Relative-Price Changes as Aggregate Supply Shocks
Revisited: Theory and Evidence*
Hassan Afrouzi†

Saroj Bhattarai‡

Edson Wu§

Columbia University
and NBER

University of Texas
at Austin

University of Texas
at AustinThis Version: April 30, 2024

Abstract
We provide theory and evidence that relative price shocks can lead to aggregate inflation
and act like aggregate supply shocks. We show empirically that exogenous and positive oil
price shocks have a positive impact not only on headline U.S. inflation but also on core U.S.
inflation and a negative impact on U.S. real activity. We use a multi-sector monetary modelwith arbitrary input-output linkages and heterogeneity in price stickiness and analyticallycharacterize how sectoral shocks propagate to the aggregate economy and across sectors. We
empirically validate our analytical characterization using panel IV local projections, by showingthat the responsiveness of sectoral prices to oil price shocks is in line with what is predicted by
our analytical results. To highlight the importance of input-output linkages and heterogeneityof price stickiness in the dynamics and persistence of aggregate inflation, we perform anexperiment in our model using the aftermath of COVID-19 to show that even in the absence of
aggregate slack, relative price changes can generate persistent aggregate inflation movements
and match the behavior of headline and core inflation. We also show the critical role played bymonetary policy in the transmission of these relative price changes to the aggregate economy.
JEL Codes: E32, E52, C67
Key Words: Relative Price Changes, Aggregate Supply Shocks, Oil Price Shocks, Input-Output
Linkages, Core Inflation, Post-Covid Inflation* We thank Larry Ball and Felipe Schwartzman for very helpful comments. We thank Raphael Schoenle for generously
sharing data on frequency of price adjustment across U.S. sectors.
†
Department of Economics, 1105A IAB, 420 West 118th St, New York, NY 10027. hassan.afrouzi@columbia.edu.
‡
Department of Economics, 2225 Speedway, Stop C3100, Austin, TX 78712. saroj.bhattarai@austin.utexas.edu.
§
Department of Economics, 2225 Speedway, Stop C3100, Austin, TX 78712. edsonwu91@gmail.com.

1

Introduction

Commodity price increases and supply chain disruptions have recently been at the forefront of
discussions about possible drivers of high and persistent inflation worldwide. For instance, the top
panel of Figure 1 shows that following the Covid pandemic, supply chain pressures and commodity
prices increased substantially. The middle panel of Figure 1 shows that this in turn coincided withan increase in import inflation and headline inflation in the U.S. In addition, the middle panel of
Figure 1 highlights that both core inflation and import inflation, excluding petroleum, also rose
persistently and have remained high in the U.S. Finally, the bottom panel of Figure 1 shows howmonetary policy kept interest rates low and stable for an extended period during the run-up of
inflation and that after raising it, the unemployment rate, one of the most important measures ofaggregate slack in the economy, remained remarkably stable.
But how can relative price changes cause aggregate inflation? This is especially puzzling because
in simple multi-sector models (with no cross-sector input-output linkages and no heterogeneity
in price stickiness), such shocks, which cause “relative price” changes across sectors, do not affectaggregate inflation. In particular, aggregate inflation dynamics in these models is determinedthrough a Phillips curve that only involves the aggregate GDP gap. In other words, once aggregate
GDP gap dynamics is taken into account, these models predict no additional role for relative pricemovements in determining aggregate inflation.
We present both theoretical and empirical evidence that questions this narrative. We set up
a two-sector monetary model with input-output linkages where a downstream sector uses theother sector’s output as a production input, and where sectors differ in the duration of nominal
price changes. We show that in such an environment, aggregate inflation dynamics are determinedthrough a Phillips curve that involves not just the aggregate GDP gap, but also relative (acrosssectors) price gaps.
We show analytically that this additional role for relative price changes comes about due to
two forces: production linkages and heterogeneous price stickiness across sectors. In particular,
both model ingredients are sufficient on their own to generate such a new role for relative pricechanges. When both features are present, they interact in non-trivial ways, but this interaction cannevertheless still be understood in terms of economic mechanisms driven by model primitives.
Viewed in this way, relative price changes in our model are indeed akin to aggregate supply shocks(Ball and Mankiw, 1995), as they affect aggregate inflation even while holding aggregate GDP gap

1

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Figure 1: Recent evolution of prices, interest rates, and unemployment rate
Notes: This figure plots consumer headline and core inflation in the U.S. using the PCE index, import and import excluding petroleum inflationin the U.S. using the BLS import price index, energy inflation using the IMF energy index, and the New York Fed index of global supply chainpressure. It also plots the Federal funds rate and the unemployment rate. The time period is 2018:01-2024:01. The units are percentages for
inflation measures and for unemployment rate. The global supply chain pressure measure is normalized such that a value of zero represents theindex’s average value and a positive value represents how many standard deviations the index is above the average value.

2

constant.1
We solve our two-sector model in closed form to further illustrate how shocks to the upstream
sector propagate to aggregate and sectoral inflation. While solving for equilibrium, it is essential totake a stance on monetary policy reaction and we provide results that can accommodate various
monetary policy rules. Our key result is that an exogenous increase in relative price of the upstream
sector passes through to the downstream sector and generates inflation due to input output linkages.
Moreover, this inflationary pass-through to the downstream sector is greater if the input share of
the upstream sector is larger and it is more persistent (compared to the inflation persistence in the
upstream sector) if the downstream sector has greater price stickiness.
Empirically, we use the theoretical results as a guiding framework to investigate how recent
inflation dynamics were affected by relative price changes. First, we show that exogenous oil priceshocks that drive up producer prices in the energy sector in the U.S. have a significant positive effectnot only on headline inflation, but also on core inflation.2 That is, such shocks pass through toaggregate inflation even after removing their direct and mechanical own-sector effect, as predictedby our model with production networks.These same shocks cause a contraction in real activity as
they decrease real consumption and increase the unemployment rate. The evidence thus clearlysuggests that relative price changes originating from global oil commodity markets act as negative
aggregate supply shocks in the U.S.3
Second, we show that exogenous oil price shocks that drive up producer prices in the energy
sector in the U.S. have heterogeneous effects on consumer prices across various sectors. Our
empirical framework is a panel local projection with instrumental variables. Using the predictions
from the model on a sufficient statistic for sectoral characteristics that drive such heterogeneous
effects, we show that indeed our empirical results are consistent with the theoretical predictions. In
particular, the pass-through of relative price of energy to consumer prices is higher for sectors thathave a greater input share of energy and lower for sectors that have more rigid prices.
Finally, to highlight the importance of input-output linkages and heterogeneity of price stickiness in the dynamics and persistence of aggregate inflation, we perform an experiment in acalibrated version of our model using the aftermath of COVID-19 to show that even in the absenceof aggregate slack, relative price changes can generate persistent aggregate inflation movements.
1

The mechanism in Ball and Mankiw (1995) is however, different from the one in our paper.
We isolate exogenous variation in producer prices of the energy sector in the U.S. using the oil supply news shock ofKanzig (2021) as an instrumental variable.
3
As we show in detail later, these broad patterns are qualitatively present even if exclude the recent time period withlarge oil price shocks, the post-Covid period.
23Moreover, our calibrated model matches well the behavior of headline and core inflation, generating patterns similar to those in the middle panel of Figure 1. Using counterfactual exercises weshow how the monetary policy rules, the role of the upstream sector as a production input for thedownstream sector, as well as higher price flexibility in the upstream sector all contribute to thequantitative results that enable us to match the patterns in Figure 1.
Our paper builds on multi-sector sticky price models where price stickiness is heterogeneous
across sectors. Aoki (2001) and Benigno (2004) in two-sector models showed how heterogeneous
price stickiness across sectors leads to a role for relative price changes on aggregate inflation andanalyzed optimal monetary policy implications. Chapter 6 in Woodford (2003) has a detailed
discussion of inflation dynamics and optimal policy in two-sector sticky price models. Moreover,in models with both sticky prices and wages (Erceg, Henderson, and Levin, 2000, Blanchard andGali, 2007, Gali, 2008, Lorenzoni and Werning, 2023), the real wage gap plays a similar role to that
played by the relative price gap in our model. The continuous time sticky price and wages model in
Lorenzoni and Werning (2023) has a particularly similar structure to our model. We do not model
sticky wages or multiple production factors, but instead focus on understanding the role of acrosssector input-output linkages in a simple model where analytical results are derived under various
monetary policy rules.
Some recent papers study quantitative implications of sectoral shocks in multi-sector models. For instance, Ruge-Murcia and Wolman (2022) considers a multi-sector model with sectoral
shocks and assesses the role of relative price changes in a model without input-output linkages
while Carvalho, Lee, and Park (2021) study propagation of sectoral shocks in a model with sectoral
heterogeneity in price stickiness and a round-about production structure. Our focus in this paper is on how transition dynamics of relative prices can lead to aggregate and sectoral inflation
dynamics similar to what we observed in the post-Covid period after we allow for the roles of bothheterogeneous price stickiness and a distinct upstream sector.
Our paper is also closely related to previous work on multi-sector models with production
networks and nominal rigidities, such as Pasten, Schoenle, and Weber (2020), La’O and TahbazSalehi (2022), Rubbo (2023), and Afrouzi and Bhattarai (2023). Our model in this paper is simpler,with two sectors, as it is specifically tailored to understanding post-Covid inflation dynamics
in a highly transparent set-up. Our theoretical contribution is the focus on the interaction oftransition dynamics of relative prices and monetary policy in generating differential aggregate
and sectoral inflation dynamics. We also provide empirical support for the model predictions,especially with regards to heterogeneous effects across sectors of a relative price of energy shock,4

using dis-aggregated sectoral price data.
On the empirical front, our paper is also related to Minton and Wheaton (2023) who explore
the effects of oil shocks on sectoral producer prices using the Kanzig (2021) shock as an IV for oil
prices and estimate how the heterogeneous effects are governed by sectoral characteristics. Our
analysis is different, and is thus complementary to their results, in three dimensions. First, we
specifically use the closed-form solution for the sectoral statistic that should be the determinant of
this pass-through according to our model, which is a specific interaction of price stickiness andinput-output linkages. Second, we use the Kanzig (2021) shock as an IV for (relative) producer pricesof energy. Third, using this IV strategy, we estimate the pass-through from (relative) producer priceof energy to consumer prices.

2

Model and Theoretical Results

We base our analysis on the theoretical model of Afrouzi and Bhattarai (2023), which is a multin-sector New Keynesian model with arbitrary production linkages, heterogeneous price stickinessacross sectors, and both aggregate and sectoral shocks. Here, we consider a special case with two
sectors: “Upstream” (e.g., energy) and “Downstream” (e.g., core) where, in particular, the core sector
uses the upstream sector’s output as an input.
Thus, the model we consider here is a very special case of the model in Afrouzi and Bhattarai(2023); however, this special case allows us to go much further in deriving analytical representations for the particular set of questions that motivate this study. In particular, we use this special
framework to rigorously study (1) the mechanisms for how shocks to upstream but flexible sectors
can cause persistent spillover inflation in downstream but sticky sectors, and (2) how different
monetary policies can accommodate or mitigate such inflationary pressures.
In the rest of this section, we briefly describe the precise environment of our model, and thendiscuss the economic mechanisms that drive the role of the relative price changes in determining
aggregate inflation.4
2.1. Short description of the modelTime is continuous and runs forever. The economy consists of a representative household that
consumes an aggregate basket of goods produced by two sectors: “upstream” (Sector 1) and “downstream” (Sector 2). The aggregate consumption of this household is defined by an aggregation of
4

For a detailed description of this model in a general set-up, see Afrouzi and Bhattarai (2023).

5

these products, denoted by¶ µ¶
C 1,t β C 2,t 1−β
Ct =
β
1−β
µ

Given a vector of prices (P 1,t , P 2,t ) for the sectoral goods, the aggregate consumption bundle ispriced atβ1−β

P t = P 1,t P 2,twhich is only a function of sectoral prices. P t is therefore the CPI of this economy. The householdalso supplies labor in a competitive labor market at nominal wage Wt . Similar to baseline New
Keynesian models, labor is the only primary factor of production.
The household’s utility over consumption and leisure is given by ln(C t ) − L t . These preferences
imply that the nominal wage is proportional to the aggregate nominal demand Wt = M t ≡ P t C t . In
log-linearized terms, this implies that, with perfect foresight, the household’s inter-temporal Euler
equation can be written as
i t = ċ t + πt = ṁ t

(1)where πt = ∂t ln(P t ) is the instantaneous inflation rate, i t is the nominal interest rate, and ċ t and ṁ t
are the growth rate of log consumption and log nominal demand, respectively. Moreover, with noinvestment, government spending or imports and exports, the aggregate GDP of this economy isgiven by Y t ≡ C t .
On the firm side, each sector i ∈ {1, 2} consists of a unit measure of monopolistically competitive
firms with Calvo-type sticky prices, where firms change their prices at each period with an i.i.d.
Poisson rate of θi > 0. Importantly, θi can be different across sectors. These intermediate firms use
labor and final goods of other sectors to produce and meet the demand of a final good producer intheir sector.
In sector i ∈ {1, 2}, this final good producer uses a CES production function to exclusively demand
the product of the intermediate firms within its sector and produce its final product. These final
goods are then used by the household for consumption or by intermediate goods producers of all
sectors as inputs, forming an arbitrary production network.
For any i , j ∈ {1, 2}, we let a i j denote the expenditure share of firms in sector i on the final goodof sector j . In our two-sector economy with only one upstream sector, this structure is summarized
by three shares: a 11 and a 22 , which capture the expenditure shares of firms from their own sectors’
final good, and importantly, a 21 , which captures the expenditure share of firms in the downstream

6

sector from the final good of the upstream sector.
With constant returns to scale production functions, it follows that the log-linearized deviationof the marginal cost of firms in sector i from its level in an efficient steady-state is only a function ofprices and the nominal wage given by
mc i ,t = αi m t + a i i p i ,t + a i ,−i p −i ,t − z i ,t(2)where small letters denote deviations from the log-linearized steady-state and z i ,t is a sector-specific
Hicks-neutral productivity shock. Moreover, αi is the share of labor in sector i ’s production function,m t = w t is the nominal wage coinciding with nominal aggregate demand, a i ,−i is the expenditure
share of sector i from the other sector (a 21 for i = 2 and 0 for i = 1), p i ,t is the sector i ’s own final
good price, and p −i ,t is the final good price of the other sector. Constant returns to scale implies
αi + a i ,−i = 1 for i ∈ {1, 2}.
In the spirit of a standard New Keynesian model, we can also define the counterfactual conceptof a “desired” price for firms, which captures the linearized best response function of a firm in sector
i under flexible prices. Letting p i∗,t denote this desired price, it follows thatp i∗,t = ωi ,t + mc i ,t(3)where ωi ,t is a sector-specific markup shock. Thus, p i∗,t captures the fact that if firms had flexible
prices they would set their prices equal to their marginal cost plus a term that captures the deviationof their markups from the steady state. However, prices are not flexible and firms that do get toreset their prices at each period, choose them in a forward-looking manner to maximize the present
discounted value of their profits in the histories of events where they are stuck with their prices in
the future.
The result of this optimization problem, in log-linearized terms, is that firms that reset theirprices target a weighted average of their expected future desired prices, weighted by the probabilityof price adjustment. Denoting these reset prices by p i#,t , this object is given by the following(forward-looking) differential equation under perfect foresightṗ i#,t = (ρ + θi )(p i∗,t − p i#,t )(4)

Finally, since price changes are staggered, aggregate sectoral prices are simply an average of all
past reset prices, weighted by the probability of price adjustment. Denoting the aggregate price ofsector i by p i ,t , it evolves according to the following (backward-looking) differential equationṗ i ,t = θi (p i#,t − p i ,t )7

(5)

with the initial price level at time 0, p i ,0− , given. Going forward, for analytical convenience we willconsider the limit where ρ/θi → 0, ∀i ∈ {1, 2}.
2.2. Sectoral and aggregate Phillips curves
Together, Equations (2) to (5) across the two sectors characterize the supply side of the economy interms of two sectoral Phillips curves:
π̇1,t = (1 − a 11 )(1 − a 22 )λ2 θ12 r t − α1 θ12 x t(6)π̇2,t = −(1 − a 11 )(1 − a 22 )λ1 θ22 r t − α2 θ22 x t(7)where λ1 and λ2 are the Domar weights of sectors 1 and 2, respectively, in the zero-inflation efficient
steady-state, and are given by:
µ
¶
1
a 21
λ1 =
β + (1 − β)1 − a 11
1 − a 221−β
λ2 =1 − a 22(8)Moreover, r t ≡ (p 1,t − p 2,t ) − (p 1,t − p 2,t ) f is the relative price gap of sector 1 to sector 2, whichmeasures the gap between the current relative price and the flexible level of this relative price atftime t , and x t ≡ y t − y t is the GDP gap of this economy. It it worth recognizing that both the flexibleflevel of output, y t , and the flexible relative price, (p 1,t − p 2,t ) f , are independent of monetary policy
due to classical dichotomy in the flexible price economy. They are given by:
µ
¶
¡
¢f
¢
¢
1
a 21 ¡
1 ¡p 1,t − p 2,t =1−
ω1,t − z 1,t −ω2,t − z 2,t
1 − a 11
1 − a 22
1 − a 22f

y t = λ1 (z 1,t − ω1,t ) + λ2 (z 2,t − ω2,t )Finally, we can combining our sectoral Phillips curves, we can also derive the aggregate Phillips
curve of this economy asπ̇t = (1 − a 11 )(1 − a 22 )(βλ2 θ12 − (1 − β)λ1 θ22 )r t − (βα1 θ12 + (1 − β)α2 θ22 )x t
|
{z
} |
{z
}
Inflation due to relative price gaps

(9)

Inflation due to aggregate slack

which shows a key theoretical property of our model: aggregate inflation dynamics are not solely
determined by the aggregate GDP gap, but also depend on relative price changes, and specifically,
they depend on the relative price gap, r t . We next discuss the economic reasons for why the relative
price gap shows up in the aggregate Phillips curve, Equation (9), of our economy and also elaborateon the implications.

82.3. Discussion of why relative price gaps appear in the Phillips curves
Equations (6) and (7) show that in our network economy with potentially heterogeneous pricestickiness across sectors, relative price distortions affect sectoral inflation dynamics independentlyof the GDP gap. For instance, even if monetary policy were to fully stabilize the GDP gap (x t ≡fy t − y t ), inflation rates across sectors would still vary until relative prices are at their flexible levels.
The terms that multiply r t determine the effect of relative price distortions on inflation dynamics,
which resemble similar terms in multisector New Keynesian models as in Aoki (2001), Benigno(2004), Woodford (2003) that do not feature production networks. Equations (6) and (7) also clarify
that in this simple framework, the network amplifies the importance of these relative price gaps as
the Domar weight of each sector multiplies r t in the sectoral Phillips curve of the other sector. To
see why this amplifies the inflationary effects of sectoral shocks on other sectors, note that Domar
weights are bounded below by the expenditure share of their sector with this inequality binding
when there are no input-output linkages; i.e.,
λi ≥ βi , ∀i , with equality if a i , j = 0, ∀i , j(10)Thus, we see that with input-output linkages the impact of relative price gaps increases for all
sectoral inflation dynamics.
Moreover, on implications for aggregate inflation dynamics shown in Equation (9), note that
relative price gaps are also generally relevant except for the knife-edge case where
βλ2 θ12 = (1 − β)λ1 θ22(11)

One special case under which this condition holds is when there are no input-output linkages
a i , j = 0, and all sectors have the same price stickiness θ1 = θ2 . This is the familiar case of thestandard New Keynesian model where this multi-sector economy aggregates to a single-sector
economy, and where aggregate inflation is only affected by the aggregate slack in that economy.
2.4. Spillover Inflationary Effects of Relative Price Shocks
One key feature of this model is that the relative price of different sectors at time zero, r 0 , is a statevariable of this economy. Thus, when initial relative prices are distorted—i.e. when r 0 deviates fromits steady-state level—inflation is inherently and endogenously persistent, even without any shocks.
In this section, we study this endogenous persistence within our simple two-sector input-output
economy. To this end, we study this economy for a distorted value of r 0 —that could stem fromprevious shocks that happened before time 0—and characterize the transition path of sectoral andaggregate inflation rates back to the steady state under different monetary policy regimes.
9More precisely, we will generate such distortions in relative prices by considering a one-timepermanent shock to the productivity of the upstream sector. To see why this constitutes a disturbance in r 0 , suppose the economy is in a zero-inflation steady state at time 0, so that nominal
prices are constant over time and the deviations of all objects, including r , from their steady-statevalues are zero. We then consider a one-time permanent, unanticipated, and negative shock to the
productivity of the upstream sector. Such a shock would increase the price of the upstream sector’s
final good and would eventually lead to a new steady state where relative prices are different fromthe initial steady state. But note that from the perspective of this new steady-state, where there havebeen no shocks since time 0, the initial relative price gap at time 0, r 0 , is distorted.
2.4.1. No Monetary Response. We start by considering a monetary policy regime that does not
respond to the shock, that is, it keeps nominal demand constant (ṁ t = 0), which implies that
nominal interest rates are fixed over time, as seen from Equation (1).
Proposition 1. Suppose the economy is in a zero inflation steady state at time t = 0 and consider aone-time permanent shock to the productivity or the wedge of the upstream sector at that time. In
the absence of any monetary policy response after the shock,p
1. Inflation in the upstream sector decays at the rate of ξ1 = θ1 1 − a 11 :∂π1,t ¯¯
¯ = e −ξ1 t∂π1,0 z1
2. Spillover inflation in the downstream sector is proportional to the input share of that sector
from the upstream sector, a 21 , positive along the whole transition path, and more persistentpthan inflation in the upstream sector if and only if ξ1 > ξ2 ≡ θ2 1 − a 22 :µ¶∂π2,t ¯¯
ξ2a 21
ξ2 e −ξ1 t − ξ1 e −ξ2 t¯ =∂π1,0 z1 1 − a 22 ξ2 + ξ1
ξ2 − ξ1
Proof. Considering the deviations of prices from the new steady-state after a shock to relative prices,let p 1,0 and p 2,0 denote these log-deviations of prices in sectors 1 and 2 at time 0, right after theshock. Assuming that prior to the shock to sector 1’s productivity or wedge, the economy was in a
steady state with zero inflation, the relationship between p 1,0 and p 2,0 is given by the input-output
matrix as:
p 2,0 =a 21
p 1,0
1 − a 22(12)Given that prices are sticky, we are interested in how prices in sectors 1 and 2 start from thesevalues and converge to the steady state. Assuming that monetary policy does not respond along the10transition path; i.e., m t = 0, ∀t ≥ 0 (which also implies that i t = 0, ∀t ≥ 0), we note that0 = m t = βp 1,t + (1 − β)p 2,t + y t

(13)

f

Noting that (p 1,t − p 2,t ) f = y t = 0 along the path as well (because there are no shocks after time 0),
we haver t = p 1,t − p 2,tf

x t = y t − y t = y t = −p 1,t + (1 − β)r t
Plugging these into Equation (6), we havep̈ 1,t = π̇1,t = (1 − a 11 )(1 − β)θ12 r t − (1 − a 11 )θ12 (−p 1,t + (1 − β)r t )= (1 − a 11 )θ12 p 1,t(14)

which is second order differential equation only in terms of p 1,t with the initial condition that p 1,0 isgiven as well as the boundary condition that p 1,t should converge back to its steady state at p 1,t = 0.
It follows that
p 1,t = p 1,0 e −ξ1 t ,ξ1 = θ 1p

1 − a 11

(15)

Now, plugging the expression for r t and x t , as well as the solution to p 1,t into Equation (7), we havep̈ 2,t = π̇2,t = ξ22 p 2,t −a 21 2
ξ2 p 1,0 e −ξ1 t
1 − a 22(16)

which is a second order differential equation in p 2,t with the initial condition that p 2,0 is given
as well as the boundary condition that p 2,t should converge back to its steady state at p 2,t = 0. It
follows that
p 2,t =´
p 1,0 ³ 2 −ξ1 t
a 21
2 −ξ2 tξe−ξe
1
1 − a 22 ξ22 − ξ21 2(17)

where p 1,0 captures the initial distortion in relative prices caused by the shock to sector 1. Differentiating the solutions for p 1,t and p 2,t , we have:∂π1,t ¯¯
¯ = e −ξ1 t∂π1,0 z1µ¶∂π2,t ¯¯a 21ξ2ξ2 e −ξ1 t − ξ1 e −ξ2 t¯ =∂π1,0 z1 1 − a 22 ξ2 + ξ1
ξ2 − ξ1(18)(19)

To provide a sense of how the solution looks like, Figure 2 plots these impulse responses forillustrative numerical values that assign a higher stickiness to the downstream sector. As is clear,11

inflation in the downstream sector is more muted on impact but persists much longer.

Figure 2: Inflationary effects of a permanent shock to the relative price of the upstream sector
Notes: The figure shows the response of each sector’s inflation rate to a permanent shock to the relative price of the
upstream sector in the absence of any monetary policy response. The shock is normalized such that inflation in the
upstream sector increases by one percent on impact.

To examine Proposition 1 further analytically, let us consider the “cumulative response of
inflation (CIR)” generated by the shock in each sector, defined as the area under the impulse
response of inflation in each sector. The CIR in the upstream sector is given by ξ−11 (by design, as wehave normalized the shock to generate a one percent increase in inflation on impact). The moreinteresting case is the CIR in the downstream sector, which is given by
CIRπ2 =

a 21
× CIRπ11 − a 22(20)

which shows that, in the absence of any monetary response, the total spillover of inflation from the
upstream to the downstream sector is proportional to the input share of the downstream sector
from the upstream sector, a 21 , multiplied by the cumulative expenditure share of the downstreamP1nsector by itself, 1−a= ∞n=0 a 22 . This is a key result that shows how relative price shocks can
22
generate persistent spillover inflation in downstream sectors. In particular, note that without the
input-output linkages, the spillover effect is zero. Moreover, in the absence of price stickiness, thespillover effect is also zero, since relative prices would adjust immediately to the shock.
Moreover, to understand the short-run effects of this inflationary shock, we can also consider
the impact pass-through of inflation in the upstream sector to the downstream sector, which is
12

given by
ξ−1∂π2,0 ¯¯a 21× −1 1 −1¯ =z∂π1,0 1 1 − a 22 ξ2 + ξ1

(21)

We see that this pass-through is proportional to the long-run pass-through above, but is now
ξ−11adjusted by the term ξ−1 +ξ
−1 . This new term captures the relative duration of price stickiness in the2

1

two sectors. In particular, if the upstream sector is more flexible than the downstream sector, thenthis immediate pass-through is dampened, as it would take longer for the downstream firms to get
the opportunity to increase their prices in response.
2.4.2. Spillover Effects with Soft Landing. We now move to considering a monetary policy regime
that engineers a soft landing, that is, it keeps GDP gap at zero (x t = 0, ∀t ≥ 0).
Proposition 2. Consider a one-time permanent shock to relative prices at time zero so that r 0 ̸= 0.
Conditional on monetary policy engineering a perfect soft-landing by setting x t = 0, ∀t ≥ 0:
1. The relative price converges back to its steady state exponentially:q
r t = r 0 e −ξ̄t where ξ̄ = (1 − a 11 )(1 − a 22 )(λ2 θ12 + λ1 θ22 )(22)with the nominal prices of each sector evolving according to:
p 1,t =λ2 θ12r e −ξ̄t ,2 0

p 2,t = −λ1 θ22 + λ2 θ1

λ1 θ22r0e
λ1 θ22 + λ2 θ12

−ξ̄t

(23)

2. The relative price shock causes endogenously persistent aggregate inflation on the path,
proportional to r t :Ãπt = ξ̄λ1 θ22
λ1 θ22 + λ2 θ12!
− β rt(24)

Proof. Part 1. On a path where monetary policy engineers x t = 0, ∀t ≥ 0, we can add and subtract
the sectoral Phillips curves in Equations (6) and (7) to re-write them as:r¨t = (1 − a 11 )(1 − a 22 )(λ2 θ12 + λ1 θ22 )r t
π̇1,t

π̇2,t

λ2 θ1

λ1 θ22+2=0These are both second-order differential equations, which, subject to the boundary conditions r 0
given and stability of prices uniquely characterize the path of both price indices over time. To see
this note that, subject to these boundary conditions, the first equation implies:q−ξ̄tr t = r 0 e , ξ̄ ≡ (1 − a 11 )(1 − a 22 )(λ2 θ12 + λ1 θ22 )13

while the second one implies:λ1 θ22p +2 1,t

λ1 θ22 + λ2 θ1=⇒ p 1,t =λ2 θ12λ2 θ12
λ1 θ22 + λ2 θ12r e −ξ̄t ,2 0

λ1 θ22 + λ2 θ1

p 2,t = 0, ∀t ≥ 0

p 2,t = −(25)

λ1 θ22
λ1 θ22 + λ2 θ12

r 0 e −ξ̄tPart 2. Having specified the path of sectoral prices, we can now calculate the aggregate price level
and inflation rate asÃ
p t = βp 1,t + (1 − β)p 2,t = β −Ã=⇒ πt = −ξ̄ β −λ1 θ22
λ1 θ22 + λ2 θ22

λ1 θ22
λ1 θ22 + λ2 θ22

!
rt

!
rt

The first takeaway from Proposition 2 is that relative price distortions at an initial period canindeed cause fluctuations in aggregate inflation, even in the absence of any further shocks and any
fluctuations in aggregate slack in the economy. Note that this is a key feature of our multi-sector
economy because in the standard New Keynesian model, divine coincidence holds, such that in theface of technology shocks, closing the aggregate slack of that economy eliminates any inflationary
effects of such shocks.
The second takeaway is that given the positive relative price response along the path (i.e.,r t > 0), whether the shock is inflationary or deflationary in terms of the CPI inflation rate along theλ1 θ 2path depends on the sign of the term β − ζ where ζ ≡ λ θ2 +λ2 θ2 . To see why, note that a GDP gap
1 2

2 1

stabilization policy is essentially a price targeting rule that fully stabilizes a certain price index.5 In
our case, this price index is ζp 1,t + (1 − ζ)p 2,t = 0 as shown in Equation (25). Subtracting this priceindex from the CPI index, we can then see that along the transition path
p t = βp 1,t + (1 − β)p 2,t = (β − ζ)r t =⇒ πt = ξ̄(ζ − β)r t(26)

So an increase in the relative price of the upstream sector leads to aggregate inflation if and only if
ζ > β. This is a central point to our analysis as we can prove the following result.
Proposition 3. Suppose prices are more flexible in the upstream sector in the sense that its networkppadjusted frequency is larger (ξ1 = θ1 1 − a 11 > ξ2 = θ2 1 − a 22 ). Then, an increase in the relative
price of the upstream sector caused by a permanent shock as in Proposition 2 is CPI inflationary if
5Earlier versions of this result were shown in Galí (2015) and Woodford (2003) in the context of sticky price-sticky
wage economies as well as two sector sticky price economies with no input-output linkages. More recently, Rubbo(2023) proved this in multi-sector sticky price economies with arbitrary input-output linkages.

14and only if
Ã
!
ξ21
β
ζ > β ⇐⇒ a 21 >× 2 −1
λ2
ξ2(27)

Proof. Follows from definition of ζ and the expression for the the Domar weights λ1 and λ2 .
Equation (27) shows the importance of input-output linkages in this simple economy for generating inflation at the aggregate level due to relative price shocks to more flexible sectors. In
particular, note that with no across sector input-output linkages; i.e., a 21 = 0, the condition in
Equation (27) always fails under the assumptions of the proposition. Thus, even if heterogeneous
price stickiness across sectors was present, with no across sector input-output linkages, i.e., a 21 = 0,
it would not generate inflation at the aggregate level with GDP gap targeting.
2.5. An Experiment for the Post-COVID-19 Inflation
We finish this section by performing an experiment in a calibrated version of our model to show how
relative price changes can generate persistent aggregate inflation movements consistent with our
motivating Figure 1. We use the aftermath of COVID-19 as a case study for this experiment. We also
do counterfactual analyses to isolate the role of different forces in accounting for post COVID-19
inflation dynamics.
2.5.1. Calibration of a two-sector economy. For this experiment, we first divide the sectors in thedata to a flexible upstream group and a sticky downstream group to calibrate the network and theprice stickiness parameters of our two-sector stylized model. This calibration is described in detailin Section 6.1.
Parameter
β
θ1
θ2
a 11
a 21
a 22

Description
Upstream sector consumption share
Upstream sector frequency of price adjustment
Downstream sector frequency of price adjustment
Cost share of upstream sector on upstream sector
Cost share of downstream sector on upstream sector
Cost share of downstream sector on downstream sector

Value
0.1
0.29
0.09
0.31
0.13
0.47

Table 1: Calibrated parameters and description.

2.5.2. Results. We then shock the relative price of the upstream sector in the model in line with
Propositions 1 and 2 and consider the following monetary policy reaction: For the first T periods,
monetary policy does not react and keeps interest rates fixed (endogenously), and then for theremaining periods, it sets the interest rate to fully stabilize the GDP gap and engineer a soft-landing.
15

Figure 3 shows the response of the price of the two sectors for different values of T . The bluelines are the path of prices under no monetary response, in which case both prices rise in responseto the inflationary relative price shock. Once the economy reaches a soft-landing T the central bankstabilizes the GDP gap, and the nominal prices of the two sectors converge back to a new steadystate that is consistent with this policy per Proposition 2. We see that when monetary policy does
not react, both prices rise at a relatively faster rate, but once the soft-landing policy is implemented,
one price falls while the other one rises to reach the new steady state.

Figure 3: Inflationary effects of a permanent shock to the relative price of the upstream sector
Notes: The figure shows the response of each sector’s price level to a permanent shock to the relative price of the
upstream sector in absence of a monetary response in blue. Each red line then shows the path of price contingent onmonetary policy switching to a soft-landing policy at that time.

Figure 4 shows the response of 12 month inflation in each sector. As expected, inflation inboth sectors rise initially due to the base effect of prices being stable before the shock. Once thisbase effect is gone, prices fall faster in the upstream sector, especially after the soft landing policy
is implemented. The consequence is that at some point inflation in the upstream sector decays
quickly, while inflation in the downstream sector is more persistent.
Finally, Figure 5 is meant to map the model to the motivating evidence in Figure 1 by showing
the responses of aggregate inflation, inflation in the downstream sector (i.e. a sticky sector thatis meant to capture the behavior of core inflation), as well as inflation in the relatively flexible
upstream sector.
Here, we have chosen the size of the shock to match a peak aggregate inflation of 7 percent, and16

Figure 4: Inflationary effects of a permanent shock to the relative price of the upstream sector
Notes: The figure shows the response of each sector’s inflation rate to a permanent shock to the relative price of the
upstream sector in the absence of any monetary policy response until some time T , for alternative values of T , after
which monetary policy switches to a soft-landing policy.

we have chosen T = 16 months so that monetary policy switches to soft-landing 16 months after theshock, in line with the path of interest rates in Figure 1. With these two parameters, this admittedly
very stylized model generates the following patterns consistent with Figure 1: the relative priceshock generates persistent aggregate inflation movements in the economy; core inflation peaks ataround 5 percent and proceeds to cross aggregate inflation at around 20 months after the onset of
inflation. Both of these predictions of the model are consistent with the Post-Covid-19 inflation
dynamics episode. In particular, the model explains the behavior of the core inflation rate pretty
well due to a one-time shock to the relative price of the flexible upstream sector.

17

Figure 5: Inflationary effects of a permanent shock to the relative price of the upstream sector
Notes: The left panel shows the impulse responses of inflation rates in the upstream and downstream sectors after a
shock to relative price of the upstream sector, where monetary policy does not respond for the first 16 months after
the shock and then switches to a soft-landing policy. The right panel shows the response of aggregate inflation alongwith the downstream sector’s inflation to the same shock under the same policy. The shock size is such that aggregate
inflation peaks at 7 percent after 12 months.

18

2.5.3. Counterfactual results. We now do several counterfactual exercises that illuminate the roleof various model features that drive our results.
First, we do a policy counterfactual where the central bank stabilizes the GDP gap from the
beginning while keeping the same shocks and model parameters as in our baseline exercise. This
exercise will illustrate the extent to which the rise of aggregate inflation in Figure 5 can be attributed
to monetary policy keeping interest rates constant. The results are in Figure 6 and they show that
aggregate inflation would have peaked at a bit above 3 percent, which is considerably lower than
the 7 percent in Figure 5. Moreover, note that under such policy, the inflation in the upstream sector
would also have been slightly less pronounced while inflation in the downstream sector would havebeen negative throughout.

Figure 6: Inflationary effects of a permanent shock to the relative price of the upstream sector
Notes: The left panel shows the impulse responses of inflation rates in the upstream and downstream sectors after a
shock to relative price of the upstream sector, where monetary policy does not respond for the first 16 months after
the shock and then switches to a soft-landing policy. The right panel shows the response of aggregate inflation alongwith the downstream sector’s inflation to the same shock under the same policy. The shock size is such that aggregate
inflation peaks at 7 percent after 12 months in the baseline calibration. Policy rule is GDP gap at zero starting from t = 0.

Second, we do a model counterfactual where we shut down the role of upstream sector as asource of intermediate inputs to the downstream sector by setting a 21 = 0. The results are in Figure 7
and show that in such a case, as there is no spillover of upstream sector shock to the downstream
sector, there is no inflation in the downstream sector at all. Moreover, aggregate inflation peaks atslightly above 4 percent.
19Figure 7: Inflationary effects of a permanent shock to the relative price of the upstream sector
Notes: The left panel shows the impulse responses of inflation rates in the upstream and downstream sectors after a
shock to relative price of the upstream sector, where monetary policy does not respond for the first 16 months after
the shock and then switches to a soft-landing policy. The right panel shows the response of aggregate inflation alongwith the downstream sector’s inflation to the same shock under the same policy. The shock size is such that aggregate
inflation peaks at 7 percent after 12 months in the baseline calibration. Model counterfactuals based on no upstream
sector as a production input for the downstream sector: a 21 = 0.

20

Finally, we do a model counterfactual where we shut down the role of heterogeneous pricestickiness across sectors by setting θ2 = θ1 . The results are in Figure 8 and show that in such acase, as the downstream sector has a higher price flexibility, inflation increases by more and thus
aggregate inflation peaks at above 8 percent, higher than the baseline results of 7 percent in Figure 5.
Note however, that as price stickiness is the same across the two sectors now, the dynamics ofinflation are identical. As a result, unlike in Figure 5, the inflation is the downstream sector is neverhigher, and is not more persistent, than aggregate inflation.
Taken together, these counterfactual exercises help highlight how the monetary policy rules, therole of the upstream sector as a production input for the downstream sector, as well as higher priceflexibility in the upstream sector all contribute to the results in Figure 5 that enable us to match thepatterns in Figure 1.

Figure 8: Inflationary effects of a permanent shock to the relative price of the upstream sector
Notes: The left panel shows the impulse responses of inflation rates in the upstream and downstream sectors after a
shock to relative price of the upstream sector, where monetary policy does not respond for the first 16 months after
the shock and then switches to a soft-landing policy. The right panel shows the response of aggregate inflation alongwith the downstream sector’s inflation to the same shock under the same policy. The shock size is such that aggregate
inflation peaks at 7 percent after 12 months in the baseline calibration. Model counterfactual results based on same
price stickiness across sectors: θ2 = θ1 .

3

Empirical Framework and Results

We now present some empirical evidence on exogenous changes to relative price of energy affecting
aggregate inflation and real activity in the U.S. We also present evidence that such exogenous
21

relative price changes affect consumer prices heterogeneously across sectors in the U.S. and that
this sectoral heterogeneity is consistent with the predictions of our theoretical model.
3.1. Aggregate effects of relative price of energy shocks
We start by showing aggregate effects of exogenous changes in relative price of energy in the U.S.
This allows us to assess empirically whether shocks to relative prices act like negative supply shocks
in the aggregate.
3.1.1. Specification. Our empirical approach is a local projection instrumental variables (LP-IV)
technique. To isolate exogenous variation, we instrument relative PPI energy prices (which are PPIenergy prices relative to aggregate PPI prices) in the U.S. with the oil supply news shock of Kanzig(2021) and estimate dynamic effects of such exogenous changes in relative PPI energy prices on
PCE headline and core inflation.6 In addition, we also estimate effects on measures of real activity
such as the unemployment rate and (real) consumption. More specifically, we run³
PPI energyt
PPI energyt −1 ´log(Y t +h ) − log(Y t −1 ) = α(h) + β(h) × log(
) − log()
PPIt
PPIt −1
³
´
K
X
+
γ(h)
log(Y
)
−
log(Y
)
t −k
t −k−1
k
+

k=1
J
X

³
PPI energyt −k
PPI energyt −k−1 ´)−log() + εtζ(h)log(kPPIt −k
PPIt −k−1
k=1

(28)
(29)
(30)

where Y t is the outcome of interest and β(h) is the parameter of interest that gives us the impulse
response coefficient.
We use the following outcome variables: headline PCE, PCE core, unemployment Rate, and (real)
PCE consumption.7 Relative PPI energy price is defined as a simple geometric mean of the relative
Oil and gas extraction PPI and Petroleum and coal products manufacturing PPI (relative to aggregate
PPI).8 We use K = 12, J = 12. We instrument log(

PPI energyt
PPI energy) − log( PPIt −1 t −1 ) with the Kanzig (2021)
PPIt

oil supply news shock. Standard errors are robust to heteroskedasticity and autocorrelation. The
results are robust when we also control for lagged real wages, measured as the ratio between averagehourly earnings of production and nonsupervisory employees, total private and PCE core.
6

We are thus isolating exogenous variation in wholesale energy prices in the U.S. and estimating its dynamic
pass-through to retail prices.
7
We retrieve these data from FRED. The Appendix provides details on data sources and construction. For theunemployment rate, we do not take its log.
8
We define it as a simple geometric average of oil and gas extraction and petroleum and coal products PPI. That
1¢
1 ¢¡
¡
is, PPI energy pricest ≡ PPI Oil and gas extractiont2 PPI Petroleum and coal productst2 . A direct PPI energy is notavailable from the BLS for a long time window.

223.1.2. Results. We show that relative energy price shocks lead to an increase both in headline
inflation and core inflation. Furthermore, they also lead to a contraction in economy activity. Thisevidence is thus consistent with the idea that relative price shocks act like negative aggregate supply
shocks.
To establish this result, we first document in Figure 9 that the oil supply news shock of Kanzig(2021) has a positive and significant effect on (relative) PPI energy prices.9 This effect is present evenif we exclude the COVID-19 period, as shown in Panel B of Figure 9. To give a sense of magnitudes,
we note that a one unit shock of Kanzig (2021) leads of to a 10.88% increase in Brent oil prices on
impact.10 The pass-through here to PPI prices in the U.S. is thus about half of the effect on Brent oil
prices. We then use this shock of Kanzig (2021) as an IV for the relative PPI energy prices to show
our main aggregate results. Figure 9 thus serves to show the relevance of the oil supply news shockof Kanzig (2021) as an IV for PPI energy prices.
The first row of Figure 10 shows impulse responses of U.S. headline inflation and core inflation
to an exogenous increase in the relative price of energy, where the oil supply news shock of Kanzig(2021) is the IV.11 We observe that relative energy price shocks lead to an increase in not just headline
inflation, but also core inflation. The positive effects on core inflation depict how these shocks
have second-round pass-through effects on various sectors in the economy since measures of core
inflation deliberately exclude the direct effect of energy prices. The peak effects of these relative
energy price shocks happen fairly quickly, even on core inflation. Moreover, the initial effects arealso significant. This is indeed what our model predicts given that the oil and energy sector is arelatively flexible price sector, which leads to immediate, but transient, effects on prices.
The second row of Figure 10 shows that these shocks cause a contraction in economic activity, as
after some delay, the unemployment rate increases while (real) consumption expenditure decreases.
The effects build up slowly and peak around 24 months. Taken together, the two rows of Figure 10
show that relative price of energy shocks act like negative aggregate supply shocks.
Figure 10 is based on using data for the full sample period, 1986:01-2023:06.12 Figure 11 below
shows results for an alternate sample period, from 1986:01-2020:03. These show that the results,
both on inflationary effects as well as on an eventual economic contraction, are robust to excluding
the large oil price shocks of the pandemic period.
9

The shaded area in the Figures corresponds to 68% and 90% confidence intervals.
Figure A1 shows the impulse response of Brent oil prices after a one unit oil supply news shock.
11
The responses are of the inflation rate in the future compared to the initial period for a one percent initial period
increase in the relative price of energy.
12
Our estimation sample starts at 1986:01 because the Oil and gas extraction PPI and the Petroleum and coal products
manufacturing PPI start in 1986:01.
10

23

Panel A: Energy PPI Relative Prices, 1986:01-2023:06

0.12
0.1
0.08
0.06
0.04
0.02
0
-0.02
-0.04

0

6

12

18

24

Horizon (in months)

30

36

42

48

36

42

48

Panel B: Energy PPI Relative Prices, 1986:01-2020:03

0.15

0.1

0.05

0

-0.05

0

6

12

18

24

Horizon (in months)

30

Figure 9: Relative PPI energy prices impulse responses to an oil supply news shock
Notes: This figure plots impulse responses of relative energy PPI. The measure is relative to the aggregate PPI. This measure is defined as thesimple geometric average of relative Oil and gas extraction PPI and relative Petroleum and gas extraction PPI. The shock is the oil supply news
shock from Kanzig (2021). The dependent variable is measured in log and the independent variable is in units of the shock. The shock is such thata unit shock leads to a 10.88% increase in the Brent oil prices on impact. Sample period: Panel A: 1986:01 - 2023:06. Panel B: 1986:01 - 2020:03.
Standard errors are robust to heteroskedasticity and autocorrelation. The shaded area corresponds to 68% and 90% confidence intervals.

24

Panel A: PCE

0.15

Panel B: core PCE

0.08
0.06

0.1

0.04
0.02

0.05

0
-0.02

0

-0.04
-0.05

0

6

12

18

24

30

Horizon (in months)

36

42

-0.06

48

Panel C: Unemployment Rate

0.15

0

6

12

18

24

30

Horizon (in months)

36

42

48

42

48

Panel D: Real PCE Quantity Index

0.15
0.1

0.1

0.05
0.05

0
-0.05

0

-0.1
-0.05
-0.1

-0.15
0

6

12

18

24

30

Horizon (in months)

36

42

-0.2

48

0

6

12

18

24

30

Horizon (in months)

36

Figure 10: Impulse responses to a shock to the relative price of energy
Notes: This figure plots impulse responses of PCE headline inflation, PCE core inflation, the unemployment rate, and the real PCE quantity index.
The shock is to the relative price of energy. The relative price of energy is measured as a simple geometric mean of relative Oil and gas extraction
PPI and relative Petroleum and coal products PPI (relative to the aggregate PPI) and is instrumented by the oil supply news shock by Kanzig(2021). Both the dependent variable and the independent variable are expressed in log. Hence, the coefficients represent elasticities. Sample
period: 1986:01 - 2023:06. Standard errors are robust to heteroskedasticity and autocorrelation. The shaded area corresponds to 68% and 90%
confidence intervals. First stage F-stat: Panel A: 111.0882. Panel B: 105.6962. Panel C: 113.7576. Panel D: 135.4382.

25

Panel A: PCE

0.14

Panel B: core PCE

0.08

0.12

0.06

0.1
0.04

0.08
0.06

0.02

0.04

0

0.02
-0.02

0
-0.02

0

6

12

18

24

30

Horizon (in months)

36

42

-0.04

48

Panel C: Unemployment Rate

0.1

0

6

12

18

24

30

Horizon (in months)

36

42

48

42

48

Panel D: Real PCE Quantity Index

0.15
0.1

0.05

0.05
0

0

-0.05
-0.1

-0.05

-0.15
-0.1

0

6

12

18

24

30

Horizon (in months)

36

42

-0.2

48

0

6

12

18

24

30

Horizon (in months)

36

Figure 11: Impulse responses to a shock to the relative price of energy
Notes: This figure plots impulse responses of PCE headline inflation, PCE core inflation, the unemployment rate, and the real PCE quantity index.
The shock is to the relative price of energy. The relative price of energy is measured as a simple geometric mean of relative Oil and gas extraction
PPI and relative Petroleum and coal products PPI (relative to the aggregate PPI) and is instrumented by the oil supply news shock by Kanzig (2021).
The dependent variable and the independent variable are expressed in log. Hence, the coefficients represent elasticities. Sample period: 1986:01 2020:03. Standard errors are robust to heteroskedasticity and autocorrelation. The shaded area corresponds to 68% and 90% confidence intervals.

26

3.1.3. Robustness. We now discuss some results from a sensitivity analysis to our sample period
and specification. Figure A2 in the Appendix reports results if we use the sample period of 2008:012023:06, thereby focusing only on the time period following the financial crisis. In addition, Figure
10 is based on a specification that does not use additional variables as controls. Figure A3 in the
Appendix reports results where we use lagged real wages as controls. Comparing Figure 10 with
Figures A2 and A3 shows that the results are robust to these changes in sample period and additional
controls.
3.2. Heterogeneous Sectoral Effects of a Relative Price of Energy Shock
Underlying the aggregate inflation response to the relative price of energy shock discussed above isa distribution of sectoral inflation responses. Our model solution revealed sufficient statistics thatpredict how the sectoral inflation responses should look like, as given in (21)13 . We now estimate
these heterogeneous sectoral inflation responses and show that they align with the predictions of
the model in terms of sectoral characteristics that govern such heterogeneity. We use data startingin 1998.
3.2.1. Reduced-form results. We first show that our IV has a positive and significant effect on
sectoral PCE prices. More importantly, we show that its interaction with our sufficient statistics does
correctly predict the strength of pass-through of oil supply shocks to sectoral PCE prices. These
results are thus the “reduced-form” results underlying the IV results we will show next.
We use a panel local projection specification to estimate the effect of the oil supply news shockof Kanzig (2021) on U.S. sectoral PCE prices. More specifically, we run(h)(h)
log P j t +h − log P j t −1 = β(h)0 + β1 × Kanzigt + β2 ×

+

12
X
k=1

θj

³ aji
1 − a j j θjγ(h)(log P j t −k − log P j t −k−1 ) +
k

12
X
k=1

p

p

´
1− aj j× Kanzigtp
1 − a j j + θi 1 − a i i

ζ(h)× Kanzigt −k + ϵ j tkwhere P j t is the PCE price index of category j at time t and i indexes the IO sector that receives theshock. In our case, i is the total energy sector. The main coefficient of interest is given by β(h)2 . Wecompute Driscoll-Kraay standard errors.
In our main results, we exclude PCE categories for which Petroleum and coal products were
included in them in 1997.14 The excluded PCE categories are: Motor vehicle fuels, lubricants, and13

We measure the sufficient statistics in standard deviations.
Oil and gas extraction has zero personal consumption expenditure. Therefore, there is no PCE category that includes
Oil and gas extraction.
14

27

fluids; Fuel oil and other fuels; and Pharmaceutical and other medical products.15 The Appendix
provides further detail on how we construct the sector specific interaction term using data, where
we again note that the expression for that term is guided by our theoretical model that provides thesufficient statistic in (21).
Figure 12 shows that the Kanzig (2021) shock has a positive average effect on sectoral PCE pricesthat is relatively short-lived.16 Critically however, when we consider the interaction effect (β(h)
2 ) thatis guided by the sufficient statistic from the model, we see a significant degree of heterogeneity
in sectoral pass-through that impacts both the magnitude and the persistence of the effect of theshock. Moving from the 25th to the 75th percentile of the distribution of the sufficient statistic leads
the response to a one-unit Kanzig shock to increase by 0.3 basis points on impact, 1.5 basis points
after 3 months, and 3 basis points after 36 months.17
To provide a sense of the quantitative differences in effects across sectors, we now report total
effects on prices and how they vary across the distribution of the sufficient statistic. The (total)
responses on impact of the 25th, 50th, and the 75th percentiles of the distribution of the sufficient
statistic are 3.60, 3.69, and 4.00 basis points, respectively. The responses after three months of the
25th, 50th, and the 75th percentiles of the distribution of the sufficient statistic are 11.0, 11.3, and12.5 basis points, respectively. Finally, the responses after 36 months of the 25th, 50th, and the75th percentiles of the distribution of the sufficient statistic are 16.0, 16.7, and 19.1 basis points,
respectively. The bottom row of Figure 12 shows that results are robust to using a pre-Covid sample
period.
3.2.2. IV Results. In this subsection, we argue that the oil supply news shocks affects sectoral PCE
prices through its impact on relative PPI energy prices. That is, building on the “reduced-form”
results we presented in the previous subsection, we now present IV results where we use the oil
supply news shock as an IV for relative PPI energy prices.
We employ a panel local projection instrumental variables (panel LP-IV) technique. We consider
the effect of changes of PPI energy prices relative to PPI prices on U.S. sectoral prices, instrumenting
15

The petroleum and coal products accounted for 43% of the Motor vehicle fuels, lubricants, and fluids purchasers’
value ex-transportation cost in 1997. It accounted for 41% of the Fuel oil and other fuels purchasers’ value extransportation cost in 1997. Finally, it accounted for 0.009% of the Pharmaceutical and other medical products
purchasers’ value ex-transportation cost in 1997.
16
The shaded area in the Figures in the text corresponds to 68% and 90% confidence intervals.
17
The 25 percentile of the distribution of the sufficient statistics is 0.008153 and the 75 percentile is 0.042397. β(0)2 =(36)0.0011634, β(3)=0.0044282,
and
β=0.0090165.
Then,
the
differencein
response
after
a
one
unit
shock
becomes
2
2
(3)
β(0)
2 × (0.042397 − 0.008153) × 1 = 0.0000398 log-points ≈ 0.00398% ≈ 0.3 basis points, on impact, β2 × (0.042397 −0.008153) × 1 = 0.0001516 log-points ≈ 0.0151% ≈ 1.5 basis points after 3 months, and β(36)2 × (0.042397 − 0.008153) × 1 =0.000309 log-points ≈ 0.0308% ≈ 3 basis points.

28

6

#10-3

Panel A: Level Coe/cient

4

0.02

2

0.015

0

0.01

-2

0.005

-4

0

-6

0

5

6

#10-3

12

18

24

30

Horizon (in months)

36

Panel B: Interaction Coe/cient

0.025

42

-0.00548

Panel C: Level Coe/cient

0

6

18

24

30

Horizon (in months)

36

42

48

42

48

Panel D: Interaction Coe/cient

0.025

4

12

0.02

3
0.015

2
1

0.01

0

0.005

-1
0

-2
-3

0

6

12

18

24

30

Horizon (in months)

36

42-0.005

48

0

6

12

18

24

30

Horizon (in months)

36

Figure 12: Estimated panel Local Projections coefficients to a Kanzig (2021) shock
Notes: This figure plots the estimated panel Local Projections coefficients to an oil supply news shock, where the dependent variable is thesectoral PCE price index. Reduced form specification. The dependent variable is measured in log and the independent variable is in units ofthe shock. The shock is such that a unit shock leads to a 10.88% increase in the Brent oil prices on impact. Sample period: Panel A, B: 1998:01 2023:06. Panel C, D: 1998:01-2020:03. Standard errors are Driscoll-Kraay. The shaded area corresponds to 68% and 90% confidence intervals.

29

it using the oil supply news shock of Kanzig (2021). More specifically, we run³
PPI energyt
PPI energyt −1 ´(h)(h)
log P j t +h − log P j t −1 = β0 + β1 × log(
) − log()
PPIt
PPIt −1p´ ³³ aji
θj 1 − a j j
PPI energyt
PPI energyt −1 ´
×
log(
)
−
log(
)
+ β(h)
×pp
2
1 − a j j θ j 1 − a j j + θi 1 − a i i
PPIt
PPIt −1
+
+

12
X
k=1
12
X

(log P j t −k − log P j t −k−1 )
γ(h)
k

³
PPI energyt −k−1 ´PPI energyt −k)−log() + ϵj t
ζ(h)
×
log(
k
PPIt −k
PPIt −k−1
k=1

where P j t is the PCE price index of category j at time t . When we look at the effect of relative energy
price changes on sectoral inflation in the U.S., we are mainly interested in how the heterogeneity of
response of sectoral inflation depends on our model implied sufficient statistics. Thus, the maincoefficient of interest is given by β(h)2 . We again compute Driscoll-Kraay standard errors.
Figure 13 shows that exogenous changes in the relative price of energy lead to, on average, anincrease in sectoral PCE prices. Furthermore, sectors with a higher value of our sufficient statistic
indeed respond relatively more to these shocks, as given by the positive estimates for β(h)2 . Movingfrom the 25th to the 75th percentile of the distribution of the sufficient statistic leads the response
to a one percent increase in the relative price of energy to increase by 0.07 basis points on impact,
0.28 basis points after 3 months, and 0.55 basis points after 36 months18 .
To provide a sense of the quantitative differences in effects across sectors, we now report total
effects on prices and how they vary across the distribution of the sufficient statistic. The responses
on impact of the 25th, 50th, and the 75th percentiles of the distribution of the sufficient statistic are
0.67, 0.69, and 0.75 basis points, respectively. The responses after three months of the 25th, 50th,
and the 75th percentiles of the distribution of the sufficient statistic are 2.16, 2.23, and 2.44 basis
points, respectively. Finally, the responses after 36 months of the 25th, 50th, and the 75th percentilesof the distribution of the sufficient statistic are 1.37, 1.50, and 1.93 basis points, respectively. The
bottom row of Figure 13 shows that the results are robust to using a pre-Covid sample period.
3.2.3. Robustness and Extensions. In this subection, we show that our result is robust to includingtime fixed effects or sector fixed effects in the panel local projection specification. Furthermore, weshow evidence that our sufficient is indeed informative about the pass-through through placebo
The 25 percentile of the distribution of the sufficient statistics is 0.008153 and the 75 percentile is 0.042397. β(0)2 =(36)0.0216634, β(3)=0.0820985,
and
β=0.163326.
Then,thedifferencein
response
after
a
one
percent
increasein2
2(0)
the relative price of energy becomes β2 × (0.042397 − 0.008153) × 1% = 0.000741841% ≈ 0.07 basis points on impact,
(36)
β(3)
2 × (0.042397 − 0.008153) × 1% = 0.00281138% ≈ 0.28 basis points after 3 months, and β2 × (0.042397 − 0.008153) ×
1% = 0.005592936% ≈ 0.55 basis points after 36 months. One percentage point is equal to 100 basis points.
1830

Panel A: Level Coe/cient

0.08

Panel B: Interaction Coe/cient

0.4

0.06

F-stat = 49.9697

0.3

0.04
0.02

0.2

0
0.1

-0.02
-0.04

0

-0.06
-0.08

0

6

12

18

24

30

Horizon (in months)

36

42

-0.1

48

Panel C: Level Coe/cient

0.08

0

6

18

24

30

Horizon (in months)

36

42

48

42

48

Panel D: Interaction Coe/cient

0.4

0.06

12

0.3

0.04
0.2

0.02
0

0.1

-0.02
0

-0.04
-0.06

0

6

12

18

24

30

Horizon (in months)

36

42

-0.1

48

0

6

12

18

24

30

Horizon (in months)

36

Figure 13: Estimated panel Local Projections coefficients to a shock to the relative price of energy
Notes: This figure plots the estimated panel Local Projections coefficients to a shock to the relative price of energy, where the dependent variable
is the sectoral PCE price index. The relative price of energy is instrumented by the oil supply news shock from Kanzig (2021). The dependent
variable and the independent variable are expressed in log. Hence, the coefficients represent elasticities. Sample period: Panel A, B: 1998:01 2023:06. Panel C, D: 1998:01 - 2020:03. Standard errors are Driscoll-Kraay. The shaded area corresponds to 68% and 90% confidence intervals.
F-stat: 49.9697.

31

tests. Finally, we present several extensions.
Placebo Tests. One may be concerned that the significant interaction coefficients we find might bepresent even if we use the sufficient statistics with relation to sectors that are not directly affectedby oil supply shock. To address that, we run the same regression as in the panel local projection IV
results subsection constructing the sufficient statistics corresponding to the following IO sectors:
Ambulatory health care services, Hospitals, Insurance carriers and related activities, and Legal
services19 . Since oil supply shocks do not affect directly the PPI price in these sectors, we expect theinteraction coefficient to be non-positive over the entire horizon. Figure 14 shows the results thatare consistent with what we would expect.
Panel A: Level Coe/cient

0.2

Panel B: Interaction Coe/cient
0

0.1

-0.02

0
-0.1

-0.04
0

6

0.2

12

18

24

30

36

Horizon (in months)
Panel C: Level Coe/cient

42

48

0

6

0

6

0

6

0

6

0.02

0.1

12

18

24

30

36

42

48

12

18

24

30

36

42

48

12

18

24

30

36

42

48

18

24

30

36

42

48

Horizon (in months)
Panel D: Interaction Coe/cient

0

0
-0.1

0

6

0.2

12

18

24

30

36

Horizon (in months)
Panel E: Level Coe/cient

42

-0.02

48

0.05

0.1

0

0
-0.1

-0.05
0

6

0.2

12

18

24

30

36

Horizon (in months)
Panel G: Level Coe/cient

42

48
0.1

0.1

0.05

0

0

-0.1

Horizon (in months)
Panel F: Interaction Coe/cient

0

6

12

18

24

30

Horizon (in months)

36

42

-0.05

48

Horizon (in months)
Panel H: Interaction Coe/cient

12

Horizon (in months)

Figure 14: Estimated panel Local Projections coefficients to a shock to the relative price of energy
Notes: This figure plots the estimated panel Local Projections coefficients to a shock to the relative price of energy, where the dependent variable
is the sectoral PCE price index. The relative price of energy is instrumented by the oil supply news shock from Kanzig (2021). The dependent
variable and the independent variable are expressed in log. Hence, the coefficients represent elasticities. Sample period: 1998:01 - 2023:06. PanelA, B: Ambulatory health care services. F-stat: 50.3411. Panel C, D: Hospitals. F-stat: 50.3452. Panel E, F: Insurance carriers and related activities.
F-stat: 51.46013. Panel G, H: Legal services. F-stat: 50.496. Standard errors are Driscoll-Kraay. The shaded area corresponds to 68% and 90%
confidence intervals.

19

These are IO sectors with a very small share of cost accounted for Oil and gas extraction (211), Petroleum and coalproducts (324), and Utilities (22)32Sectoral Quantity Responses. Besides the heterogeneous sectoral price responses, we also present
the responses of sectoral quantities, using the same panel local projection IV specification. Thus,
we use real PCE quantities of various sectors as the dependent variable. Figure 15 shows theresults, which depict negative interaction coefficients, as expected and consistent with the positive
interaction coefficients in Figure 13 for sectoral prices.20 Moving from the 25th to the 75th percentileof the distribution of the sufficient statistic leads the response to a one percent increase in therelative price of energy to decrease by 0.22 basis points on impact and 0.68 basis points after 36
months.21
Sensitivity Analysis. We now report results from some important sensitivity analysis. First, we
run an alternative specification including time fixed effects, which should account for common
shocks that affect all PCE categories. Figure A4 in the Appendix shows the results. Next, we runan alternative specification including sector fixed effects which should account for time invariant
sectoral heterogeneity. Figure A5 in the Appendix shows the results. In both cases, the results are
similar to our baseline results.
Finally, throughout our analysis, we assumed that the total energy sector was represented byboth oil and gas extraction and petroleum and coal products. We now show that our results arerobust to considering oil and gas extraction only as the oil sector. For this analysis, we do not
exclude any PCE category in the panel regressions. The reason is because the oil and gas extraction
sector is not consumed as a final consumption for any category. Therefore, there is no mechanicaleffect on sectoral PCE prices. Figure A6 in the Appendix shows the results for prices and Figure A7
in the Appendix for quantities. They are similar to our baseline results.

4

Extension

In this section, we present evidence suggesting that changes in global supply chain pressures mightalso act as negative aggregate supply shocks in the U.S.. We document that increased pressuresin global supply chains are linked to increases in domestic inflation and a reduction in economic
activity. Moreover, global supply chain pressure first manifests most strongly in import prices ofindustrial supplies and materials, thereby suggesting a link with intermediate inputs as in ourtheoretical model.
20

See Ghassibe (2021) for an analysis of sectoral consumption responses to a monetary policy shock and an interpretation of the results based on input-output linkages.
21
The 25th percentile of the distribution of the sufficient statistic is 0.008153 and the 75th percentile is 0.042397.
(0)β2 = −0.0668064, β(36)= −0.19911. Then, the difference in response after a one percent increase in the relative price of2energy becomes β(0)×(0.042397− 0.008153) × 1% = −0.00228% ≈ −0.22 basis points on impact and β(36)22 × (0.042397 −0.008153) × 1% = −0.00682% ≈ −0.68 basis points after 36 months.

33

Panel A: Level Coe/cient

0.4
0.3

F-stat = 49.9697

0.1

0.2

0

0.1

-0.1

0

-0.2

-0.1

-0.3

-0.2
-0.3

Panel B: Interaction Coe/cient

0.2

0

6

12

18

24

30

Horizon (in months)

36

42

-0.4

48

Panel C: Level Coe/cient

0.3

0

6

12

18

24

30

Horizon (in months)

36

42

48

42

48

Panel D: Interaction Coe/cient

0.2
0.1

0.2

0

0.1

-0.1
0

-0.2

-0.1
-0.2

-0.3

0

6

12

18

24

30

Horizon (in months)

36

42

-0.4

48

0

6

12

18

24

30

Horizon (in months)

36

Figure 15: Estimated panel Local Projections coefficients to a shock to the relative price of energy
Notes: This figure plots the estimated panel Local Projections coefficients to a shock to the relative price of energy, where the dependent variable
is the sectoral PCE quantity index. The relative price of energy is instrumented by the oil supply news shock from Kanzig (2021). The dependent
variable and the independent variable are expressed in log. Hence, the coefficients represent elasticities. Sample period: 1998:01 - 2023:06.
Standard errors are Driscoll-Kraay. The shaded area corresponds to 68% and 90% confidence intervals.

34

To support this finding, we use the New York Fed Global Supply Chain Pressure Index (GSCPI)
as a measure of global supply chain pressures in a local projection framework, as in Subsection 3.1.
We focus on the period before the COVID-19 pandemic to ensure that our results are not driven byunusually high shocks or endogenous movements in the GSCPI.
Our analysis first shows that rising global supply chain pressures correlate with higher importprices, which we conjecture is a main channel through which global supply chain pressures affectdomestic activity. In particular, as shown in Panel A of Figure 16, a one unit innovation in the
GSCPI is associated with approximately 0.15 log-points increase, after 24 months, in import prices
of industrial supplies and materials, which serve as inputs for firms. Moreover, more broadly, as
shown in Panel B of Figure 16, a one unit innovation in the GSCPI is associated with approximately
0.06 log-points increase, after 24 months, in over import prices. Panels C and D of show results for
PCE prices for durables and non-durables, which have a lower pass-through compared to importprices. The effects are nevertheless still significant.
Next we present results related to aggregate prices and economic activity. The first row of Figure
17 shows impulse responses of U.S. headline inflation and core inflation to an innovation in the
GSCPI. We observe that innovations in the GSCPI lead to an increase in both headline inflation andcore inflation, although the effect on core inflation is less precisely estimated. The second row of
Figure 17 shows that innovations in the GSCPI are associated with contraction in economy activity,
as after some delay, the unemployment rate increases, while (real) consumption expenditure
decreases. Taken together, the two rows of Figure 17 suggest that global supply chain pressures canact as negative aggregate supply shocks.

35Panel A: Import Prices Industrial Supplies and Materials

0.25
0.2

0.08

0.15

0.06

0.1

0.04

0.05

0.02

0

0

-0.05

0

6

12

18

24

30

Horizon (in months)

36

42

-0.02

48

Panel C: PCE Durable Goods Prices

0.05

0.04

0.03

0.03

0.02

0.02

0.01

0.01

0

0

0

6

12

18

24

30

Horizon (in months)

36

0

6

42

-0.01

48

12

18

24

30

Horizon (in months)

36

42

48

42

48

Panel D: PCE Non-Durable Goods Prices

0.05

0.04

-0.01

Panel B: Import Prices

0.1

0

6

12

18

24

30

Horizon (in months)

36

Figure 16: Impulse responses to a global supply chain pressure innovation
Notes: This figure plots impulse responses of import price inflation, import price industrial supplies and materials inflation, PCE durable
goods price inflation, and PCE non-durable goods price inflation. The independent variable is the NY Fed Global Supply Chain Pressure
Index. The dependent variable is expressed in log, while the independent variable is expressed in units of the index. Controls for 12 lags of log
industrial production change, log real wage changes, log PCE changes, log PCE core changes, unemployment changes, and log real personal
consumption expenditures. Sample period: 1998:01 - 2020:03. Standard errors are robust to heteroskedasticity and autocorrelation. The shaded
area corresponds to 68% and 90% confidence intervals.

36

Panel A: PCE

0.025

20

0.02

#10-3

Panel B: PCE core

15

0.015

10

0.01
5

0.005

0

0
-0.005

0

6

12

18

24

30

Horizon (in months)

36

42

-5

48

Panel C: Unemployment

0.03

6

12

18

24

30

Horizon (in months)

36

42

48

42

48

Panel D: Real PCE quantity

0.01

0.025

0

0.02

-0.01

0.015

-0.02

0.01

-0.03

0.005

-0.04

0
-0.005

0

0

6

12

18

24

30

Horizon (in months)

36

42

-0.05

48

0

6

12

18

24

30

Horizon (in months)

36

Figure 17: Impulse responses to a global supply chain pressure innovation
Notes: This figure plots impulse responses of PCE headline inflation, PCE core inflation, the unemployment rate, and the real PCE quantity index.
The independent variable is the NY Fed Global Supply Chain Pressure Index. The dependent variable is expressed in log, while the independent
variable is expressed in units of the index. Controls for 12 lags of log industrial production change, log real wage changes, log PCE changes, log
PCE core changes, unemployment changes, and log real personal consumption expenditures. Sample period: 1998:01 - 2020:03. Standard errors
are robust to heteroskedasticity and autocorrelation. The shaded area corresponds to 68% and 90% confidence intervals.

37

5Conclusion

In this paper, we show how relative price changes cause aggregate inflation in a multi-sector sticky
price model with input-output linkages. We present a two-sector calibrated model that can accountfor recent headline and core inflation dynamics in the U.S., where the shock that drives inflation is ashock to an upstream sector that has a low relative price duration. Empirically, using dis-aggregated
PCE price data, we show that exogenous changes to the relative price of energy have heterogeneouspass-through to PCE sectoral prices, as predicted by our model.

References
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Approach,” NBER Working Paper No. 31218.
A OKI , K. (2001): “Optimal Monetary Policy Responses to Relative-Price Changes,” Journal of Monetary Economics, 48(1),55–80.
B ALL , L., AND N. G. M ANKIW (1995): “Relative-Price Changes as Aggregate Supply Shocks,” The Quarterly Journal of
Economics, 110(1), 161–193.
B AQAEE , D. R., AND E. FARHI (2020): “Productivity and Misallocation in General Equilibrium,” The Quarterly Journal of
Economics, 135(1), 105–163.
B ENIGNO, P. (2004): “Optimal Monetary Policy in a Currency Area,” Journal of International Economics, 63(2), 293–320.
B LANCHARD, O., AND J. G ALI (2007): “Real Wage Rigidities and the New Keynesian Model,” Journal of Money, Credit
and Banking, 39(s1), 35–65.
C ARVALHO, C., J. W. L EE , AND W. Y. PARK (2021): “Sectoral Price Facts in a Sticky-Price Model,” American Economic
Journal: Macroeconomics, 13(1), 216–56.
E RCEG , C. J., D. W. H ENDERSON , AND A. T. L EVIN (2000): “Optimal monetary policy with staggered wage and pricecontracts,” Journal of Monetary Economics, 46(2), 281–313.
G ALI , J. (2008): Monetary Policy, Inflation, and the Business Cycle: An Introduction to the New Keynesian Framework.
Princeton University Press.
G ALÍ , J. (2015): Monetary Policy, Inflation, and the Business Cycle: An Introduction to the New Keynesian Framework and
Its Applications. Princeton University Press.
G HASSIBE , M. (2021): “Monetary policy and production networks: an empirical investigation,” Journal of Monetary
Economics, 119, 21–39.
K ANZIG , D. R. (2021): “The Macroeconomic Effects of Oil Supply News: Evidence from OPEC Announcements,”
American Economic Review, 111(4), 1092–1125.
L A’O, J., AND A. TAHBAZ -S ALEHI (2022): “Optimal Monetary Policy in Production Networks,” Econometrica, 90(3),1295–1336.
L ORENZONI , G., AND I. W ERNING (2023): “Wage Price Spirals,” Manuscript.
M INTON , R., AND B. W HEATON (2023): “Hidden Inflation in Supply Chains: Theory and Evidence,” Manuscript.
PASTEN , E., R. S CHOENLE , AND M. W EBER (2020): “The Propagation of Monetary Policy Shocks in a Heterogeneous
Production Economy,” Journal of Monetary Economics, 116, 1–22.
RUBBO, E. (2023): “Networks, Phillips curves, and Monetary policy,” Econometrica, 91(4), 1417–1455.
RUGE -M URCIA , F. J., AND A. L. W OLMAN (2022): “Relative Price Shocks and Inflation,” Working Paper 22-07, Federal
Reserve Bank of Richmond.
W OODFORD, M. (2003): Interest and Prices: Foundations of a Theory of Monetary Policy. Princeton, NJ: Princeton
University Press.

38

6

Appendix

6.1. Data and sources
Variable
PCE Price Index
PCE Core Price Index
Unemployment Rate
Real PCE Quantity IndexPPIPPI Oil and gas extraction
PPI Petroleum and Coal Products Mfg
PCE Price Indices by Type of Product
Real PCE by Type of Product, Quantity Indices
IO Use Table Before Redefinitions PRO
PCE Bridge at Summary level
Frequency of price adjustment
Import Matrices Before Redefinitions SUM
PCE Energy Price Index
Import Price Index
Import Price Ex-Petroleum Index
Average hourly earnings
PCE Durable Goods Price Index
PCE Non-Durable Goods Price Index
PCE Goods Price Index
PCE Services Price Index
Real PCE Goods Quantity Index
Real PCE Services Quantity Index
Oli Supply News Shock
Global Supply Chain Pressure Index

SourceSeries Code

St. Louis FRED
St. Louis FRED
St. Louis FRED
St. Louis FRED
St. Louis FRED
St. Louis FRED
St. Louis FRED
Table 2.4.4U.
Table 2.4.3U.
BEA
BEA
Pastel et al. (2020)
BEA
St. Louis FRED
St. Louis FRED
St. Louis FRED
St. Louis FRED
St. Louis FRED
St. Louis FRED
BEA: Table 2.4.4U.
BEA: Table 2.4.4U.
BEA: Table 2.8.3.
BEA: Table 2.8.3.
https://github.com/dkaenzig/oilsupplynews
https://www.newyorkfed.org/research/policy/gscp...

PCEPI
PCEPILFEUNRATEDPCERA3M086SBEAPPIACOPCU21112111
PCU32413241

DNRGRG3M086SBEAIR
IREXPET
AHETPIDDURRG3M086SBEA
DNDGRG3M086SBEA

Table A1: Variables and data used in the regressions.

PPI energy. We construct a measure of PPI energy by calculating a simple geometric mean between
the PPI oil and gas extraction and the PPI petroleum and coal products mfg. That is,
¡
1 ¢¡
1 ¢
PPI energyt ≡ PPI oil and gas extractiont/2 PPI petroleum and coal products mfgt/2
Input-Output table (A) and Personal consumption expenditures (β). We use the 1997 IO use
table before redefinition in producers’ value at the Summary level disaggregation. We disregard
the distinction between commodities and industries and assume that each industry produces only
one commodity. Furthermore, we exclude the government sectors (GFGD, GFGN, GFE, GSLG,
GSLE), Scrap, used and secondhand goods (Used), Noncomparable imports and rest-of-the-world
adjustment (Other)22 . After this, we end up with 66 sectors. For the empirics, we also perform thefollowing two processes: (1) we collapse the retail summary sectors into a single retail sector. That
22

Baqaee and Farhi (2020) adopts a similar procedure.

39is, we collapse Motor vehicles and parts dealers (441), Food and beverage stores (445), Generalmerchandise stores (452), and Other retail (4A0) into a single retail sector; (2) we collapse Oil andgas extraction (211) and Petroleum and coal products (324) into a single Total oil sector. We end up
with 62 sectors.
Frequency of price adjustment. We use data from Pasten, Schoenle, and Weber (2020). The data
comes at a more disaggregated level than the disaggregation we use (Summary level). We aggregate
it into our disaggregation level by taking the simple average of frequency of price adjustment amongindustries within our disaggregation level for which we have data.
Sufficient Statistics for PCE categories. An important component of our analysis is the NIPA
PCE bridge table. We use the 1997 PCE bridge table. For each PCE category, the rows of thebridge table shows the commodities included in it, the producers’ value of the commodity, andthe transportation costs and trade margins required to move the commodity from producer toconsumer.
We are interested in

h a

ji

1−a j j θ jθjp

1−a j jp
1−a j j +θi 1−a i ipij is PCE category

where j is a PCE category. We do notdirectly observe the cost shares in terms of PCE categories, a j i , their frequency of price adjustment
θ j , or their own category input share a j j . However, we do observe the IO commodities that compose
this PCE category, along with its producers’ value, transportation costs, and trade margins.
To overcome this limitation, to calculate the sufficient statistic, we take a weighted average ofthe sufficient statistic for each IO sector that is included in j ’s PCE category. The weights are givenby the share of PCE purchasers’ value ex-transportation cost accounted for the respective IO sector.
We include wholesale margins and retail margins as rows in the bridge. These would correspond to
the Wholesale Trade (42) and the consolidated Retail Sector (441, 445, 452, 4A0). The reason why
we exclude transportation cost is because at the Summary level, we cannot assign to which one of
the transportation sectors (481, 482, 483, 484, 486, 487) this cost refers to. Similarly, the reason why
we collapse the retail sectors into one retail sector is because we cannot assign the margin to thecorresponding IO retail sector.
Two sector calibration. In the theory section, we use a two-sector model with an upstream sector
and a downstream sector. We define the upstream sector as the Oil and gas extraction (211),
Petroleum and coal products (324), Utilities (22), Primary metals (331), Wholesale trade (42), Farms(111CA), Other real estate (ORE), and Federal Reserve banks, credit intermediation, and related
activities (521CI) sectors. All other sectors are defined as downstream sectors. For the frequency
of price adjustment, we first calculate the continuous time FPA, then we calculate the sectoral

40

duration 1/θi . Then, we take the simple average of the sectoral duration among sectors that belong
to the upstream and downstream sectors. Finally, we recover the upstream and downstream FPA
by calculating θ j = 1/duration j , j ∈ {upstream, downstream}. To construct A and β we use the IO use
table, collapsing the IO sectors that belong to upstream and downstream sectors. We end up withthe following objects:

β=


A=



βupstream
βdownstream

a 11 a 12
a 21 a 22





=



=

0.10030.8996

0.3102 0.3668
0.1346 0.4703



where the sector 1 is the upstream sector, and sector 2 is the downstream sector. Finally, θupstream
00.2899
0
=

Θ=
0
θdownstream
00.092041

6.2. Additional results for aggregate effects
Panel A: Brent Oil Prices, 1987:05-2023:06

0.2
0.15
0.1
0.05
0
-0.05
-0.1

0

6

12

18

24

Horizon (in months)

30

36

42

48

36

42

48

Panel B: Brent Oil Prices, 1987:05-2020:03

0.2
0.15
0.1
0.05
0
-0.05
-0.1

0

6

12

18

24

Horizon (in months)

30

Figure A1: Impulse responses to a Kanzig shock
Notes: This figure plots impulse responses of Brent Oil prices. The shock is the oil supply news shock from Kanzig (2021). The dependent variable
is measured in log and the independent variable is in units of the shock. In panel A, a one unit shock leads to a 10.88% increase in oil prices on
impact. Standard errors are robust to heteroskedasticity and autocorrelation. The shaded area corresponds to 68% and 90% confidence intervals.

42Panel A: PCE

0.2

Panel B: core PCE

0.1

0.15

0.05

0.1

0

0.05
-0.05

0

-0.1

-0.05
-0.1

0

6

12

18

24

30

Horizon (in months)

36

42

-0.15

48

Panel C: Unemployment Rate

0.15

6

12

18

24

30

Horizon (in months)

36

42

48

42

48

Panel D: Real PCE Quantity Index

0.3

0.1

0.2

0.05

0.1

0

0

-0.05

-0.1

-0.1

-0.2

-0.15
-0.2

0

0

6

12

18

24

30

Horizon (in months)

36

42

-0.3

48

0

6

12

18

24

30

Horizon (in months)

36

Figure A2: Impulse responses to a shock to the relative price of energy
Notes: This figure plots impulse responses of PCE headline inflation, PCE core inflation, the unemployment rate, and the real PCE quantity index.
The shock is to the relative price of energy. The relative price of energy is measured as a simple geometric mean of relative Oil and gas extraction
PPI and relative Petroleum and coal products PPI (relative to the aggregate PPI). Sample period: 2008:01 - 2023:06. Both the dependent variable
and the independent variable are expressed in log. Hence, the coefficients represent elasticities. Standard errors are robust to heteroskedasticity
and autocorrelation. The shaded area corresponds to 68% and 90% confidence intervals.

43

Panel A: PCE

0.14

Panel B: core PCE

0.08

0.12

0.06

0.1
0.04

0.08
0.06

0.02

0.04

0

0.02
-0.02

0
-0.02

0

6

12

18

24

30

Horizon (in months)

36

42

-0.04

48

Panel C: Unemployment Rate

0.15

0

6

12

18

24

30

Horizon (in months)

36

42

48

42

48

Panel D: Real PCE Quantity Index

0.15
0.1

0.1

0.05
0.05

0
-0.05

0

-0.1
-0.05
-0.1

-0.15
0

6

12

18

24

30

Horizon (in months)

36

42

-0.2

48

0

6

12

18

24

30

Horizon (in months)

36

Figure A3: Impulse responses to a shock to the relative price of energy
Notes: This figure plots impulse responses of PCE headline inflation, PCE core inflation, the unemployment rate, and the real PCE quantity index.
The shock is to the relative price of energy. The relative price of energy is measured as a simple geometric mean of relative Oil and gas extraction
PPI and relative Petroleum and coal products PPI (relative to the aggregate PPI). The specification uses lagged real wages as controls. Both thedependent variable and the independent variable are expressed in log. Hence, the coefficients represent elasticities. Sample period: 1986:01 2023:06. Standard errors are robust to heteroskedasticity and autocorrelation. The shaded area corresponds to 68% and 90% confidence intervals.
First stage F-stat: Panel A: 84.77. Panel B: 78.55. Panel C: 113.10. Panel D: 116.99.

44

6.3. Robustness and extensions on sectoral effects
Time Fixed Effects Regressions. In this subsection we run an alternative specification includingtime fixed effects which should account for common shocks that affect all PCE categories. Figure
A4 shows that our sufficient statistics does predict the response of sectoral inflation to oil supply
shocks correctly. Finally, we consider robustness in which we add time fixed effects, and in which
we add sector fixed effects. That is, in the time fixed effects specification, we run
p
³ aji
´ ³
θj 1 − a j j
PPI energyt
PPI energyt −1 ´(h)log P j t +h − log P j t −1 = β1 ×× log() − log()
pp
1 − a j j θ j 1 − a j j + θi 1 − a i i
PPIt
PPIt −1
+

12
X
k=1

(log P j t −k − log P j t −k−1 ) + F E t + ϵ j tγ(h)kinstrumenting the change in the relative prices of energy with the oil supply news shock from Kanzig(2021). F E t is the time fixed effect.
Sector Fixed Effects Regressions. In this subsection we run an alternative specification including
sector fixed effects which should account for time invariant sectoral heterogeneity. Figure A5 shows
the result. For the sector fixed effects specification, we run
p
³ aji
´ ³
θ
1− aj j
PPI energyt −1 ´
PPI energytjlog P j t +h − log P j t −1 = β(h)
×
)
−
log(
)
×
log(
p
p
1
1 − a j j θ j 1 − a j j + θi 1 − a i i
PPIt
PPIt −1
+

12
X
k=1

γ(h)
(log P j t −k − log P j t −k−1 ) + F E j + ϵ j tkwhere F E j is the sector fixed effect.
Oil and gas extraction as the oil sector. Throughout our analysis, we assumed that the total oil
sector was represented by both oil and gas extraction and petroleum and coal products. In thissubsection, we show that our results are robust to considering oil and gas extraction as the oil sector.
For this analysis, we don’t exclude any PCE category. The reason why we do this is because the oiland gas extraction sector is not consumed as a final consumption for any category. That is, thepersonal consumption expenditures for the oil and gas extraction sector is zero. Therefore, there isno mechanical effect on sectoral PCE prices. Figure A6 shows the results for prices and Figure A7 forquantities.

45

Panel A: Interaction Coe/cient

0.4

F-stat = 58.0717

0.3

0.3

0.2

0.2

0.1

0.1

0

0

-0.1

0

6

12

18

24

30

Horizon (in months)

36

42

-0.1

48

Panel A: Interaction Coe/cient

0.5
0.4

Panel B: Interaction Coe/cient

0.4

0

6

18

24

30

Horizon (in months)

36

42

48

42

48

Panel B: Interaction Coe/cient

0.4

F-stat = 61.6266

12

0.3

0.3

0.2

0.2
0.1

0.1

0

0
-0.1

0

6

12

18

24

30

Horizon (in months)

36

42

-0.1

48

0

6

12

18

24

30

Horizon (in months)

36

Figure A4: Estimated panel Local Projections coefficients to a shock to the relative price of energy
Notes: This figure plots the estimated panel Local Projections coefficients to a shock to the relative price of energy, where the dependent variable isthe sectoral PCE price index. The relative price of energy is instrumented by the oil supply news shock from Kanzig (2021). The dependent variable
and the independent variable are expressed in log. Hence, the coefficients represent elasticities. Panel A: All PCE categories. 1998:01-2023:06.
F-stat: 58.0717. Panel B: All PCE categories. 1998:01-2020:03. Panel C: Ex-PCE categories with positive Petroleum and coal products or Oil and gas
extraction producers’ value. 1998:01-2023:06. F-stat: 61.6266. Panel D: Ex-PCE categories with positive Petroleum and coal products or Oil andgas extraction producers’ value. 1998:01-2020:03. Standard errors are Driscoll-Kraay. The shaded area corresponds to 68% and 90% confidence
intervals.

46

Panel A: Level Coe/cient

0.1
0.08

0.2

0.06

F-stat = 49.9279

0.15

0.04

0.1

0.02

0.05

0

0

-0.02

-0.05

-0.04
-0.06

Panel B: Interaction Coe/cient

0.25

0

6

12

18

24

30

Horizon (in months)

36

42

-0.1

48

Panel C: Level Coe/cient

0.1

0

6

12

18

24

30

Horizon (in months)

36

42

48

42

48

Panel D: Interaction Coe/cient

0.25
0.2
0.15

0.05

0.1
0.05
0

0
-0.05

-0.05

0

6

12

18

24

30

Horizon (in months)

36

42

-0.1

48

0

6

12

18

24

30

Horizon (in months)

36

Figure A5: Estimated panel Local Projections coefficients to a shock to the relative price of energy
Notes: This figure plots the estimated panel Local Projections coefficients to a shock to the relative price of energy, where the dependent variable
is the sectoral PCE price index. The relative price of energy is instrumented by the oil supply news shock from Kanzig (2021). The dependent
variable and the independent variable are expressed in log. Hence, the coefficients represent elasticities. Specification with sector fixed effects.
Panel A and B: 1998:01-2023:06. Panel C and D: 1998:01-2020:03. Standard errors are Driscoll-Kraay. The shaded area corresponds to 68% and
90% confidence intervals. F-stat: 49.92

47

Panel A: Level Coe/cient

0.1

Panel B: Interaction Coe/cient

0.4

F-stat = 50.6754

0.3

0.05

0.2
0
0.1
-0.05

-0.1

0

0

6

12

18

24

30

Horizon (in months)

36

42

-0.1

48

Panel C: Level Coe/cient

0.08

6

12

18

24

30

Horizon (in months)

36

42

48

42

48

Panel D: Interaction Coe/cient

0.35
0.3

0.06

0.25

0.04

0.2

0.02

0.15

0

0.1

-0.02

0.05

-0.04
-0.06

0

0
0

6

12

18

24

30

Horizon (in months)

36

42

-0.05

48

0

6

12

18

24

30

Horizon (in months)

36

Figure A6: Estimated panel Local Projections coefficients to a shock to the relative price of energy
Notes: This figure plots the estimated panel Local Projections coefficients to a shock to the relative price of energy, where the dependent variable
is the sectoral PCE price index. The relative price of energy is instrumented by the oil supply news shock from Kanzig (2021). The dependent
variable and the independent variable are expressed in log. Hence, the coefficients represent elasticities. The sufficient statistic is created withrelation to Oil and gas extraction sector. Sample: All PCE categories. Panel A, B: 1998:01 - 2023:06. Panel C, D: 1998:01 - 2020:03. Standard errors
are Driscoll-Kraay. The shaded area corresponds to 68% and 90% confidence intervals. F-stat: 50.6754

48

Panel A: Level Coe/cient

0.4

-0.05

0.2

-0.1

0.1

-0.15

0

-0.2

-0.1

-0.25

-0.2

-0.3
0

6

12

18

24

30

Horizon (in months)

36

42

-0.35

48

Panel C: Level Coe/cient

0.4

0

6

12

18

24

30

Horizon (in months)

36

42

48

42

48

Panel D: Interaction Coe/cient

0.05
0

0.3

-0.05

0.2

-0.1

0.1

-0.15

0

-0.2

-0.1

-0.25

-0.2
-0.3

F-stat = 50.6754

0

0.3

-0.3

Panel B: Interaction Coe/cient

0.05

-0.3
0

6

12

18

24

30

Horizon (in months)

36

42

-0.35

48

0

6

12

18

24

30

Horizon (in months)

36

Figure A7: Estimated panel Local Projections coefficients to a shock to the relative price of energy
Notes: This figure plots the estimated panel Local Projections coefficients to a shock to the relative price of energy, where the dependent variable
is the sectoral PCE quantity index. The relative price of energy is instrumented by the oil supply news shock from Kanzig (2021). The dependent
variable and the independent variable are expressed in log. Hence, the coefficients represent elasticities. The sufficient statistic is created withrelation to Oil and gas extraction sector. Sample: All PCE categories. Panel A, B: 1998:01 - 2023:06. Panel C, D: 1998:01 - 2020:03. Standard errors
are Driscoll-Kraay. The shaded area corresponds to 68% and 90% confidence intervals. F-stat: 50.6754

49