Download What is the Welfare Social Cost of Oil Price?

What is the Welfare Social Cost of Oil Price?
Marc Joëts
Tovonony Raza…ndrabey
(March 2015)
Abstract
In this study, we assess the welfare social cost of oil price ‡uctuations for an oil importing country. To that end, we rely on an open economy dynamic and stochastic general
equilibrium (DSGE) model that o¤ers microfoundations of the propagation mechanisms
at play from oil price to consumers’ welfare. First, we uncover that the extent of social
welfare loss from oil price increase depends on the nature of shocks - supply, demand and
speculative - underlying oil price dynamics. Second, we uncover that welfare loss resulting
from an increase of crude oil price is less pronounced with oil fundamental shocks - with
the rise in demand that might compensate entirely the resulting welfare loss following oil
demand shocks - than oil speculative demand shocks.
Keywords: Oil price; Welfare; DSGE model
Ipag Lab, Ipag Business School and EconomiX-CNRS, University of Paris Ouest,
[email protected]
y
EconomiX-CNRS, University of Paris Ouest Nanterre la Défense, France. [email protected]
1
France.
1
Introduction
The recent and unprecedented surge observed in energy prices, and especially in the price of
crude oil, from 2003 to 2008, has given rise to heated public and academic debates about the
true nature of these shocks. Due to the potential impact of these huge movements on most
economies (Sadorsky, 1999; Hamilton, 2003; Edelstein and Kilian, 2007; Kilian, 2008; among
others), the e¤ectiveness of economic policies strongly depends on the identi…cation of the
major causes of oil prices movements. Since Greenspan’s (2004) intervention regarding the
existence of speculators in oil market, a popular view of the origins of the price surge has
been that these movements cannot be attributed to economic fundamentals - such as changes
in the conditions of supply and demand - but were caused by the increasing …nancialization
of commodities. This …nancialization should in turn cause volatility clustering phenomena,
extreme movements, higher comovements between oil, …nancial assets, and commodity prices,
as well as an increased impact of …nancial investors’ decisions (such as hedge funds, swap
dealers, . . . ).
While several papers have documented the speci…c nature of oil price (see among others,
Büyüksahin et al., 2009; Büyüksahin et al., 2010a; Büyüksahin et al., 2010b; Alquist and
Kilian, 2010; Silvennoinen and Thorp, 2010; Brunetti et al., 2011; Hamilton and Wu, 2012; and
Joets, 2013) limited works have been done about the welfare consequence of these movements.
However, this question appears to be of primary importance from both the economic and
the political point of view. For instance, the recent …nancialization of oil price and the
potential welfare social consequences raise the economic question of the trade-o¤ between
private and public interest, since …nancialization is often de…ned as being bene…cial from the
private perspective without any bene…cial considerations from a social planner’s point of view.
Politically, the debate is even more relevant since it lends credibility to the regulation of the
markets for commodity derivatives in the same way that the G20 governments try to regulate
…nancial markets by limiting speculative behavior.
In this study, we investigate the welfare social cost of oil price ‡uctuations depending on
the origin of shocks - i.e. oil supply shock, oil demand shock, speculative demand shock. To
that end, we rely on an open economy dynamic stochastic equilibrium model. This framework
allows us to see the shock which a¤ects the most the oil price and the consequence in terms of
welfare in an oil importing country. Namely, it has the advantage of o¤ering a microeconomic
perspective to macroeconomic oil shocks by evaluating the propagation mechanisms at play
from oil price to the consumers welfare. It also o¤ers a structural analysis of the two main
2
channels of the impact of oil price ‡uctuations on macro-economic variables. First, unexpected
rise in the crude oil price increases the production cost of domestic goods. This is the supply
channel that re‡ects the e¤ect of oil price shocks on the production process of …rms. Second,
unexpected rise in the crude oil price renders re…ned energy prices more expensive and, hence,
results to households’income loss - the demand channel. This leads to reduction of demand
of other goods and services in the economy, and to reallocation of available income towards
goods that are energy-e¢ cient.
It appears that social welfare is a¤ected in di¤erent ways depending on initial shocks.
Fundamental shocks have usually less impact on welfare than speculative shocks. More precisely, fundamental shocks from physical supply and demand conditions are largely anticipated
compared to speculative ones. In consequence, the welfare cost is lower when the fundamental component of the oil price is dominant, since households and …rms usually smooth their
consumption and their use of re…ned products. However, when speculative shocks occur, evolution of the oil price seems to be more uncertain and then future evolution less predictable
leading to more impact on welfare.
The remainder of the paper is organized as follows: section 2 reviews the litterature on
the link between oil price and macroeconomic variables; section 3 describes the data issues
and presents the model; section 3 discusses the wefare consequence of oil price shocks; and
section 4 concludes.
2
Oil price and Macreoconomic
Since 1970s, the interaction between oil and macroeconomic has attracted attention in the
economic literature.1 Since then, the debate about the relationship between oil price and
macroeconomic aggregates has growing with the price of crude oil and prices increases have
often been viewed (especially in the U.S.) as the main factor explaining periods of excessive
in‡ation, low productivity and slow economic growth. In order to understand the social
welfare consequence of oil price movements in the U.S., this Section highlights facts and
di¢ culties that have led economists and politics to consider the strong relationship between
oil price and macroeconomic performance. It also discusses the important debate regarding
the endogeneous and exogeneous components of oil price and examines the nature of oil price
1
According to the literature, this interest emerges from the speci…c macroeconomic context in the United
States during 1970s: poor macroeconomic performance, period of strong dependence on imported oil, and
exceptional disruptions in the global oil market (see, Kilian 2008 for more details).
3
shocks.
2.1
How oil price shocks may a¤ect economic?
Given the important role that crude oil plays at both macroeconomic and microeconomic
levels, the impact of oil price ‡uctuations on households and …rms has attracted signi…cant
attention among economists and policymakers. As suggested by Kilian (2008) this particular
interest has emerged from the common belief that the consequence of the energy prices increases in general, and crude oil price in particular tends to be di¤erent from other goods.2
In the literature two standard approaches have been opposed to explain the e¤ects of oil price
shocks to real output. In the …rst view, the relationship between oil and economy comes from
the supply channel corresponding to a term-of-trade shocks following an exogeneous increase
of imported crude oil price. Crude oil is considered here as an intermediate input in‡uencing domestic economy through the e¤ects on production decision (see among others, Kim
and Loungani 1992; Backus and Crucini 2000). However, this approach has been confronted
to several well-known problems about the role of oil on the value added of the production.
Indeed as discussed by Rotemberg and Woodford (1999), Barsky and Kilian (2004), and Kilian (2008), under standard assumptions of perfect competition, gross output is composed by
value added (labor and capital) and imported oil. Since oil does not enter in value added,
it is common in the literature that the e¤ect of oil price shocks does not shift the demand
curve for labor and capital services. Then, holding labor and capital constant, the e¤ect of oil
price on gross output must be small.3 It remains that even if it exists, the impact of oil price
on domestic output through the supply channel should be bounded by the cost share of oil,
which is also theoretically and empirically very small. Despite some theoretical improvements
to account for previous limitations (see, Rotemberg and Woodford 1996; Atkeson and Kehoe
1999; and Finn 2000) there is so far no empirical support for the supply channel hypothesis.4
In response to these di¢ culties, another strand of literature has been developed focusing
2
Four reasons are often discussed promoting this common perception: (i) oil prices ‡uctuations are usually
more volatile than other goods, (ii) oil price ‡uctuations seem to be determined by exogeneous events, such as
political context in the Middle East, (iii) the demand for crude oil is inelastic with regards to supply shocks,
and (iv) major crude oil price increases have often been followed by economic recession.
3
This conclusion can be partially mitigate if we drop the assumption of perfect competition and allow …rms
to …xe mark-up pricing of all cost components, including imported oil (Rotemberg and Woodford 1996).
4
See Kilian (2008) for more details.
4
on the demand side of the economy. Here the e¤ect of oil price shocks can be seen as the
reduction in the demand for goods and services rather than an aggregate supply shock for the
U.S. economy. Since then, several papers have demonstated the interest to consider oil price
shocks as an aggregate demand shocks for the U.S. economy (see, Lee and Ni 2002; Bernanke
2006; Hamilton 2008; Kilian 2008).5 In the propagation of oil price shocks on economy,
four direct mechanisms are usually at play in the demand channel. The …rst mechanism is
the discretionary income e¤ ect6 , where after an oil price increase consumers reallocate their
consumption pattern to the detriment of other goods and services since they have less money
to spend. The second mechanism comes from the uncertainty e¤ ect, where oil price shocks
may create uncertainty in future price patterns diminishing the readiness of consumers to
spend or allocate their earning and wages through an "option value to wait".7 ,8 Implicit
in the latter e¤ect is the irreversibility condition in purchase decisions. If this condition is
dropped it remains, according to the literature, that higher oil price will a¤ect consumer
behavior through a precautionary saving e¤ ect since consumers smooth their consumption
patterns in response to perceived future income losses and unemployment. Finally, the last
mechanism is directly related to the decrease of comsumption of durables requiring energy.
Indeed, after a positive oil price shock the consumption of energy-using durables tends to
decline by an operating cost e¤ ect (see, Davis 1987; Hamilton 1988; Bresnaban and Valley
1993; Hamilton 2008, to name few).9 These four direct e¤ects on the aggregate demand
following an oil price shock may often be accompagnied by indirect e¤ects coming from shifts
in consumption expenditures. In some sectors, change in expenditure pattern can cause, in a
second-round e¤ect, intersectoral and intrasectoral reallocations of labor and capital leading
5
As discussed by Kilian (2008), this view is widely shared by policymakers (see for instance Bernanke
2006b).
6
As discussed by Kilian (2008), it is important to note that this e¤ect implies that higher prices is the
consequence of imported crude oil price as opposed to domestic oil price, leading to income transfert from the
U.S. to abroad. Indeed, in the case of higher domestic oil price, the transfert of income will be cancelled at
the aggregate level since it will be characterized by a transfert from one consumer to another.
7
See Henry (1974), Bernanke (1983), Brennan and Schwartz (1985), Majd and Pindyck (1987), Brennan
(1990), Gibson and Schwartz (1990), Bloom et al. (2007), Bloom (2009), and Bredin et al. (2011) for the
impact of uncertainty at both macro and micro levels. For the impact of oil price uncertainty to economic
activity, see Pindyck (1991), Favero et al. (1994), Lee et al. (1995), Elder and Serletis (2009, 2010), Kellogg
(2014), and Jo (2014). For the reverse relationship (i.e. from macroeconomic uncertainty to oil price), see
Pindyck (1980), Litzenberger and Rabinowitz (1995), Van Robays (2013), and Joëts et al. (2015).
8
The uncertainty e¤ect is often cited as one of the main factor exacerbating the asymmetry in the oil
price-economic activity nexus. As discussed by Kilian (2014), the asymmetric responses of real output through
uncertainty channel may comes from the fact that uncertainty e¤ect may serve to amplify the e¤ects of
uncexpected oil price increases and to o¤set the e¤ects of unexpected oil price decreases.
9
It is important to note that this e¤ect is speci…c to the durables considered (for instance motor vehicules).
5
to unemployed resources, exacerbating the initial e¤ect of oil price shocks on real economy
(especially on prices and nominal wages). These indirect e¤ects are more delayed than direct
ones but can be much larger, and may arise as higher energy input costs or higher wage
demand feed through to consumers prices.10 This is especially because they could lead to a
self-sustaining spiral of increasing wages and prices which results in a more persistent impact
of in‡ation.11
2.2
Where do oil price shocks come from?
Since the early 1970s, it has been an important debate in the literature regarding the origins
of oil price shocks.12 This discussion has been accompagnied by re‡exions regarding the endogeneous and exogeneous natures of oil prices with respect to the U.S. macroeconomic.13 As
shown by the literature several factors may impact oil price movements such as ‡ow supply
and ‡ow demand shocks, and increase speculative demand shocks. Among the shocks, the
conventional misperception suggests that oil prices have been so far supply-driven and that
exogeneous events such as OPEC cartels’ decision, embargoes, and the political instability
in the Middle East have been responsible for major oil price shocks.14 Potential examples
of theses events are the Arab oil embargo of 1973-74 just after the Yom Kippur War, the
Iranian Revolution of 1978-79, the Iran-Iraq War of 1980-88, the OPEC collapse of 1986, the
invasion of Kuwait of 1990, the Afghan War of 2001, the Venezuelan crisis and Iraq War of
2002-03, and the Libyan uprising of 2011. However, as pointed out by Kilian (2014), while
some events were exogeneous with respect to the U.S. economy they did not cause oil price
shocks. For instance, the Yom Kippur War in 1973 did not constitute a shock to the ‡ow
10
According to many economists, these second-round e¤ects are often considered as the primary channel
under which energy prices in general and oil price in particular may a¤ect economy (see, David and Haltiwanfer
2001; Lee and Ni 2002; Bernanke 2006; Hamilton 2008, among others).
11
It is important to note that this conclusion is somewhat general and that this second-round e¤ect can
be di¤erent across countries. For the U.S., the direct e¤ect is often more important than the indirect one
given the fact that nominal wages are not enough ‡exible (i.e. the price-wage ratio remains constant) while
the conclusion is heterogeneous for the euro area (see, Baumeister et al. 2010). Indirect e¤ects can also be
in‡uenced by monetary policy reaction (see, Baumeister et al. 2010).
12
Before this date (back to 1920s) there was no global market for crude oil and the price of oil in the U.S.
was regulated by the government agencies (such as the Texas Railroad Commission). This system ended in
the beginning of 1970 when the U.S. ceased to be a net exporter of crude oil.
13
In this context, endogeneity refers to the causality from global macroeconomic to crude oil prices. Exogeneity refers to the exogeneous component of the crude oil price which can be attributed to political events
in the Middle East.
14
See, Hamilton (2003).
6
supply because no producing facilities were damaged.15 The Iranian Revolution and the oil
supply discruption in Iran did not coincide with oil price surge in late 1970. Furthermore,
Kilian (2008a,b) have evidenced that exogeneous oil supply shocks associated to events in the
Middle East have little predictive power for the percent change in the real price of oil.
Competting to this view is the strand of literature which consider that oil prices are endogeneous with respect to global macroeconomic conditions suggesting that ‡ow demand associated with the global business cycle has been the primary source of oil prices ‡uctuations16
(see, Mabro 1998; Barsky and Kilian 2002, 2004; Kilian 2008a; and Kilian 2009, among others). Since then, empirical papers have provided overwhelming evidence that oil prices since
1973 have been driven by global demand shocks (see among others, Kilian 2008a,b; Kilian
2009a,b; Kilian and Hicks 2013; Kilian and Murphy 2012, 2014).17 One of the most relevant
example point out by Barsky and Kilian (2002) is the 1973-74 oil price episode where the
dramatic oil price increase was explain by 75% of the aggregate demand conditions and 25%
of exogeneous events. Another interesting example, which has lead to heated public debates
among politics and researchers, is the recent oil price surge after 2003 and in particular in
the period of 2007-08 of economic turmoil. While the common wisdom has suggested that
the sharp price increase was the consequence of speculative behaviors in the market18 (see,
Fattouh et al. 2013 for a discussion), the recent literature supports the conclusion that the
surge in the oil price during this period was mainly caused by shifts in the ‡ow demand driven
by the global business cycle (see, Kilian 2009; and Kilian and Hicks 2013; Kilian and Murphy 2012, 2014; Joëts et al. 2015). Most importantly, the literature has further evidenced
that most shocks that seem to be exogeneous at the origins are actually the consequence of
the global macroeconomic context.19 Several historical episodes have been indeed linked the
15
Actually, the Arab-Israeli War of 1973 was not on the territory of oil producing economies and therefore
did not a¤ect crude oil production.
16
Note that ‡ow demand here refers to demand for oil that is consumed immediately for producing re…ned
products (such as gasoline, diesel, heating oil, ...) rather than the one in anticipation of future higher oil price
evolution, often called speculative demand.
17
One exception stressed by Kilian and Murphy (2013) is the 1990 period where the ‡ow supply shocks
played an important role.
18
The standard interpertation is that oil traders in spot markets buy crude oil now and store it in anticipation
of future higher oil prices.
19
Theoretically, Green and Porter (1984) and Rotemberg and Saloner (1986) have demonstrated that oil
cartels are determined to an important extent by the macroeconomic environment. Empirically, one example
is the Arab oil embargo of 1973-74 which did a¤ect the oil supply channel was endogeneous to the U.S. economy
(see, Barsky and Kilian 2002; Kilian 2008a).
7
strategy of oil cartels and embargoes to macroeconomic forces.20
The fact that oil price has been mainly demand-driven in post-1973 period does not imply
that other shocks have not a¤ected price dynamics. Indeed, as stressed by the literature, the
price of crude oil can depend on several shocks occuring simultaneously.21 While the impact
of the ‡ow demand for crude oil re‡ecting the state of the global business cycle appeared,
especially during the recent period, to be the main contribution of price movements, other
shocks have been at play in the oil market history. For instance, the oil price shocks of 197980 was driven in part by ‡ow demand and in part by increase in speculative demand for oil
in anticipation to an oil supply disruption in the Persian Gulf rather than the ‡ow supply
disruptions associated with the Iranian revolution of 1978-79.22 The oil price increase was
further powered by speculative demand pressures from 1981 to the collapse of OPEC in 1986,
whereas the impact of ‡ow demand started to decrease from the beginning of 1981. According
to Kilian and Murphy (2014), a ‡ow supply shock associated to the Iran-Irak War moderately
supported crude oil price in late 1980 early 1981. Unlike many commentators stressed, the
1986 price episode was the result of the Saudi Arabia crude oil production cut rather than the
collapse of OPEC. Simultaneously with the ‡ow supply, is a drop in the speculative demand
which reinforced the oil price decrease. The period of price surge surrounding the invasion of
Kuwait in 1990 also appears, according to the literature, to be the consequence of simultaneous shocks of an unexpected ‡ow supply disruption and an unexpected increase in speculative
demand working in the same direction (see, Kilian and Murphy 2014).23 The Venezuelan
crisis and the Iraq War of 2002-03 meanwhile, lead to a considerable oil production fall at the
end of 2002 and early 2003.24 Together with the oil supply shock is an increase in speculative
demand in anticipation of the Iraq War which lead to a sharp oil price increase. The litera20
See for instance Terzian (1985) about the explaining role of the dollar depreciation in OPEC’s strategy in
1970s. The ‡uctuation of the real interest rates in 1970s was also made responsible to the formation of carterls
(see, Green and Porter 1984; and Rotemberg and Saloner 1986).
21
Kilian (2009), Baumeister and Peersman (2013), and Kilian and Murphy (2012, 2014) were among the …rst
to disentangle these di¤erent shocks on the real price of oil.
22
See Barsky and Kilian (2002) and Kilian and Murphy (2014).
23
It is important to note that the conclusion regarding the e¤ects on price of shifts in speculative demand
for oil in this period are not clear cut. While Kilian (2009a) presented evidence of this e¤ect, Hamilton (2009a)
rejected this hypothesis in favor of oil supply shocks. Recently Kilian and Murphy (2014) resolves this puzzle
by showing that both shocks were at play during the oil price surge in 1990 (two third of oil supply shock and
one third of speculative demand shock).
24
As notice by Kilian (2008a), the combined e¤ect on oil production was of similar magnitude to the supply
shocks of the 1970s.
8
ture has also pointed out that depending on the shocks (‡ow supply, ‡ow demand, speculative
demand) the response of the crude oil price does not follow the same pattern. For example,
the period immediately after the invasion of Kuwait in 1990, the Afghan War in 2001, the
Iraq War in 2002-03, and the …nancial turmoil of 2007-08 are characterized by sharp spikes
in oil prices. The Iran-Irak war in 1980 and the 1999 OPEC meeting are, in contrast, de…ned
by small price movements (see, Barsky and Kilian 2004). In other words, the absorption of
shocks of price are not the same and deeply depends on the context of the market and the
nature of the disturbances. This re‡exion can be extended to the social impact of the di¤erent
shocks through the crude oil price. It is therefore of primary importance in our context to
disentangle each type of shocks (i.e. endogeneous and exogeneous) to examine the welfare
social consequence of oil price movements on the U.S. economy.
2.3
What is the e¤ect of oil price movements on consumers welfare?
As the literature evidenced, knowing the underlying reasons for a change in oil prices is of
primary importance to determine the crude oil price dynamic and the economic repercusions.
For instance, recent studies have shown that the e¤ects of oil price on the euro area and the
U.S. economies vary considerably depending on the source of oil price movements (see, Kilian
2009; Peersman and Van Robays 2009; and Baumeister et al. 2010).25 To simplify let’s assume
that we want to evaluate the e¤ect of an unexpected exogeneous oil price shock on domestic
economy.26 As previously discussed, higher imported crude oil will have two main immediate
e¤ects on real GDP in oil-importing economies: (i) the reduction of the income of domestic
households (purchasing power)27 through an increase of the prices of re…ned products, and (ii)
an increase of producting cost of output. Recent empirical studies suggest that the domestic
supply channel is weak compared to the demand one.28 Understanding the impact of oil price
‡uctuations on consumers welfare is therefore quantify how the prices of imported crude oil
change the total consumption and expenditures patterns of households. In other words, it is to
25
Bodenstein et al. (2012) proved that the optimal response of monetary policy is also di¤erent depending
on the source of oil price shocks.
26
Note that here we willingly do not consider the endogenous component of oil price (i.e. oil prices movements
following a ‡ow demand shock from global economic activity).
27
Recall that incomes are transferred abroad because we consider a shock from imported crude oil rather
than an increase in domestically produced crude oil.
28
See, Lee and Ni (2002) and Kilian and Park (2009) for empirical evidences of the predominance of the
demand channel. See Kilian (2014) for a discussion.
9
understand the pass-through of higher oil price on purchasing power by the demand channel.29
At a disaggregate level, the implicit question behind the welfare evolution is how price-elastic
the total real consumption (energy and non-energy) is. Empirically, some studies have evidenced the e¤ect of higher oil price on energy consumption, such as the demand of gasoline,
electricity, heating oil and coal and natural gas (see among others, Dahl and Sterner 1991;
Reiss and White 2005; Hughes et al. 2008; Edelstein and Kilian 2007, 2009). However, conclusions are somewhat di¤erent between studies. While Edelstein and Kilian (2007) using
a bivariate model estimated that the responses of demand of gasoline, heating oil and coal,
and electricity are respectively around
0:48,
1:47 and
0:15 after one year30 , Reiss and
Matthew (2005) identi…ed using a structural model a short-run electricity price elasticity of
electricity demand of
0:39 and Dahl and Sterner (1991) through a comprehensive survey re-
ported a short-run gasoline price elasticity of gasoline demand between
0:08 and
0:41.31 ,32
Looking at the e¤ect of higher energy prices on consumer expenditures, Kilian (2008) illustrated that it takes repeated unanticipated gasoline price increases to generate large e¤ects on
households consumption. Putting in parallel the e¤ect of higher oil price through the prices
of re…ned products and the transmission channel to consumers, futher investigations reveal
that on the long-run the consequence of 1 percent increase in energy prices is a maximum
reduction in the associated discretionary income of
0:04 percent (see, Kilian 2008). This
response is quite small compared to the e¤ect on total consumption ( 0:15). As discussed by
Kilian (2008), it can be the consequence of two factors: (i) the demand for energy may decline
over time as households change their consumption patterns more e¢ ciently (i.e. driving less,
upgrade their home-heating,...), and (ii) households reduce their consumptions because they
increase their demands for precautionary saving and due to the presence of an operating cost
e¤ect. It appears that a statistically signi…cant e¤ect of precautionary saving of
0:07 percent
is at play for services on the period 1970-2006, the e¤ect on durables and nondurables other
29
As discussed by Hamilton (2012) measuring the in‡ation pass-through is a leading question among policymakers.
30
Contrary to the conventional wisdom (i.e. the demand of gasoline is inelastic) gasoline consumption
responds immediately after an unanticipated energy price increase. The large response of heating oil and coal
can be explained by the storage property of energy allowing households to delay purchases. Finally, the small
decline of electricity demand can be explained by its unstorable property.
31
Hughes et al. (2008), meanwhile, by splitting the sample into two periods found a decline of the gasoline
price elasticity of gasoline demand in 1975-80 compared to 2001-06. Illustrating the time-varying nature of
price elasticities (see also, Baumeister et al. 2010; and Baumeister and Peersman 2013a,b).
32
See Kilian (2008) for a discussion.
10
than vehicles, in contrast, is statistically insigni…cant. Meanwhile, the e¤ect of an operating
cost e¤ect is illustrated by the excessive response of vehicles compared to other goods (around
0:60).33 Taking all these e¤ects together, it appears that higher energy prices in general, and
crude oil price in particular a¤ects the aggregate consumption and then consumers welfare
but the e¤ects seems to be, according to the literature, rather small.
It questions the existence of other transmission pattern than the aggregate real consumption
on which oil price shocks a¤ect consumers through the demand channel. As illustrated by the
literature, a central point of the theory of the demand channel is how energy price shocks a¤ect
households’ expenditure patterns. This channel of transmission is illustrated particularly
in the automobile indystry where consumers tend to buy smaller and more energy-e¢ cient
cars in response to purchasing power losses. Edelstein and Kilian (2007, 2009) were among
the …rst to quanti…ed the e¤ect of oil price increase on speci…c types of expenditures and
to documented a highly signi…cant drop of
0:76 percent in the overall demand of motor
vehicles and parts.34 Authors further evidenced that given the increase households’demand
for more energy-e¢ cient cars the elasticity of demand for new automobiles is about
0:71. An
operating cost e¤ect can be additionally documented by comparing the responses following
an energy price increase of unit light truck sales compared to the unit heavy truck sales,
respectively
3
1:05 percent and
0:86 percent.35
Data issues and Model speci…cation
This section presents the framework of the dataset as well as the model speci…cation and
estimation procedure. It also provides a discussion about the symmetric and asymmetric
economic responses to unexpected oil price increases.
33
See Kilian (2008), and Edelstein and Kilian (2007, 2009).
Among the e¤ect, they also observe a decline of 1:25 percent of pleasure boats, 1:05 percent for pleasure
aircraft, and 1:58 percent in recreational vehicles (see, Edelstein and Kilian 2007; and Kilian 2008).
35
Another e¤ect of energy price shocks could be transmitted on …rms’investment expenditures (see, Hamilton
2008). However, we do not discuss this pattern because, to date, there is no empirical evidence of the e¤ect
(see, Kilian 2008).
34
11
3.1
The dataset
An important concern when modeling the impact of crude oil on the U.S. real output
and more speci…cally on consumers welfare is the proxy to use for oil price and the sample
period to consider. Indeed, empirical literature evidenced that results regarding the impact
of oil prices on GDP are sensitive to the choice of price measure.36 While there is so far
no consensus about which oil price to use, economic intuition suggests that in a context of
global oil market, the price of imported crude oil should be a better proxy than the domestic one to assess the impact on real output. Indeed, as stressed in Section 2 the e¤ect of
higher domestic oil price should be cancelled at the aggregate level since it is characterized
by a transfert from one consumer to another (see, Kilian 2008; and Kilian and Vigfusson
2011a). On the contrary, while Hamilton (2010) suggests that the U.S. producer crude oil
price is a better proxy than the U.S. re…ners’acquisition cost to apprehend the e¤ect of price
on output because it is highly related with gasoline price, Mork (1986), Eldelstein and Kilian (2009), and Kilian (2010) caution against this view. The arguments against Hamilton
(2010)’s approach are however di¤erent between studies. For instance, Mork (1986) considers
that the U.S. producer price cannot be considered as a true market price since it has been
regulated by government, meanwhile Eldelstein and Kilian (2009) and Kilian (2010) show
that the gasoline price is a best candidates for retail price faced by consumers and …rms. The
recent literature has then considered the price of the re…ners’ acquisition cost for imported
crude oil because that price is likely to be a better proxy for the price of oil in global markets
than the U.S. price of domestic crude oil which was regulated during the 1970s and early 1980s.
With the question of the proxy of oil price use, another fundamental di¤erence between studies
is whether the price oil is expressed in real or nominal terms. While a consensus has emerged
since 1973 in favor of the real price of oil37 , many other studies use the nominal price of oil to
investigate the impact on GDP. The theoretical argument behind this choice is that the real
price of oil after 1973 simply re‡ected in‡ation adjustments while the nominal price remained
immobile for some periods. Following this intuition, the real price of oil in the post 1973
period should not echo shocks in the oil market while nominal does. However, as point out
36
The empirical literature has so far considered the West Texas Intermediate (WTI) crude oil price, the U.S.
re…ners’acquisition cost for imported crude oil, and for domestic crude oil, and the price of U.S. producers as
the leading proxies.
37
See, Mork (1989), Lee et al. (1995), Kilian (2008b), Edelstein and Kilian (2007, 2009), Elder and Serletis
(2009, 2010), Kilian and Vigfusson (2011a,b), among others.
12
by Kilian and Vigfusson (2011a), and Alquist et al. (2013), the nominal oil price should be
more prone to react to in‡ation innovations rather the real price since it is free to adjust to
in‡ation pressures and monetary disturbances. Moreover, given that the transmissions of oil
price shocks to the economy is expressed in real terms the focus on the real price of oil make
more economic sense. We follow the mainstream of the recent literature considering the real
price of oil de…ned as the U.S. re…ners’acquisition cost for imported crude oil reported by the
Energy International Agency (EIA). The sample period goes from 1964Q1 to 2013Q4 and the
the price is de‡ated by the U.S. consumer price index.38
3.2
Symmetric vs. asymmetric economic responses to oil price shocks
After the sharp crude oil price decrease in 1986 following the shut down of the Saudi Arabia
crude oil production39 and the economic repercussions40 , a large interest has emerged among
economists regarding the potential asymmetric41 responses of macroeconomic aggregates in
oil-importing countries to unexpected oil price decreases and increases (see among others, Li
et al. 1995; Davis and Haltiwanger 2001; Balke et al. 2002; Hamilton 1996, 2003; Kilian
and Vigfussion 2011a,b; Herrera et al. 2011; and Venditti 2013).42 This interest has growing
recently with the successive major unexpected crude oil price declines in 1998 during the asian
economic crisis, and in late of 2008 during the global …nancial turmoil. In the literature, the
rationale of asymmetric reactions of real output following an unexpected oil price increase
comes from the existence of potential additional indirect e¤ects of price movements.43 These
indirect e¤ects have been discussed in the literature through three main channels: (i) the
reallocation e¤ect (Hamilton, 1988), (ii) the uncertainty e¤ect (Bernanke 1983; and Pindyck
1991), and (iii) the role of the monetary policy of the Federal Reserve (Bernanke et al. 1997).
38
In Section "ROBUSTNESS", we check for the sensitivity of our results with respect to alternative oil price
measures.
39
During this period, many commentators considered that the rise of the crude oil price was the consequence
of the OPEC collaspe in 1986. Rather, it has been evidenced that it was mainly the result of an unilateral
crude oil production reduction from Saudi Arabia to compensate for higher oil production elsewhere in the
world (given the lack of cooperation from OPEC members). See Kilian (2014).
40
It has been more the absence of major economic expansion following the price decline in 1986 compared
to the apparent economic decline in 1979 after a sharp price increase which emerged interest in the potential
asymmetric responses of U.S. macroeconomic aggregates.
41
Here by asymmetric we discuss the weaker impact of energy price decrease than increase and do not evoke
extreme forms of asymmetric behaviors like the net oil price increase speci…cation of Hamilton (1996, 2003,
2009, and 2010).
42
See, Kilian (2008) and Hamilton (2009) for a discussion.
43
As stressed by the literature, the direct e¤ect of an increase of imported crude oil price on real output is
symmetric (see, Kilian and Vigfusson 2011b).
13
In period of unexpected real oil price increase, both the reallocation and the uncertainty e¤ects
lead investment and consumption expenditures to drop. The e¤ect of the former is through
the intersectoral and intrasectoral shifts throughout the economy causing labor and capital
to be unemployed, whereas the latter comes from the fact that …rms and consumers delay
investments and consumptions via an "option value to wait" (see, Elder and Serletis 2009,
2010; Anderson et al. 2011; Kellogg 2014; and Jo 2014 for recent empirical studies at both
micro and macro levels).44 In contrast, in periods of unexpected real oil price decline, both
e¤ects (reallocation and uncertainty) will partially o¤set the increased expenditures driven
by higher purchasing power leading to a smaller economic expansion (see, Kilian and Vigfusson 2011b for a discussion).45 The third factor potentially responsibles of the asymmetric
economic responses to oil price shocks is the role of the Federal Reserve. The asymmetry
arises because in periods of unexpected real oil price increase, the Federal Reserve tends to
increase the interest rate to o¤setting the e¤ect of the crude oil price on in‡ation, thereby
amplifying the economic contraction, while in periods of unexpected price decrease the Federal Reserve does not.46 As discussed by Kilian and Vigfusson (2011b), much of the empirical
works have considered for one of these channels only, and have been in support of asymmetries without explicitly test for this hypothesis.47 One exception is the study of Kilian and
Vigfusson (2011a) who proposed a simple impluse-response based Wald test for asymmetric
transmission encompassing all potential transmission channels previously discussed. Another
approach is the slope-based test developed by Balke et al. (2002). While both approaches
seem to be comparable according to Hamilton (2010), it remains some important di¤erences
between them as discussed by Kilian and Vigfusson (2011b). First, the test used by Balke et
al. (2002) are not designed to assess the degree of the asymmetric transmission of oil price
44
Note that for both channels, the quantitative importance of the e¤ect depends on how important the real
price of oil is for investments and consumptions. This e¤ect is also bounded by the share of oil in the pattern
of consumptions and investments (see, Kilian 2008; Kilian and Vigfusson 2011b for a discussion).
45
The fundamental di¤erence between the Bernanke-Pindyck framework and the one of Hamilton is that the
former de…nition is related to uncertainty at horizon relevant to investment decisions (such as years or decade),
while the latter is more likely current uncertainty (see, Kilian and Vigfusson 2011b; and Joëts et al. 2015).
46
To date, there is no theoretical model justifying the role of monetary policy in explaining asymmetry,
and most of empirical studies have so far imposed this speci…city in estimation procedure without provide
any econometric justi…cations. One exception is the paper of Balke et al. (2002) who explicitly tests for this
hypothesis and …nd no signi…cant evidence. This in line with a large literature showing that the impact of
the Federal Reserve in explaining asymmetry is weak (see, Hamilton and Herera 2004; Carlstrom and Fuerst
2006; Herera and Pasavento 2009; Nakov and Pescatori 2010; Kilian and Lewis 2011; and Kilian and Vigfusson
2011b for a general discussion).
47
Another important limitation of earlier studies is that the asymmetric transmissions are based on invalid
censored VAR models (see, Balke et al. 2002; and Kilian and Vigfusson 2011a).
14
innovations to real output while the one developed by Kilian and Vigfusson (2011a) does.
Second, the model used in Balke et al. (2002) imposes a recursive ordering which implicitly
treats the real output as predetermined, whereas the general intuition since early 1970s is
that the price of oil is endogenous with respect to economic activity (see Mabro 1998; Barsky
and Kilian 2002, 2004; Kilian 2008a; and Hamilton 2009 to name few). Third, estimation
of Balke et al. (2002) is based on data starting on January 1965, while oil price movements
before 1973 cannot be represented by standard dynamic models (see, Kilian and Vigfusson
2011b; and Alquist and Kilian 2013). Econometrically, Kilian and Vigfusson (2011a,b) further
demonstate that standard sloped-based tests for asymmetry are not su¢ cent for judging the
degree of asymmetry in impulse response functions.
Considering that impulse response approaches are more appropriated than slope-based to test
for asymmetric response of real GDP to unexpected oil price shocks, the remaining question
is what is the empirical evidence of such e¤ect in the literature. Kilian and Vigfusson 2011a,b
show that whatever the oil price considered (nominal price, real price or the U.S. re…ners’
acquisition cost for imported crude oil) there is no evidence of asymmetric responses to unexpected price shocks of typical magnitude during the period 1974-2009.48 Herera et al. (2010)
recently extended the analysis at both aggregate and disaggregate levels for industrial sectors. They …nd signi…cant evidence against symmetry at the disaggregate level after a shock
of typical magnitude, especially for chemicals, transit equipment, petroleum and coal, plastics
and rubber, primary metals, and machinery. For shocks of higher magnitude, they found
rejection of the null of symmetry for plastics and rubber, chemicals, and transit equipments.49
For both magnitudes, any e¤ects on motor vehicles are found. Whatever the framework of the
analysis, empirical evidence for asymmetry appears to be mixed and subjects to cautions. In
particular, there is evidence against symmetry only in the case of very large oil innovations,
episodes that are quite limited in oil market history. Moreover, as point out by Kilian and
Vigfusson (2011b), the rejection of symmetry during large oil price innovations is based on
the net increase measure of Hamilton (1996, 2003) known to be an extreme forms of asymmetry whereas a more conventional measure, as the one de…ned by Mork (1989), vanishes
48
They …nd statistically signi…cant evidence against symmetry for high magnitude only, such as two-standard
deviation shocks. However, it is important to note that two thirds of all oil price innovations occuring historically are of typical magnitude, such as one-standard deviation (see, Kilian and Vigfusson 2011b). Moreover,
the asymmetric e¤ect of two-standard deviation shocks should be considered with cautions since they include
the period of the recent …nancial crisis.
49
However, as point out by Kilian and Vigfusson (2011b) their results are sensitive to data mining.
15
the rejection of the symmetry. Since no empirical evidence are found in favor of asymmetric
transmission, we assume a symmetric speci…cation in the transfert of oil price to consumers
welfare.
3.3
The model speci…cation
In order to quantify the social cost of oil price ‡uctuations on economy, we rely on an open
economy dynamic stochastic general equilibrium model which describes the behavior of a net
oil-importer. This framework has the advantage of o¤ering a microeconomic perspective to
macroeconomic oil shocks by evaluating the propagation mechanisms at play from oil price to
the consumers welfare. It also o¤ers a more ‡exible approach than to consider closed economy
setting since here the price of oil is determined endogeneously in global oil markets whereas
assumed to be exogeneous.50 The oil net importing country that is considered is populated by
four types of agents: (1) home …rms that produce non-oil intermediate goods, oil-importing
…rms that import crude-oil in the international market and set re…ned-oil prices, …nal good
…rms that bundle non-oil and re…ned-oil intermediate goods to produce homogenous goods
to be used in consumption, investment and government expenditures, (2) households that
consume, own capital and supply labor, (3) government that issues domestic real bonds to
…nance its expenditures and lump-sum transfer to households, (4) and a central bank that
conducts monetary policy and uses the interest rate as the instrument rule. The derivation
of the complete equilibirum conditions is standard and is de¤ered to Appendix A for the sake
of clarity.
3.3.1
Households
Individual household h consumes a bundle of …nal consumption good ct (h), owns capital kt (h)
that they lend to intermediate good …rms either as a form of investment it (h) or as a change
in the capital utilization rate ut and supply monopolistically labor Lt (h) to intermediate good
…rms. Moreover, households have access to …nancial markets by buying or selling domestic
real bonds bt (h) issued by the government and behave in a Ricardian fashion in the sens
that they can save or borrow in order to substitute their consumption intertemporally. Thus,
50
Most of existing studies that focus on the relationship between oil price ‡uctuations and economy using
DSGE models have either assume exogeneous real price of oil (see, Leduc and Sill 2004; Carlstrom and Fuerst
2006; Montoro 2010; Kormilitsina 2011; Natal 2012, to name few) or are based on closed economy models (see,
Bodenstein et al. 2008; Nakov and Pescatori 2010a,b). One recent exception is the paper of Bodenstein et al.
(2012) which investigates the monetary policy responses to oil price ‡uctuations.
16
household h values each period a discounted stream of future utilities
W t = Et
1
X
k
Ut+k (ct+k (h); hat+k ; Lt+k (h))
(1)
k=0
that depends on an external habit hat = hgZ;t1 ct
consumption ct
1.
1
that is a constant fraction h of last period
The variable gZ;t de…ne the evolution of the labor-augmenting technology
process Zt and determine the nature, deterministic or stochastic, of the growth trend of real
variables. The period t utility function is de…ned as51 :
Ut (
where
B
t
)=
B
t
1+
L (Lt )
t
hgZ;t1 ct 1
ln ct
1+
!
denotes the intertemporal substitution or preference shock,
supply shock and
L
t
denotes the labor
denotes the intertemporal elasticity of labor supply. Households therefore
value positively the net change in the level of consumption and negatively additional hours
supplied into employment.
3.3.2
Firms
Final private good …rms produce consumption and investment goods using a bundle of non-oil
ht and oil ot intermediate-goods produced by domestic and oil importing intermediate …rms,
respectively. The production function that transforms intermediate goods into …nal output is
given by:
qtC
qtI
=
(1
=
(1
C)
I)
1
C
1
I
C 1
C
hC
t
hIt
1
I
I
+
1
C
+
C
1
I
I
o•It
C
C 1
C 1
C
o•C
t
1
I
I
= ct
(2a)
I
I
1
= it +
(ut ) gZ;t1 kt
1
(2b)
where the last equality is derived from the market clearing condition (24). The parameter
i
for i = fC; Ig denotes the constant elasticity of substitution between non-oil and oil interme-
diate goods, and
i
represents the weight of energy in the production process of …nal private
consumption and investment goods. We assume that …nal producers bear a certain cost, at
51
The intensive form representation adopted in this paper lead us to assume a logarthmic utility function in
consumption (Christo¤el et al., 2008).
17
least in the short run, when changing the level of their consumption of energy. Therefore,
adjusted-level of energy-consumption is de…ned as:
o•it = 1
i
t
oit for i = fC; Ig
where we follow Christo¤el et al. (2008) and assume that the adjustment cost function is
given by:
i
t
where
i
=
i
2
1
i
O;d
t
oit =qti
oit 1 =qti
2
1
1
for i = fC; Ig
> 0. This speci…cation allows the model to have smooth response of oil energy
share in the production process of …nal private consumption and investment goods following
a change in the relative price of oil energy. However, the level of oil energy is allowed to jump
following a change in the total demand.
O;d
t
represents oil demand shock and is assumed
O;d
t
where
to evolve according to
ln
3.3.3
O;d
t
=
O;d
O;d ln t 1
+
O;d
t
iid N 0;
2
O;d
(3)
Oil market
We assume without loss of generality that the supply of the crude oil is exogenous and evolves
according to:
ln ot = 1
O;s
ln (o) +
O;s ln ot 1
+
O;s
t
where
O;s
t
where o denotes the steady state value of crude oil supply and
O;s
t
iid N 0;
2
O;s
(4)
denotes oil supply shocks
which may come from exogeneous events. For instance, a negative shock may be interpreted as
an exogenous disruption of the supply of crude oil. It permits to capture historical exogenous
events in the world oil production such as embargoes, social and political events in the Middle
East, and OPEC decisions.
At the demand-side, there exists a continuum of local retailer …rms which import crude
oil in the global market and distribute to …nal good …rms re…ned oil they produce. Moreover,
oil importing …rms behave monopolistically on staggered basis à la Calvo when setting the
home currency re…ned oil price pO;t . They face marginal cost which is identical across …rms
18
and which in real terms is de…ned as:
M CO;t = pO;t =pO;t
(5)
where pO;t = PO;t =Pt denotes the international real oil-price de‡ated by the U.S. consumer
price index as in Kilian (2009) and Baumeister and Peersman (2013).52
Finally, the international price of oil which is denominated in U.S dollar is assumed to
evolve according to:
ln pO;t = 1
pO
ln (pO ) +
pO
ln pO;t
1
+
pO
t
(6)
where pO denotes the steady state value of crude oil price. As stressed by the literature,53
the dynamics of crude oil price is assumed to depend on exogenous shocks that a¤ect the
oil market and endogeneous shocks that a¤ect oil-importing countries. Thus, in a similar
vein, the oil price innovation
PO
t
corresponds to unexpected ‡ow demand, ‡ow supply and
oil market speci…c demand.
3.3.4
Disentangling source of oil price shocks
As …rst pointed out by Kilian (2009), to model the global framework of oil market it is important to disentangle the shocks that may a¤ect crude oil price. The literature has identi…ed
three type of shocks, namely the ‡ow supply, the ‡ow demand, and the oil market speci…c
demand (i.e. speculative demand or demand for oil stocks) shocks. Since not all so-called
shocks follow the same pattern the e¤ect on price is di¤erent54 and the consequence on consumers welfare should be also conditioning on the type of shocks. To disentangle each shock
52
In case of study that considers oil-importing country other than the United States, the expression of real
marginal cost reduces to the following equation:
M CO;t =
t
pO;t
pO;t
where t = Et Pt =Pt denotes the cpi-based real exchange rate vis-à-vis the United States and Et denotes the
U.S. Dollar bilateral nominal exchange rate that gives the home-currency price of one unit of dollar.
53
See, Kilian (2009), Baumeister et al. (2010), Alquist and Kilian (2010), Alquist et al. (2013), Baumeister
and Peersman (2013), Kilian and Murphy (2012, 2014), to name few.
54
See, Barksy and Kilian (2004) and Joëts et al. (2015).
19
in oil price ‡uctuations, we assume the following expression of oil price innovation
pO
t
where 0
dde
o
f und
o
1 and (1
=
|
f und
o
dde O;d
o
t
1
{z
dde
o
O;s
t
fundamental (demand and supply) shocks
+ 1
} |
f und
o
{z
pO
t :
O;m
t
speculative shocks
(7)
}
represents the proportion of fundamental shocks in oil price, composed by
dde )
o
which are respectively shocks to the ‡ow demand (
O;d
t )
for crude
oil re‡ecting the state of the global business cycle and shocks to the ‡ow supply of oil (
f und
o
ground.55
1
corresponds to shocks to the speculative demand (
O;m
)
t
O;s
t ).
for oil stocks above the
Equation (7) is therefore in line with the literature by disentangling the di¤erent
contemporaneous structural shocks at play in oil price dynamics.56
4
The welfare consequence of oil price shocks
The literature identi…es two main channels of the impact of oil price ‡uctuations on macroeconomic variables. First, unexpected rise in the crude oil price increases the production cost
of domestic goods by raising the price of investment goods. This is the supply channel that
re‡ects the e¤ect of oil price shocks on the production process of …rms. Second, unexpected
rise in the crude oil price renders re…ned energy prices more expensive and, hence, results to
households’income loss. This leads to reduction of demand of other goods and services in the
economy, and to reallocation of available income towards goods that are energy-e¢ cient. In
either case, the impact of oil price increase on macroeconomic aggregate variables, in particular
the consumption, is negative to the extent that depends on the nature of shocks hitting oil
price dynamics. In turn, changes in the consumption primarily determine the level of welfare
changes in (1). Using the estimates of structural parameters in Table 1, we compute the second
order log-linear approximation of the welfare function around steady-state. Depending on all
possible values of the proportion of fundamental
f und
o
and demand
dde
o
shocks, let us depict
in Figure 1 the welfare changes that result from oil shocks of di¤erent natures. That is,
55
As discussed by Kilian and Murphy (2014), his shock is also often called "speculative demand shock" since
it involves a forward- looking strategy in anticipation of higher oil prices.
56
See, Kilian (2009), Baumeister et al. (2010), Alquist and Kilian (2010), Alquist et al. (2013), Baumeister
and Peersman (2013), Kilian and Murphy (2012, 2014), to name few.
20
Figure 1: Welfare impact of Oil price shock
The change in welfare that follows oil price shocks is represented in the vertical axis. In
turn, the proportion of ‡ow demand shocks and of fundamental shocks are represented in the
left-hand-side and right-hand-side of the horizontal axis, respectively. It is clear that the oil
price innovation that induces the larger welfare loss to households is the speculative oil demand
shocks as can be seen in the bottom of Figure 1. Recall that oil market speci…c shocks re‡ect
expectation shift of agents in the physical oil market about the future demand conditions of
crude oil. These shocks, by their very nature, do not enter into decisions of domestic agents and
are largely unanticipated. Therefore, the impact on aggregate variables such as consumption
21
and production is large, and leads to a greater loss in welfare. In contrast, oil demand shocks
are the result of changes in economic condition such as consumption preference of households
and production decision of …rms. The resulting higher demand increases domestic income and
compensates the adverse e¤ect of the resulting increase of oil price. As shown in the upper-left
of Figure 1, the welfare loss is extremely low. It is equal to
the fundamental demand shocks are at play (
reasonable range values of
f und
o
and
dde ,
o
f und
o
=
dde
o
3e
5
for situation where only
= 1). More interestingly, for a
demand shocks induce a we‡are gain. Finally, the
welfare loss that results from oil supply shocks is less severe compared to speculative demand
shocks. Indeed, …rms smooth the response of energy share in the production process following
change in the relative price of energy. This is also in line with …ndings in the literature which
state that the e¤ect of supply shocks on oil price dynamics is small.
5
Conclusion
In this paper, we o¤er a structural analysis of the welfare social cost of oil price ‡uctuations
depending on the origin of shocks - i.e. oil supply shock, oil demand shock, speculative
demand shock. Namely, we rely on the dynamic stochastic general equilibrium model to o¤er
microfoundations of the propagation mechanisms at play from oil price to the consumers’
welfare of oil importing countries. First, we uncover that the extent of social welfare loss from
oil price increase depends on the nature of shocks underlying oil price dynamics. Second,
speculative oil demand shocks induce a large welfare loss for consumers. This is mainly the
result of the very nature of oil market speci…c shocks which re‡ect expectation shift of agents
in the physical oil market and are unanticipated by domestic agents. Third, the resulting
social wefare loss that stems from oil demand shocks is extremely low. Indeed, the rise in
demand that is at the origin of the oil price increase - re‡ecting the endogenous nature of oil
price dynamics with respect to economic activity - might compensate enterily the resulting
welfare loss. Forth, in the line with the recent …ndings in the literature, we uncover that
welfare loss that results from oil supply shocks is less severe compared to speculative demand
shocks.
Therefore, we uncover that welfare loss resulting from an increase of crude oil price is less
pronounced with oil fundamental shocks than oil speculative demand shocks. More precisely,
fundamental shocks from physical supply and demand conditions are largely anticipated by
domestic agents compared to speculative ones. In consequence, the welfare cost is lower when
22
the fundamental component of the oil price is dominant, since households and …rms usually
smooth their consumption and their use of re…ned products. However, when speculative
shocks occur, evolution of the oil price seems to be more uncertain and then future evolution
less predictable leading to more impact on welfare.
23
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24
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25
A
The model
We consider a country that is populated by four types of agents: (1) home …rms that are
composed of a continuum of monopolistic competitive …rms in the unit interval [0; 1] indexed
by f that produce non-oil intermediate goods, a continuum of oil-importing …rms in the unit
interval [0; 1] indexed by f that imports crude-oil in the international market and behave
monopolistically when setting re…ned-oil prices, and a …nal good …rms that bundles non-oil
and re…ned-oil intermediate goods to produce homogeneous goods to be used in consumption,
investment and government purchases, (2) households h 2 [0; 1] supposed to be a monopolistic
supplier of individual labor indexed by L(h), (3) a government, (4) and a central bank.
In line with the balanced-growth path theory, we assume that real variables share the
same evolution as the labor-augmenting technology process Zt . The latter is assumed to
evolve according to:
gZ;t =
Zt
Zt 1
where speci…cation of gZ;t will determine the nature, deterministic or stochastic, of the growth
trend. Therefore, to render the model stationary, we scale real variables by Zt and nominal
variables by the consumer price level Pt . This transformation leads to the intensive form
representation of the economy that has a well-de…ned steady-state. Concerning notation,
variables expressed in intensive form are represented by lower-case letters. For instance,
ct = Ct =Zt and pH;t = PH;t =Pt represent respectively the stationary level of consumption and
relative price of domestic goods. However, there are some noteworthy exception when scaling
the level of capital and wage. Given the predetermined nature of the capital stock and the
convention that Kt represents the stock of capital at the end of period, the stationary level of
capital stock is de…ned as kt = Kt =Zt .57 Moreover, given the assumption that nominal wage
evolves in line with labor-augmenting productivity growth, it is necessary to scale it both
with Zt and Pt . That is, stationary level of real wage is de…ned as wt = Wt =Zt Pt . Similarly,
the stationary level of real domestic bond is de…ned as bt = Bt =Zt Pt . Finally, it is important
to note that the level of hours worked Lt is already stationary and no further transformation
is needed.
57
With the notation of capital stock "in the begining of the period", we need to scale it by lagged level of
labor-augmenting productivity. That is, stationary level of capital stock is de…ned as kt+1 = Kt+1 =Zt .
26
A.1
Households
We follow Christiano et al. (2005) and Stähler and Thomas (2012) and assume that the law
of motion for capital is given by:
kt = (1
where
I
t
)gZ;t1 kt
1
+
I
t
1
S gZ;t
is de…ned to be the investment shock, and S ( ) =
it
it
it
(8)
1
gZ;t itit 1
I
2
gZ
2
is a positive
cost function for changing the level of investment which has the following properties: S(1) = 0,
S 0 (1) = 0 and S 00 (1) > 0. In turn, gZ represents the steady-state gross rate of the labouraugmenting productivity growth gZ;t and
I
> 0 represents the investment adjustment cost
parameter.
Each period, individual households consume a bundle of …nal good ct (h), invest a bundle
of good it (h) to increase their stock of capital and buy or sell nominal bond issued by the
government bt (h). In turn, they receive each period factor income in form of dividends divt (h)
from home and import intermediate …rms, return on real e¤ective capital stock rtk minus the
cost associated with variations in the degree of capital utilisation ut , labor income wt (h) and
lump-sum tax or transfer tt , and receive or pay interest on nominal bonds. Therefore, budget
constraint of an individual household is given by:
ct (h) + pI;t it (h) + bt (h) = inct (h) +
Q
t 1 Rt 1 (gZ;t
where pI;t = PI;t =Pt is the relative price of investment good,
to the presence of domestic …nancial intermediation,
t
Q
t
t)
1
bt
1 (h)
(9)
is the risk premium shock due
= Pt =Pt
1
rate and Rt represents the gross nominal interest rate. The variable
is the gross CPI in‡ation
Q
t
measures shocks to the
domestic bonds risk premium over the risk-free rate of the central bank due to the presence
of domestic …nancial intermediation. Moreover, inct (h) represents the individual household’s
total income and is given by:
inct (h) = divt (h) + rtk ut
where
(ut ) gZ;t1 kt
1 (h)
+ wt (h)Lt (h) + at (h)
tt
(ut ) is the cost associated in changing the degree of capital utilisation ut with
0. Formally, we follow Christo¤el et al. (2008) and assume that:
(ut ) =
u;1 (ut
1) +
27
u;2
2
(ut
1)2
(1) =
In turn, at (h) is a net cash in‡ow from participating in a state-contingent securities which
guarantees identical wage-income and optimal allocations in equilibrium across households,
namely under staggered wage setting with households supplying di¤erentiated labor.58
A.1.1
Optimization problem
Taking into account the assumption of perfect insurance market, each individual household
chooses fct+k ; bt+k ; kt+k ; it+k ; ut+k g1
k=0 to maximize the discounted futur value of its utility
(1) subject to its budget constraint (9) and the law of motion for capital (8). The …rst order
conditions of this maximization problem is standard and are given by:
t
B
t
=
hgZ;t1 ct
ct
t+1
1 = Et
t
t+1
Qt = Et
t
pI;t = Qt
Et
rtk
=
0
I
t
1
(
Qt+1
1
(10a)
1
(gZ;t+1
t+1 )
1 Q
t Rt
h
1
k
gZ;t+1
rt+1
ut+1
S gZ;t
I
t+1
it
it
t+1
(10b)
(ut+1 ) + (1
S 0 gZ;t
1
S 0 gZ;t+1
t
it
it
it+1
it
gZ;t
1
gZ;t+1
)Qt+1
it
it
1
it+1
it
i
+
)
(10c)
(10d)
2
(10e)
(ut )
where Qt is the marginal value of capital also interpreted as the "marginal Q" of Tobin.
A.1.2
Wage setting
Households are assumed to supply monopolistically labor to domestic intermediate good …rms.
Each period, a constant fraction (1
W)
of households are able to adjust their real wages.
They choose w
~to (h) that maximize their lifetime utility (1) subject to budget constraint (9)
and to labor demand from domestic intermediate good …rms that is given by:
Lt+k (h) =
wt+k (h)
wt+k
1+ W;t+k
W;t+k
Lt+k
58
It implies perfect insurance markets and that in equilibrium, household’s individual variables Xt (h) for
X = fc; L; k; w; b; divg will be equal to the corresponding aggregate variables Xt .
28
The elasticity of substitution among di¤erent types of labor
W;t+k
is assumed to be time-
varying and to evolve randomly according to
ln (1 +
where
W;t
W;t )
= ln (1 +
W)
+
W;t
denotes the wage markup shock and
where
W;t
,! i.i.d N 0;
2
W
denotes the steady state labor elasticity
W
of substitution. In turn, whenever households are not allowed to adjust their contracts, wage
is indexed to last period CPI in‡ation rate
= Pt
t 1
1 =Pt 2
(Erceg et al., 2000; Smets
and Wouters, 2003; and Adolfson et al., 2007) and period t monetary authority’s possibly
time-varying gross in‡ation objective
t
according to the following indexation rule:
w
wt (h) =
t 1
1
t
W
wt
1 (h)
t
where
w
denotes the indexation parameter of wages to past in‡ation. The …rst order condi-
tions to this optimization problem yields the following expression of wage setting equation:
w
~to =
1
fW;t
(11)
2
fW;t
where
1
fW;t
=
1+
1 B L
W;t t t ({w;t Lt )
2
fW;t
=
1
W;t {w;t Lt
t
+
1
(1 + W;t ) + W Et fW;t+1
n
o
1 W
1 2
W
E
(
)
f
t+1
W t
W;t+1
t
t+1
We assume that there exists a dispersion between individual wages (Schmitt-Grohe and
Uribe, 2007; and Christo¤el et al., 2008). Thus, individual and aggregate labor are linked
R1
according to 0 Lt (h)dh = {w;t Lt where {w;t is a measure of wage dispersion that is de…ned
as:
{w;t = (1
W)
w
~to
wt
1+ W;t
W;t
w
+
W
t 1
1
t
t
W
wt 1
wt
!
1+ W;t
W;t
{w;t
1
(12)
Finally, given that all households that are allowed to adjust wage each period choose the
same level of optimal wage w
~to whilst those that do not adjust index wage to past CPI in‡ation
and central bank’s in‡ation objective, the expression of aggregate real wage index is de…ned
29
as:
2
wt = 4
A.2
w
W
t 1
1
t
W
wt
t
1
!
1
W;t
~to )
W ) (w
+ (1
1
W;t
3
W;t
5
(13)
Intermediate Firms
In the domestic market, there exist two types of intermediate-good …rms that behave as
monopolistic suppliers of their di¤erentiated intermediate-goods: a continuum of non-oil
intermediate-good …rms ht (f ) which produce a di¤erentiated non-oil intermediate-goods that
are sold domestically to …nal-good …rms and a continuum of local retailer …rms ot (f ) that
import crude-oil in international market and sell it to …nal-good …rms. It is assumed that the
number of …rms lies in the unit mass f 2 [0; 1].
A.2.1
Non-oil intermediate good …rms
Non-oil intermediate good …rms use both labor Lt (f ) and e¤ective capital stock k~t (f ) to
produce output according to the following constant returns to scale technology:
a
t
ht (f ) =
a
t
h
i
k~t (f )
H
[Lt (f )]1
H
(14)
is the aggregate productivity shock and
a …xed cost. To choose the optimal
level of factors of production Lt (f ) and k~t (f ), …rms minimize real cost expressed in terms of
where
the relative domestic producer price index (PPI) pH;t = PH;t =Pt subject to the production
function (14) and take as given the PPI-adjusted real wage wt =pH;t and the rental cost of
capital rtk . The solution to this cost minimization problem yields the standard expressions of
the capital-labor ratio and marginal cost. That is,
k~t (f )
Lt (f )
=
M CH;t (f ) =
H
1
1
a
t
H
wt =pH;t
k~t
=
k
Lt
rt
wt =pH;t
1
H
1
H
(15a)
rtk
H
= M CH;t
(15b)
H
It mainly shows that the capital-labor ratio and marginal cost are identical across intermediate
…rms given that the right-hand side of the equations does not depend on individual …rm
characteristics. Moreover, non-oil intermediate …rms are assumed to be a monopilistic supplier
of their good. They o¤er goods to meet demand (18) from …nal good …rms and set prices
30
pH;t (h) in staggered fashion à la Calvo (1983). That is, each period, a constant fraction
(1
H
H)
of randomly selected …rms are able to adjust prices p~oH;t (f ) whilst a constant fraction
set current prices in function of past domestic PPI in‡ation
period t in‡ation objective of monetary authority
rule:
1
t
H
H;t 1
pH;t (f ) =
t
H;t 1
= PH;t
1 =PH;t 2
and
according to the following indexation
H
pH;t
1 (f )
t
Firms that are allowed to change prices maximize the discounted sum of their expected
pro…ts subject to …nal good …rms’ demand (18) and the expression of marginal cost (15b).
Price setting maximization problem yields the following …rst order condition that characterizes
domestic intermediate good …rm’s optimal pricing decision:
p~oH;t
pH;t
=
1
fH;t
2
fH;t
where
1
fH;t
=
t {H;t ht
p
H;t
2
fH;t
=
t {H;t ht
p
H;t
where the term 1 +
p
H;t
1
1
p
H;t
1+
+
H Et
M CH;t +
n
H
H;t
1 H
t+1
H Et
(
1
fH;t+1
H;t+1 )
1
2
fH;t+1
o
denotes the time-varying mark-up of prices over marginal costs at
domestic intermediate-goods level and is assumed to evolve according to the following rule:
ln 1 +
where
p
H;t
p
H;t
= ln 1 +
p
H
p
H;t
+
where
p
H;t
iid N 0;
2
p
H
is a domestic good markup shock or domestic …rm cost-push shock. As for house-
holds wage setting, we assume that there exists a dispersion between individual producer
prices. Therefore, individual and aggregate intermediate good prices are linked according to
R1
0 pH;t (f )df = {H;t pH;t where {H;t is a measure of non-oil intermediate good price dispersion
that is de…ned as:
{H;t = (1
H)
p~oH;t
pH;t
p
1+
H;t
p
H;t
H
+
H;t 1
1
t
H
H;t
H
!
p
1+
H;t
p
H;t
{H;t
1
Finally, given that all …rms that are allowed to adjust price each period choose the same level
31
of optimal price p~oH;t whilst those that do not adjust index price to past CPI in‡ation and
central bank’s in‡ation objective, the aggregate non-oil producer price price index is de…ned
as:
2
pH;t = 4
A.2.2
1
t
H
H;t 1
H
pH;t
H
1
t
!
1
p
H;t
+ (1
H)
1
p
H;t
p~oH;t
3
p
H;t
5
Oil intermediate good …rms
Oil retailers are assumed to behave as a monopolistic …rm when setting their home currency
price of oil p~oO;t . They set prices in staggered fashion à la Calvo (1983) where only a fraction
(1
O)
of randomly selected oil-importing …rms is able to set new prices p~oO;t each period.
In turn, the fraction
O
of importing …rms that keeps their prices unchanged are assumed
to simply follow an indexation rule that is function of the last period CPI in‡ation and the
in‡ation target of the monetary authority. That is,
1
t
O
O;t 1
pO;t (f ) =
O
pO;t
1 (f )
t
Oil importing …rms that are allowed to adjust prices maximize the discounted sum of their
expected pro…ts subject to …nal good …rms’ demand (19) and the expression of marginal
cost (5). Price setting maximization problem yields the following …rst order condition that
characterizes oil importing …rms’optimal pricing decision:
p~oO;t
pO;t
=
1
fO;t
2
fO;t
t {O;t ot
1
p
O;t
t {O;t ot
1
p
O;t
1+
+
p
O;t
O Et
n
M CO;t +
O
O;t
1 O
t+1
O Et
(
n
o
1
fO;t+1
1
O;t+1 )
2
fO;t+1
o
where
1
fO;t
=
t {O;t ot
p
O;t
2
fO;t
=
t {O;t ot
p
O;t
1
1
1+
+
p
O;t
O Et
M CO;t +
n
O
O;t
1 O
t+1
O Et
(
1
fO;t+1
O;t+1 )
1
2
fO;t+1
o
As for the domestic intermediate good …rms, {O;t represents the price dispersion across re…nedoil …rms and the term 1 +
p
O;t
denotes the time-varying mark-up of prices over marginal
costs at the re…ned-oil intermediate-goods level. Moreover, given that …rms that are able to
32
adjust choose the same prices p~oO;t , aggregate re…ned-oil price index pO;t is de…ned as:
2
pO;t = 4
A.3
A.3.1
1
t
O
O;t 1
O
pO;t
O
t
1
!
1
p
O;t
+ (1
O)
1
p
O;t
p~oO;t
3
p
O;t
5
Final good …rms
Final private consumption, investment and public consumption goods
Final private consumption good …rms produce homogeneous goods qtC using a bundle of nonC
oil hC
t and oil ot intermediate-goods. The production function that transforms intermediate
goods into …nal output is given by:
qtC
where
C
= (1
C)
1
C
hC
t
C 1
C
+
1
C
C
o•C
t
C 1
C
C
C 1
denotes the constant elasticity of substitution between non-oil and oil intermediate
goods, and
C
represents the weight of energy in the production process of …nal private
consumption goods.
The bundle of non-oil and oil inputs are respectively an aggregation of a continuum of
di¤erentiated home-produced and oil-imported intermediate goods. The aggregation technology is assumed to be a CES function as is standard in the literature. Therefore, taken as
given the price of domestic pH;t (f ) and oil-imported pO;t (f ) intermediate gods, …rms optimal
allocation of di¤erentiated inputs that minimizes their total expenditures yields respectively
the following demand for individual domestic and oil-imported intermediate goods:
hC
t (f ) =
oC
t (f ) =
pH;t (f )
pH;t
pO;t (f )
pO;t
p
1+
H;t
p
H;t
p
1+
O;t
p
O;t
hC
t
oC
t
In turn, the optimal allocation of expenditure between the bundle of non-oil hC
t and oilC
imported oC
t intermediate goods to produce …nal private consumption-good qt is given by:
33
hC
t
= (1
o•C
t
C)
p•C
O;t
=
C
pt
pH;t
pt
! C
C
qtC
(16a)
qtC
(16b)
where the adjusted oil aggregate price indices p•C
O;t is given by:
p•C
O;t
"
= 1
C 0
t
C
t
C
oC
t =qt
C
oC
t 1 =qt 1
#
1
pO;t
whereas the aggregate consumption price index is given by:
h
pt = (1
1
C ) (pH;t )
C
+
C
p•C
O;t
1
C
i
1
1
C
(17)
Final investment-good …rms have the same structure as …nal consumption good …rms.
They produce homogeneous goods qtI using a bundle of non-oil hIt and oil oIt intermediategoods. In turn, …nal public consumption good qtG are produced using only a bundle of domestic
intermediate goods hG
t in contrast to private consumption and investment goods.
A.3.2
Aggregate demand of intermediate goods
Aggregate demand of individual domestic and oil-imported intermediate goods are obtained
by aggregating individual demand across …nal good …rms. Therefore, total aggregate demand
for individual domestic intermediate goods is given by:
ht (f ) =
pH;t (f )
pH;t
p
1+
H;t
p
H;t
ht
(18)
I
G
C
I
G
where ht (f ) = hC
t (f ) + ht (f ) + ht (f ) and ht = ht + ht + ht . In turn, total aggregate
demand for individual oil-imported intermediate goods is given by:
ot (f ) =
pO;t (f )
pO;t
34
p
1+
O;t
p
O;t
ot
(19)
I
C
I
where ot (f ) = oC
t (f ) + ot (f ) and ot = ot + ot .
A.4
Authorities
A.4.1
Government
Each period, the government is subject to the following budget constraint:
bdt + tt =
Q
t 1 Rt 1 (gZ;t
t)
1 d
bt 1
+ gt
(20)
where gt is the government spending commonly de…ned in the litterature. Without loss of
generality and given that detailed …scal policy analysis is beyond the scope of this paper,
government budget balances each period through lump-sum transfer to households. That is,
if government run de…cit, it will be …nanced by lump-sum tax (tt > 0). In turn, if government
run surplus, it will be rebated to households as a lump-sum transfer (tt < 0). Moreover, we
assume that public spending is determined exogenously and evolves according to:
ln gt = (1
A.4.2
G ) ln g
+
G ln gt 1
G
t
+
(21)
Central bank
To close the model, let us assume that monetary authority follows an instrument rule rather
than optimizing a speci…c loss function. Monetary authority adjust nominal interest rate in
response to deviation of headline CPI in‡ation from its target and to output gap. Following
Smets and Wouters (2003), policy maker adopts the following interest rate rule:
Rt
=
R
Rt 1
R
R
r
t
yt
y
t
where y represents the steady-state output,
and
t
= ln
t
ry 1
R
t
R
r
yt
y
exp(
yt
1
iid N 0;
2
R
represents the headline CPI in‡ation objective. The latter is assumed to
t
t
(22)
is a monetary policy shock
follow a …rst-order autoregressive process
where
R
t )
=
t 1
+
t
where
represents the in‡ation targeting shock.
35
t
iid N 0;
2
A.5
Market clearing
Labor clears when the aggregate labor supply of households is equal to the aggregate labor
demand of intermediate …rms. In a similar way, capital market clears when the e¤ective use
of capital services equals demand from intermdiate …rms in di¤erent sectors. For intermediate
good …rms, market clears when the supply of their products equals domestic demands in (18)
and (19). Moreover, aggregating over domestic non-oil intermediate good …rms f yields the
aggregate real ressource of the economy that consists of non-oil goods ht . That is,
yt = {H;t ht
which in nominal term is de…ned as:
py;t yt = pH;t ht
(23)
For …nal good …rms, market clears when supply of …nal goods equals demand. That is,
qtC
= ct
qtI
= it +
(ut ) gZ;t1 kt
(24)
1
qtG = gt
From the aggregate ressource constraint (23) and the optimal allocation of expenditure beI
G
C I
tween domestic (hC
t ; ht ; ht ) and oil-imported (ot ; ot ) bundle de…ned in (16), one derive the
following aggregate ressource constraint:
pY;t yt = ct + pI;t it +
(ut ) gZ;t1 kt
1
+ pH;t gt
pO;t
where
c
t
i
t
(1
=
1
c
t
(
1
=
1
i
t
36
c)
t
C
C
c )0 ot =qt
t oC =q C
t 1 t
1
i
I
I
i 0 ot =qt
t oI =q I
t 1 t
1
c C
t ot
+
i I
t ot
(25)
B
Estimation procedure
B.1
Calibration
As for Smets and Wouters (2007), real variables are assumed to evolve along deterministic
balance growth path at annual constant rate of 1:6 percent. It corresponds to quarterly
constant growth rate of 0:4 percent with the parameter gzc hence, …xed at 1:004. The discount
factor
is set so as to obtain a steady state nominal interest rate of 2:5 percent on annual
basis. The depreciation rate of capital
is …xed at standard value of 0:025 that implies an
annual rate of depreciation of 1 percent. The steady state government spending ratio gy is
set at 18 percent.
The share of capital
in the non-oil intermediate-good …rms’production function is kept
…xed at standard value of 0:30. It roughly implies a steady-state share of labor income relative
to intermediate output of 70 percent. The steady-state wage mark-up
W
is set to be equal to
0:5 as in Smets and Wouters (2003, 2007). For price mark-up in non-oil and oil intermediategood …rms, we follow Christo¤el et al. (2008) and set
p
H
and
p
O
to be equal to 0:35.
We assume as in Bodenstein et al. (2011) that the steady state oil share in total consumption of households
C
and that used in production of …nal investment goods
I
are …xed at
0:023 and 0:028, respectively. These values correspond to a total oil share of 4:2 percent in
the U.S. economy.
B.2
Prior
In the following, we present the prior distribution of the remaining parameters to be estimated.
Namely, priors for each parameter are de…ned so as to cover a wide range of values used in
the literature. The prior distribution is depicted in Table 1.
The behavioral parameters are assumed to follow either a normal, gamma or beta distribution. The parameter h that describes the habit preference of households is assumed to
be beta distributed with mean that is set at 0:7 as in Smets and Wouters (2003, 2007). As
is standard in the literature, we assume that the inverse of intertemporal elasticity of labor
supply
follows a normal distribution with a mean of 2. However, the standard error is set
at 0:75 so as to cover a wide range of values used both in the micro- and macro-literature.
The constant elasticity of substitution between non-oil and oil intermediate goods in the
production function of …nal consumption (
C)
and …nal investment ( I ) goods is assumed to
follow a gamma distribution. The mean is set to 0:4 according to the value found in Bodenstein
37
et al. (2011) with a standard deviation equal to 0:25. In a similar vein, we follow Christo¤el
et al. (2008) and set the investment cost function parameter in the law of motion for capital
I,
the oil adjustment cost parameters in the production process of …nal good consumption
C
and that of …nal good investment
I
to follow gamma distribution with mean 5:0, 2:5, 2:5
and standard deviation 0:50, 1:0, 1:0, respectively.
The Calvo and indexation parameters are assumed to follow beta distribution both for
intermediate-good prices and wage. We assume as in Smets and Wouters (2007) that the
average durations of wage and price nominal rigidity last two quarters, corresponding to a
value of Calvo probability of 0:5. However, the standard error is set to 0:10 in order to cover
a wide range of value generally used in the literature. The indexation parameters in turn
are also assumed to follow a beta distribution with mean 0:5 but with rather large value of
standard error equal to 0:15.
The priors of parameters describing monetary policy reaction function are quite standard.
We mainly follow Smets and Wouters (2007). Namely, the interest rate smoothing parameter
R
is set to follow a beta distribution with mean and standard deviation equal to 0:75 and
0:10, respectively. The rest of the monetary policy reaction function parameters are assumed
to follow a normal distribution.
For the autoregressive parameters of the shock processes, the priors are set uniformly and
are assumed to be a beta distribution with mean 0:5 and standard deviation 0:20, following
Smets and Wouters 2007. Similarly, the standard errors of the innovations are uniformly given
a lose prior and thus, assumed to follow an inverted gamma distribution with a mean of 0:10
and 2 degrees of freedom.
For parameters
phy
o
and
dde
o
that characterize the di¤erent natures of oil price (supply,
demand and market speci…c) shocks, they are assumed to be beta distributed with mean 0:5.
The standard error is set to 0:20 in order to cover a wide range values, re‡ecting the little
prior information available for these parameters.
38
B.3
Data description
The data used to estimate the deep parameters of the model are de…ned as follow:
ytdata = ln((gdpt /civt )/(deft /100))
cdata
= ln((const /civt )/(deft /100))
t
idata
= ln((invt /civt )/(deft /100))
t
wrtdata = ln(waget /(deft /100))
pdata
= ln(opricet /(deft /100))
O;t
odata
= ln(oprodt )
t
idata
= fedfundt
t
data
t
= deft /deft-1
where,
gdp: United States, Gross Domestic Product, Total, Current Prices, Seasonally Adjusted, Annual Rate, USD, Source: U.S. Bureau of Economic Analysis (BEA).
cons: United States, Expenditure Approach, Personal Consumption Expenditures, Total, Seasonally Adjusted, Annual Rate, USD, Source: U.S. Bureau of Economic Analysis
(BEA).
inv: United States, Expenditure Approach, Gross Private Domestic Investment, Fixed
Investment, Total, Seasonally Adjusted, Annual Rate, USD, Source: U.S. Bureau of
Economic Analysis (BEA).
wage: United States, Earnings, Average Hourly Earnings, Production & Non-Supervisory
Employees, Total Private, Seasonally Adjusted, USD, Source: U.S. Bureau of Labor Statistics (BLS).
oprice: United States Crude Oil Imported Acquisition Cost by Re…ners, Dollars per
Barrel, Source: Energy Information Administration. Before 1974: Crude Oil, Average of U.K. Brent, Dubai & West Texas Intermediate, End of Period, USD, Source:
Macrobond.
oprod: World BP Statistical Review of World Energy, Oil, Production, Barrels, Source:
39
Macrobond. Before 1973Q1: World Oil Production - World VOLN, Source: Datastream
(code: WDOPPOI).
civ: United States, Population Level, Civilian noninstitutional population, 16 years and
over, Seasonally Adjusted, Source: U.S. Bureau of Labor Statistics (BLS). Before 1976:
Federal Reserve Economic Data (FRED).
def : United States, Consumer Price Index, All Urban Consumers, All Items, , Seasonally Adjusted, U.S. Bureau of Labor Statistics (BLS), 2009=100.
fedfund: E¤ective Federal Funds Rate, Percent, Quarterly, Not Seasonally Adjusted,
Source: Federal Reserve Bank of St. Louis.
In this study, we adopt a balanced-growth path speci…cation. Therefore, it is necessary to
provide the observation equations that link the data to the observed variables of the model.
To that end, let us denote with upper script "obs" variables that are observed in the model.
The observation equation is therefore de…ned as:
ytobs = ytdata
ytdata
1 = ln(yt )
ln(yt
cobs
= cdata
t
t
cdata
t 1 = ln(ct )
ln(ct
iobs
= idata
t
t
idata
t 1 = ln(it )
ln(it
wrtobs = wrtdata
oobs
= odata
t
t
wrtdata
1 = ln(wrt )
odata
t 1 = ln(ot )
ln(ot
1)
1)
1)
+ ln(gzc)
+ ln(gzc)
+ ln(gzc)
ln(wrt
1)
1)
+ ln(gzc)
+ ln(gzc)
data
pobs
O;t = pO;t = ln(pO;t )
Rtobs = ln(1 + (idata
=400)) = ln(Rt )
t
obs
t
= ln(
data
)
t
= ln(
t)
where gzc denotes the steady value of the growth rate gZ;t of the labor-augmenting technology
process. It is worth noting that representing variables in terms of logarithm permits to take
log-linear approximation of the model around steady state. It is done by using the identity
xt = exp(~
xt ) where x
~t = ln(xt ) for xt = fyt ; ct; : : :g, and by letting Dynare linearize the model
around the steady state value of x
~t .
40
C
Tables
Table 1: Prior and Posterior estimation
Parameter
h
C
I
I
C
I
W
H
O
W
H
O
R
r
ry
r y
B
L
G
Q
I
a
o;d
o;s
PO
phy
o
dde
o
Prior
Posterior
Distribution Mean(Std/Df)
Mean
Mode
IC(10%)
Behavioral parameters
Beta
0:70(0:10)
0:8309
0:8277
0:7965
Normal
2:00 (0:75)
0:5904
0:5000
0:5000
Gamma
0:40 (0:25)
0:5288
0:8515
0:0847
Gamma
0:40 (0:25)
0:2144
0:1636
0:0375
Gamma
5:00 (0:50)
4:6655
4:7656
4:3156
Gamma
2:50 (1:00)
3:0364
2:9556
2:1005
Gamma
2:50 (1:00)
1:6179
1:7594
0:8821
Price and Wage setting parameters
Beta
0:50 (0:10)
0:6741
0:6709
0:6180
Beta
0:50 (0:10)
0:9490
0:9500
0:9477
Beta
0:50 (0:10)
0:4643
0:4091
0:3261
Beta
0:50 (0:15)
0:7427
0:4994
0:5987
Beta
0:50 (0:15)
0:5924
0:5514
0:5414
Beta
0:50 (0:15)
0:5408
0:7102
0:4399
Monetary Policy parameters
Beta
0:75 (0:10)
0:9395
0:9576
0:9198
Normal
1:50 (0:25)
1:4940
1:3873
1:2938
Normal
0:125 (0:05)
0:1993
0:2539
0:1431
Normal
0:125 (0:05)
0:3048
0:2832
0:2711
Autoregressive parameters
Beta
0:50 (0:20)
0:8858
0:9023
0:8081
Beta
0:50 (0:20)
0:8030
0:8046
0:7585
Beta
0:50 (0:20)
0:9945
0:9930
0:9911
Beta
0:50 (0:20)
0:1236
0:0978
0:0301
Beta
0:50 (0:20)
0:6406
0:6194
0:5218
Beta
0:50 (0:20)
0:9034
0:9223
0:8714
Beta
0:50 (0:20)
0:0944
0:0461
0:0252
Beta
0:50 (0:20)
0:4271
0:2545
0:1565
Beta
0:50 (0:20)
0:9847
0:9840
0:9732
Beta
0:50 (0:20)
0:9807
0:9824
0:9666
Oil price shocks
Beta
0:50 (0:20)
0:2234
0:2482
0:0784
Beta
0:50 (0:20)
0:7995
0:7829
0:7104
41
IC(90%)
0:8695
0:7054
0:8731
0:3779
5:0100
3:9242
2:3816
0:7361
0:9500
0:5964
0:8939
0:6459
0:6419
0:9596
1:6894
0:2538
0:3403
0:9701
0:8548
0:9980
0:2104
0:7461
0:9368
0:1610
0:6791
0:9962
0:9962
0:3669
0:8774
Parameter
G
B
Q
I
L
A
PO
O;d
O;s
R
D
Prior
Posterior
Distribution
Mean(Std/Df)
Mean
Mode
IC(5%)
Technology and preferences innovations
Inv. Gamma
0:10(2:00)
0:0339
0:0342
0:0303
Inv. Gamma
0:10(2:00)
0:0239
0:0223
0:0178
Inv. Gamma
0:10(2:00)
0:0308
0:0296
0:0233
Inv. Gamma
0:10(2:00)
0:0415
0:0417
0:0340
Inv. Gamma
0:10(2:00)
0:1515
0:1429
0:1035
Inv. Gamma
0:10(2:00)
0:0187
0:0174
0:0147
Oil shocks
Inv. Gamma
0:10(2:00)
0:8750
0:7486
0:4833
Inv. Gamma
0:10(2:00)
0:0604
0:0452
0:0250
Inv. Gamma
0:10(2:00)
0:0213
0:0212
0:0194
Monetary policy innovations
Inv. Gamma
0:10(2:00)
0:0119
0:0118
0:0118
Inv. Gamma
0:10(2:00)
0:0129
0:0123
0:0118
Graphics
42
IC(90%)
0:0376
0:0300
0:0400
0:0489
0:1961
0:0223
1:2085
0:0967
0:0232
0:0120
0:0141