil
(price of oil divided by the consumer price index) to the global economic con-
ditions. Hamilton (2005), Kilian (2007) and Kilian (2008) show that global
macroeconomic ‡uctuations have an impact on the price of oil. Therefore,
when we analyse the e¤ects of oil price shocks on the economy, we have to
take into account the causes of the oil price increases and their e¤ects on the
macroeconomic variables as well. It is believed that the major source of oil
price hikes in 1970s was the reduction in the oil supply. In the case of a pure
supply shock, macroeconomic variables are a¤ected by the oil supply disrup-
tion through higher oil prices. On the other hand, if an increase in oil price
is caused by a demand shock, there might be additional transmission channels
1

---

that a¤ect the macroeconomic variables. For example, if an increase in oil
demand is caused by a foreign productivity shock, a small open economy will
su¤er from the higher oil import bills while also enjoying the cheaper consump-
tion goods import, as well as higher exports due to the higher demand from
the rest of the world. In other words, in‡ationary e¤ects of oil price increases
will be limited. We argue that the faster economic growth coming from higher
productivity growth in developing countries ultimately raised oil demand of
these countries, fostering the real price of oil in the world market.1 Table 1
shows the trend of higher productivity growth of emerging markets, such as
China, India, Turkey and other East European countries in the last decade.
Following Gali and Monacelli (2005) we develop a sticky-price, small open
economy (SOE) dynamic stochastic general equilibrium (DSGE) model by
which we can analyse the e¤ects of foreign productivity shocks and oil sup-
ply shocks on oil prices, as well as the macroeconomic variables of a SOE.
Speci…cally, we assume that the world economy is composed of a domestic
SOE and a continuum of other small open economies (the rest of the world, or
ROW). E¤ectively, a SOE has a negligible e¤ect on the world economy, hence
oil demand and price are determined by the ROW, which can be regarded as
a closed economy. Oil price is determined endogenously in the model, hence
the model enables us to investigate the channels through which shocks that
cause oil price hikes and other macroeconomic variables interact. Oil supply is
assumed to be exogenous and follows a …rst-order autoregressive (i.e. AR(1))
process. Production process involves labour and oil as factors of production.
In this setting, we are able to analyse the e¤ects of oil supply shocks and for-
eign productivity shocks on the SOE. Additionally, general equilibrium e¤ects
of stronger commitments of the central banks to the low and stable in‡ation,
lower oil dependency and openness are analysed using our model. Finally, we
analyze the welfare implications of alternative monetary policy regimes.
The remainder of the paper is organised as follows. In section two the basic
structure of the model is laid out. The oil market equilibrium and the equilib-
rium conditions of the foreign economy are derived in section three. Impulse
responses and sensitivity analysis are outlined in section four. Section …ve
1 Our point of view is supported by IMF sta¤ reports (see, for example, World Economic
Outlook, April 2007). See also Campolmi (2007).
2

---

compares the welfare outcomes of some alternative monetary policy regimes.
Section six concludes.
2
The Small Open Economy Model
In this section, we develop an open economy DSGE model with staggered
prices. It shares its basic features with many new Keynesian SOE models, in-
cluding the benchmark models of Gali and Monacelli (2005) (GM thereafter)
and Clarida, Gali and Gertler (2001) (CGG thereafter). In these models, the
world economy is considered as consisting of a domestic SOE and a contin-
uum of other SOEs (or ROW), all represented by a unit interval. The SOE
has negligible e¤ect on the ROW, hence ROW can be regarded as a single
closed economy. We assume that the SOE and the ROW have preferences
and technologies in common, and all the goods produced are traded. In order
to highlight our interest in a single SOE and its interlinkages with the for-
eign economy, variables without superscripts refer to the home economy, while
variables with a star indicate the foreign economy variables.
In order to capture oil shocks, we follow Blanchard and Gali (2007) by
introducing a non-produced oil input in the production function. Contrary
to their analysis, however, the price of oil is endogenously determined in our
model.
2.1
Households
A representative household is in…nitely-lived and seeks to maximize
1
C1
N 1+'
E
t
t
t
0 X
(1)
1
1 + '
t=0
where U (C
N 1+'
t
t; Nt) = C1
t
is the period utility function, N
1
1+'
t denotes hours
of work and Ct is a composite consumption index de…ned by
1
1
Ct = h(1 ) C( 1)= + C( 1)=
H;t
F;t
i =( 1)
where CH;t and CF;t are CES indices of consumption of domestic and foreign
goods, given by
"=(" 1)
=(
1)
CH;t = Z 1CH;t(j)(" 1)="dj
; CF;t = Z 1(Ci;t)( 1)= di
0
0
3

---

where Ci;t = hR1C
0
i;t(j)(" 1)="dji"=(" 1) is an index of the quantity of goods
imported from country i 2 [0;1] and consumed by domestic households, j 2
[0; 1] indicates the goods varieties and " > 1 is the elasticity of substitution
among goods produced within a country. 0 <
< 1 indicates the expenditure
share of the imported goods in the consumption basket of households. We
assume that the degree of substitutability between domestic and foreign goods
( > 0) is the same as the degree of substitutability between goods produced
in di¤erent foreign countries. The period budget constraint of the household
is given by
1
Z
1
1
PH;t(j)CH;t(j)dj +Z Z Pi;t(j)Ci;t(j)djdi+Et Q D
t;t+1
t+1
Dt +WtNt +Tt:
0
0
0
(2)
Conditional on the optimal allocation of expenditures between domestic
and imported goods
CH;t = (1
) PH;t
C
C
P
t and CF;t =
PF;t
t
,
t
Pt
the budget constraint can be written as
PtCt + Et Q
D
t;t+1
t+1
Dt + WtNt + Tt
(3)
where Pt = [(1
)P 1
+ P 1
]1=(1
) is the consumer price index (CPI)
H;t
F;t
and the price indices for domestically produced and imported goods are
1=(1 ")
1=(1
)
PH;t = Z 1PH;t(j)1 "dj
; PF;t = Z 1P1 di
i;t
0
0
where Pi;t = hR1P0i;t(j)1 "dji1=(1 ") is a price index for goods imported from
country i. Qt;t+1 is the stochastic discount factor, Dt+1 is the nominal pay-o¤
in period t + 1 of the portfolio held at the end of period t including the shares
in …rms, Wt is the nominal wage and Tt is lump-sum transfers and/or taxes.
The behaviour of household is also characterized by an intratemporal op-
timality condition
W
C N ' =
t
(4)
t
t
Pt
and a Euler equation
P
R
( Ct+1
t
)
tEt
= 1
(5)
Ct
Pt+1
4

---

where Rt = 1=EtfQt;t+1g is the return on a riskless bond paying o¤ one unit of
domestic currency in period t+1. Equations (7) and (6) are the log-linearized
forms of the equations (4) and (5).
wt
pt = ct + 'nt
(6)
1
ct =
(rt
Et f t+1g
) + Et fct+1g
(7)
where lower case letters denote the logs of the respective variables (now and
thereafter),
=
log , log Rt = log(1 + rt) t rt is the nominal interest rate
and t+1 = pt
pt 1 is the CPI in‡ation between t and t + 1.
2.2
In‡ation, Real Exchange Rate and UIP Condition
The bilateral real exchange rate Qi;t is de…ned as Qi;t = Ei;tPit , where E
P
i;t is
t
the bilateral nominal exchange rate (domestic currency price of country i’s
currency) and P i is the aggregate price index for country i’s consumption
t
goods. Therefore, Qi;t is the ratio of the two country’s CPI’s, both expressed
in domestic currency. The law of one price is assumed to hold for each good.
Hence, the log-linearized real e¤ective exchange rate can be written as
qt = pF;t
pt
(8)
where qt = R1q0i;tdi is the log e¤ective real exchange rate. Then using the
log-linearized formula for the CPI index around a symmetric steady state, the
CPI, domestic price level and real exchange rate can be linked through the
following equation
pt = pH;t +
q
1
t:
(9)
We assume that households in foreign economy face exactly the same opti-
mization problem with identical preferences. However, noting that the foreign
economy as a whole is in fact a closed economy with the in‡uence from the
domestic economy being negligible, C = C
and P = P
. Equations (6)
t
F;t
t
F;t
and (7) continue to hold for the foreign economy with each variable replaced by
a corresponding starred variable. Under complete international …nancial mar-
kets assumption and no-arbitrage, Euler equations from both countries can be
combined to achieve a risk sharing condition. Ignoring the irrelevant constant
5

---

that depends on the initial conditions2, the log-linearized version of the risk
sharing equation can be written as
1
ct = c +
q
t
t:
(10)
The assumption of complete …nancial markets yields another important
relationship. Using rt = log Rt =
logQt;t+1 and its foreign country coun-
terpart for each country i; then aggregating over the countries, will yield the
uncovered interest parity condition (UIP)
Et f et+1g = rt r
(11)
t
where et is the (log) nominal e¤ective exchange rate.
Combining this with the de…nition of the real exchange rate and log-
linearizing around the steady state, one can write the UIP condition in terms
of the real exchange rate as
Et f qt+1g = (rt Etf t+1g) (r E
t
tf t+1g):
(12)
2.3
Firms
Each …rm produces a di¤erentiated good indexed by j 2 [0;1] with a produc-
tion function
Yt(j) = [AtNt (j)] Od(j)1
(13)
t
where Od(j) is the amount of oil used in production by …rm j, (log) produc-
t
tivity at = log(At) follows an AR(1) process at =
a
,
a t 1 + "a
t
f"atg is i.i.d. and
a 2 [0; 1). Assuming that …rms take the price of each input as given, cost
minimization of the …rm implies
(1
)(1
)WtNt(j) = Od(j)P
t
O;t
(14)
which holds for each …rm j. PO;t is the price of oil which is in fact determined
endogenously in our model, as will be explored later.
is an employment
subsidy, whose role is discussed in detail in GM and also in the appendix. The
nominal marginal cost is
(1
)W
M Cn =
t
:
t
A N
(j)1
t
t(j)
1Odt
2 See Gali and Monacelli (2005) for detailed derivations and explanation on this issue.
6

---

Utilising equation (14), the marginal cost can be written as
(1
) W P 1
t
M Cn =
O;t :
t
(1
)(1
)At
Therefore, one can derive the (log) real marginal cost in terms of domestic
prices mct, which is identical for each …rm, as (ignoring a constant)
mct = wt + (1
)pO;t
at
pH;t:
(15)
Yt = hR1Y0t(j)(" 1)="dji"=(" 1) represents an index for the aggregate do-
mestic output, like the one assumed for consumption goods. Aggregating (13)
over all …rms and log-linearizing to …rst order yields
yt = at + nt + (1
)od:
(16)
t
2.3.1
Price Setting
We assume that …rms set prices according to Calvo (1983) framework, in which
only a randomly selected fraction (1
) of the …rms can adjust their prices
optimally. Thus,
is the probability that …rm j does not change its price in
period t. Then the …rm’s optimal price setting strategy implies the following
marginal cost-based Phillips Curve
H;t =
Et f H;t+1g + dmct
(17)
where
= (1 )(1
) and dmctisthe(log)deviationofrealmarginalcostfrom
its ‡exible price equilibrium level.
2.4
Equilibrium Conditions
2.4.1
Goods Market Equilibrium
The equilibrium condition in the goods market requires that the production of
domestic goods satis…es
1
Yt(j) = CH;t(j) + Z Ci (j)di
H;t
0
where, Ci (j) is country i’s demand for good j produced in the home coun-
H;t
try. Using the optimal allocation of expenditures for the SOE and the ROW,
7

---

the real exchange rate de…nition and the assumption of symmetric preferences
and aggregating across goods, we obtain
P
1
Y
H;t
t =
C
Q
di :
P
t
(1
) +
Z 1 i;t
t
0
First order log-linearization around the symmetric steady state yields
1
yt = ct + (pt
pH;t) + (
)qt:
(18)
Using equation (9), one can write the goods market equilibrium as
(2
)
1
yt = ct +
q
1
t:
(19)
Equation (19) can be combined with c = y and equation (10) to obtain
t
t
(1
)
yt = y +
q
t
(2
)
(1
)2
t
(20)
Combining equation (19) with Euler equation and (9) gives (ignoring a
constant)
1
(2
)(
1)
yt = Et fyt+1g
(rt
Et f H;t+1g)
E
(1
)
t f qt+1g : (21)
2.4.2
Marginal Cost and In‡ation Dynamics
Within a general equilibrium framework, the relation between marginal cost
and economic activity can be established by combining the labour supply and
demand relations with the market clearing condition in the goods market, as
stressed by GM and CGG. Equation (15) can be written as
mct
=
at + (wt
pt) + (1
)(pO;t
pt)
(pH;t
pt)
=
at + ( ct + 'nt) + (1
)epO;t+( )q
1
t
(22)
where we make use of equations (6), (9). epO;t = pO;t pt istherealpriceof
oil (the relative price of oil with respect to CPI). Then using (16) and cost
minimization condition for …rms, and …nally (10), we can write the previous
equation for the real marginal cost in terms of the domestic output and pro-
ductivity, world output, real exchange rate, and the real price of oil
mct =
1at +
2y
+
t
3yt +
4 epO;t+ 5qt
(23)
8

---