How Oil Shocks Propagate: Evidence on the
Monetary Policy Channel*
Wataru Miyamoto†Thuy Lan Nguyen‡

Dmitriy Sergeyev§

December 10, 2023

Abstract
Using high-frequency responses of oil futures prices to prominent oil market news,
we estimate the effects of oil supply news shocks when systematic monetary policy
is switched off by the zero lower bound (ZLB) and when it is not (normal periods) inJapan, the United Kingdom, and the United States. We find that negative oil supply
news shocks are less contractionary (and even expansionary) at the ZLB compared tonormal periods. Inflation expectations increase during both periods, while the shortnominal interest rates remain constant at the ZLB, pointing to the importance of monetary policy for oil shock propagation.

Keywords: oil price shocks, high-frequency identification, zero lower bound, systematic
monetary policy
JEL Classification: E5, E7, G4* The views expressed in this paper are those of the authors and do not represent the views of the Fed-

eral Reserve Bank of San Francisco or the Federal Reserve System. Any errors are ours. We thank Regis
Barnichon, Christiane Baumeister, Martin Bodenstein, James Cloyne, John Cochrane, Riccardo Degasperi,
Laurent Ferrara, Yuriy Gorodnichenko, Oscar Jorda, Diego Kanzig, Neil Mehrotra, Dmitry Mukhin, Emi
Nakamura, Maurice Obstfeld, Carolin Pflueger, Ricardo Reis, Jon Steinsson, Ludwig Straub, Ivan Werning, Dan Wilson, Christian Wolf, and seminar and conference participants at the Universitat Autonoma
de Barcelona, Bocconi University, Texas A&M University, UC Berkeley, the 2023 Barcelona Summer Forum, Copenhagen Business School, 2023 CSEF-IGIER Symposium, Banque de France, 22nd Macro FinanceWorkshop at the University of Chicago, 2023 NBER Summer Institute, NYU Abu Dhabi, 2022 System Energy meeting, 2023 SED, Trinity College Dublin, 2023 T2M, Workshop on Emirical Macroeconomics fortheir helpful feedback and discussions. Chiara Bargellesi, Ethan Goode, Roberto Patino, and Aren Yalcin
provided excellent research assistance.
† The University of Hong Kong, wataru.miyamoto1@gmail.com.
‡ Federal Reserve Bank of San Francisco and Santa Clara University, thuylan.nguyen00@gmail.com.
§ Bocconi University, Department of Economics, dmytro.sergeyev@unibocconi.it.

1Introduction

Oil price changes are among the most prominent macroeconomic disturbances. They arelarge and sudden, especially when caused by wars involving oil producers. Oil pricechanges affect all countries at the same time because crude oil is an internationally tradedcommodity. Moreover, according to the conventional supply-side view, it is difficult formonetary policy to stabilize both output and inflation in the face of oil price changes because inflation and output move in opposite directions. Recent events, such as the oil
price increase in 2021-22, the 2022 Russian invasion of Ukraine, and the burst of high inflation worldwide in 2021-22, reignited interest in exploring the impact and mechanismsof the effects of oil price changes.
The fact that most post-WWII recessions in the United States followed oil price spikes
has inspired a vast empirical literature on oil shock effects (Hamilton, 1983; Kilian, 2009;
Kilian and Murphy, 2012; Baumeister and Hamilton, 2019; Kanzig, 2021). This literature
has documented substantial effects of oil shocks on macroeconomic variables, relying
on a variety of econometric approaches to identify oil shocks. At the same time, howexactly oil shocks propagate is still unclear. Theoretical literature proposes aggregate
supply channels, such as variations in the cost of production, which can be amplified
by markup endogeneity (Rotemberg and Woodford, 1996) and production network nonlinearities (Baqaee and Farhi, 2019), as well as aggregate demand channels, such as theinteraction between nominal price stickiness and real wage rigidity (Blanchard and Gali,
2009) and the presence of financially constrained households (Chan et al., 2022; Auclert
et al., 2023).
One aggregate demand channel stands out. It stems from the observation made in
Bernanke, Gertler and Watson (1997) that most post-WWII recessions in the United States
have followed monetary policy hikes. This raises the possibility that the estimated effectsof oil shocks on real activity are also driven by systematic monetary policy reaction tothese shocks. Such logic is central in standard New Keynesian models (Woodford, 2003).
In particular, the central bank may tighten monetary policy following an oil price spike
because the inflation rate increases, or inflation expectations go up, or because the central bank fears a future inflation rate increase. Such systematic monetary policy reactions
can exacerbate the direct adverse effect of oil price spikes on output. Moreover, New
Keynesian models can imply that oil price spikes are expansionary (Eggertsson, 2008;
Bodenstein, Guerrieri and Gust, 2013), for example, if the central bank does not change
the short-term nominal interest rate following an oil price spike. Intuitively, with higher
inflation expectations and a constant nominal interest rate, the real interest rate drops,
stimulating aggregate economic activity by increasing consumption and investment de2

mand.
In this paper, we empirically evaluate the role of monetary policy in oil shock propagation. We leverage the fact that several countries have recently experienced zero lower
bound (ZLB) episodes, when the short-term nominal interest rate—a standard conventional monetary policy tool—stayed close to zero.1 This allows us to compare the effectsof oil shocks during the ZLB periods, when monetary policy did not respond actively,
and the normal periods, when the short-term nominal interest rate was not constrainedby the ZLB. Specifically, we examine how Japan, the United Kingdom, and the UnitedStates responded to oil shocks between 1975:1 and 2019:12, differentiating between the
ZLB and the normal periods.
Our primary focus is on Japan because it has the longest ZLB experience, which started
at the end of 1995. Moreover, Japan experienced several business cycles during the ZLB
periods, making it possible to average out the effects of potentially differential impactsof shocks during booms and busts. In addition, Japan was a net oil importer throughout
our sample. Looking at the data in other countries, such as the United Kingdom and theUnited States, is helpful because the ZLB periods do not coincide, which alleviates theconcern that some global factor could be responsible for results in all countries.
To extract exogenous and unexpected variation in oil prices, we build on the recent literature that uses high-frequency data to identify macroeconomic shocks (Kuttner, 2001;
Gürkaynak, Sack and Swanson, 2004; Gertler and Karadi, 2015; Nakamura and Steinsson,
2018a). In particular, we follow Kanzig (2021), who uses the changes in oil futures prices
in a tight window around the Organization of the Petroleum Exporting Countries (OPEC)
production announcements. The series of oil futures price changes then becomes an external instrument in an oil market vector-autoregression (VAR), allowing us to estimate
structural oil shocks, which we refer to as oil supply news shocks. These shocks change
oil prices on impact and oil production gradually.
Using the state-dependent local projections method (Jorda, 2005), we estimate that oil
supply news shocks are less contractionary, and at times even expansionary, in the ZLB
compared to the normal periods. In particular, in our baseline specification using monthly
data from Japan, industrial production increases by 1.3 percent after one year during the
ZLB periods following a shock that increases the oil price by 10 percent. Outside of the
ZLB periods, industrial production falls by up to 1 percent 12 months after the shock.
The differences in the two responses are statistically significant at conventional levels. It
is particularly remarkable that the increase in industrial production in response to thenegative oil shock during the ZLB periods is significantly different from zero at some
1 In practice, the short-term nominal interest can go slightly below zero. This has led researchers to referto the bound as the effective lower bound. In this paper, we will use the term ZLB to refer to the effective
lower bound.

3

horizons. The unemployment rate in Japan exhibits similar patterns with the opposite
sign: it decreases significantly in the ZLB periods, while it stays near zero or increases
outside of the ZLB. Since Japan has long periods with a zero nominal interest rate, we
also estimate the effects of oil supply shocks using quarterly macro variables. Consistent
with the results from industrial production and the unemployment rate, oil supply news
shocks cause real per capita gross domestic product (GDP), consumption, and investment
to increase in the ZLB periods and decrease (or do not change) outside of the ZLB.
To explore the relevance of the monetary policy channel, we estimate the responses of
the Bank of Japan target interest rate (the Call rate) and 5-year nominal interest rates, realized inflation, and inflation expectations. In the ZLB periods, the short-term interest rate
does not react to oil supply news shocks, and the 5-year rate increases slightly. In contrast,
during the normal periods, both the short and 5-year rates increase considerably after an
oil price increase, and these changes are statistically different from those during the ZLB
periods. Moreover, inflation expectations react more during the ZLB. These results are
consistent with the channel that works through ex ante real interest rate movements. At
the same time, we do not observe a stronger reaction of realized inflation during the ZLB
periods. In fact, realized inflation increases more in the normal periods.
Our estimated effects of oil supply news shocks in the United Kingdom and the UnitedStates are consistent with those in Japan. For example, in the United States, industrial production increases by 0.9 percent after 15 months following a shock that increases the oil
price by 10 percent. Outside of the ZLB period, industrial production falls up to 0.8 percent. The difference in the two responses is statistically significant at conventional levels,and the ZLB response is significantly above zero at the 5 percent level for multiple horizons. The unemployment rate repeats this pattern with the opposite sign. The nominalinterest rate responds more in the normal than in the ZLB periods, and both expected andrealized inflation rates respond positively in the two periods. The results in the United
Kingdom are qualitatively similar. These findings imply that the patterns obtained inJapan are not a particular feature of the Japanese economy.
We extend our main analysis in a number of ways. First, we consider alternative oil
supply shocks obtained in two prominent recent studies: Kilian (2009) and Baumeisterand Hamilton (2019). These papers rely on structural VAR identification of oil supply
shocks. We find that the differences between the responses of the Japanese economy in
the ZLB and the normal periods following oil supply shocks identified as in Kilian (2009)
are not statistically significant. This is consistent with Wieland (2019), who also used theseoil supply shocks to estimate the response of the Japanese economy during and outside of
the ZLB. At the same time, the oil supply shocks identified as in Baumeister and Hamilton(2019) produce qualitatively similar results to our baseline findings. These differences can4potentially be attributed to the fact that the oil supply shocks in Kilian (2009) do not movethe oil price significantly, while they do in Baumeister and Hamilton (2019). Second, we
estimate the responses of several other variables, such as output without oil production,exchange rates, and stock market prices, all of which exhibit differential responses acrossthe ZLB and the normal periods. We estimate the reaction of economic activity in countries that experienced near-constant nominal interest rate periods, such as Canada andthe euro area, and countries that did not experience their own ZLB episodes, and we do
not find evidence of differential responses. Third, we investigate subsample propertiesof our results and re-estimate results following a refined version of the oil supply news
shock that corrects for a potential information revelation effect (Jarociński and Karadi,
2020; Degasperi, 2021). We find largely similar results. Fourth, we measure the effects
of positive and negative oil supply news shocks, and the effects of the shocks in booms
and recessions and find no difference. Finally, we discuss the sensitivity of our results tovariations in the number of control variables used in our regressions.
The last part of the paper presents a stylized model based on Galı́ and Monacelli (2002)
and consisting of a small open economy and the rest of the world, where oil supply shocks
propagate through aggregate supply, aggregate demand (via monetary policy), and international spillovers that affect both aggregate supply and demand. We formally illustrate
the mechanisms of oil shock propagation and compare our empirical results to numericalresponses to oil supply shocks in this model.
Related literature. Our paper contributes to the literature that studies the role of monetary policy in shock propagation and, in particular, a differential impact of shocks during
the ZLB (or constant nominal interest rate periods) and the normal periods. On the aggregate demand side, Miyamoto, Nguyen and Sergeyev (2018) and Ramey and Zubairy(2018) estimated higher government spending multipliers in the ZLB periods than outside of it in Japan and the United States, respectively. Different from these papers, we
focus on the shocks traditionally attributed to aggregate supply disturbances.
We contribute to the supply-side literature by analyzing state-dependent responses
of several countries to oil shocks identified using high-frequency techniques. Bernanke,
Gertler and Watson (1997) showed that most of the U.S. macroeconomic response to oilshocks is due to a systematic monetary policy.2 Their analysis relies on the triangular
VAR identification of oil shocks and a counterfactual simulation with a fixed policy interest rate in the spirit of Sims and Zha (2006). This method aims to remove systematic
2 Hamilton and Herrera (2004) show that the quantitative importance of monetary policy in propagating

oil shocks in Bernanke, Gertler and Watson (1997) depends on the lag order of the estimated VAR. Kilianand Lewis (2011) argue that Volcker’s 1979 tightening is crucial for estimating a strong response by the Fed
to oil price shock in Bernanke, Gertler and Watson (1997).

5monetary policy effects but can be subject to the Lucas critique.3 Unlike Bernanke, Gertler
and Watson (1997), we directly estimate our results from the episodes with fixed interest
rates. Garin, Lester and Sims (2019) find that positive total factor productivity shocks, measured by Fernald (2014), are more expansionary in the ZLB than in the normal periods in
the United States. As mentioned above, Wieland (2019) finds no difference in Japanese
output reactions to oil supply shocks identified as in Kilian (2009). Our results rely on
the oil shocks identified using a high-frequency approach. Moreover, we use data fromseveral countries, which is essential when studying relatively short ZLB periods. Unlike
Garin, Lester and Sims (2019) and Wieland (2019), we find that shocks that depress aggregate supply increase output during the ZLB periods relative to the normal periods.
Finally, our findings are consistent with the indirect evidence in Datta, Johannsen, Kwon
and Vigfusson (2021). The authors estimate that oil prices and equity returns are morepositively correlated in the recent past than before and that both variables become more
responsive to macroeconomic news, consistent with the prediction of a model where the
ZLB alters the economic environment.
Our paper also speaks to the literature on unconventional monetary policies. A constant short-term nominal interest rate, which we use to define ZLB episodes, does not
logically imply that the medium- or long-term rates are constant. Swanson and Williams(2014b,a) estimate that, while the monetary policy rate is nearly constant during ZLB
episodes, the medium- and long-term rates continue to respond to macroeconomic news.
Such behavior can be caused by an active use of unconventional monetary policies, suchas quantitative easing and forward guidance. Consistent with these findings we also findthat longer term nominal interest rates respond to oil supply news shocks. However,these responses tend to be smaller during the ZLB episodes than during the normal periods. Debortoli et al. (2020) estimate a time-varying-coefficient structural VAR driven byshocks identified through the long-run and sign restrictions. They found no evidence fordifferential responses of macro variables to identified macroeconomic shocks. In contrast,
we use a high-frequency identification of oil supply news shocks and find significantly
different responses of macro variables during the ZLB and normal periods.
The rest of the paper is organized as follows. Section 2 starts by explaining how wemeasure the effects of oil supply news shocks on the aggregate economy and summarizes
the data. We then present the main results for Japan in Section 3 and the United Kingdom
and United States in Section 4. We describe our sensitivity analysis in Section 5. Section 6presents a stylized model and compares its numerical predictions to our empirical results.
Section 7 concludes. Online Appendix A lists the data sources, Appendix B and C collect
3 Wolf and McKay (2022) extend the Sims and Zha (2006) methodology by incorporating the expecta-

tions effects via additional information about the responses of economic variables to news shocks. Importantly, this method assumes that people are aware of counterfactual policy changes.

6figures omitted from the main text, and Appendix D presents model details.

2

Measurement, Data, and ZLB Definition

This section describes our empirical specification, details the data used for estimation,and concludes by defining ZLB periods.

2.1

Measurement of Oil Shock Effects

We measure the effects of oil supply news shocks in three steps: we define a daily oil
supply surprise series, use it as an external instrument in an oil market VAR to identify oil supply news shocks, and employ these shocks to estimate state-dependent local
projections.
High-frequency identification. To isolate exogenous and unanticipated changes in oil
prices, we follow Kanzig (2021) and use a high-frequency approach, which has beenused widely in monetary economics (Kuttner, 2001; Gürkaynak, Sack and Swanson, 2004;
Gertler and Karadi, 2015; Nakamura and Steinsson, 2018a). The main idea relies on theobservation that the oil market is dominated by a few large players, one of which—the
Organization of Petroleum Exporting Countries (OPEC)—is responsible for about half of
the world’s oil production. OPEC is an intergovernmental organization that coordinates
its oil production during conference meetings that end with public announcements about
oil supply changes. Asset prices, particularly oil futures prices, react immediately to theseannouncements. Hence, looking at oil futures price changes in a narrow window of one
day around OPEC announcements reveals unanticipated and arguably exogenous news
about the future oil supply.4
Our implementation closely follows Kanzig (2021). First, we extract the first principle
component of the daily price changes of the West Texas Intermediate (WTI) crude oil
futures with maturities from one to twelve months in a narrow window around the OPEC
announcements. These futures contracts are the most liquid contracts with the longest
sample size, starting in 1983. We aggregate the daily first principle component up to amonthly frequency by summing the values if there were more than one OPEC meeting
during a particular month. As Kanzig (2021), we will refer to this monthly series as the oil
supply surprise series.

4 The size of the window is motivated by the fact that the exact time of the announcement is unavailable

in the initial part of our sample.

7External instruments approach. The information contained in the OPEC announcements summarized by the oil supply surprise series is only a subset of all news about
oil supply changes affecting the oil market. In addition, this series can be subject to ameasurement error.5 As a result, we do not use the series as a shock. Instead, following
Stock and Watson (2012) and Mertens and Ravn (2013), we employ the oil supply surpriseseries as an external instrument—a variable that is correlated with the shock of interest
but not the other shocks—in an oil market VAR.
Formally, consider a VAR(p) process of the formp

Yt = C + ∑ Bl Yt−l + Ut ,l =1

where p is the number of lags, Yt is an n × 1 vector of endogenous variables, Ut is an n × 1
vector of reduced-form errors with the variance-covariance matrix Σ, C is an n × 1 vector
of constants, { Bl } are n × n matrices of coefficients. The reduced-form errors are related
to an n × 1 vector of uncorrelated structural shocks Et linearly as Ut =SEt , where S is an
unknown n × n matrix. If we order the oil supply news shocks to be the first element of
Et , the goal is to identify the first column of matrix S, which we denote as S1:n,1 .
Let zt be an external instrument, that is, the oil supply surprise series in our application. If it is a valid instrument, it must be correlated with the shock of interest, i.e.,
E [zt E1,t ] ̸= 0, where E [·] is the expectations operator, and uncorrelated with the othershocks, i.e., E [zt Ek,t ] = 0 for k = 2, 3, . . . , n. Under this assumption, we can write
S2:n,1 = E [zt U2:n,t ] /E [zt U1,t ] ,and the whole vector S1:n,1 equals ( x, xS2:n,1 )′ , where x is a normalization constant which
can take any value. We will normalize x so that the shock E1,t increases oil price on impact
by 10 percent. Having computed S1:n,1 , we obtain the oil supply news shock Eb1,t from theestimated reduced-form error terms Ubt . We will refer to these shocks as oil supply news
shocks or oil shocks, for brevity. Importantly, to be able to estimate Eb1,t , the structural shock
E1,t has to be invertible, which would allow us to recover these shocks from current andpast values of the variables entering the oil market VAR (Nakamura and Steinsson, 2018b;
Stock and Watson, 2018). In Section 3.1, we present evidence supporting the assumptionthat the shock E1,t is invertible.

5 A high-frequency identification of monetary policy shocks faces a similar challenge (Nakamura andSteinsson, 2018a). Nevertheless, in Section 5.4, we present the results based on the specification where theoil supply surprise series is used directly as a shock.

8

The state-dependent effects of oil supply news shocks. Finally, to evaluate the impactof oil supply news shocks on a variable of interest yt during and outside of the ZLB
periods, we estimate a series of regressions at each horizon h from h = 0 to H of the
form6
i
h
y
y
y
yt+h − yt−1 =It−1 · α A,h + β A,h Ptoil + ψ A,h ( L) xt−1
i
h
y
y
y
y
oil
+ (1 − It−1 ) · α B,h + β B,h Pt + ψB,h ( L) xt−1 + ϵt+h ,(1)where It−1 is the indicator variable that takes the value of one if the economy is in the ZLB
in period t − 1, and zero otherwise, and the subscripts A and B indicate the ZLB and theynormal periods, respectively, Ptoil is the log real oil price, and the controls ψ A,h ( L) xt−1 arelags of the variable of interest, the unemployment rate, and the measure of oil supply news
shock Eb1,t . We use 12 lags with monthly data and 4 lags with quarterly data. In principle,
the estimation does not require the addition of these controls when the data are infinite. In
practice, however, our sample is far from infinite. In this case, it is helpful to increase thesignal-to-noise ratio of the oil supply news shocks by removing the variation predictedby past values of the variable of interest, the variation attributed to business cycles but
unrelated to the oil supply news shocks (we achieve this by adding the unemploymentrate), and the variation attributed to past oil supply news shocks. In some cases, there are
additional controls, which we specify separately.
Moreover, instead of directly regressing the variables of interest on the oil supply news
shock Eb1,t , we instrument the log of oil price Ptoil with the shock Eb1,t . There are two main
reasons to do this. First, the shock Eb1,t is a generated regressor whose measurement error needs to be accounted for when computing standard errors. Instead, generated instruments do not require standard error correction under very general conditions, as explained in Section 6.1 of Wooldridge (2010).7 Second, an instrumental variable approachynaturally normalizes the impulse responses. Specifically, the estimated coefficients β A,hyand β B,h can be interpreted as the impulse response of variable y at horizon h to a 1 percent
change in real oil price upon impact of oil supply news shocks. We use heteroskedasticity and autocorrelation consistent (HAC) standard errors and statistics that are robust toboth arbitrary heteroskedasticity and autocorrelation. We choose automatic bandwidth
6 The variables of interest, such as industrial production, real GDP, real aggregate consumption, and real

aggregate investment are in logs, while nominal interest rates, the unemployment rate, the inflation rate,inflation expectations, and trade balance to GDP ratio are in levels, that is, we do not apply logs.
7 We compare our baselines results to those where we use the shocks E
b1,t directly in equation (1) in placeoilof the log oil price Pt . The results reported in Appendix Figure B.1 are virtually identical. Coibion and
Gorodnichenko (2012) present similar findings in a different context and argue that the generated regressor
problem is likely to be minimal when the generated regressor is a residual rather than a fitted variable froma regression.

9

selection in the estimation.
Finally, the state-dependent specification allows us to test the null hypothesis that theyyresponses are identical in the two periods, that is, β A,h = β B,h .

2.2

Data

We estimate the four-variable oil market VAR using the log levels of the following monthly
variables. The real oil price is the WTI spot oil price deflated by the U.S. consumer priceindex. For world industrial production, we use the Baumeister and Hamilton (2019) index, which covers the OECD countries plus six major economies (Brazil, China, India,
Indonesia, the Russian Federation, and South Africa). Together, these countries jointly
represent 75 percent of world’s GDP. World oil inventories are OECD petroleum stocks
from Kilian and Murphy (2014). World oil production comes from the U.S. Energy Information Administration.8 The detailed description of the data sources is in Appendix
A. Because of the availability of oil futures data, the oil supply surprise series covers ashorter period between 1983:4 and 2019:12, but the external instrument VAR uses data
between 1974:1 and 2019:12 to estimate oil supply news shocks. The VAR includes a constant term and has 12 lags.
We use monthly and quarterly macro data for three advanced countries—Japan, theUnited Kingdom, and the United States—that have experienced a sufficiently long period
where the nominal interest rate is at the ZLB. The sample period is between 1975:1 and2019:12, which corresponds to the sample of the extracted oil supply news shock Eb1,t . We
exclude the COVID pandemic by dropping data after 2019:12.

2.3

ZLB Definition

We define the ZLB periods as those when the short-term nominal interest rate—the standard instrument of conventional monetary policy—was close enough to zero that it did
not respond substantially to macroeconomic developments. In particular, the ZLB periods for Japan are October 1995 to June 2006 and January 2009 to December 2019. Thisdefinition is similar to Wieland (2019), who follows the previous literature on the timingof the ZLB spell in Japan. This period of the ZLB in Japan coincides with a 0.5 percent
cutoff before 1998 and 0.25 percent after that. We define the ZLB periods in the United
Kingdom and the United States as the months during which each country’s short-term
nominal interest rate is at or below 0.5 percent. The ZLB period in the United States was

8 Unlike Kanzig (2021), we do not directly use the U.S. industrial production and inflation rate in the oilmarket VAR. This is because the United States can exhibit a state-dependent response of these two variables.

10

Figure 1: The oil supply surprise series and oil supply news shock.
Oil Supply News ShockOil Supply Surprise Series

10

2
5

1

0

0
-1

-5

-2
-10
1985

1990

1995

2000

2005

2010

2015

2020

1980

Year

1990

2000

2010

Year

Notes: The left panel plots the oil supply surprise series from 1983:4 to 2019:12. The right panel presents the oil supply news shock
Eb1,t from 1975:1 to 2019:12, estimated using a four-variable oil VAR instrumented by the oil supply surprise series. The details are in
Section 2.1.

between 2008:11 and 2016:11.9 According to our definition, the United Kingdom experienced two ZLB episodes: 2009:4–2010:9 and 2012:2–2018:7.10 Finally, as mentioned in the
introduction, we rely only on the stance of the conventional monetary policy to define
ZLB episodes. We estimate the responses of longer-term rates to analyze if these alternative policies managed to overcome the ZLB constraint.

3

Oil Supply News Shocks and their Effects in Japan

This section presents the estimates of the oil supply news shocks and their effects on
the Japanese economy when the nominal interest rate is at the zero lower bound andoutside of it. Specifically, we present the results for real monthly variables, including
industrial production and the unemployment rate, then quarterly variables, such as realGDP, real private consumption, and real investment per capita. Finally, we examine the
New Keynesian mechanism by estimating the responses of the nominal interest rate andinflation expectations.

3.1

Oil Supply News Shocks

We start by describing properties the oil supply surprise series. First, the left panel of Figure 1, which plots the series, illustrates that OPEC announcements had a sizable impact
on the oil futures prices in both directions throughout our sample. Second, the external
9 This 0.5 percent cutoff results in a ZLB period similar to Ramey and Zubairy (2018). Lowering thecutoff to 0.25 percent shrinks the ZLB period to 2008:12-2015:12, however, the estimation results remain
qualitatively similar.
10 The U.K. interest rate rose just above 0.5 percent during 2009:5-2010:8. Our results do not materiallychange if we define this period as ZLB as well.

11

Figure 2: Impulse responses of real oil prices.
Real Oil Price Response% response

15

Di,erence in Real Oil Price Responses

Normal (Japan)
ZLB (Japan)

15
10

10

5
5
0
0

-5
0

5

10

15
20
Months

25

30

0

35

5

10

15
20
Months2530

35Notes: The left panel plots the impulse response functions and one-standard-deviation (HAC) confidence bands for the real oil pricein the ZLB (thick blue line) and in the normal (thin gray line) periods. The Japanese ZLB definition is used to break the full sample
into the ZLB and normal periods. The right panel plots the differences in the responses in the ZLB and normal periods along with the
90 percent (dark gray area) and 95 percent (light gray area) confidence bands.

instrument approach to estimating the oil supply news shocks requires the oil supply surprise series to be a relevant instrument. The first-stage regression of the oil price residuals
from the VAR on the instrument, which is the oil news surprise series, yields an F-statisticof 19.9, well over a recommended threshold of 10 (Montiel Olea et al., 2021). The instrument explains 3.6 percent of the variation in the oil price residual. Third, we find evidence
supporting the assumption of the invertibility of the oil supply news shocks. Specifically,
we test whether the oil supply surprise series jointly Granger causes the four variablesin the oil VAR (Giannone and Reichlin, 2006; Forni and Gambetti, 2014; Plagborg-Møller
and Wolf, 2022). The p-value for the Wald test of no Granger causality null hypothesis is0.90.11
The right panel of Figure 1 plots the estimate of the oil supply news shocks Eb1,t from1975:1 to 2019:12. There is no noticeable difference between the different parts of thesample in terms of the size and frequency of the shocks. There was a relatively large
negative shock in February 1986, followed by a positive shock of similar size in August
1986.
Since the estimated oil supply news shocks are used as an instrument for the real oil
price in equation (1), we also report the F-statistics from the first-stage regression of thelog real oil price on this instrument. The smallest value of the F-statistics using the datafrom 1975:1 to 2019:12 for horizons up to 36 months is 16.3, well above 10. As mentioned
earlier, we estimate the responses to an oil supply news shock by directly regressing variables of interest on this shock using the local projections method. These additional results,
reported in Appendix B, are consistent with the baseline results presented next.
11 This result also holds when we test for Granger causality using first-differences, a shorter sample from1983:4 to 2017:12, and a 6-variable VAR as in Kanzig (2021) instead of the 4-variable VAR as in our baseline
specification.

12

Before turning to the analysis of the Japanese economy, in Figure 2, we plot the responses of the real oil prices to the oil supply news shock that increases the real oil priceon impact by 10 percent. We use the ZLB definition for Japan and generate these responses by estimating equation (1) with the real oil price as the variable of interest. Thereis some evidence that the shock in the ZLB periods leads to a more persistent increasein the real oil price than that in the normal periods. The differences between the real oil
price responses in the ZLB periods and those in the normal periods are statistically different at the 5 percent level at horizons of 1 and 19 months after the shock, as seen from theright panel of Figure 2. However, the responses in the two subperiods are qualitatively
similar.12

3.2

Real Economy

The top left panel of Figure 3 shows the responses of industrial production (a volume
measure) to a 10 percent increase in real oil prices driven by the oil supply news shocks athorizons up to 36 months after the shock. The error bands show a one-standard-deviation
confidence interval. In normal times, industrial production slowly falls, declining almost
1 percent one year after the shock. This decline reverts around two years after the shock.
In the ZLB periods, the response of industrial production increases to just above 1 percent
one year after the shock, and it is statistically different from zero at the 5 percent level athorizons between 11 and 14 months. The difference between the two responses of industrial production in the ZLB and the normal periods are in the bottom left panel of Figure
3. This difference is statistically significant at the 10 percent level at horizons between 9
and 18 months and at the 5 percent level at horizons between 10 and 14 months after theshock.13 Appendix Figure B.1 shows that using the oil supply news shock directly as aregressor in specification (1) in place of the oil price keeps the results virtually unchanged.
Oil supply news shocks also lead to different labor market dynamics in the ZLB andthe normal periods. The top right panel of Figure 3 plots the responses of the unemployment rate to a 10 percent increase in real oil prices driven by the oil supply news shocks
in both the normal and the ZLB periods. Initially, the responses of the unemployment
rate to an increase in real oil prices are negative and not significantly different from zero.
Then, the unemployment rate increases up to 0.03 percentage points during normal times
at the one-year horizon, while it decreases 0.08 percentage points in the ZLB periods a
12 A higher persistence of the oil supply news shocks in the ZLB period implies a larger disruption inaggregate economic activity under the conventional supply-side view. Our estimation below presents evidence to the contrary.
13 The Anderson and Rubin (1949) p-values, which take into account the fact the instrument in specification (1) can be weak, are higher, but the difference in the industrial production response is significant at the
10 percent level at horizons of 12 and 13 months.

13

Figure 3: Japanese industrial production and unemployment rate impulse responses.
Unemployment Rate

Industrial Production
0.05%pt response% response10-1Normal
ZLB

0

5

10

15
20
Months

25

30

0
-0.05
-0.1
0

35

5

Di,erence in Industrial Production

4

10

15
20
Months

25

30

35

30

35

Di,erence in Unemployment Rate
0.1

%pt

%pt

2

0

0
-0.1

-2
0

5

10

15
20
Months

25

30

-0.2

35

0

5

10

15
20
Months25

Notes: Each figure in the top panel plots the impulse response functions and one-standard-deviation confidence bands of industrial
production and the unemployment rate in Japan in the ZLB (thick blue line) and in the normal (thin gray line) periods. The lower
panels present the differences in the responses of industrial production and the unemployment rate in the normal and ZLB periods,
with the 95 percent (dark gray area) and 90 percent (ligh gray area) confidence bands.

year after the shock. This decrease is statistically significant at the 5 percent level at horizons between 5 and 24 months after the shock. We test the differences in the responses in
the normal and ZLB periods, and the p-values are below 5 percent for horizons between
16 and 22 months, after the shock, except in month 21, as depicted in the bottom-rightpanel of Figure 3.14
Long ZLB spells in Japan allow us to perform estimation using quarterly data. Figure
4 plots the impulse responses of real per capita GDP, private consumption, and private
investment, government purchases, and net exports in Japan to a 10 percent increase in
the real oil price driven by the oil supply news shock. We sum all monthly shocks withina quarter to obtain quarterly oil supply news shocks that we use as the instrument inequation (1). The controls are identical to those described in Section 2.1, and the numberof lags at quarterly frequency is four. Consistent with the monthly real variables, weobserve that real GDP, consumption, and investment per capita responses are larger in
the ZLB periods than in the normal periods. In particular, GDP virtually does not change
on impact but increases above 0.4 percent after one year at the ZLB. It remains roughly
14 The Anderson and Rubin (1949) p-values are below 10 percent for horizons 16 to 22 months, again

excluding month 21.

14

constant in the normal periods. Appendix Figure C.1 plots the difference in responses in
the ZLB and normal periods.15
Figure 4: Japanese quarterly variable impulse responses.
Real GDP per capita% response

0.6

Normal
ZLB

0.4
0.2
0
0

2

4
Quarters

68Real Investment per capita

Real Consumption per capita
0.8

2% response% response

0.6
0.4
0.2
0

1
0

-0.2
0

2

4
Quarters

6

-1

8

0

2

Real Government Purchases per capita

6

8

Net Exports over GDP
0.2% response

0.5% response

4
Quarters

0

0.1
0
-0.1
-0.2

-0.5
0

2

4
Quarters

6

-0.3

8

0

2

4
Quarters

68Notes: Each figure plots the impulse response functions and one-standard-deviation confidence bands of real GDP, real consumption,
real investment, real government purchases (all per capita), and nominal trade balance over nominal GDP in Japan to an oil supply
news shock that increases the oil price by 10 percent on impact in the ZLB (thick blue line) and the normal (thin gray line) periods.
The estimated specification is in equation (1). The sample is from 1975:Q1 to 2019:Q4. The differences in the impulse responses acrossthe ZLB and the normal periods are plotted in Figure C.1.

Interestingly, the point estimate for government purchase responses are also higher in
the ZLB periods than outside of it. However, the standard errors are substantial, so thedifferences in government purchase responses in the two periods are not statistically different at conventional significance levels. Finally, the trade balance exhibits a differential
response across the two states as well.16 The difference between the responses in the ZLB
15 From now on, we present the difference in responses in the ZLB and normal periods in Appendix C.
16 To estimate the response of the real trade balance at various horizons, we normalize the change in the15and normal periods is negative a year after the shock. This is consistent with the fact that
aggregate consumption and investment increase at the ZLB relative to the normal period,
which can drive an increase in demand for imports.17

3.3

Interest Rates, Inflation, and Inflation Expectations

One possible explanation for the observed differences in the responses of real macro variables in Japan to oil supply news shocks is that the monetary policy stance during these
periods differs. To inspect this mechanism, we estimate the responses of nominal interest
rates, inflation, and inflation expectations to an oil supply news shock. In the specification for the nominal interest rates, we add 12 lags of the CPI inflation rate and the real oil
price in addition to the controls described in Section 2.1.18
The top left panel of Figure 5 plots the impulse response of the short-term nominal interest rate to a 10 percent increase in real oil prices driven by the oil supply news shocks.
In the ZLB periods, the response of the nominal interest rate stays near zero and is precisely estimated, as one would expect from the ZLB periods. In normal times, the shortterm nominal interest rate does not change on impact, but then it gradually increases by
0.4 percentage points one year after the shock. Appendix Figure C.2 plots the differencein the responses of the short-term nominal interest rate, as well as of the other variables
discussed in this subsection. The short-term nominal interest rate difference is significant
at conventional levels for the first 15 months. In addition, the response in the normal periods is significantly different from zero at the 5 percent significance level from horizonsof 1 to 15 months.
As mentioned earlier, the longer-term rates can vary even when the short-term nominal rate is constant at zero. The top right panel of Figure 5 presents the response of the
5-year nominal government bonds yield. This longer rate behaves qualitatively similar tothe short rate, with the important difference being that it increases significantly but mildly
during the ZLB periods. In addition, in the normal periods, this longer rate rises less than
the short rate. Appendix Figure C.2 presents the differences in responses of these interest
rates, together with the conventional confidence intervals. The differences are significant
up to 6 months and at horizon of 14 months.
nominal trade balance by the nominal GDP just before the shock. That is, we use ( NXt+h − NXt−1 )/Yt−1
as the left-hand variable.
17 Section 5.2 presents the responses of the real exchange rate.
18 We add the inflation rate because it is typically an important factor that central bankers take into
account when choosing monetary policy. We add the real oil price because it can have information abovethat contained in the lags of the oil supply shocks. The two variables can help predict the nominal interest
rates and increase the signal-to-noise ratio in our regressions. In practice, however, the results are virtuallyunchanged without these two controls.

16

Figure 5: Interest rates, inflation, and inflation expectations responses in Japan.
Short-term Nominal Interest Rate
0.45-year Nominal Bond Yield

0.3

NormalZLB%pt response%pt response

0.6

0.2
0

0.2
0.1
0

-0.2
0

5

10

15
20
Months

25

30

0

35

5

15
20
Months

25

30

35

30

35

12-month PPI in.ation

12-month CPI in.ation1% response

0.4% response

10

0.2
0

0.5
0
-0.5
-1

-0.2
0

5

10

15
20
Months

25

30

0

35

5

10

15
20
Months25

4Q ahead CPI In.ation Expectation%pt response

0.4
0.2
0
-0.2
0

2

4
Quarters

68Notes: The figures plot the impulse response functions and one-standard-deviation confidence bands of the short-term nominal interest rate, 5-year nominal interest rate, CPI inflation rate, PPI inflation rate, and CPI inflation expectations in Japan in the ZLB (thickblue line) and in the normal (thin gray line) periods. The responses are to an oil supply shock that increases the real oil price by 10
percent on impact. The differences in responses across ZLB and the normal periods are in Figure C.2.

The reaction of the CPI inflation rate to the oil shock is plotted in the middle left panelof Figure 5. The inflation rate, measured as the 12-month percentage change in the consumer price index, increases in in the normal periods about 0.3 percentage points after 8
months from the shock and reverts after 17 months. In the ZLB periods, the inflation rate
does not react at the beginning and shows a moderate increase of 0.15 percentage points
20 months after the shock. The middle right panel of the same figure presents the reactionof the producer price index (PPI) inflation rate. The behavior qualitatively repeats the behavior of the CPI inflation rate. However, the response of the PPI inflation rate during the17

ZLB periods is more pronounced than the response of the CPI inflation rate.19
The bottom panel of Figure 5 demonstrates the impulse responses of the one-yearahead inflation expectations at quarterly frequency. We use the Japanese Center for Economic Research (JCER) CPI inflation forecast to proxy for inflation expectations.20 Inflation expectations increase 0.3 percentage points in the ZLB one quarter after the shock,which is statistically significant at the 5 percent level. The inflation expectations responsein the normal periods is close to zero on impact and becomes negative after one year. The
differences of the responses between the ZLB and normal periods are significant at the 4,5, and 7 quarter horizons. These results imply that the ex ante real ante interest rate falls
during the ZLB periods but increases in the normal periods.

4

Oil Supply News Shocks Effects in the U.K. and U.S.

Since Japan is not the only country that has experienced ZLB episodes, we now investigate the effects of oil supply news shocks in the United Kingdom and the United States,
both of which faced a near-zero interest rate in the recent past. The results provide additional evidence that oil supply news shocks have differential impacts during and outsideof the ZLB periods, suggesting that the results using Japanese data are not specific only
to Japan or to the period when Japan was in a liquidity trap.

4.1

Real Economy

Panel (a) of Figure 6 plots the impulse responses of industrial production to a 10 percent
increase in real oil prices driven by an oil supply news shock, and the difference is in Appendix Figure C.3. Both in the United States and United Kingdom, the difference between
the industrial production responses in the ZLB and normal periods becomes positive andstatistically significant a few months after the shock. Moreover, in these countries, theindustrial production responses become positive and statistically different from zero in
the ZLB period several months after the shock. For example, in the United States, industrial production increases nearly 1 percent one year after the shock. In contrast, industrial
production falls in the normal period: the responses are negative and statistically different from zero. These results are qualitatively consistent but numerically and statistically
19 The diminished reaction of price indices to oil shocks during the ZLB, relative to the normal period,aligns with Watanabe and Watanabe (2017) finding that goods level price inflation in Japan has shown
reduced variability since the mid-1990s.
20 Alternative inflation expectations datasets are too short to estimate the effects of oil shocks on inflation
expectations in the normal periods in Japan. For example, the Consensus Economics Forecast data for Japan
started in 1989.

18

more pronounced compared to the results in Japan.
Figure 6: Industrial production and unemployment rate responses in the U.S. and U.K.
(a) Industrial production
2

0.5

1

% response% response

United States
1

0
-0.5

0

5

0
-1

NormalZLB-1United Kingdom

10

15
20
Months

25

30

0

35

5

10

15
20
Months

25

30

35

25

30

35

(b) Unemployment rate
United Kingdom

United States
0.2%pt response%pt response

0.2

0Normal
ZLB

-0.2
0

5

0
-0.2
-0.4

10

15
20
Months

25

30

0

35

5

10

15
20
Months

Notes: Each figure plots the impulse response functions and one-standard-deviation confidence bands. Panel (a) shows industrial
production responses in the United Kingdom and the United States in the ZLB (thick blue line) and in the normal (thin gray line)
periods. Panel (b) plots unemployment rate responses in the United Kingdom and the Unites States in the ZLB (thick blue line) andin the normal (thin gray line) periods. Figure C.3 plots the differences in the responses of these variables in the ZLB and outside of it.

The labor market responses, which we plot in Panel (b) of Figures 6 and C.3, mirror
the responses of industrial production. Specifically, the unemployment rate in the UnitedStates and the United Kingdom falls after a negative oil supply news shock that increases
the oil price in the ZLB period a few months after the shock. These ZLB responses are
statistically different from zero and from those in the normal periods.

4.2

Interest Rates, Inflation, and Inflation Expectations

To investigate whether the monetary policy channel can be responsible for the above differences in the United States and the United Kingdom, we estimate the effects of oil supply news shocks on the nominal variables. Panel (a) of Figure 7 shows that responsesof the short-term nominal interest rate in the ZLB periods remain zero. In contrast, theresponses in the normal periods are positive and statistically different from those in the
ZLB periods for a few initial months, as shown in Figure C.4. Although the results are
19

noisier compared to Japan. The 5-year nominal yields respond to oil shocks in the twocountries both during and outside the ZLB. Nevertheless, the responses during the ZLB
are statistically different from those in the normal periods at several horizons. The inflation rate behavior in the ZLB and normal periods are indistinguishable in the UnitedStates. In the United Kingdom, the initial inflation responses in both periods are close
to each other. However, inflation in the ZLB periods starts falling substantially after one
year.
We close this section by describing the behavior of inflation expectations. We focus onhouseholds’ inflation expectations because this group of economic agents is responsible
for consumption choices. In addition, recent literature, such as Weber et al. (2022) andCandia et al. (2023), documents that inflation expectations of firm managers are closer
to those of households than of professional forecasters. In the bottom panel of Figure 7,
we plot the responses of the median one-year-ahead inflation expectations in the UnitedStates using the Michigan Survey of Consumers data and in the United Kingdom using
the Bank of England/Ipsos Inflation Attitudes Survey data. The former survey collects
data monthly, while the latter is a quarterly survey. As in the case of regressions withquarterly Japanese data, we construct quarterly oil supply news shocks by adding up theshocks within the same quarter. In both countries, we observe an increase in inflation
expectations on impact in both the ZLB and normal periods. In the United States, theresponse in the normal periods is larger than that in the ZLB periods: the reaction in thenormal periods reaches 0.24 percentage points compared to 0.1 percentage point in the
ZLB periods.21 In contrast, the response in the ZLB periods in the United Kingdom islarger than the response in the normal periods: the ZLB largest response is almost 0.5
percentage points compared to less than 0.1 percentage point in the normal periods.
Overall these results parallel those in Japan in Section 3.3. Specifically, the reaction of
the nominal interest rates and expected inflation indicate the differential reaction of theex ante real interest rate in the ZLB and normal period.

21 Figure B.2 shows the response of one-year ahead inflation expectations by professional forecasters

using the data from Consensus Economics. There is also evidence of a stronger reaction of the expectationsin the normal period, however, the difference is smaller than in the case of the U.S. consumers.

20

Figure 7: Interest rates and inflation in the the United States and United Kingdom(a) Short-term nominal interest rate
United Kingdom

United States

0.4

0.3
%pt response%pt response

0.3
0.2
0.1
0
Normal
ZLB

-0.1
0

5

10

15
20
Months

25

30

0.2
0.1
0
-0.1
0

35

5

10

15
20
Months

25

30

35

25

30

35

25

30

35

(b) 5-year nominal government bond yield
United Kingdom

United States
0.2%pt response%pt response

0.3
0.2
0.1
0

Normal
ZLB

-0.1
0

5

0.1
0
-0.1

10

15
20
Months

25

30

0

35

5

10

15
20
Months(c) CPI inflation rate
United Kingdom

United States
0.2% response% response

0.4
0.2
0
-0.2

0

5

-0.2
-0.4

Normal
ZLB

-0.4

0

-0.6
10

15
20
Months

25

30

0

35

5

10

15
20
Months(d) Median household inflation expectations
United Kingdom

United States
0.6%pt response%pt response

0.3
0.2
0.1
0

Normal
ZLB

-0.1
0

5

0.4
0.2
0

10

15
20
Months

25

30

35

0

2

4
Quarters

68Notes: Each figure plots the impluse response functions and one-standard-deviation confidence bands the central bank interest rate,
the 5-year nominal yield on government bonds, the CPI inflation rate, and household inflation expectations responses to the oil supply
shock that increases the real oil price by 10 percent in the United States and United Kingdom in the ZLB (thick blue line) and in thenormal (thin gray line) periods. The U.S. inflation expectations are 12-month-ahead inflation expectations from the Michigan Survey
21
of Consumers measured at monthly frequency. The U.K. inflation expectations are 4-quarter-ahead inflation expectations from the
Bank of England/Ipsos Inflation Attitudes Survey measured at quarterly frequency. Figure C.4 plots the differences in the responsesof these variables in the ZLB and outside of it.

5

Other Shocks, Variables, Countries, and Specifications

Our estimates for Japan are consistent with those in the United States and the United
Kingdom, suggesting that the less contractionary (and even expansionary) effects of anoil supply news shock at the ZLB are not particular to Japan. We now extend our analysis
in several dimensions to provide new insights and explore the sensitivity of the results
just presented. First, we estimate the effects of alternative oil shocks using two prominent identifications of these shocks in the literature. Second, we look into the responsesof additional variables to oil supply news shocks. Third, we estimate the effects in theeconomies areas that experienced near-ZLB episodes, such as Canada and the euro area,
and countries that were far away from the ZLB constraint, such as Mexico, Sweden, andthe Republic of Korea. Finally, we check how our main results in Sections 3 and 4 change
when we vary our benchmark specification in a number of ways, such as the sample size,
exclusion of influential historical episodes, and modification of control variables.

5.1

Other Oil Shocks

We begin by analyzing the effects of oil supply shocks, identified through alternative
methods, to demonstrate the importance of oil shocks identification for our findings.
This analysis clarifies why our baseline results differ from those of Wieland (2019), whichfound no difference in Japanese industrial production and unemployment rate responses
to oil supply shocks.
We focus on two prominent identification strategies for oil supply shocks. The firstone is the oil supply shocks identified in Kilian (2009), also used in Wieland (2019). We
will refer to these oil supply shocks as the Kilian shocks. The second set of oil supply
shocks is from Baumeister and Hamilton (2019), which we will call the BH shocks. To
identify oil supply shocks in a structural VAR, Kilian (2009) assumes that there is no shortrun reaction of the oil supply to changes in the real oil price.22 In contrast, Baumeisterand Hamilton (2019) do not restrict the oil supply elasticity to be small and estimate it
to be a much larger number of 0.15. Baumeister and Hamilton (2019)’s identification
strategy of oil supply shocks recovers a series of oil supply shocks that is substantiallymore important in accounting for the historical oil price movements than Kilian (2009)’s
identified oil supply shocks. We use these two oil supply shocks in the same way as inour baseline specification described in Section 2.1.
Appendix Figure B.3 plots the impulse responses of the Japanese industrial production
and unemployment rate to the Kilian (first row) and BH (second row) shocks. The results
22 Kilian and Murphy (2012) later modified this assumption with an alternative that the short-run priceelasticity of the oil supply is small or, more specifically, less than 0.0258.

22

based on the Kilian shocks are consistent with Wieland (2019).23 In contrast, the responses
of industrial production and the unemployment rate to the BH shocks are qualitatively
similar to our baseline estimation using oil supply news shocks. In particular, industrial
production increases in the ZLB periods but decreases in the normal periods, and theunemployment rate decreases in the ZLB periods but increases in the normal periods.
The differences between the responses of the unemployment rate to BH shocks in the ZLB
period and those in the normal period are not statistically significant, while the industrial
production responses are significantly different at 10 percent at the horizon of 20 and 21
months after the shock, as can be seen in Figure C.5.
What can be behind the different effects of these shocks? As displayed in the top
right panel of Figure B.5, the Kilian (2009) oil supply shocks generate a response of thereal oil price that is not statistically different from zero, consistent with one of his main
results that his oil supply shocks are not an important driver of the historical oil pricevariations. This observation might explain why these shocks do not generate statisticallysignificant responses of the real variables in the United States, as reported in Kilian (2009).
Additionally, this could account for the lack of different responses of real variables at the
ZLB and outside of it in Japan, as shown in our Figures B.3 and B.4. At the same time,
the response of the real oil price to the BH shock (the bottom right panel of Figure B.5) is
more significant than that to the Kilian shock, but still not as precise as the response of thereal oil price to the oil supply news shocks identified in Kanzig (2021) (the top left panelof Figure B.5). Since we use all these shocks to instrument the oil price in specification(1), it is not surprising that the standard errors following the BH shocks are somewhat
larger compared to those following the Kanzig shocks. Notably, when we regress thereal variables on the shocks directly (i.e., without instrumenting), the effects of the BH oil
supply shocks become much more precise, as seen in panel (b) of Figure B.4.
We close this section by presenting the responses of the Japanese economy to anotheroil shock estimated in Kilian (2009). This shock is ordered last in a triangular identificationof his three-variable VAR, making it effectively a residual to the oil supply and global
aggregate demand shocks, which come first and second. Kilian (2009) refers to this shockas the oil-market specific demand shock. When normalized to increase the oil price, thisshock reduces U.S. GDP and, at the same time, increases the U.S. CPI, unlike his oil supply
shock that does not change U.S. GDP and CPI. As shown in Figure B.6, where we use
23 Wieland (2019) does not use the Kilian shocks to instrument for the real oil price. He uses the shocks

directly in equation (1) instead of the oil price. We present the estimation based on this direct approach inAppendix Figure B.4 Panel (a). These responses between the ZLB and normal periods are not statisticallysignificant. Note that our responses are not identical to the responses in Figure 6 (panels B and C) in
Wieland (2019) because of at least two differences. First, we compute the Kilian shocks using the 1973:22019:12 sample instead of the 1973:2-2015:9 sample in Wieland (2019). Second, following our analysis in
Section 3, we start our sample in 1975:1 instead of starting in 1986:1 as in Wieland (2019).

23

this shock to estimate the responses in Japan, the results are qualitatively similar to ourbaseline.

5.2

Other Variables

Production without oil. Our analysis used a measure of industrial production that includes mining, such as oil extraction. This raises a concern that oil price variations canmechanically affect the mining sector’s output. This problem can be potentially more
pronounced in the United States, where the importance of oil production has grown in
the last two decades following the shale oil extraction boom. To address this concern, we
present the responses of industrial production in the United States, the United Kingdom,
and Japan only for the manufacturing sector in Panel (a) of Figure B.7 and for industrial
production when we remove oil production for the United States in Panel (b). Our main
findings remain qualitatively unchanged.
Stock market response. If oil supply news shocks lead to different responses in aggregate economic activity during and outside of the ZLB, it is logical to expect this pattern tobe reflected in financial markets. To investigate this possibility, we estimate the responseof the U.S. stock market represented by the S&P 500 index.24 The left panel of Figure B.8
plots the reaction of the S&P 500 index estimated using specification (1) on monthly data.
The results confirm our previous finding that the U.S. economy responds positively to theshocks at the ZLB and negatively in the normal periods. The positive response is significant at almost all horizons at the 5 percent significance level, while the negative response
is only significant at this level at the 13-month horizon.
In addition to looking at the stock market data at a monthly frequency, we leverage
the fact that stock market data are also available at a higher daily frequency. This allows
us to use the oil supply surprise series directly to measure the importance of monetary
policy for oil shock propagation. Specifically, we estimate a state-dependent specification
where a log-change of the S&P500 index is projected on the oil supply surprise series. We
use ten lags of the S&P 500 index as only controls. The sample covers all OPEC pressconference announcements between January 1, 1983 and December 31, 2019. The rightpanel of Figure B.8 presents the results, which are consistent with the monthly data results
and our earlier findings on the responses of aggregate economic activity. The different
stock market responses based on the direct use of the oil supply surprise series reinforces
24 We primarily look at the US stock market for two reasons. First, it is the biggest stock market in theworld. Second, the recent literature, documenting the presence of the global financial cycle (Rey, 2015;
Miranda-Agrippino and Rey, 2022), notes that financial market developments are correlated across countries.

24

our main results based on the oil supply news shock.
Exchange rates. Another financial variable that can exhibit different responses during
the ZLB and the normal periods is exchange rates. This can be due to the differential
response of trade balance and monetary policy we estimated earlier.25 Figure B.9 showsthat the real exchange rate depreciates in the ZLB period and appreciates in the normal
periods during the first two years after the shock, although the responses in the normal
periods are not statistically significant at conventional levels. This reaction is in line witha relative tightening of monetary policy during normal times.
Unconventional monetary policy. During the ZLB periods, central banks often use unconventional monetary policies, such as forward guidance (announcements about future
conventional monetary policy) or quantitative easing (purchases of long-term private andpublic financial assets). As a result, central banks can potentially respond to oil priceshocks even during the ZLB periods. One way to assess this possibility is to look at
longer-term nominal interest rates, which we did in Sections 3.3 and 4.2. We found evidence of the reaction of long-term rates to oil supply news shocks. An alternative assessment tool is a measure of monetary policy stance summarized by the shadow rate (Wuand Xia, 2016). The shadow rate is a synthetic short-term nominal interest rate that is estimated to be consistent with the part of the yield curve that is above zero. By construction,
the shadow rate closely follows the actual short-term nominal interest rate when the ZLB
constraint does not bind, but it may go negative when the ZLB constraint is active. Figure
B.10 presents the impulse responses of the shadow rate to an oil supply news shock in the
ZLB periods in the United States. To be consistent with the estimation of the interest rate
responses in Sections 3.3 and 4.2, we add the lags of inflation rate and real oil price as controls. Using updated data from Wu and Xia (2016), we estimate projections on the sample
from 1990:1 to 2019:12 and report the ZLB shadow rate responses only.26 The shadow rate
falls significantly after an oil price hike. This pattern is consistent with the expansion ofreal economic activity during the ZLB we obtained earlier. One reason why the shadow
rate might fall after the oil price spike is that the inflation rate is typically below target
during ZLB episodes, potentially making central bankers less concerned about inflationand more concerned about a possible output decline following oil price spikes.
25 Most macro models emphasize the role of trade balance and monetary policy in determining exchange
rates. However, the exchange rate disconnect puzzle (Obstfeld and Rogoff, 2000)—the absence of correlation between exchange rate and macro fundamentals—is still standing. See Engel and Wu (2023)for recent
progress in identifying the effects of macro variables on the exchange rate.
26 The normal period response of the shadow rate is qualitatively similar to the response of the short-term
nominal rate in Figure 7 but nosier at longer horizons.

25

5.3

Other Countries

Canada and the euro area. Japan, the United States, and the United Kingdom experienced clear episodes when the interest rate was constant. Two more economies experienced close-to-zero interest rate episodes: Canada and the euro area. Figure B.11 plots
their short-term nominal interest rates. We define the ZLB period to be between 2009:4
and 2017:4 in Canada and 2012:7–2019:12 in the euro area. It is important to note that theinterest rates continued changing even when they were close to zero in both economies,
which is why it is reasonable to expect noisier results.
Figure B.12 demonstrates a general lack of difference in responses of industrial production and unemployment in the ZLB and normal periods in Canada and the euro area.
In contrast to the results in Japan, the United Kingdom, and the United States, there issome evidence that the initial response of industrial production goes up by more, and theunemployment rate goes down by more in the normal period than in the ZLB period in
the euro area. In Canada, while not significant, the point estimates are consistent with
our results for Japan, the United States, and the United Kingdom.
Placebo countries. We next present the responses of three other countries—Mexico,
Sweden, and the Republic of Korea—that did not experience ZLB during the Global Financial Crisis. We chose them among the OECD countries and ensured they are locatedin different parts of the world. Figure B.13 shows that neither industrial production nor
unemployment rates respond differently in the normal and the ZLB periods based on
the U.S. definition of the ZLB period. Only Mexico shows some signs of the expansionary effect of oil shocks during the U.S. ZLB period, which can be driven by international
spillovers from an expansion in the United States following an increase in oil prices.

5.4

Other Specifications

Subperiod analysis. The advantage of showing results from several countries that experienced ZLB episodes is that these episodes may not coincide, providing evidence fromdifferent subperiods. In practice, however, the ZLB episodes in the United States and theUnited Kingdom occur almost simultaneously and partly overlap with the ZLB periods
in Japan. To avoid the potential spillover of the United States during its ZLB period toother countries, we estimate the reaction of the Japanese industrial production and theunemployment rate in the normal and the ZLB periods when we shorten the sample tobefore the start of the ZLB period in the United States. Specifically, we choose the ending
date for the sample to be June 2006, corresponding to the end of the first ZLB sub-period
in Japan. The results, plotted in Figure B.14, qualitatively repeat the patterns for the full26

sample estimation in Figure 3.
The first half of 2008 was marked by the world plunging into the Global Financial
Crisis, with recession in Japan starting in March 2008. At the same time, the oil pricecontinued rising until July 2008, partly due to rising oil demand in China and a stableoil supply in oil-producing countries (Hamilton, 2009). Such a coincidence may have an
important effect on the estimation of the oil supply news shocks on economic activity. To
investigate this possibility, we re-estimate the responses of Japanese industrial production
and the unemployment rate using specification (1), where we not only have dummies for
the ZLB and the normal periods as defined above, but also a third dummy that equals one
during 2008:3-2008:7, which effectively dummies out this period. Figure B.15 presents the
responses of Japanese variables during the ZLB and normal periods, and we do not add
the responses during 2008:3-2008:7 to the figure. The responses of industrial production
and the unemployment rate in the ZLB period remain virtually unchanged comparedwith our baseline results. However, the point estimate responses in the normal periods
become less contractionary than before, consistent with the hypothesis that the developments in 2008 may be important for generating a negative relationship between economic
activity and the oil supply news shocks. This point can also be seen in Figure B.14 where
the point estimates in the normal periods are less contractionary than in our baseline results. Finally, if we were to assign the 2008:3-2008:7 period to the ZLB episode, we would
estimate a weaker expansionary effect of the shocks in Japan during the ZLB episode.27
The United States responded to the large oil price swings of the 1970s by introducing rationing of gasoline. To check if these episodes affect our U.S. results, we estimate
the responses of U.S. industrial production and the unemployment rate with the sample
starting in 1986:1, following Ramey and Vine (2011). Figure B.16 shows that our results
are robust to shortening of the sample. The only notable difference is that the normal
period responses become more persistent than our baseline results in Figure 6.
Controls. In Section 2.1, we argued in favor of using controls, such as a lagged dependent variable, lagged oil shocks, and the lagged unemployment rate, to enhance thesignal-to-noise ratio of the oil supply news shocks. To verify this claim, we present results
obtained without these controls. Appendix Figure B.17 displays the impulse response
functions of Japanese industrial production and the unemployment rate, where we haveyyomitted controls ψ A,h ( L) xt−1 and ψB,h ( L) xt−1 from equation (1). While the point estimates are similar to those with controls, the standard errors increase significantly. This
motivates the inclusion of the controls. Furthermore, Appendix Figure B.18 demonstrates
27 We thank Christiane Baumeister for pointing out the importance of the developments in the first halfof 2008.

27

that our findings hold up even when we add additional controls, such as the lagged inflation rate and the lagged 1-year nominal government bond yield.28
Information effect. In monetary economics, a high-frequency approach to identifying
monetary policy shocks is subject to a criticism that it cannot distinguish between a true
shock and the information revelation about the state of the economy by a central bank(Nakamura and Steinsson, 2018a). The same criticism may apply to the announcements
by OPEC. For example, OPEC may have better information about the state of the global
oil market than market participants themselves. To check whether our results are driven
by the information revelation about the state of the economy, we use recent insights fromthe monetary shocks identification literature (Cieslak and Schrimpf, 2019; Cieslak andPang, 2021; Jarociński and Karadi, 2020) that were applied to OPEC announcements in
Degasperi (2021). The idea is to separate the movements in the oil supply surprise series on the days of the OPEC announcements into those that positively co-move with thestock market, and are likely to represent the information revelation effect, and those that
co-move negatively, and are likely to proxy true oil supply surprises. We use the S&P 500
stock price index to measure the stock market reaction. The advantage of using the U.S.
stock market index is that it may not react strongly to monetary policy in Japan, which,as we illustrated above, can influence the sign of the stock market reaction. Figure B.19
presents the results for Japan based on the oil supply news shocks that were estimatedusing a part of the oil supply surprise series that generates a negative comovement between the U.S. stock market and the real oil price. The results are qualitatively similar tothe baseline results: the difference in industrial production and unemployment responses
in the normal and the ZLB periods remain significant.29
Sign of oil shocks. The strength of the effects of macroeconomic shocks can also depend on the sign of these shocks (Barnichon et al., 2022). This can be rationalized by,for example, nonlinearities in macro models, such as downward nominal wage rigidity,
which binds when a shock reduces nominal wages but is slack when it increases them. In

28 The results are not sensitive to using two or five-year nominal interest rates.
29 One can object to even using the U.S. stock market by arguing that the U.S. economy entered the ZLB

in 2008 and the S&P 500 changed the sign of its co-movement with the oil supply series after that, as we
previously illustrated. To address this concern, we re-estimate the results in Figure B.19 by removing a period when the U.S. short-term nominal interest rate was constant. Specifically, we choose a sample between
1975:1 and 2006:6. The main finding that the shock that increases the real oil price is less contractionary
remains true even in this case.

28

Figure C.8, we present the results from estimating the following specification
i

 h
y
y
y
yt+h − yt−1 =I Eb1,t ≥ 0 · α A,h + β A,h Eb1,t + ψ A,h ( L) xt−1

 h
i
y
y b
y
y
b
+ I E1,t < 0 · α B,h + β B,h E1,t + ψB,h ( L) xt−1 + ϵt+h ,where I(Eb1,t < 0) is an indicator variable that equals one when the shock Eb1,t is negativeand zero otherwise, and I(Eb1,t ≥ 0) = 1 − I(Eb1,t < 0). We do not find evidence foryysign-dependent effects. Figure C.8 shows that the difference βbA,h − βbB,h is not statisticallysignificant from zero at conventional levels.
Expansions and recessions. Aggregate economic variables may also react differently toshocks depending on the state of the economy. For example, there is evidence that government purchases have different impacts on GDP in expansions and recessions (Auerbachand Gorodnichenko, 2013). Since ZLB episodes often coincide with recessions, the resultsthat we obtain can potentially be driven by the different impacts of the oil supply news
shocks in recessions and booms. To explore this possibility, we estimate state-dependent
responses of Japanese macro variables to the oil supply news shocks using a specificationin equation (1) with the same controls but where the dummy variable takes a value of one
if Japan is in a recession and zero if it is in an expansion. We use the Cabinet Office ofJapan dating of business cycles.30 If our results in Section 3.2 were driven only by the different responses in recessions and expansions, we should be able to detect the difference
across recessions and booms. Figure B.20 plots the responses of industrial production
and the unemployment rate in recessions and booms, and Figure C.9 plots the difference.
The difference in industrial production responses is not statistically different from zeroat conventional levels at all horizons, the difference in the unemployment rate is barely
different from zero at 10 percent level at horizons of 18 and 22 months. We interpret thisresult as not being strong evidence for different responses across recessions and booms.31
Doing without external instruments. In our baseline analysis, we assumed that the
four-variable oil market VAR spans all the relevant information to estimate the series ofthe oil supply news shocks Eb1,t , an assumption for which we could find supporting evi30 The data can be found at https://www.esri.cao.go.jp/en/stat/di/rdates.html. For example, according to this dating, Japan experienced a recession from March 2008 to March 2009 during the
Global Financial Crisis.
31 It is sometimes argued that the entire ZLB experience in Japan coincides with a long recession. We
cannot separate the effects of this long recession from a constant interest rate period. However, following
Section 6.2 in Miyamoto et al. (2018), we note that in modern macro models that generate different responses
in booms and busts, a crucial indicator is labor market tightness, which did not exhibit drastically different
behavior before and during the ZLB.

29

dence. Nevertheless, for completeness, we now show the responses using an alternative
strategy, where we directly use the oil supply surprise series zt as a shock. More precisely,
we first regress the series on twelve lags four variables from the oil VAR and extract theresidual.32 We then estimate specification (1), replacing the log oil price with the residual
just obtained. The advantage of this approach is that it does not require the invertability
assumption. However, we can only use the sample where the oil supply surprise series isavailable, namely 1983:4-2019:12. The left panel of Figure B.21 shows that industrial production in Japan responds differentially in the ZLB and normal periods, consistent withour baseline results. The estimates are, however, much noisier, which is expected froma shorter sample and less-frequent independent variable. The magnitudes of the point
estimates are larger than those in our baseline estimation, which can be related to the fact
that, unlike in our baseline estimation, the response of the real oil price peaks at higher
than 10 percent level after several months following the shock. The right panel of Figure
B.21 presents the responses of the unemployment rate. The standard errors are large, preventing us from making any statistical statements. However, the point estimates paint asimilar picture to our baseline results.

6

Oil Shocks in an Open Economy New Keynesian Model

This section examines a standard Open Economy New Keynesian model with oil shocks
with the following two goals. First, we formalize the intuition that oil market shocks
that increase oil price can sometimes be expansionary. Second, we present a stylized
quantitative exercise aimed at quantifying the model-implied effects of oil price spikes onmacro variables under constant nominal interest rate monetary policy.

6.1

The Model

Our model is a version of Galı́ and Monacelli (2002) extended with oil intermediate inputs used by firms in the spirit of Bodenstein, Guerrieri and Gust (2013).33 It consists ofa small open home country and a foreign country representing the world economy. The
small open economy is intended to approximate Japan. Each country has a representative
household that consumes home and foreign goods with home-biased preferences, saves
32 This step is not necessary and does not change the results. However, by doing so, we make sure thatthe oil supply surprise series is not predicted by other oil variables. This step also relates the exercise to
the internal instrument approach (Ramey, 2011; Plagborg-Møller and Wolf, 2021), where the instrument is
added to the VAR and ordered first.
33 Galı́ and Monacelli (2002) is a working paper of the classical Gali and Monacelli (2005) paper. The key
difference between the two is that the working paper features two countries, a small open economy and theworld economy, while the published version has a continuum of small open-economies.

30

via complete domestic and international asset markets, and supplies labor to domestic
firms. Monopolistically competitive firms produce differentiated goods from domestic
labor and oil using a constant-returns-to-scale production function. These firms set theirnominal prices in domestic currencies and change them infrequently a la Calvo. Only foreign country receives a stochastic endowment of oil in each period. All goods, including
oil, cannot be stored. In addition, all goods are traded globally, implying the law of one
price.34
The foreign country—the world economy—can be described by the following loglinearized equilibrium conditions, which we derive in Appendix D. Aggregate consumption follows the Euler equation:
 ∗




1 ∗
it − Et π F,tEt cb∗t+1 − cb∗t =+1 − ι ,σ(2)where asterisks denote foreign country variables, cb∗t is the log deviation of world con∗sumption from its steady state, it∗ is the nominal interest rate, π F,t+1 is both a consumer
price index (CPI) and producer price index (PPI) inflation rate because the world economy
is closed, ι is the steady-state nominal interest rate, and σ is the inverse of the intertemporal elasticity of substitution. The world variables satisfy the Phillips curve
 ∗

∗
∗
π F,t
= κζ ∗ cb∗t + βEt π F,trt ,+1 + κψo b(3)where ζ ∗ and ψo∗ are composite parameters that represent the sensitivities of firm’s marginal
costs to consumption cb∗t and the real oil price b
rt , which is expressed in units of foreign
goods, κ is the sensitivity of inflation to changes in the marginal cost.35 The main difference between a standard closed economy model and this world economy is the lastterm in the Phillips curve equation, κψo∗brt , which relates changes in the real oil price andinflation. The foreign central bank sets the interest rate according to the Taylor rule∗it∗ = ι + φ∗π π F,t,(4)where the inflation target is zero, the effective lower bound is not explicitly introduced,
and φ∗π is non-negative. Finally, the equilibrium real oil price is determined in the world’s

34 This stylized model can be extended in many realistic dimensions that we do not pursue here. It canfeature non-rational expectations (Milani, 2009), incomplete markets within (Chan et al., 2022; Auclert et al.,2023) and across (Itskhoki and Mukhin, 2021) countries, local or dollar currency pricing (Gopinath andItskhoki, 2022), production and storage of oil (Pindyck, 2001), and many more.
35 The composite coefficients κ, ζ ∗ , ψ∗ , are expressed in equations (D.24), (D.27), and (D.28) in AppendixoD through preferences and production function parameters.

31

oil market:b
rt = ϕc cb∗t − ϕo b
ot∗ ,

(5)

where bot∗ is the oil endowment and ϕc , ϕo are positive.36 This equation implies that anincrease in the world economic activity or a decrease in the oil supply lead to an increasein the real oil price.
Home country consumption dynamics follows a similar Euler equation
Et [cbt+1 ] − cbt =1( i t − Et [ π t +1 ] − ι ) ,σ(6)while the home-produced goods inflation rate obeys the following Phillips curve
π H,t = κζ H cbt + βEt [π H,t+1 ] + κψob
rt + κζ F cb∗t + κψq qbt ,(7)

where, in addition, to the channels present in the Phillips curve of the foreign countryin equation (3), the term κζ F cb∗t incorporates the effect of global aggregate demand on
domestic inflation, and the last term shows the influence of the real exchange rate qbt on
the marginal costs of home firms and, hence, the inflation rate. The real exchange rateis defined as the price of foreign goods in home goods unit, so an increase in qbt is areal depreciation. When the global aggregate demand drops, foreign residents purchasefewer home goods, reducing marginal costs of home firms and, hence, the inflation rate.
In addition, when the home currency depreciates in real terms (bqt increases), oil becomes
more expensive to buy at home for any level of the real oil price b
rt denominated in foreign
goods. As a result, home firms’ marginal costs and the inflation rate go up.
The central bank at home follows the Taylor ruleit = ι + φπ π H,t ,(8)where ϕπ ≥ 0. The link between the CPI and PPI inflation rates is
πt = π H,t +

1−Ω
∆b
qt ,
Ω

(9)

where Ω ∈ [0, 1] is the share of home goods in home household spending, which represents the degree of home bias. The second term expresses the effect of real depreciationof domestic currency on the consumption basket inflation.
With complete financial markets, there is perfect risk sharing across countries, so the

36 The composite coefficients ϕ and ϕ are in equations (D.25) and (D.26).
co32

real exchange rate is proportional to the difference in consumption in the two countries:
qbt = σ (cbt − cb∗t ) .

(10)

The production of home goods is a sum of home and foreign demand for home goods
ybH,t =Ω
1 − Ω∗Ω ( 1 − Ω ) + ( 1 − Ω ∗ ) γn
∗
b
b
c
+
c
+
· qbt .
t
Ω + 1 − Ω∗
Ω + 1 − Ω∗ t
Ω + 1 − Ω∗Ω(11)where 1 − Ω∗ is the proportion of consumption that foreign households allocate to home
goods.37 The last two terms express two forces that take into account that oil shocks affecthome country through the world economy. The presence of cb∗t captures the spillover ofworld consumption demand to domestic goods. The term featuring the real exchange
rate qbt measures the strength of the expenditure switching effect between foreign to home
goods, which crucially depends on the elasticity of substitution between home and foreign goods γn .
We look into the consequences of a one-time unanticipated negative global oil supply
shock bo0∗ = bo ∗ < 0 that reverts back to its steady-state value of zero with probability
α ∈ [0, 1].38 There are no other sources of uncertainty.
Finally, instead of explicitly representing the zero lower bound on the nominal interest rate, we assume that the nominal interest rate stays constant following an oil priceshock. This assumption retains the key property of the ZLB that the interest rate does not
respond to developments in the economy. At the same time, it avoids the need to introduce additional notation. See Nakamura and Steinsson (2014) for a similar treatment in
the context of fiscal multipliers.

6.2

The Effects of Oil Shocks

We start by presenting the responses of foreign goods production, which equals consumption, and the inflation rate. We look for a unique bounded Markov equilibrium where
37 As Appendix D formally shows, we assume that foreign demand for domestic goods is proportional

to the size of the home country. Because we consider a limit when the size of the home country tends tozero (the small open economy assumption), both home production and foreign demand for home goods
shrink to zero. However, their ratio stays positive in the limit.
38 In our empirics, we use the oil supply news shocks that affect the oil price immediately but the actual
oil supply gradually with a lag of several months. In this stylized model, where oil cannot be stored and theprice of oil is determined in the spot market, oil supply news can only affect current oil price through otherforward-looking macro variables, such as consumption. Because of this, we choose to focus on the realized
oil supply shocks in this model. From a perspective of a small open economy, the distinction between
oil supply news and oil supply shocks may not be crucial when the key manifestation of the shock is anincrease in the oil price. Finally, in our numerical exercise, we employ quarterly calibration, which brings
the supply news shocks closer to the realized supply shocks.

33

Figure 8: The World Economy.
EE

PC'

EE

PC

PC'

PC

Notes: Both panels show the response of the world economy to a decline in oil supply when monetary policy is active (the left panel)
and when it does not respond following an oil shock (the right panel).

∗∗ r } are linear functions of oil supply b
endogenous variables {cb∗t , π F,tot∗ . The Phillipst+1 , i t , b
curve and the Euler equation (together with the Taylor rule) areκ (ζ ∗ + ψo∗ ϕc ) ∗ κψo∗ ϕocb +o∗ ) ,(−b
1 − βα1 − βαφ∗ − α ∗π .
cb∗ = − π
(1 − α ) σ F

π F∗ =(12)(13)

Figure 8 plots the two equations under the assumption that monetary policy is active,that is, φ∗π > 1 (the left panel), and when monetary policy does not change following an
oil shock, that is, φ∗π = 0 (the right panel). The upward-sloping Euler equation on theright panel is due to the fact that higher inflation in the absence of the response of thenominal interest rate reduces the real interest rate and increases aggregate consumption.
For the unique bounded solution to exist, the Euler equation should be steeper than thePhillips curve when they have slopes with the same sign.39
A decline in the oil supply results in an upward shift in the Phillips curve in bothpanels of Figure 8. Intuitively, a decline in the oil supply increases the real oil price,which, in turn, pushes up the inflation rate.
Under active monetary policy, the central bank increases the nominal interest rate suchthat the real interest rate rises, reducing aggregate output. At the same time, under theconstant nominal interest rate policy, the real rate falls, stimulating the world economy.
Similarly to the world economy, we can represent the Phillips curve and Euler equa-

39 Formally, we focus on the parameters that satisfy (1 − βα ) (1 − α ) σ + κ ( φ∗ − α ) ( ζ ∗ + ψ∗ ϕ ) > 0. Thisπo cinequality always holds when the monetary policy is active. When φ∗π = 0, however, the inequality restricts

the parameter space.

34

Figure 9: The Small-Open Economy.
EE'

PC'

EE

EE'

PC

PC'

PC

EE

Notes: Both panels show the response of the small-open economy to a decline in oil supply when the monetary policy is active (the left
panel) and when it does not respond following the oil shock (the right panel). Both panels assume that the world economy’s output
declines following an increase in the oil price.

tion of the home economy asκ ζ F − ψq σ ∗κ ζ H + ψq σ
κ
cb +
ψob
r+
cb ,
πH =
1 − αβ1 − αβ1 − αβφπ − αcb = −Ω
π H + (1 − Ω) cb∗ .
σ (1 − α )

(14)
(15)

The two equations closely resemble the world equations (12) and (13), with the exception of additional terms. When the oil supply decreases, real oil prices increase, pushingdown global demand cb∗ when the world monetary policy tightens, the case we will focus
on. The last term in the Phillips curve encapsulates two global forces. First, a slowdown
in global demand leads domestic marginal costs and inflation to fall. Second, to keep
the marginal utility of consumption equalized in both countries as required by equation(10), the home currency depreciates in real terms. This makes the purchase of oil fromthe global market costlier and consequently increases the marginal costs of production at
home. The net effect of these two forces is ambiguous, and it depends on the degree of
openness of the home country. In Figure 9, we plot equation (14) when monetary policyin the rest of the world actively responds to the oil shock. In the graph, we assume thatthe second force is stronger, so a decrease in the oil supply pushes the PC to shift to theleft.
In addition, when there is a decline in global economic activities, the last term in the
Euler equation implies that the EE line shifts to the left, as plotted in Figure 9. The reason
is that a decline in global economic activity, which is expected to revert in the future,appreciates home currency in real terms over time. This, in turn, reduces home inflation
and, hence, increases the real interest rate for any level of the nominal interest rate. As aresult, domestic aggregate demand falls.
In equilibrium, as demonstrated in Figure 9, a decline in oil supply that increases theoil price can also be expansionary when the leftward shift in the Euler equation is small
35

enough, which is the case with a sufficiently high degree of home bias, i.e., when thecoefficient Ω is close to one.40
Table 1: Calibration Parameters
β = 0.99
σ −1 = 1
φ−1 = 0.5γn = 0.5Ω = 0.8
α = 0.58
φπ = φ∗π = 1.5
γy = 0.1
ωoy = 0.057
1 − θ = 0.25
Composite parametersκ = (1 − θ ) (1 − βθ ) /θ = 0.086(1+γy φ)ωoy
ψo∗ = ψo = 1+γy φωoy = 0.077
1+ ω γ φoy y= 2.167(1−ωoy )γy 1−ωoyζ H = 1+γy φωoy σ + φ Ω+1Ω−Ω∗ = 2.05Ω∗ = Ω − ωoy / 1 − ωoy = 0.558

ϕo =Discount factor
Intertemporal elasticity of substitution
Frisch elasticity of labor supply
Elasticity of substitution between home and foreign goods
Share of home goods in home consumption basket
Persistence of oil shocks
Taylor rule coefficient on inflation
Elasticity between labor and oil in production
share of oil in production
Probability of price adjustmentζ ∗ = 1 − ωoy (σ + φ) / 1 + ωoy γy φ = 2.769


 

 
ϕc = 1 + γy φ + 1 − ωoy σ / 1 − ωoy γy = 5.167(1+ φγn )(1−ωoy )= 1.27
ψq = 1−ΩΩ ·1+γy φωoy
1− ω

∗

oy
ζ F = 1+γy φωφ Ω1+−1Ω−Ω∗ = 0.808oyι = − log β = 0.01

Numerical exercise. To illustrate the quantitative importance of the highlighted channels, we calibrate the model by choosing the values used in the recent macro literature.
The quarterly calibration parameters are listed in Table 1.41 Most of the parameters aretaken from Gali and Monacelli (2005). The exceptions are the share of oil in production,
which come from Bodenstein et al. (2013). The persistence of oil shocks is set to 0.58
(half life of five months) to match the maximum point estimate decline in Japanese aggregate consumption by 0.2 percent in the normal period following a shock that increases
oil prices by 10 percent. The elasticity of substitution between home and foreign goods
consumption is set to 0.5 and between labor and oil in production to 0.3. We chose thesesomewhat lower than usual values to highlight the short-run effects of oil supply shocks.
The weight of home goods in the home consumption basket is Ω = 0.8, which is set toapproximate this value in Japan.42
Under these parameters and a shock to oil supply that increases oil prices by 10 percent, world consumption falls 0.18 percent under active monetary policy and increases 1
40 Notethat for the bounded solution
to be unique, the following condition must holdσ (1 − αβ) (1 − α) + κ ( φπ − α) ζ H + ψq σ Ω > 0. This condition always holds when the central bank actively responds to the oil shock, i.e., φπ > 1. However, when φπ = 0, the above condition restricts the setof model parameters.
41 We use quarterly calibration because we estimate the response of consumption and GDP in Japan using
quarterly variables.
42 This value is lower than the one typically used for the U.S., but higher that that for euro area countries.

36

percent when the nominal interest rate is constant. The home economy’s consumption
falls 0.2 percent when monetary policy is active both at home and abroad, while homeconsumption increases 0.9 percent when monetary policy does not respond at home but
responds in the rest of the world. The ZLB consumption response is larger than the maximum estimated response of Japanese consumption at the ZLB of 0.7 percent, presented in
Figure 4. Nevertheless, this stylized numerical exercise captures our empirical result that
the ZLB response is larger than the absolute value of the response in the normal period.
The model allows us to look at other variables. For example, home production increases by 1.1 percent when home monetary policy does not respond (but foreign monetary policy does), and it falls by 0.2 percent when home monetary policy is active. Furthermore, using equation (11), we can decompose the 1.1 percent change in output into
0.67 percent due to a higher aggregate demand at home, −0.04 percent due to a lower foreign demand, and 0.42 percent due to expenditure switching, suggesting the importanceof the international spillovers of the oil price variations.

7

Conclusion

This paper presents new evidence on the effects of oil supply news shocks when thenominal interest rate is not responsive due to the ZLB constraint. We focus on Japan,
which has the longest spell at the ZLB, and supplement with evidence from the United
Kingdom and the United States, which have also experienced considerable periods with
fixed interest rates. We find that oil supply shocks are less contractionary in the ZLB
period than in the periods outside of the ZLB in Japan, the United Kingdom, and theUnited States. Notably, we document that these economies expand following an oil priceincrease during the ZLB periods. In addition, we find that inflation expectations rise afteran oil supply news shock, while the nominal interest rate remains at zero during the ZLB
and increases in normal periods. This suggests that the monetary policy channel can playa significant role in the transmission of oil shocks.

37References
A NDERSON , T. and R UBIN , H. (1949). Estimation of the parameters of a single equation
in a complete system of stochastic equations. Annals of Mathematical Statistics, 20, 46–63.
A UCLERT, A., M ONNERY, H., R OGNLIE , M. and S TRAUB , L. (2023). Managing an Energy
Shock: Fiscal and Monetary Policy. Tech. rep., Mimeo, Stanford.
A UERBACH , A. J. and G ORODNICHENKO , Y. (2013). Fiscal multipliers in recession andexpansion. In A. Alesina and F. Giavazzi (eds.), Fiscal Policy after the Financial crisis, 2,
University of Chicago Press, pp. 63–98.
B AQAEE , D. R. and FARHI , E. (2019). The macroeconomic impact of microeconomic
shocks: Beyond hulten’s theorem. Econometrica, 87 (4), 1155–1203.
B ARNICHON , R., D EBORTOLI , D. and M ATTHES , C. (2022). Understanding the size of thegovernment spending multiplier: It’s in the sign. The Review of Economic Studies, 89 (1),
87–117.
B AUMEISTER , C. and H AMILTON , J. D. (2019). Structural interpretation of vector autoregressions with incomplete identification: Revisiting the role of oil supply and demand
shocks. American Economic Review, 109 (5), 1873–1910.
B ERNANKE , B. S., G ERTLER , M. and WATSON , M. (1997). Systematic monetary policy
and the effects of oil price shocks. Brookings papers on economic activity, 1997 (1), 91–157.
B LANCHARD , O. and G ALI , J. (2009). The macroeconomic effects of oil shocks: Why are
the 2000s so different from the 1970s? In J. Gali and M. Gertler (eds.), International
Dimensions of Monetary Policy., University of Chicago Press.
B ODENSTEIN , M., G UERRIERI , L. and G UST, C. J. (2013). Oil shocks and the zero boundon nominal interest rates. Journal of International Money and Finance, 12, 941–967.
C ANDIA , B., C OIBION , O. and G ORODNICHENKO , Y. (2023). The macroeconomic expectations of firms. In Handbook of Economic Expectations, Elsevier, pp. 321–353.
C HAN , J., D IZ , S. and K ANNGIESSER , D. (2022). Energy prices and household heterogeneity: Monetary policy in a gas-tank. Available at SSRN 4255158.
C IESLAK , A. and PANG , H. (2021). Common shocks in stocks and bonds. Journal of Financial Economics, 142 (2), 880–904.

38

— and S CHRIMPF, A. (2019). Non-monetary news in central bank communication. Journalof International Economics, 118, 293–315.
C OIBION , O. and G ORODNICHENKO , Y. (2012). What can survey forecasts tell us about
information rigidities? Journal of Political Economy, 120 (1), 116–159.
D ATTA , D. D., J OHANNSEN , B. K., K WON , H. and V IGFUSSON , R. J. (2021). Oil, equities,
and the zero lower bound. American Economic Journal: Macroeconomics, 13 (2), 214–253.
D EBORTOLI , D., G AL Í , J. and G AMBETTI , L. (2020). On the empirical (ir) relevance of thezero lower bound constraint. NBER Macroeconomics Annual, 34 (1), 141–170.
D EGASPERI , R. (2021). Identification of expectational shocks in the oil market using opec
announcements. manuscript, University of Warwick.
E GGERTSSON , G. B. (2008). Can tax cuts deepen recessions? Federal Reserve Bank of New
York, December.
E NGEL , C. and W U , S. P. Y. (2023). Liquidity and exchange rates: An empirical investigation. The Review of Economic Studies, 90 (5), 2395–2438.
F ERNALD , J. (2014). A Quarterly, Utilization-Adjusted Series on Total Factor Productivity.
Tech. rep., Federal Reserve Bank of San Francisco.
F ORNI , M. and G AMBETTI , L. (2014). Sufficient information in structural vars. Journal of
Monetary Economics, 66, 124–136.
G AL Í , J. and M ONACELLI , T. (2002). Monetary policy and exchange rate volatility in asmall open economy.
G ALI , J. and M ONACELLI , T. (2005). Monetary policy and exchange rate volatility in asmall open economy. The Review of Economic Studies, 72 (3), 707–734.
G ARIN , J., L ESTER , R. and S IMS , E. (2019). Are supply shocks contractionary at the zlb?
evidence from utilization-adjusted tfp data. Review of Economics and Statistics, 101 (1),
160–175.
G ERTLER , M. and K ARADI , P. (2015). Monetary policy surprises, credit costs, and economic activity. American Economic Journal: Macroeconomics, 7 (1), 44–76.
G IANNONE , D. and R EICHLIN , L. (2006). Does information help recovering structural
shocks from past observations? Journal of the European Economic Association, 4 (2-3),
455–465.
39

G OPINATH , G. and I TSKHOKI , O. (2022). Dominant currency paradigm: A review. Handbook of International Economics, 6, 45–90.
G ÜRKAYNAK , R. S., S ACK , B. P. and S WANSON , E. T. (2004). Do actions speak louder
than words? the response of asset prices to monetary policy actions and statements.
The Response of Asset Prices to Monetary Policy Actions and Statements (November 2004).
H AMILTON , J. D. (1983). Oil and the macroeconomy since world war ii. Journal of political
economy, 91 (2), 228–248.
— (2009). Causes and consequences of the oil shock of 2007-08. Paper presented at Brookings
Institution.
— and H ERRERA , A. M. (2004). Comment: oil shocks and aggregate macroeconomic
behavior: the role of monetary policy. Journal of Money, credit and Banking, pp. 265–286.
I TSKHOKI , O. and M UKHIN , D. (2021). Exchange rate disconnect in general equilibrium.
Journal of Political Economy, 129 (8), 2183–2232.
J AROCI ŃSKI , M. and K ARADI , P. (2020). Deconstructing monetary policy surprises-therole of information shocks. American Economic Journal: Macroeconomics, 12 (2), 1–43.
J ORDA , O. (2005). Estimation and inference of impulse responses by local projections.
American Economic Review, 95 (1), 161–182.
K ANZIG , D. (2021). The macroeconomic effects of oil supply news: Evidence from opec
announcements. American Economic Review, 111 (4), 1092–1125.
K ILIAN , L. (2009). Not all oil price shocks are alike: Disentangle demand and supply
shocks in the crude oil market. American Economic Review, 99 (3), 1053–1069.
— and L EWIS , L. T. (2011). Does the fed respond to oil price shocks? The Economic Journal,
121 (555), 1047–1072.
— and M URPHY, D. (2012). Why agnostic sign restrictions are not enough: Understanding
the dynamics of oil market var models. Journal of the European Economic Association,
10 (5), 1166–1188.
— and M URPHY, D. P. (2014). The role of inventories and speculative trading in the global
market for crude oil. Journal of Applied econometrics, 29 (3), 454–478.
K UTTNER , K. N. (2001). Monetary policy surprises and interest rates: Evidence from thefed funds futures market. Journal of monetary economics, 47 (3), 523–544.
40

M ERTENS , K. and R AVN , M. O. (2013). The dynamic effects of personal and corporate
income tax changes in the united states. American economic review, 103 (4), 1212–47.
M ILANI , F. (2009). Expectations, learning, and the changing relationship between oil
prices and the macroeconomy. Energy Economics, 31 (6), 827–837.
M IRANDA -A GRIPPINO , S. and R EY, H. (2022). The global financial cycle. In Handbook ofinternational economics, vol. 6, Elsevier, pp. 1–43.
M IYAMOTO , W., N GUYEN , T. L. and S ERGEYEV, D. (2018). Government spending multipliers under the zero lower bound: Evidence from japan. American Economic Journal:
Macroeconomics, 10 (3), 247–277.
M ONTIEL O LEA , J. L., S TOCK , J. H. and WATSON , M. W. (2021). Inference in structuralvector autoregressions identified with an external instrument. Journal of Econometrics,
225 (1), 74–87, themed Issue: Vector Autoregressions.
N AKAMURA , E. and S TEINSSON , J. (2014). Fiscal Stimulus in a Monetary Union: Evidence
from US Regions. American Economic Review, 104 (3), 753–92.
— and — (2018a). High-frequency identification of monetary non-neutrality: the information effect. The Quarterly Journal of Economics, 133 (3), 1283–1330.
— and — (2018b). Identification in macroeconomics. Journal of Economic Perspectives,
32 (3), 59–86.
O BSTFELD , M. and R OGOFF , K. (2000). The six major puzzles in international macroeconomics: is there a common cause? NBER macroeconomics annual, 15, 339–390.
P INDYCK , R. S. (2001). The dynamics of commodity spot and futures markets: a primer.
The energy journal, 22 (3).
P LAGBORG -M ØLLER , M. and W OLF, C. K. (2021). Local projections and vars estimate thesame impulse responses. Econometrica, 89 (2), 955–980.
— and W OLF, C. K. (2022). Instrumental variable identification of dynamic variance decompositions. Journal of Political Economy, 130 (8), 2164–2202.
R AMEY, V. A. (2011). Identifying Government Spending Shocks: It’s all in the Timing. The
Quarterly Journal of Economics, 126 (1), 1–50.
— and V INE , D. J. (2011). Oil, automobiles, and the us economy: How much have things
really changed? NBER Macroeconomics Annual, 25 (1), 333–368.
41

— and Z UBAIRY, S. (2018). Government spending multipliers in good times and in bad:Evidence from us historical data. Journal of Political Economy, 126 (2), 850–901.
R EY, H. (2015). Dilemma not trilemma: the global financial cycle and monetary policy independence. Tech. rep., National Bureau of Economic Research.
R OTEMBERG , J. and W OODFORD , M. (1996). Imperfect competition and the effects of energy price increases on economic activity. Journal of Money, Credit and Banking, 28 (4),550–77.
S IMS , C. A. and Z HA , T. (2006). Does monetary policy generate recessions? Macroeconomic Dynamics, 10 (2), 231–272.
S TOCK , J. H. and WATSON , M. W. (2012). Disentangling the Channels of the 2007-2009 Recession. Tech. rep., National Bureau of Economic Research.
— and — (2018). Identification and estimation of dynamic causal effects in macroeconomics using external instruments. The Economic Journal, 128 (610), 917–948.
S WANSON , E. T. and W ILLIAMS , J. C. (2014a). Measuring the effect of the zero lower
bound on medium-and longer-term interest rates. American economic review, 104 (10),3154–3185.
— and — (2014b). Measuring the effect of the zero lower bound on yields and exchange
rates in the uk and germany. Journal of International Economics, 92, S2–S21.
WATANABE , K. and WATANABE , T. (2017). Price rigidity at near-zero inflation rates: Evidence from japan. CARF Working Papers.
W EBER , M., D’A CUNTO , F., G ORODNICHENKO , Y. and C OIBION , O. (2022). The subjective inflation expectations of households and firms: Measurement, determinants, andimplications. Journal of Economic Perspectives, 36 (3), 157–184.
W IELAND , J. F. (2019). Are negative supply shocks expansionary at the zero lower bound?
Journal of Political Economy, 127 (3), 973–1007.
W OLF, C. K. and M C K AY, A. (2022). What Can Time-Series Regressions Tell Us About Policy
Counterfactuals? Tech. rep., National Bureau of Economic Research.
W OODFORD , M. (2003). Interest and Prices: Foundations of a Theory of Monetary Policy.
Princeton University Press Princeton, NJ.
W OOLDRIDGE , J. M. (2010). Econometric analysis of cross section and panel data. MIT press.
42

W U , J. C. and X IA , F. D. (2016). Measuring the macroeconomic impact of monetary policy
at the zero lower bound. Journal of Money, Credit and Banking, 48 (2-3), 253–291.

43

Online Appendix
A

Data Details

This section details data sources.
1. Industrial production. Monthly industrial production data for all countries (i.e., Japan, UK, US,as well as Canada, Eurozone, Mexico, the Republic of Korea, and Sweden) are taken from Haver
Analytics. The series name is “Industrial production excluding construction, seasonally adjusted
2015=100.” For all countries, the data are from 1974:1 to 2019:12.
2. Unemployment rate. The unemployment rate data for all countries are taken from the OECD
database. The series name is Unemployment rate (monthly), Total, All persons.
3. Inflation rate. CPI data for all countries are taken from the OECD database. The subject of the series
is “CPI: 01-12 All items, not seasonally adjusted, 2015=100.” Core CPI data (2015=100, not seasonallyadjusted) for all countries are downloaded from Haver Analytics, which populates data from theOECD Major Economic Indicator (MEI) database. The codename for the series is PCXG N023. We
seasonally adjusted core CPI using X-12-ARIMA in Stata.
4. Inflation expectations. The inflation expectations for Japan come from the Japan Center for Economic Research (JCER). The US inflation expectations are 12-month ahead median inflation expectations from the Michigan Survey of Consumers measured at monthly frequency. The UK inflation
expectations are 4-quarter ahead median inflation expectations from the Bank of England/Ipsos Inflation Attitudes Survey measured at quarterly frequency.
5. Short-term nominal interest rate.
(a) For Japan, the short-term nominal interest rate is the uncollateralized overnight call rate from
July 1985. Prior to that date, we use the collateralized overnight call rate. Both data series aretaken from the Bank of Japan website.
(b) For the United States and the United Kingdom, the short-term interest rate is the overnightinterbank rate downloaded from Haver Analytics, with a ticker FRUO, which populates datafrom OECD MEI.
(c) For the Euro Area, the short-term nominal interest rate is the 3-month treasury yield, downloaded from the Global Financial Database (GFD).
6. Long-term nominal interest rate. For all countries, the long-term nominal interest rate is the 5-year
government bond yield. Data are taken from the GFD.
7. Shadow rate. The U.S. shadow rate series is from Wu and Xia (2016). The updated version of theseries was downloaded from Jing Cynthia Wu personal website: https://sites.google.com/
view/jingcynthiawu/.
8. Nominal and real exchange rates. The nominal and real exchange rates for all countries are takenfrom the BIS, end of period.
9. Oil VAR data. All four variables for the VAR are taken from Kanzig (2021).

44

B

Additional Figures and Tables
Figure B.1: Japan impulse responses using OLS vs. baseline specification with instruments.

Notes: Each row displays the impulse response functions and one-standard-deviation confidence bands for the responses of Japaneseindustrial production and the unemployment rate to oil price shocks, as identified in Kanzig (2021). The OLS estimates (thick blueline) represent the results obtained by regressing the variables of interest directly on the oil supply news shocks. Meanwhile, theBaseline estimates illustrate the responses of these same variables to the real oil price, which is instrumented by the oil supply news
shock

Figure B.2: Responses of inflation expectations in the United States in the ZLB and normal periods.
United States (Consensus Economics)% response

0.1
0.05
0
-0.05
0

2

4
Quarters

68Notes: The figure plots the impulse response function and one-standard-deviation confidence bands for the professional forecasters’(Consensus Economics) inflation expectations in the Unites States in the ZLB (thick blue line) and normal (thin gray line) periods.

45

Figure B.3: Japan industrial production and unemployment rate: alternative oil supply shocks.
(a) Kilian (2009) oil supply shocks
Industrial Production

Unemployment Rate
0.4
%pt response% response

15
10
5
0
Normal
ZLB

-5
0

5

0.2
0
-0.2

10

15
20
Months

25

30

35

0

5

10

15
20
Months

25

30

35

30

35

(b) Baumeister and Hamilton (2019) oil supply shocks
Industrial Production

Unemployment Rate
1.5
%pt response% response20-2
Normal
ZLB

-4
0

5

1
0.5
0
-0.5

10

15
20
Months

25

30

35

0

5

10

15
20
Months25

Notes: Each figure plots the impulse response functions and 68 percent confidence bands of industrial production and the unemployment rate in Japan to oil shocks identified in Kilian (2009) and Baumeister and Hamilton (2019). Figure C.5 plots the differences in the
responses of these variables in the ZLB and outside of it.

46

Figure B.4: Japanese real variables responses to different oil supply shocks: OLS estimation(a) The Kilian oil supply shocks(b) The Baumeister-Hamilton oil supply shocks

Notes: Each row plots the impulse response functions and 68 percent confidence bands for the responses of Japanese industrial
production and the unemployment rate to oil supply shocks, as identified in Kilian (2009) and Baumeister and Hamilton (2019), using
OLS estimation instead of IV. The estimation period is from 1975:1 to 2019:12. Note that the oil supply shocks lead to an increase inreal oil prices.

47

Figure B.5: Real oil price response to different identified oil shocks.
To Kilian Oil Supply Shocks

10% response% response

To Kanzig Oil Supply News Shocks

5

2
0
-2

0

0

5

10
15
Months0

20

5

To Kilian Precautionary Shocks
4% response% response

20

To BH Oil Supply Shocks

8
6
4
2
0

10
15
Months

3
2
1
0

0

5

10
15
Months

20

0

5

10
15
Months20

Notes: Each figure plots the impulse response functions and 90 percent confidence bands for the responses of oil price to oil priceshocks identified in Kanzig (2021) (oil supply news shock), Kilian (2009) (oil supply and oil-market specific demand shocks), andBaumeister and Hamilton (2019) (oil supply shocks). In the case of the Kanzig (2021) shocks, we use the whole sample of 1974:1 to
2019:12 to estimate the response of oil prices.

Figure B.6: Japan impulse responses to Kilian (2009) oil-market specific demand shocks.
Unemployment Rate

Industrial Production
0.1%pt response% response

1
0.5
0
-0.5
-1

Normal
ZLB

-1.5
0

5

10

15
20
Months

25

30

0.05
0
-0.05
-0.1

35

0

5

10

15
20
Months2530

35Notes: Each figure plots the impulse response functions and 68 percent confidence bands for the responses of Japanese industrial
proudction and unemployment rate to oil price shocks identified in Kilian (2009) oil-market specific demand shocks. Figure C.6 plots
the differences in the responses of these variables in the ZLB and outside of it.

48

Figure B.7: Non-oil output responses in Japan, the United Kingdom, and the United States.
(a) Manufacturing Industrial Production
Japan

2

0
-1
Normal
ZLB

-2
0

5

% response% response1% response

United Kingdom

United States
0.5
0
-0.5

1
0

-1
-1
10

15
20
Months

25

30

35

0

5

10

15
20
Months

25

30

35

0

5

10

15
20
Months25(b) Non-Oil Industrial Production
United States% response

0.5
0
-0.5
-1
0

5

10

15
20
Months2530

35Notes: This figure plots the impulse response functions and one-standard-deviation confidence bands of the responses of manufacturing industrial production in Japan, the Unites States, and the United Kingdom, and non-oil industrial production in the United States(lower panel) in the ZLB (thick blue line) and outside of it (think gray line) to an oil supply news shock that increases the real oil priceby 10 percent on impact. Formally, we estimate equation (1) using data from 1975:1 to 2019:12.

Figure B.8: The S&P 500 responses to oil supply news shocks and surprises.
S&P 500 (monthly)

S&P 500 (daily)

15

NormalZLB

104% response% response

6

2
0
-2

Normal
ZLB

-4
0

5

5
0
-5

10

15
20
Months

25

30

0

35

5

10

15

20

25

30

35

Days

Notes: This figure plots the impulse response functions and one-standard-deviation confidence bands of the responses of the S&P 500
index to the oil supply news shock (left) and to the oil supply surprise series (right) both of which increase the oil price by 10 percent
on impact. The left panel presents the results based on the specification (1) using monthly data, while the right panel uses daily data.
The daily estimation uses 10 lags of the daily stock price as the only controls.

49

30

35

Figure B.9: Real exchange rate responses.
Japan

1

0

-2

% response% response2% response

United Kingdom

United States20-2
Normal
ZLB

-4
0

5

10

15
20
Months

25

30

35

0

5

0.5
0
-0.5
-1

10

15
20
Months

25

30

0

35

5

10

15
20
Months25

Notes: Notes: Each figure plots the impulse response functions and one-standard-deviation confidence bands of the responses of
the real effective exchange rates in Japan, the United States, and the United Kingdom. An increase in the real exchange rate is a
depreciation. The differences are plotted in Figure C.7.

Figure B.10: Shadow rate impulse responses in the United States in the ZLB period.

Notes: This figure plots the impulse response function and one-standard-deviation confidence bands of the responses of the shadowinterest rate in the Unites States in the ZLB.

Figure B.11: The short-term nominal interest rates.
Canada25

Euro Area

8

20

6

%

%

15
10

4
2

5
0
0
1980

1985

1990

1995

2000

2005

2010

2015

1995

Year

2000

2005

2010

2015

Year

Notes: Each panel presents central bank’s policy rate for each country. The shaded areas are the zero lower bound periods defined in
Section 5.3.

50

30

35

Figure B.12: Industrial production and unemployment rate responses in Canada and the euro area.
(a) Industrial production
Euro Area

Canada1% response% response

1
0.5
0
-0.5

0

-1
-1
0

5

10

15
20
Months

25

30

0

35

5

10

15
20
Months

25

30

35

25

30

35

(b) Unemployment rate
Euro Area

Canada0.05

0.2%pt response%pt response

0.3

0.1
0

0
-0.05
-0.1

-0.1
0

5

10

15
20
Months

25

30

0

35

5

10

15
20
Months

Notes: Each figure plots the impulse response functions and one-standard-deviation confidence bands of the responses. Panel (a)shows industrial production responses in Canada and the Euro Area in the ZLB (thick blue line) and in the normal (thin gray line)
periods. Panel (b) plots unemployment rate responses in Canada and the Euro Area in the ZLB (thick blue line) and in the normal(thin gray line) periods.

51

Figure B.13: Responses in other countries: Korea, Mexico and Sweden.
(a) Republic of Korea(b) Mexico(c) Sweden

Notes: Each figure plots the impulse response function and one-standard-deviation confidence bands of the responses of industrial
production (left panels) and the unemployment rate (right panels) in Republic of Korea, Mexico and Sweden in the ZLB (thick blueline) and in the normal (thin gray line) periods, where the ZLB period is defined based on the behavior of the short term nominalinterest rate in the US.

52

Figure B.14: Industrial production and unemployment rate responses in Japan when ZLB is 1995:10-2006:6.
Unemployment Rate

Industrial Production
0.1%pt response% response

2
1
0
-1

Normal
ZLB

-2
0

5

0
-0.1
-0.2

10

15
20
Months

25

30

0

35

5

10

15
20
Months2530

35Notes: The impulse responses and one-standard-deviation confidence bands of industrial production and unployment rate to an oil
supply news shock that increases oil price by 10 percent in the ZLB (think blue line) and normal (thin gray line) periods. The estimation
sample is from 1975:1 to 2006:6.

Figure B.15: Industrial production and unemployment rate responses in Japan without 2008:3-2008:7.
Industrial Production

Unemployment Rate2
%pt response% response010Normal
ZLB

-1
0

5

10

15
20
Months

25

30

-0.05
-0.1
-0.15
0

35

5

10

15
20
Months2530

35Notes: The figures plot impulse response functions and one-standard-deviation confidence bands of industrial production (left) and
unployment rate (right) to an oil supply news shock that increases oil price by 10 percent in the ZLB (thick blue line) and normal (thingray line) periods. The results based on specification when the 2008:3-2008:7 period is dummied out.

Figure B.16: Industrial production and unemployment rate responses in the US: the 1986:1-2019:12 sample.
Industrial Production

1

Unemployment Rate
0.3
%pt response% response

0.5
0
-0.5
-1

Normal
ZLB

-1.5
0

5

0.2
0.1
0
-0.1
-0.2

10

15
20
Months

25

30

35

0

5

10

15
20
Months2530

35Notes: The figures plot the impulse response functions and one-standard-deviation confidence bands of industrial production (left)
and unployment rate (right) to an oil supply news shock that increases oil price by 10 percent in the ZLB (thick blue line) and normal(thin gray line) periods in the United States. The sample is from 1986:1 to 2019:12.

53

Figure B.17: Japanese industrial production and unemployment rate responses: no controls
Industrial Production

Unemployment Rate
0.05

1

%pt response% response20-1
Normal
ZLB

-2
0

5

10

15
20
Months

25

30

0
-0.05
-0.1
-0.15

35

0

5

10

15
20
Months2530

35Notes: Each figure plots the impulse response functions and one-standard-deviation confidence bands of the responses of Japaneseindustrial proudction and unemployment rate to oil supply news shocks that increase the real oil price by 10 percent on impact in the
ZLB (thick blue line) and the normal (thin gray line) periods. The controls only include a constant and lags of dependent variable,
unlike the baseline specification that features the unemployment rate and the lags of the oil supply news shocks.

Figure B.18: Japanese industrial production and unemployment rate responses: additional controls
Industrial Production

Unemployment Rate
0.1
%pt response% response10-1Normal
ZLB

-2
0

5

10

15
20
Months

25

30

0.05
0
-0.05

35

0

5

10

15
20
Months2530

35Notes: Each figure plots the impulse response functions and one-standard-deviation confidence bands of the responses of Japaneseindustrial proudction and unemployment rate to oil supply news shocks that increase the real oil price by 10 percent on impact in the
ZLB (thick blue line) and the normal (thin gray line) periods. In addition to the baseline specification control variables (the lagged
left-hand variable, unemployment rate, and the oil supply news shocks), we add two nominal variables to the list of controls: the lagsof inflation rate and lags of 1-year nominal interest rate.

Figure B.19: Industrial production and unemployment rate responses in Japan (without info revelation).

Notes: Each figure plots the impulse response functions and one-standard-deviation confidence bands of industrial production (left)
and unployment rate (right) to a modified oil supply news shock that increases oil price by 10 percent in the ZLB (thick blue line)
and the normal (thin gray line) periods. A modified oil supply news shock was obtained by only using only a part of the oil supply
surprise series that generates a negative comovement between oil prices and the U.S. stock market index (Degasperi, 2021).

54

Figure B.20: Japanese industrial production and unemployment rate responses in booms and busts.
Unemployment Rate
0.15

1

0.1

%pt response% response

Industrial Production
2

0-1Expansion
Recession

-2
0

5

10

15
20
Months

25

30

0.05
0
-0.05
-0.1
0

35

5

10

15
20
Months2530

35Notes: Notes: Each figure plots the impulse response functions and one-standard-deviation confidence bands of the responses ofJapanese industrial production and the unemployment rate in recessions and booms following a 10-percent increase in real oil pricegenerated by the oil supply news shock. The difference is plotted in Figure C.9.

Figure B.21: Japanese Industrial Production and Unemployment Rate Responses: the oil supply surpriseseriesIndustrial Production

8

Unemployment Rate
0.4
%pt response% response

6420Normal
ZLB

-2
-4
0

5

10

15
20
Months

25

30

0.2
0
-0.2
-0.4
-0.6
-0.8

35

0

5

10

15
20
Months2530

35Notes: Each figure plots the IRFs and 68% confidence bands of the responses of Japanese industrial proudction and unemployment
rate to an oil supply suprise that increase the real oil price by 10 percent on impact.

55

C

Additional Figures: Differences in Estimates
Figure C.1: Difference in quarterly impulse responses in Japan.
Di,erence in Real GDP per capita

0.5

0

-0.5
0

2

4
Months6

Di,erence in Real Consumption per capital

8

Di,erence in Real Investment per capita
3

1

2
0.5

1
0

0
-1
0

2

4
Months

6

0

8

2

4
Months68

6

8Di,erence in NX/Y

Di,erence in Real Government Purchases per capita

1.5

0

1
0.5

-0.2

0
-0.4

-0.5
-1

-0.6
0

2

4
Months

6

0

8

2

4
Months

Notes: Each figure plots the difference between the responses of real GDP, real consumption, real investment, real government purchases (all per capita), and nominal trade balance over nominal GDP in Japan to the oil supply news shock that increase the oil priceby 10 percent on impact across the ZLB and in the normal periods. The estimated specification is in equation (1). The sample is from
1975Q1 to 2019Q4. Each plot also presents the 90-percent (dark grey) and 95-percent (light grey) confidence bands. The levels of theimpulse responses are plotted in Figure 4.

56

Figure C.2: Difference in interest rates, inflation, and inflation expectations responses in Japan.
Di,erence in Short-term Nominal Interest RateDi,erence in 5-year Nominal Bond Yield

0.4
0.1

%pt

0.2
0

0

-0.2

-0.1

-0.4

-0.2

-0.6
-0.8

-0.3
0

5

10

15
20
Months

25

30

35

0

Di,erence in CPI

5

10

15
20
Months25

30

35

Di,erence in 12-month PPI in.ation

0.4

2

%pt

0.2
1

0
-0.2

0

-0.4
-0.6

-1
0

5

10

15
20
Months

25

30

35

0

5

10

15
20
Months25

30

35

Di,erence in 4Q ahead CPI In.ation Expectation
0.6
0.4
0.2
0
-0.2
-0.4
0

2

4
Months68Notes: The figures plot the difference in impulse responses of the short-term nominal interest rate, 5-year nominal interest rate, CPI
inflation rate, PPI inflation rate, and CPI inflation expectations across ZLB and normal periods in Japan. The errors bands are 90- and95-percent confidence intervals. The corresponding impulse responses in the ZLB and normal periods are in Figure 5.

57

Figure C.3: Difference in industrial production and unemployment rate responses in the US and UK.
(a) Difference in the industrial production responses
United Kingdom

United States
3

2

2

1.5
1

1

0.5

0

0

-1

-0.5
0

5

10

15
20
Months

25

30

0

35

5

10

15
20
Months

25

30

35

25

30

35

(b) Difference in the unemployment rate responses
United Kingdom

United States
0

0

-0.2

-0.2

-0.4
-0.4
-0.6
-0.6
0

5

10

15
20
Months

25

30

0

35

5

10

15
20
Months

Notes: Each figure plots the mean and one standard-deviation confidence bands of the responses. Panel (a) shows industrial production responses in the United Kingdom and the Unites States in the ZLB (blue) and in the normal (grey) periods. Panel (b) plots
unemployment rate responses in the United Kingdom and the Unites States in the ZLB (blue) and in the normal (grey) periods. The
levels of the impulse responses are plotted in Figure 6.

58

Figure C.4: Difference in interest rates and inflation in the the United States and United Kingdom.
(a) Short-term nominal interest rate difference
United Kingdom

United States
0.4
0.2

0.2

0

0

-0.2

-0.2

-0.4

-0.4

-0.6
0

5

10

15
20
Months

25

30

0

35

5

10

15
20
Months

25

30

35

25

30

35

25

30

35

(b) 5-year nominal government bond yield difference
United States

United Kingdom

0.3

0.2

0.2
0.1

0

0
-0.2

-0.1
-0.2

-0.4
0

5

10

15
20
Months

25

30

0

35

5

10

15
20
Months(c) CPI inflation rate difference
United Kingdom

United States
0.4
0

0.2

-0.2

0

-0.4
-0.2
-0.6
-0.4
-0.8
0

5

10

15
20
Months

25

30

0

35

5

10

15
20
Months(d) Household inflation expectations difference
United Kingdom

United States
0.1

0.6

0

0.4

-0.1

0.2

-0.2

0

-0.3
-0.2
0

5

10

15
20
Months

25

30

0

35

2

4
Months68Notes: Each figure plots the mean, 90- and 95-percent confidence intervals of the difference in the responses of the central banknominal interest rate, the 5-year nominal yield on government bonds, and the CPI inflation, and the household inflation expectationsin the Unites States and the United Kingdom in the ZLB (thick blue line) and in the normal (thin grey line) periods. All the units on
thy Y axes are percentage points. The levels of the impulse responses are plotted in Figure 7.

59Figure C.5: Difference in responses of Japan industrial production and unemployment rate: different oil
supply shocks.
(a) Kilian (2009) oil supply shocks
Di,erence in Industrial Production

Di,erence in Unemployment Rate

30
0.2
20

0

10

-0.2

0

-0.4

-10

-0.6
-0.8
0

5

10

15
20
Months

25

30

35

0

5

10

15
20
Months

25

30

35

30

35

(b) Baumeister and Hamilton (2019) oil supply shocks
Di,erence in Industrial Production

Di,erence in Unemployment Rate

2

6

1

4

0

2

-1

0

-2

-2

-3
0

5

10

15
20
Months

25

30

0

35

5

10

15
20
Months25

Notes: Each figure plots the mean, 90- and 95-percent confidence intervals of the difference in the responses of industrial production
and the unemployment rate in Japan to oil shocks identified as in Kilian (2009) and Baumeister and Hamilton (2019). The levels of theimpulse responses are plotted in Figure B.3.

Figure C.6: Difference in responses of Japan industrial production and unemployment rate: oil-market
specific demand shock.
Di,erence in Unemployment RateDi,erence in Industrial Production
3

0.2

2

0

1

-0.2
-0.4

0

-0.6
-1

-0.8
0

5

10

15
20
Months

25

30

0

35

5

10

15
20
Months2530

35Notes: Each figure plots the mean, 90 and 95 percent confidence intervals of the difference in the responses of industrial production
and the unemployment rate in Japan to oil-market specific demand shocks identified as in Kilian (2009). The levels of the impulse
responses are plotted in Figure B.6.

60

Figure C.7: Difference in the real effective exchange rate responses.
Japan

UK

US

6

4

4

2

2

0

0

-2

-2

-4

1
0
-1
-2

0

5

10

15
20
Months

25

30

35

0

5

10

15
20
Months

25

30

35

0

5

10

15
20
Months2530

35Notes: Notes: Each figure plots the mean, 90 and 95 percent confidence intervals of the difference in the responses of the real effective
exchange rate in Japan, the United States, and the United Kingdom in the ZLB and normal periods. The levels of the impulse responses
are plotted in Figure B.9.

Figure C.8: Positive and negative oil supply shocks.
Di,erence in Industrial Production

Di,erence in Unemployment Rate
0.4

4
0.2

2
0

0

-2

-0.2

-4
0

5

10

15
20
Months

25

30

0

35

5

10

15
20
Months2530

35Notes: Notes: Each figure plots the mean, 90- (dark gray) and 95-percent (light gray) confidence intervals of the difference in the responses of the Japanese industrial production and the unemployment rate to positive and negative oil supply news shocks normalized
to change the real oil price by 10 percent.

Figure C.9: Difference in Industrial Production and Unemployment Rate: booms and busts.
Di,erence in Unemployment RateDi,erence in Industrial Production
0.1

2

0

0

-0.1
-2

-0.2
-0.3

-4
0

5

10

15
20
Months

25

30

0

35

5

10

15
20
Months2530

35Notes: Notes: Each figure plots the mean, 90- and 95-percent confidence intervals of the difference in the responses of the Japaneseindustrial production and the unemployment rate in recessions and booms following a 10-percent increase in real oil price generated
by the oil supply news shock. The levels of the impulse responses are plotted in Figure B.20.

61

D

Model Details

This section presents a standard open-economy New Keynesian model extended with demand for oil byfirms. The goal of this section is to illustrate the direct effects of oil shocks on aggregate supply, systematic
monetary policy, and the world economy.
There are two countries home (H) and foreign (F). We denote variables of foreign country with anasterisk. Each country is populated by measure n and n∗ ≡ 1 − n residents. All quantity variables are
expressed in per capita terms. Monopolistically competitive producers in home country produce varieties
with indexes i on the interval [0, n), while foreign firms on the interval [n, 1].
We describe the agent in home country. Foreign country agents description is symmetric.

D.1

Households

At home, there is a representative household with preferences represented by∞

E0 ∑ βt U (Ct , Nt ),

(D.1)

t =0

where
U (C, N ) ≡N 1+ φC 1− σ
−Θ
,
1−σ
1+φ

and Nt is labor supply, and Ct is consumption index43Ct ≡ ω

1
γn

γn −1
γn

CH,t + (1 − ω )

1
γn

γn −1
γn

 γ γ−n 1
n

CF,t

.

The indices of home and foreign goods consumption CH,t and CF,t by home residents are ϵϵ −1
  1 n
ϵ
ϵ −1
1
ϵ


,
CH,t ≡
diCH,t (i )
n


0

and

CF,t ≡ 

11−n ϵ−ϵ 1

 1 1ϵCF,t (i )

ϵ −1
ϵ

di 

,

n

where i ∈ [0, 1] is the index of individual good variety, ϵ is the elasticity of substitution across varieties,
γn is the elasticity of substitution between home and foreign goods, 1 − ω ≡ (1 − n) (1 − Ω) is a shareof foreign-good expenditures in total expenditures, and Ω ∈ [0, 1) is an index of home bias. The value ofΩ = 0 corresponds to the case of no home bias, while Ω > 0 is required for non-zero degree of home bias.
For the foreign economy, 1 − ω ∗ ≡ n (1 − Ω∗ ) is the share of home-good expenditures in total expenditures.
The household maximizes its preferences by choosing a plan {{CF,t (i )}, {CH,t (i )}, CF,t , CH,t , Ct , Nt ,43 The consumption index in foreign country is symmetric to home consumption index and equals: C ∗ ≡t∗ )(γn −1)/γn + (1 − ω ∗ )1/γn (C ∗ )(γn −1)/γn ]γn /(γn −1) , where ω ∗ is a share of foreign goods in[(ω ∗ )1/γn (CF,tH,tforeign consumption basket.

62

BH,t+1 , BF,t+1 } subject to the flow budget constraint
 n
0

 1

PH,t (i )CH,t (i )di + Et

n

∗
PF,t
( j)CF,t ( j)dj + Et [ Mt,t+1 BH,t+1 ]∗+Et Et Mt,t
+1 BF,t+1 ≤ B H,t + Et BF,t + Wt Nt + PO,t Ot + Πt − Tt ,(D.2)

∗ ( j ) are the prices of home and foreign varieties denoted in home and foreign currenwhere PH,t (i ) and PF,tcies, respectively, Et is the nominal exchange rate in units of domestic currency per foreign currency (anincrease in Et is a depreciation of home currency), PO,t is the oil price in units of home currency, Mt,t+1 and∗Mt,t+1 are prices of domestic and foreign state-contingent securities in home and foreign currencies, Wt is
nominal wage at home, Πt represent nominal profits, and Tt is nominal lump-sum taxes. The holdingsof home and foreign state-contingent securities are BH,t+1 and BF,t+1 . Ot represents the oil endowment at
home.

Price indexes, terms of trade, and real exchange rate. We define the price index of home and
n

1

1− ϵ
∗ ≡ [(1 − n )−1∗
foreign produced goods as PH,t ≡ [n−1 0 PH,t (i )1−ϵ di ]1/(1−ϵ) and PF,tdi ]1/(1−ϵ) ,n PF,t (i )and the home CPI ishi1/(1−γn )
1− γ∗ 1 − γnPt ≡ ωPH,t n + (1 − ω ) Et PF,t,(D.3)

In addition, we assume that the law of one price holds for all goods. We define the terms of trade as therelative price of imported goods St ≡ PF,t /PH,t and the real exchange rate as
Qt ≡ Et Pt∗ /Pt(D.4)

The real oil price as the nominal oil price expressed in home currency divided by the foreign producers
price index PF,t expressed in home currency:
Rt ≡

PO,t
.
PF,t

Optimality conditions. Consumption
1
CH,t (i ) =nPH,t (i )PH,t−ϵCH,t ,∗ (i )
PF,t

1
CF,t (i ) =
1−n

(D.5)

!−ϵ

∗
PF,t

CF,t ,

(D.6)

where

CH,t = ωPH,tPt − γnCt ,

CF,t = (1 − ω )∗Et PF,tPt(D.7)

 − γnCt ,(D.8)

Labor supply−

U2 (Ct , Nt )Wt=.
U1 (Ct , Nt )
Pt

63

(D.9)

where U1 (Ct , Nt ) and U2 (Ct , Nt ) are partial derivatives with respect to the first and the second arguments.
AssetsU1 (Ct+1 , Nt+1 ) Pt,·
U1 (Ct , Nt )Pt+1
U1 (Ct+1 , Nt+1 ) Pt
E∗Mt,t
· t +1 .
·+1 = βU1 (Ct , Nt )Pt+1
Et
Mt,t+1 = β(D.10)(D.11)

Foreign households. Conditions symmetric to (D.5)-(D.11) hold for foreign country. In particular, thefirst-order condition with respect to B∗H,t imply

Mt,t+1 = β

U1 (Ct∗+1 , Nt∗+1 ) Pt∗ 1/Et+1· ∗ ·.
U1 (Ct∗ , Nt∗ )
Pt+1
1/Et

(D.12)

Combining equations (D.10) and (D.12), we get
U (Ct , Nt )U1 (Ct+1 , Nt+1 )Q= 1 ∗ ∗ Qt ≡ ϕq ,U1 (Ct∗+1 , Nt∗+1 ) t+1
U1 (Ct , Nt )(D.13)

which implies that the ratio of marginal utility of consumption in the two countries multiplied by the realexchange rate is constant over time, which we denote as ϕq .

Log-linarization. We next log-linearize around the steady state where all relative goods prices are 1
and all prices and quantities are constant. Section D.8 will provide more details about steady state. For
now, we obtain
cbH,t = −γn ( pbH,t − pbt ) + cbt ,
cbF,t = −γn bet + pb∗F,t − pbt + cbt ,where hats denote log-deviations from steady state values.
The labor supply
bt − pbt .
σb
ct + φbnt = w
The Euler equation
Et [cbt+1 ] − cbt =1( i t − Et [ π t +1 ] − ι ) ,σwhere it ≡ − log Et [ Mt,t+1 ] is the safe short-term nominal interest rate and ι ≡ − log β.
The international risk sharing condition—a log-linear version of the second equality in equation (D.13)—
is1
cb∗t + qt = cbt .
σTotal consumption is
cbt = ωbc H,t + (1 − ω )cbF,t .

64

D.2

Price indices

The log-linearization of price indexes in home and foreign countries are
pbt = ω pbH,t + (1 − ω ) pbF,t = pbH,t + (1 − ω ) ( pbF,t − pbH,t ) ,pb∗t = ω ∗ pb∗F,t + (1 − ω ∗ ) pb∗H,t = pb∗F,t + (1 − ω ∗ ) pb∗H,t − pb∗F,t .
The real exchange rate is
qbt = bet + pb∗t − pbt = (ω + ω ∗ − 1) ( pbF,t − pbH,t ) .
Home relative prices are
1−ω
qbt ,
ω + ω∗ − 1
ωqbt ,pbF,t − pbt =ω + ω∗ − 1

pbH,t − pbt = −pbO,t − pbt = pbO,t − pbF,t +ωqbt .
ω + ω∗ − 1

Foreign relative prices are
1 − ω∗qbt ,ω + ω∗ − 1ω∗pb∗H,t − pb∗t = −qbt ,ω + ω∗ − 1
1 − ω∗∗∗
pbO,t− pb∗t = pbO,t− pb∗F,t +qbt .
ω + ω∗ − 1
pb∗F,t − pb∗t =

D.3

Firms

A home producer of variety i combines labor Nt (i ) and oil inputs OY,t (i ) to produce good i according to the
CES production function of the form
Yt (i ) = (1 − ωoy )1γy( ANt (i ))

γy −1
γy

1
γy

+ ωoy OY,t (i )

γy −1
γy

 γyγ−y 1,

where At is labor productivity, the intra-temporal elasticity of substitution γy is positive, and ωoy ∈ [0, 1] isthe share of oil in production. The firm is free to optimize its inputs every period. Because of the constantelasticity-of-substitution assumption about the form of the production function, the nominal marginal costof production does not depend on output and equals"
MCt = (1 − ωoy )



Wt
A

 1 − γy65

1− γ
+ ωoy PO,t y

#

1
1− γy

,

(D.14)

and the optimal labor and oil choices arePO,t −γyYt (i ),MCt
 Wt /A −γy Yt (i )Nt (i ) = 1 − ωoy
.
MCt
A


OY,t (i ) = ωoy(D.15)(D.16)

The firm resets its price infrequently in the spirit of Calvo. When allowed, a firm chooses the reset pricer (i ) to maximizes an expected discounted sum of future profits
PH,t

"
Et

∞

r
(i ) − (1 + τ ) MCt+k YH,t+k|t (i )∑ θ k Mt,t+k PH,t

#



k =0

where 1 − θ ∈ [0, 1] is the probability of price reset, YH,t+k|t (i ) is the output in period t + k conditional on
the price set in period t, and τ is the government’s proportional tax. The price is set in producer’s currency
and the firm does not differentiate between domestic and foreign consumers. In other words, the law of
one price holds for individual varieties.
The demand for variety i is∗
YH,t+k|t (i ) = nCH,t+k|t (i ) + (1 − n)CH,t+k |t (i ) =r (i )PH,t!−ϵ PH,t+k
1−n ∗CH,t+k +CH,t+k ,n∗where CH,t+k and CH,t+k are the home and foreign demand for home goods.
Firm’s optimal choice of its reset price requires

"
Et

∞

r (i )PH,tϵ
MCt+k PH,t+k·−(1 + τ )PH,t−1ϵ−1PH,t+k PH,t−1∑ θ Mt,t+k YH,t+k|t (i)
k

k =0

!#

= 0,

(D.17)

where we deflated the expression by PH,t−1 .

Log-linearization. We log-linearize around a steady state with constant prices and quantities andwhere all relative prices equal one. The marginal costs arec t = (1 − ωoy )w
bt + ωoy pbO,t .
mc
The demand for labor and oil arebt = −γy (wbt − mcc t) +n∗(1 − n ) C H
nCH
b∗H,t
cbH,t +∗
∗ cnCH + (1 − n) CH
nCH + (1 − n) CHbc t) +
oY,t = −γy ( pbO,t − mc∗
(1 − n ) C H
nCHb∗H,t ,
cbH,t +∗
∗ cnCH + (1 − n) CH
nCH + (1 − n) CH

The optimal reset price satisfies
c t − pbH,t ) + π H,t + βθEt prH,t+1 − p H,t .
prH,t − p H,t−1 = (1 − βθ ) (mc

66(D.18)

D.4

Government

The home government consists of fiscal and monetary authorities. The fiscal authority undoes monopolisticcompetition distortion by subsidizing production. Specifically, it sets the production tax τ = −1/ϵ and runs
a balanced budget each period.
The monetary authority sets the short-term safe nominal interest rate it ≡ − log Et [ Mt,t+1 ] according to
the Taylor rule that reacts to the producers price inflation rate π H,t ≡ log( PH,t /PH,t−1 ). Formally,it = ι + φπ πt ,(D.19)

where ι ≡ − log β and φπ ≥ 0. We do not explicitly introduce the zero lower bound on the interest rate
here.
The foreign government acts analogous to home government. In particular, the central bank set theinterest rate according toit∗ = ι + φ∗π π ∗H,t ,(D.20)
where φ∗π ≥ 0.

D.5

Oil

Oil is supplied as endowment that equals Ot and Ot∗ in per capita terms, and these endowments change∗ arerandomly every period. Households own oil and it cannot be stored. The oil prices PO,t and PO,tperfectly flexible and the law of one price applies to oil.

D.6

Market Clearing

Local markets. The home labor supply equals home labor demand n

1 − ωoy

Nt =





0

Wt /A
MCt

 − γyYt (i )di.

The market for every home variety i ∈ [0, 1] clears∗
YH,t (i ) = nCH,t (i ) + (1 − n)CH,t( i ).

(D.21)

The analogoes conditions hold for foreign country.

Global markets. In equilibrium, all markets clear. Specifically, all state-contingent asset markets clear∗n ( BH,t + Et BF,t ) + (1 − n) B∗H,t + Et BF,t= 0.
The oil market clears∗
nOY,t + (1 − n) OY,t
= nOt + (1 − n)Ot∗ .

and its log-linear approximation is∗
oY,t + (1 − n)OY∗ b
oY,t
= nOb
ot + (1 − n)O∗ b
ot∗ .
nOY b

67

D.7

Aggregation

The law of motion of the price index−ϵΠ1H,t= θ + (1 − θ )∗ 1− ϵ

Π F,t

1− ϵ

r
PH,t



,

PH,t−1
!1− ϵ

∗,r
PF,t

= θ + (1 − θ )

∗
PF,t
−1

.

The price dispersion in home country is∆ H,t ≡

1
n

 n
0

−ϵ

PH,t (i )PH,t
di = θ

PH,t−1PH,t

−ϵ∆ H,t−1 + (1 − θ )



r
PH,t

−ϵ
.

PH,t

Aggregate goods market clearing in home and foreign countries"(1 − ωoy )

(1 − ωoy )

1
γy

∗

1
γy

( ANt )

γy −1
γy

γy −1
γy

# γy

γy −1

+ ωoy

∗
OY,t

 γyγ−1

 γyγ−y 1yCH,t+k +1−n ∗CH,t+k
n

∗
CF,t
+k +

n
C
1 − n F,t+k=+ ωoy OY,t
1
γy

γy −1

( A Nt∗ ) γy

1
γy



=





∆ H,t ,∆∗F,t .

Value added in terms of produced goods
PO,t
PF,t
O = YH,t − Rt
O ,PH,t Y,t
PH,t Y,t
P∗
∗
∗
∗
∗
∗
ZF,t
= YF,t− O,t∗ OY,t = YF,t − Rt OY,t .
PF,tZH,t = YH,t −∗ is the demand for home and foreign-produced goods.
where YH,t and YF,t
Trade balance in units of domestically produced goods over steady state output

NXt
1
=
YH
YH
NXt∗
1
= ∗
YF∗
YF




PO,t
PO,t
Pt
YH,t +
Ot −
Ct −
O
,
PH,t
PH,t
PH,t Y,t!
∗P∗
Pt∗ ∗ PO,t ∗
∗
∗
YF,t
+ O,t
O
−
C
−
t
t
∗
∗
∗ OY,t .
PF,t
PF,t
PF,t

This formulas takes into account that the countries trade in goods and oil.

Log-linearization. Home and foreign inflation rates are
π H,t = (1 − θ ) pbrH,t − pbH,t−1 ,


∗
π F,t
= (1 − θ ) pb∗F,t,r − pb∗F,t−1 .
Combining the last two equations with the optimal reset price equation at home D.18 and a similar

68equation abroad, we get two standard Phillips curves(1 − θ )(1 − βθ )c t − pbH,t ) + βEt [π H,t+1 ] ,
(mc
θ

 ∗

(1 − θ )(1 − βθ )∗c ∗t − pb∗F,t + βEt π F,t
π F,t
=
mc
+1 .
θ

π H,t =

Goods market clearing(1 − ωoy )
=

=

AN
∗
CH + 1−n n CH

1γy! γy −1γy1γybt + ωoyn

OY∗
CH + 1−n n CH

! γy −1
γy

b
oY,t

∗
(1 − n ) C H
nCHb∗H,t ,
cbH,t +∗
∗ cnCH + (1 − n) CH
nCH + (1 − n) CH! γy −1! γy −1
γy
γy
1
∗
∗ N∗
1
O
A
γy
∗
∗
Y
b
b
(1 − ωoy ) γy
n
+
ω
oY,t
oy
t
CF∗ + 1−n n CF
CF∗ + 1−n n CF

(1 − n) CF∗
nCF
cb∗F,t +cb ,∗(1 − n) CF + nCF(1 − n) CF∗ + nCF F,tValue added

ωoy
1
b
ybH,t −
rt + pbF,t − pbH,t + b
oy,t ,
1 − ωoy
1 − ωoy

ωoy 
1
∗
b
b
z∗F,t =
yb∗F,t −rt + boy,t.
1 − ωoy
1 − ωoybz H,t =The trade balance is
O − OYcx t = ybH,t +nYHcx ∗t = yb∗F,t +
n

D.8


b
rt +

O∗ − OY∗
b
rt +
YF∗

1
qbt
ω + ω∗ − 1∗O∗ bot∗ − OY∗ b
oY,t
YF∗



oY,t
Ob
ot − OY bC1−ω
qbt + cbt ,+−YH
YH ω + ω ∗ − 1C∗
1 − ω∗− ∗ −qbt + cb∗t .
YF
ω + ω∗ − 1
Steady StateWe assume that in steady state all prices are constant and the relative prices equal one:
P
P
PO
= F = H = 1.
PPPThis implies that the real exchange rate isi1/(1−γn )(1 − ω ∗ ) ( PH /E )1−γn + ω ∗ ( PF∗ )1−γn
Q=
=E
=1
h
1−γn i1/(1−γn )P
1− γωPH n + (1 − ω ) E PF∗

E P∗

h

We get−U2 (C, N )=A
U1 (C, N )69(D.22)(D.23)

e−ι = β,
W
= A,
P
W
MC
=
= 1,
P
AP
CH = ωC,
CF = (1 − ω ) C,
YH = CH +

1−n ∗
CH ,
n

"
YH = (1 − ωoy )1γy( AN )

γy −1
γy

1
γy

γy −1
γy

# γy

γy −1

+ ωoy OY,
AN = 1 − ωoy YH ,OY = ωoy YH ,C = YH + O − OY .
Observe that that the last equation is the flow budget constraint of the country. Also note that if there
were no oil, then we would have C = YH and C ∗ = CF∗ + 1−n n CF and CH = ωC and CF = (1 − ω ) C and∗ = (1 − ω ∗ ) C ∗ . Combining these together, we get (1 − ω ) nC = (1 − n ) (1 − ω ∗ ) C ∗ andCF∗ = ω ∗ C ∗ and CH(1 − n) (1 − ω ∗ ) C ∗ = n (1 − ω ) C. The last two equations are identical. They determine the ratio: C/C ∗ =(1 − n) /n · (1 − ω ∗ ) / (1 − ω ) = (1 − Ω∗ ) / (1 − Ω) . How can we determine steady state consumption
−1

−1

1

level? The Backus-Smith condition C = ϕq σ C ∗ Q σ implies C/C ∗ = ϕq σ = (1 − Ω∗ ) / (1 − Ω).
Simplifying we get 3 equations and 2 unknowns C, N as functions of parameters and foreign consumption C ∗ . The first two equations below unambiguously determine C and AN, while the third equation is aconstraint on the parameter Θ.
(1 − n) (1 − ω ∗ ) 1 − ωoy C ∗ + nO
,nC =1 − 1 − ωoy ω



1−n
∗
∗
AN = 1 − ωoy ωC +(1 − ω ) C ,n
U (C, N )ΘN φ
− 2= −σ = A,
U1 (C, N )C
We can write symmetric equations for the foreign economy. Specifically,n (1 − ω ) 1 − ωoy C + (1 − n) O∗,(1 − n ) C =1 − 1 − ωoy ω ∗∗ω ∗ C ∗ + 1−n n (1 − ω ) C.
N =A
For the Backus-Smith condition to be satisfied, the constant ϕq has to take a certain value.
∗

1 − ωoy



C
− σ1
=
ϕ
.
q
C∗

70

Solving jointly for C and C ∗ , we get: 
1 − 1 − ωoy ω ∗ nO + 1 − ωoy (1 − ω ∗ ) (1 − n) O∗nC =ωoy 1 + 1 − ωoy [1 − (ω ∗ + ω )]


and




(1 − ω ) 1 − ωoy nO + 1 − ω 1 − ωoy (1 − n) O∗.
(1 − n ) C =ωoy 1 + 1 − ωoy [1 − (ω ∗ + ω )]∗The steady state share of home goods domestic demand in home good demand
nCH
nωC
=
∗
nCH + (1 − n) CHnωC + (1 − n) (1 − ω ∗ ) C ∗Andn (1 − ω ) C
nCF=
nCF + (1 − n) CF∗n (1 − ω ) C + (1 − n ) ω ∗ C ∗Consumption normalization. We further normalize steady state to have unit consumption in homeand foreign countries: C = C ∗ = 1.This normalization requires the following restriction on the parameters
1 = 1 − ωoy [1 + (1 − n) (Ω − Ω∗ )] + O.

1 = 1 − ωoy [1 + n (Ω∗ − Ω)] + O∗ ,Small open economy limit. In the case when n goes to zero, we get(1 − Ω ∗ ) = (1 − Ω ) +ωoy − O.
1 − ωoyO∗ = ωoy .
In this case, we haveΩnCH
1 − O∗
Ω
=
1
−
ω
=
Ω
=
.
oy
∗
nCH + (1 − n) CH
1−O
1−O
1 + Ω − Ω∗As a benchmark case, we assume that home country does not produce oil, that is, O = 0. In this case,(1 − Ω ∗ ) = (1 − Ω ) +ωoy.
1 − ωoyO∗ = ωoy ,and the share of domestic and foreign consumption arenCH= Ω 1 − ωoy ,∗nCH + (1 − n) CH
nCF= 0.
nCF + (1 − n) CF∗

71

D.9

Equilibrium

Unknowns (27).
bt ,Home quantities (6): cbt , cbH,t , cbF,t , boC,t , boY,t , nbt , it , mc
c t , π H,tHome prices (6):b
pt , pbH,t , w
∗
∗
b∗t ,
Foreign quantities (6): cb∗t , cb∗H,t , cb∗F,t , b
oC,t
,b
oY,t
,n
∗
bt∗ , it∗ , mc
c ∗t , π F,tForeign prices (6):bp∗t , pb∗F,t , w

International prices (3): b
et , qbt , pbO,tHome conditions (11 equations). Households
cbH,t = −γn ( pbH,t − pbt ) + cbt ,
cbF,t = −γn bet + pb∗F,t − pbt + cbt ,bt − pbt ,σb
ct + φbnt = w
Et [cbt+1 ] − cbt =1( i t − Et [ π t +1 ] − ι ) .
σ

The Price index
pbt = ω pbH,t + (1 − ω ) b
et + pb∗F,t .
Firms
c t = (1 − ωoy )w
bt + ωo pbO,t ,mc
bt = −γy (wbt − mcc t) +n∗(1 − n ) C H
nCHb∗H,t ,
cbH,t +∗
∗ cnCH + (1 − n) CH
nCH + (1 − n) CHbc t) +
oY,t = −γy ( pbO,t − mc
π H,t =∗
(1 − n ) C H
nCHb∗H,t ,
cbH,t +∗
∗ cnCH + (1 − n) CH
nCH + (1 − n) CH(1 − θ )(1 − βθ )c t − pbH,t ) + βEt [π H,t+1 ] .
(mcθGoods market clearing
bt + ωoy b
1 − ωoy n
oY,t =∗(1 − n ) C H
nCHbb∗H,t .
c
+
H,t
∗
∗ c
nCH + (1 − n) CH
nCH + (1 − n) CH

Government
it = ι + φπ π H,t .

72

Foreign condition (11 equations). Householdscb∗H,t = −γn ( pbH,t − b
et − pb∗t ) + cb∗t ,cb∗F,t = −γn pb∗F,t − pb∗t + cb∗N,t ,bt∗ − pb∗t ,σbc∗t + φbn∗t = w





1 ∗
Et cb∗t+1 − cb∗t =it − Et πt∗+1 − ι .
σThe price index
pb∗t = ω ∗ pb∗F,t + (1 − ω ∗ ) pb∗H,t .
Firms
c ∗t = (1 − ωoy )w
bt∗ + ωo ( pbO,t − bmcet ) ,
b∗t = −γy wbt∗ − mc
c ∗t − bat +n(1 − n) CF∗
nCF
cbF,t +
cb∗∗
nCF + (1 − n) CF
nCF + (1 − n) CF∗ F,t(1 − n) CF∗
nCF
cbF,t +
cb∗∗
nCF + (1 − n) CF
nCF + (1 − n) CF∗ F,t ∗(1 − θ )(1 − βθ )∗c ∗t − pb∗F,t + βEt π F,t
π F,t
=
mc
+1
θ

∗
∗
c ∗t +b− mc= −γy pbO,toY,tGoods market clearing∗b∗t + ωoy b(1 − ωoy )n
oY,t
=

∗
(1 − n) CF∗(1 − n ) C H
∗
b
c
+
cb .
(1 − n) CF∗ + nCF F,t (1 − n) CF∗ + nCF F,tGovernment∗it∗ = ι + φ∗π π F,t.

International conditions (3 equations).
qbt,
σqbt = bet + pb∗t − pbt ,cbt − cb∗t =∗nOY boY,t + (1 − n) OY∗ b
oY,t
= nOb
ot + (1 − n)O∗ b
ot∗ .

D.10

Euler Equations, Phillips Curves, Oil Price, and Risk Sharing

This section reduces all the equilibrium equations to only six: two Euler equations, two Phillips curves,
the Backus-Smith condition and the equilibrium on a global oil market. The unknowns are consumption∗ ), the real exchange rate q and the real price of oil expressed in units of foreign(cbt , cb∗t ), inflation (π H,t , π F,tt∗ −pb∗F,t .
goods br ≡ pbO,t − pbF,t = pbO,tEuler equations. Rewrite the Euler equation asEt [cbt+1 ] − cbt =111−ωEt [∆bq t +1 ] ,(it − Et [π H,t+1 ] − ι) − ·σσ ω + ω∗ − 173where πr,t ≡ πO,t − π F,t = ( pbO,t − pbO,t−1 ) − ( pbF,t − pbF,t−1 ) .
Foreign Euler equation


 ∗

 1
1 ∗
1 − ω∗
Et cb∗t+1 − cb∗t =it − Et π F,t·Et [∆bq t +1 ] .
+1 − ι +σσ ω + ω∗ − 1Consumption. Rewrite consumption of domestic goods through overall consumption and prices athome
cbH,t =

1−ωγn qbt + cbt ,ω + ω∗ − 1

cb∗H,t =ω∗γn qbt + cb∗t .
ω + ω∗ − 1

and abroad

And consumption of foreign goods
cbF,t = −ωγn qbt + cbt ,ω + ω∗ − 1cb∗F,t = −1 − ω∗
γn qbt + cb∗t .
ω + ω∗ − 1

andProduction. Domestic production of home goodsnωC(1 − n ) (1 − ω ∗ ) C ∗cbH,t +cb∗∗∗nωC + (1 − n) (1 − ω )CnωC + (1 − n) (1 − ω ∗ )C ∗ H,tnωC (1 − ω ) + (1 − n) (1 − ω ∗ )C ∗ ω ∗γn=cbtM +·qbt .
nωC + (1 − n) (1 − ω ∗ )C ∗
ω + ω∗ − 1

ybH,t =

wherecbtM ≡nωC(1 − n ) (1 − ω ∗ ) C ∗
b
c
+
cb∗ .
t
nωC + (1 − n) (1 − ω ∗ ) C ∗nωC + (1 − n) (1 − ω ∗ ) C ∗ tForeign production of foreign goodsyb∗F,t =(1 − n) CF∗
nCF
cbF,t +
cb∗∗
nCF + (1 − n) CF
nCF + (1 − n) CF∗ F,t=cbtM∗ −where
cbtM,∗ ≡nω (1 − ω ) C + (1 − n) (1 − ω ∗ ) ω ∗ C ∗γnqbt·n (1 − ω ) C + (1 − n ) ω ∗ C ∗ω + ω∗ − 1

n (1 − ω ) C(1 − n ) ω ∗ C ∗
b
c
+
cb∗ .
t
n (1 − ω ) C + (1 − n ) ω ∗ C ∗n (1 − ω ) C + (1 − n ) ω ∗ C ∗ t

Home marginal costs. Replace real wage (using the labor supply equation) from the labor demand
and the equation for the marginal costsc t − pbt = (1 − ωoy ) (σbmc
ct + φbnt ) + ωoy ( pbO,t − pbt ) ,

74

γy
γy
c t − pbt )
σb
ct +
(mc
1 + γy φ
1 + γy φ∗(1 − n ) C H
nCH
1
∗
b
b
+
c
+
c
∗ H,t
∗ H,t .
1 + γy φ nCH + (1 − n) CH
nCH + (1 − n) CH

bt = −n

Solve for equilibrium labor and the marginal costs
∗
1 − ωoy(1 − n ) C HnCH∗
c t − pbt =bH,t +bH,tmc
σbct + φ∗ c∗ c
1 + γy φωoynCH + (1 − n) CH
nCH + (1 − n) CH
1 + γy φ+ωoy ( pbO,t − pbt ) .
1 + γy φωoyand
σγy ωoyγy ωoycbt +( pb − pbt )1 + γy φωoy
1 + γy φωoy O,t∗(1 − n ) C H
1
nCH
∗
b
b
+
c
+
c
∗ H,t
∗ H,t .
1 + γy φωoy nCH + (1 − n) CH
nCH + (1 − n) CH

bt = −
n

Replace the CPI pbt with pbH,t in the marginal cost equation above at home∗1 − ωoy(1 − n ) C H
nCH∗
bH,t +bH,t
c t − pbH,t =σbct + φmc∗ c∗ c
1 + γy φωoynCH + (1 − n) CH
nCH + (1 − n) CH
1 + γy φ
1 + γy φ ωoy + (1 − ω ) 1 − ωoyωoy ( pbO,t − pbF,t ) +qbt .
+1 + γy φωoy
1 + γy φωoy (ω + ω ∗ − 1)
Rewrite the marginal costsc t − pbH,t =mc
1 − ωoy 
σbct + φbctM + ψo ( pbO,t − pbF,t ) + ψq qbt ,1 + γy φωoywhere

1 + γy φ ωoy,
ψo ≡1 + γy φωoy
1 + γy φ ωoy + (1 − ω ) 1 − ωoyψq ≡1 + γy φωoy (ω + ω ∗ − 1)
1 − ωoy1nωC (1 − ω ) + (1 − n) (1 − ω ∗ )C ∗ ω ∗
+
·
·
φγn
∗
1 + γy φωoy ω + ω − 1nωC + (1 − n) (1 − ω )C ∗Foreign marginal costs. A similar expression for foreign country marginal costs isc ∗t − pb∗t =
mc




1 − ωoy(1 − n) CF∗
nCF
∗
b
b
σb
c∗t + φc+cF,t
1 + ωoy γy φ
nCF + (1 − n) CF∗
nCF + (1 − n) CF∗ F,t
1 + φγy+ ωoypb∗ − pb∗t
1 + ωoy γy φ O,t75

and replace pb∗t
c ∗t − pb∗F,t =
mc




1 − ωoy(1 − n) CF∗
nCF
∗
b
b
σb
c∗t + φc+cF,t
1 + ωoy γy φ
nCF + (1 − n) CF∗
nCF + (1 − n) CF∗ F,t
1 + φγy1 − ωoy
1 − ω∗∗+ ωoc + ωoy− pb∗F,t −·qbt(1 − ωo,c ) pbO,t
1 + ωoy γy φ
1 + ωoy γy φ (ω + ω ∗ − 1)

Foreign country marginal costs arec ∗t − pb∗F,t =mci
1 − ωoy h ∗∗σbct + φbctM,∗ + ψo∗ pbO,t− pb∗F,t + ψq∗ qbt
1 + ωoy γy φwhereωoy 1 + φγy= ψo ,
1 + ωoy γy φ
1 − ωoy
1 − ω∗ψq∗ ≡ −·
1 + ωoy γy φ ω + ω ∗ − 1
1 − ωoynωCF + (1 − n) (1 − ω ∗ ) CF∗
1
φγn .
−
·
·
1 + ωoy γy φ ω + ω ∗ − 1
nCF + (1 − n) CF∗ψo∗ ≡Note that ψq∗ and ψq are not symmetric. This is because in both equations for the marginal costs the real oil
price is expressed in terms of foreign goods.

Phillips curves. The home Phillips curve is
π H,t = κi
1 − ωoy hσbct + φbctM + ψob
rt + ψq qbt
1 + γy φωoy

+ βEt [π H,t+1 ] ,and the foreign Phillips curve is
∗
π F,t
=κ



i
1 − ωoy h ∗σbct + φbctM,∗ + ψo∗b
rt + ψq∗ qbt
1 + ωoy γy φ

where
κ≡



 ∗

+ βEt π F,t+1 ,(1 − θ )(1 − βθ ).
θOil demand. The home firms demand for oil
1 − ωoy
1 − ωoy
1 + φγy M
σb
ct −
γy b
rt +
cb
1 + γy φωoy
1 + ωoy γy φ
1 + γy φωoy tnωC (1 − ω ) + (1 − n) (1 − ω ∗ )C ∗ ω ∗qbt∗+ (ω + ω − 1) ψq − 1 γy +γn.
∗nωC + (1 − n) (1 − ω )Cω + ω∗ − 1boY,t =γy76(D.24)

The foreign firm demand for oil
1 − ωoy
1 − ωoy
1 + γy φ M ∗
σb
c∗t −
γy b
rt +
cb
1 + ωoy γy φ
1 + ωoy γy φ
1 + ωoy γy φ tnωCF + (1 − n) (1 − ω ∗ ) CF∗
qbt
1
∗
+
γ
1
−
ω
1
−
ω
γn
−
(
)
y
oy
1 + ωoy γy φ
nCF + (1 − n) CF∗ω + ω∗ − 1

∗
b
oY,t
= γy

Oil market. Oil market equilibrium condition∗
nOY boY,t + (1 − n)OY∗ b
oY,t
= nOb
ot + (1 − n)O∗ b
ot∗ ,
∗ −p
b∗F,t .
which determines b
rt = pbO,t

D.11

A Small-Open Economy Limit

We now take the limit as the size of home economy approaches zero and the size of the foreign economy
approaches one, that is, n → 0 and n∗ = 1 − n → 1. Taking into account the following definitions
1 − ω = (1 − n ) (1 − Ω ) ,1 − ω ∗ = n (1 − Ω ∗ ) ,we have that in the limit the fraction of domestic goods expenditureω = Ω,ω ∗ = 1.
This implies thatn (1 − Ω ∗ )1 − ω∗= 0,=∗
ω+ω −1
1 − (1 − n ) (1 − Ω ) − n (1 − Ω ∗ )
nCH
ΩC
=
,
∗
nCH + (1 − n) CHΩC + (1 − Ω∗ ) C ∗nCF= 0,nCF + (1 − n) CF∗nωCF + (1 − n) (1 − ω ∗ ) CF∗= 0.
nCF + (1 − n) CF∗
The relative prices of home goods in units of domestic and foreign consumption baskets are
1−ω
1−Ω
qbt ,
qbt = −
ω + ω∗ − 1Ω1pb∗H,t − pb∗t = − qbt .
Ω
pbH,t − pbt = −

77





∗ ,b
The world economy. The world equilibrium consists of six unknowns yb∗F , cb∗t , πt∗ , π F,trt , it∗ and six

equations areb
rt = ϕc cb∗t − ϕo b
ot∗ ,
 ∗

∗
∗
π F,t
= κζ ∗ cb∗t + βEt π F,trt ,+1 + κψo b



 ∗ 
1 ∗
i − Et πt∗+1 − ι ,Et cbt+1 − cb∗t =σ t∗,it∗ = ι + φ∗π π F,t∗,
πt∗ = π F,tyb∗F,t = cb∗t .
∗ −pb∗F,t and
where brt ≡ pbO,t

1 + ωoy γy φ
 ,1 − ωoy γy 
1 + γy φ + 1 − ωoy σϕc =,1 − ωoy γyϕo =(1 − θ ) (1 − βθ ),
θ1 − ωoyζ∗ ≡(σ + φ) ,1 + ωoy γy φ

1 + γy φ ωoy∗
ψo =.
1 + γy φωoy

(D.25)(D.26)

κ≡(D.27)(D.28)We took into account that ψq∗ = 0, cbtM∗ = cb∗t .
Substituting oil price into the Phillips curve, we get
 ∗

∗
∗
π F,t
= κ (ζ ∗ + ψo∗ ϕc ) cb∗t + βEt π F,tot∗ ,+1 − κψo ϕo b
The value added isbz∗F,t =

1 − ωoy ϕc cb∗t − ωoy (1 − ϕo ) bot∗.
1 − ωoy

Trade balance is
cx ∗t = 0.
nSmall-open economy. The SOE block consists of six unknowns (cbt , ybH,t , πt , π H,t , it , qt ) and six equations78

1( i t − Et [ π t +1 ] − ι ) ,σrt + κζ F cb∗t + κψq qbt ,π H,t = κζ H cbt + βEt [π H,t+1 ] + κψob

Et [cbt+1 ] − cbt =

1−Ω
∆b
qt ,
Ω
it = ι + ϕπ π H,t ,πt = π H,t +qbt = σ (cbt − cb∗t ) ,ybH,t =Ω
1 − Ω∗Ω ( 1 − Ω ) + ( 1 − Ω ∗ ) γn
∗
b
b
c
+
c
+
·
qbt .
t
Ω + 1 − Ω∗
Ω + 1 − Ω∗ t
Ω + 1 − Ω∗
Ω

where


1 − ωoy
Ω
ζH =
σ+φ
,
1 + γy φωoy
Ω + 1 − Ω∗
1 − ωoy
1 − Ω∗
ζF =,φ
1 + γy φωoy Ω + 1 − Ω∗

1 − Ω (1 + φγn ) 1 − ωoy
ψq =
·
,
Ω
1 + γy φωoy
1 + γy φ ωoy,
ψo =1 + γy φωoy
and we took into account the fact that cbtM = cbt Ω/ (Ω + 1 − Ω∗ ) + cb∗t (1 − Ω∗ ) / (Ω + 1 − Ω∗ ). Note that
the Phillips curve has three additional terms compared to the standard closed-economy formulation. The
term κψob
rt shows that higher real oil price increase the marginal cost and, hence, inflation. The term κζ F cb∗t
is due to the fact that the world aggregate demand affects the demand for home products and increases
the cost of production. The term κψq qbt reflects the fact that oil prices are quoted in units of foreign goods.
This implies that absence any chance in the real oil price (in units of foreign goods), a real depreciation ofdomestic currency (an increase in qbt ) acts to increase the oil price in units of home goods, which, in turn,increases the marginal cost and inflation. Finally, note that ζ H + ζ F = ζ ∗ .
Substituting away the real exchange rate from the Euler equation and the Phillips curve, we obtain Ω(it − Et [π H,t+1 ] − ι) + (1 − Ω) Et cb∗t+1 − cb∗t ,σπ H,t = κ ζ H + ψq σ cbt + βEt [π H,t+1 ] + κψob
rt + κ ζ F − ψq σ cb∗t ,Et [cbt+1 ] − cbt =This form of the Euler equation implies that the home aggregate demand is affected by the rest of the world
because it changes the relative price of imported goods. A booming world economy has two opposing
effects on the Phillips curve. On the one hand, this boom increases demand for home goods and pushes up
inflation. On the other hand, a booming world economy appreciates the home currency in real terms andmakes oil cheaper at home. The net effect of these two forces is captured by the coefficientζ F − ψq σ =1−Ω
1 − Ω∗
φ−(1 + φγn ) σ.
∗
Ω+1−Ω
Ω

In general, the sign of this coefficient is ambiguos. However, under the empirical relevant parametersΩ = Ω∗ = 2/3, σ = 1, φ = 2, this coefficient is positive.

79

Oil demand is
1 + φγy1 − ωoy
1 − Ω∗Ω∗
bb
ct − brt ) +c+c(σbt
1 + γy φωoy
1 + γy φωoy Ω + 1 − Ω∗
Ω + 1 − Ω∗ tΩ (1 − Ω ) + (1 − Ω ∗ )qbt+ Ωψq − 1 γy +γn.
Ω + 1 − Ω∗ΩboY,t =γyTrade balance is1−Ω
cx t =ybH,t − ωoybnrt − ωoy +Ω + 1 − Ω∗


D.12



1
qbt
− ωoy boY,t −cbt .
ΩΩ + 1 − Ω∗

Neo-classical Effects

When prices are completely flexible, the Phillips curve in foreign country impliesc,∗cb∗t = ΓO
ϕo b
ot∗ .

where
ωoy
1−ωoy
ωoy
1−ωoy


1 + φγy 1−γy ωoy σ+γy ( φ+σ) .
1 + φγyγy (1−ωoy )

ωoy
1−ωoy

1 + φγyψ∗c,∗ΓO≡ ∗ o∗ =ζ + ψo ϕc
σ+φ+The consumption effect of oil supply change
c,∗
ΓO
ϕo =





 (1−γy ωoy σ)+γy ( φ+σ)ωoy
(1−ωoy )γy(σ + φ) + 1−ωoy 1 + φγy(1+ωoy γy φ)(1−ωoy )γyωoy 1 + φγy.
=ωoy + γy σ + φ − ωoy σ

The oil price(σ + φ)ot∗ (1−γy ωoy σ)+γy ( φ+σ) ϕo b
1 + φγy(1−ωoy )γy(σ + φ) 1 − ωoy
b
=−
o∗ .
ωoy + γy σ + φ − ωoy σ tbrt = −

ωσ + φ + 1−ωoyoy

A change in output normalized by a change in oil price
cb∗t
=
b
rt

D.13

ωoy (1+ φγy )ωoy +γy ( σ + φ−ωoy σ )(σ+ φ)(1−ωoy )−ωoy +γy ( σ + φ−ωoy σ )=−ωoy
1 + φγy·.
1 − ωoyσ+φA Two-state Markov ShockWith probability α, the shock persists, with the remaining probability it goes away. Oil shock b
ot∗ ∈ {bo ∗ , 0},wherebo ∗ < 0.

80

D.13.1

The World Economy

We start from the world economy. Using the equation for the oil price in equilibrium, we obtain the following Phillips curveκψo∗ ϕoκ (ζ ∗ + ψo∗ ϕc ) ∗cb +o∗ ) ,(D.29)π F∗ =(−b
1 − βα1 − βαThe Euler equation iscb∗ = −( φ∗π − α) π F∗.
(1 − α ) σ(D.30)The response of the inflation rate that solves the above two equations is
dπ F∗
= ϕo
d (−b
o∗ )
1+

κψo∗
(1− βα)> 0.
κ ( φ∗π −α)∗ + ψ∗ ϕ )ζ(co(1− βα)(1−α)σ(D.31)

There are two notable features here. First, the effect on inflation is non-negative (when the denominator ispositive). Second, when the shock is permanent, inflation response is zero. The response of inflation rate
when oil shock is such that the oil price increases by one percent is
π F∗ =

κψo∗
1− βα
.
κ ( φ∗π −α)∗1 + (1− βα)(
ζ1− α ) σ

The response of consumption (and output) that solve the Euler equation (combined with the monetary
policy rule) and the Phillips curve is
db
c∗
= −ϕo
d (−b
o∗ )
σ+

κ ( φ∗π −α)κ ( φ∗ −α)ψ∗(ζ ∗ + ψo∗ ϕc ) (1− βαπ)(1−α)(1− βα)(1−α) o
∗
=
Γnc,
≶ 0.
y
κ ( φ∗π −α)κ ( φ∗π −α)
∗
∗
∗
∗
ϕ
ϕ
ζ
+
ψ
σ
+
ζ
+
ψ
)
)
(
(
c
c
o
o
(1− βα)(1−α)(1− βα)(1−α)(D.32)∗
where Γnc,
= −ϕo ψo∗ / (ζ ∗ + ψo∗ ϕc ) is the neo-classical response. There are several notable observationsyhere. When the Taylor rule response to the inflation rate is strong enough, that is, φ∗π − α > 0, the aggregate consumption unambiguously falls following a hike in oil prices. This is because of the increase in
the real interest rate and the fall in demand for oil consumption. Second, when the shock is permanent:dbc∗ /d (−o ∗ ) = −ϕo ψo∗ /(ζ ∗ + ψo∗ ϕc ) < 0. Third, when goods prices are completely sticky, i.e., κ = 0, or thecentral bank targets a fixed real rate, i.e., φ∗π = α, the response of consumption is zero: dbc∗ /d (−o ∗ ) = 0.
∗
Fourth, the response is smaller compared to the case of completely flexible prices when φπ − α > 0.
The reaction of the oil price isκ ( φ∗ −α)br=

π
1 + (1− βα)(
ζ∗1− α ) σκ ( φ∗ −α)π
1 + (1− βα)((ζ ∗ + ψo∗ ϕc )1− α ) σϕo (−o ∗ ) .

(D.33)

Note that an oil supply decline unambiguously raises oil price when φ∗π − α > 0. The size of the oil shockthat increase the oil price by one percent equalsκ ( φ∗ −α)ϕo (−bo∗ ) =π
1 + (1− βα)((ζ ∗ + ψo∗ ϕc )1− α ) σκ ( φ∗ −α)π
1 + (1− βα)(
ζ∗1− α ) σ

81.

The log-deviation of the consumption level from its steady state c∗ following the oil supply shock that
increases oil price by one percent, b
r = 1, is∗cbκ ( φ∗π −α)ζ∗ψ∗σ (1− βα)(1−α)=−· ∗o .
κ ( φ∗π −α)1 + (1− βα)(1−α)σ ζ ∗ ζ(D.34)

When prices are flexible, i.e., κ → ∞,we have cb∗ = −ψo∗ /ζ ∗ , while when they are completely rigid, consumption does not respond, i.e., cb∗ = 0.

ZLB. All the above formulas can be applied to the case of the liquidity trap or inelastic interest rates by
setting φ∗π = 0. We have
κψo∗

dπ F∗
1− βα
> 0,
= ϕo
κα
∗
d (−b
o )
1 − (1− βα)(1−α)σ (ζ ∗ + ψo∗ ϕc )ακψ∗− (1− βα)(1o−α)σ
db
c∗
=
−
ϕ
> 0,
o
d (−b
o∗ )
1 − (1− βαακζ ∗ + ψo∗ ϕc ))(1−α)σ (∗1 − (1− βαακζdbr)(1−α)σ
= ϕo
> 0.
d (−b
o∗ )
1 − (1− βαακζ ∗ + ψo∗ ϕc ))(1−α)σ (For the equilibrium to be unique, we assume that1−ακ(ζ ∗ + ψo∗ ϕc ) > 0.
σ (1 − βα) (1 − α)The inflation rate response is
dπ F∗
dπ F∗
−
d (−b
o ∗ ) ZLB d (−bo ∗ ) normal=κ (ζ ∗ + ψo∗ ϕc ) φ∗π ϕo (1 − α) κψo∗ σ> 0.
[(1 − βα) (1 − α) σ − ακ (ζ ∗ + ψo∗ ϕc )] [(1 − βα) (1 − α) σ + κ (ζ ∗ + ψo∗ ϕc ) ( φ∗π − α)]The consumption response is
db
c∗
db
c∗
−
= ϕo hd (−bo ∗ ) ZLB d (−bo ∗ ) normal
σ+

κφ∗π
ψ∗ σ
(1− βα)(1−α) o−ακζ ∗ + ψo∗ ϕc )(1− βα)(1−α) (ihκ ( φ∗ −α)

σ + (1− βαπ)(1−α) (ζ ∗ + ψo∗ ϕc )The absolute response(1+γy φ)ωoyακ
· 1+γy φωoydbc∗(1− βα)(1−α)= ϕoκ (0− α )d (−bo ∗ ) ZLBσ+(ζ ∗ + ψ∗ ϕc )(1− βα)(1−α)

82

o

i.

D.13.2

The SOE Economy

The Euler equationcb = −Ω( φπ − α)π H + (1 − Ω) cb∗ .
σ (1 − α )The Phillips curveκ ζ H + ψq σ
κ
κ
πH =
cb +
ψob
r+
ζ F − ψq σ cb∗ .
1 − αβ1 − αβ1 − αβThe inflation rate response isπH =ζ H (1 − Ω) + ζ F − ψq σΩ
r+
cb∗ ,
 b

κ ( φπ −α)1 + σ(1−αβ)(1−α) ζ H + ψq σ Ωζ H + σψq Ω
κ1−αβ

ψo 1−καβκ ( φ −α)1 + (1−α)(π1−αβ)σThe first term represents the reaction of the economy to the world oil price, while the second term
represents the reaction to a change in the global economic activity. Specifically, a higher demand in theforeign economy increases the demand for home products and, at the same time, appreciates domestic realexchange rate making it less costly to produce conditional on an unchanged real oil price in the units offoreign goods.
The response of aggregate consumption is ψ σ−ζκ ( φ −α)( φ π − α )κ1 − Ω + σ(1−αβπ )(1−α) ζ H + ψq σ Ω ζ q +ψq Fσ
ζ H + σψq Ωψo
σ (1−α)(1−αβ)
H
∗
r.
cb −
cb =
 · ζ + σψ bκ ( φπ −α)κ ( φπ −α)q
1 + σ(1−αβ)(1−α) ζ H + ψq σ Ω
1 + (1−α)(1−αβ)σ ζ H + σψq Ω H
The response of aggregate consumption conditional on the oil supply shock that increases oil price by
one percentκ ( φ −α)( φ π − α )κ
ζ H + σψq Ω
1 − Ω + Ω σ(1−αβπ )(1−α) ψq σ − ζ Fψoσ (1−α)(1−αβ)
∗
cb −
cb =
,

 ·
κ ( φπ −α)κ ( φπ −α)
ζ
+
σψq
H
1 + σ(1−αβ)(1−α) ζ H + ψq σ Ω
1 + (1−α)(1−αβ)σ ζ H + σψq Ωwhere cb∗ is from equation (D.34).
We note that when φπ = φ∗π , we get cb = cb∗ .
Home production is
ybH,t =

Ω ( 1 − Ω ) + ( 1 − Ω ∗ ) γnΩ
1 − Ω∗
∗
b
b
c
+
c
+
·
qbt .
t
Ω + 1 − Ω∗
Ω + 1 − Ω∗ t
Ω + 1 − Ω∗ΩThis formula clearly illustrates that the oil shock affects the non-oil production through three distinct
channels corresponding to three terms in the formula: (i) a change in domestic aggregate demand; (ii) achange in foreign aggregate demand; (iii) an expenditure switching effect from foreign to domestic goods.
We replace the real exchange rate and domestic consumptionΩ1 − Ω∗Ω ( 1 − Ω ) + ( 1 − Ω ∗ ) γn
∗
b
b
+
·
c
+
c
σ (cbt − cb∗t )tΩ + 1 − Ω∗
Ω + 1 − Ω∗ t
Ω + 1 − Ω∗
Ω




Ω
Ω ( 1 − Ω ) + ( 1 − Ω ∗ ) γn σ
1 − Ω∗Ω ( 1 − Ω ) + ( 1 − Ω ∗ ) γn σ
b
=
1+
·
ct +
1−
·
cb∗t .
Ω + 1 − Ω∗ΩΩ
Ω + 1 − Ω∗
1 − Ω∗Ω

ybH,t =

83

The response of the real exchange rate isκ ( φπ − φ∗π )ψ Ω1σ1− βα)(1−α) o(qbt = σ (cbt − cb∗t ) = −σ.
 ·κ ( φπ −α)κ ( φ∗π −α)1 + σ(1−αβ)(1−α) ζ H + ψq σ Ω 1 + (1− βα)(1−α)σ ζ ∗The last expression implies that the real exchange rate does not respond when the home and foreign central
banks respond to domestic inflation in the same way, that is, φπ = φ∗π . When, however, home country isat the ZLB while foreign country actively responds to oil shock, i.e., φπ − φ∗π < 0, the real exchange rate
depreciates qbt > 0.
For uniqueness of bounded ZLB solution, the following condition must hold1−ακ
ζ H + ψq σ Ω > 0.
σ (1 − αβ) (1 − α)84