Volatility and Pass-throughDavid Berger1

Joseph Vavra2

1 Northwestern University
2 University of Chicago and NBER

May 25, 2014

Berger & Vavra(NWU and Booth)

PassthroughMay 25, 2014

Introduction

We document an robust positive relationship between the dispersion ofprice changes and exchange rate pass-through:Items with high price change dispersion have high pass-throughMonths with high price change dispersion have high pass-throughBerger & Vavra(NWU and Booth)

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Pass-through is not a single number: it varies across time
Average pass-through from 1994-2012 is 15%
But prices dispersion varies a lot across time and ignoring micro data
leads to huge time-varying bias
Pass-through varies from 8% in 1997 to upwards of 40% in 2008
0.18

NBER Recessions
Interquartile Range of Price Changes

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Empirical evidence that micro heterogeneity matters
If we want to know the IRF of a macro variable to a shock or change
in policy, how much attention needs to be paid to the distribution of
agents in the economy?
Long-standing, largely model driven debate
What would direct empirical evidence that micro matters for IRF look
like?
Measure an observed aggregate shock
Measure the observed IRF of an aggregate variableShow this observable IRF varies with micro

We will do exactly this in a particular context where it is feasible
The response of import prices to an exchange rate shock depends onthe dispersion of price changes that vary across time

Berger & Vavra(NWU and Booth)

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Understanding Our Empirical Results

To now, everything is empirical, but what might explain relationshipbetween price change dispersion and pass-through?
Imperfect "responsiveness" has been embraced by literature to explain
incomplete pass-throughBut if there is heterogeneity, has additional implications
If some …rms are more "responsive" to shocks at some points in time:
Should have more disperse price changes
Should have higher exchange rate pass-throughBerger & Vavra(NWU and Booth)

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Formally Understanding Our Empirical Results

Quantifying the importance of various channels:
Build and formally estimate model of exporting price-setters withheterogeneity a¤ecting price change dispersion and pass-throughCannot explain our empirical results:
Heterogeneity in menu costs, calvo frequencies, import intensity,
exchange rate volatility
Heterogeneity in volatility or "volatility shocks"

Can explain our empirical results:
Heterogeneity in markup elasticities or other forms of strategic
complementarities

Berger & Vavra(NWU and Booth)

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Model Implications

Large literature studying "uncertainty" or "volatility" shocks
Estimated model says dispersion and pass-through relationship not
explained by volatility shocks
Variable markup/Competition based explanations much more
promising

Berger & Vavra(NWU and Booth)

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Outline

Empirical results
Implications for Time-Varying Pass-ThroughUnderstand our result
Quantitative model estimation

Berger & Vavra(NWU and Booth)

PassthroughMay 25, 2014

Data

BLS IPP micro data underlying import price indices
Product data from survey
Record various transaction details for particular items including priceand country of origin
Over 10,000 price observations per month
Wide range of imports

IMF exchange rate data
Data on US and foreign CPI and US GDP

Berger & Vavra(NWU and Booth)

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Data Continued

Benchmark results:
All countries
Dollar priced non-petroleum goods
Bilateral exchange rates
Market based transactions
Country-sector …xed e¤ects

Berger & Vavra(NWU and Booth)

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Benchmark Pass-through Measure

How much of cumulated exchange rate movements are
passed-through when an item adjusts?
Let ∆c ei ,t be the cumulative change in exchange rate since last priceadjustment∆pi ,t = β∆c ei ,t + Zi0,t γ + ei ,tAverage medium-run pass-throughβse ( β) t-stat Nobs
R2
0.144 0.014 10.17 95284 0.067

Berger & Vavra(NWU and Booth)

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Measuring Price Change Dispersion

Want to test if there is a relationship between price change dispersion
and pass-throughMeasuring dispersion in the data:
Item-level dispersion:
Fix item j calculate dispersion of all that item’s price changes acrosstime:
DIj = disp (∆pi ,t ji = j )Month-level dispersion:
Fix month k, calculate dispersion across the price changes of all itemsin that month:
DMk = disp (∆pi ,t jt = k )Berger & Vavra(NWU and Booth)

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Item-Level Dispersion and Pass-throughLet DIi = std (∆pi ) be the standard deviation of item i’s pricechanges (conditional on adjusting)
Split sample into quintiles by XSD and within each quintile, regress∆pi ,t = βj ∆c ei ,t + Zi0,t γ + ei ,tBerger & Vavra(NWU and Booth)

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Item-Level Dispersion and Pass-Through

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Pass-Through

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0
.018

Berger & Vavra.047(NWU and Booth).076
Item-Level Standard Deviation-Quintiles

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May 25, 2014

Month-Level Dispersion

Same relationship in time-series using month-level dispersion?
For each month, calculate IQR of price changes across items
Divide time-series quintiles by IQR:

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Month-Level Dispersion and Pass-Through

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Pass-through

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3
IQR Quintile

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More Formal Test for Signi…canceMonth-level dispersion standard errors somewhat larger
But straightforward to do formal test for increasing relationship
Divide time-series into high and low dispersion months
Run the regression:h∆pi ,t = βhigh∆c ei ,t + Zi0,t γhighi

Ithigh +

h

β

low

∆c ei ,t + Zi0,t γlow

where Ithigh and Itlow are indicators for high and low dispersion.

Berger & Vavra(NWU and Booth)

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Itlow + ei ,tMay 25, 2014

Formal Test for Month-Level Dispersion PT Relationship

Split time-series in thirds by di¤erent dispersion measures:
Split

Berger & Vavra

βhigh

βlow

βhigh βlowt -stat

n

R2

IQR

0.21

0.08

0.12

4.35

62395

0.09

XSD

0.17

0.08

0.10

3.89

63095

0.09

Bloom

0.26

0.06

0.20

6.33

64204

0.08

(NWU and Booth)

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Dispersion or Frequency?
Run regressions split by DI and freq

0.35

0.3

Frequency Quintile 1 (Lowest)
Frequency Quintile 2
Frequency Quintile 3
Frequency Qunitile 4
Frequency Qunitile 5 (Highest)

Pass-Through

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1

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Item-Level Standard Deviation: Quintiles

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Product type

0.25
Differentiated Products
Other Products

Pass-Through

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1

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Item-Level Standard Deviation: Quintiles

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Robustness: Just the 2008 Recession?

Lots of things might be special about 2008 Recession
Big common shock might increase pass-throughLots of uncertainty might increase dispersion

Is our result just driven by this outlier?
If all driven by one period, maybe just a coincidence

No: All results go through Pre 2008
There is a strong link in cross-section and time-series between
dispersion and pass-through over whole sample

Berger & Vavra(NWU and Booth)

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Robustness and Additional Controls
To be less boring, just showed binned regressions. Can rerun all
results using interactions with continuous dispersion measures
Can then control for other things
Run results controlling for item-frequency, aggregate frequency,
product substitution, time-trends, seasonality, business cycle measures
All results go throughHave rerun everything for alternative sample selection and exchange
rate measures:
OECD and various individual countries instead of all-countries
Di¤erentiated/Manufactured items instead of all items
Trade weighted exchange rates
Separately for exchange rate increases and decreases
Various Additional Results

Berger & Vavra(NWU and Booth)

PassthroughMay 25, 2014

Section 2

Interpretting Our Estimates: Implications for
Pass-Through Across Time

Berger & Vavra(NWU and Booth)

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What Does Pass-Through Look Like Across Time?

First, use our empirical speci…cation to back out implied PT acrosstime under alternative parametric assumptions:
Assuming MRPT only varies because IQRt varies
ave
IQR
\t =b
MRPT
β +b
β IQRtAssuming MRPT varies for lots of reasons:

\t
MRPT

ave
IQR
freq
subs
= b
β +b
β IQRt + b
β freqt + b
β
subst

+b
β

Berger & Vavra(NWU and Booth)GDP

i .Month
GDPt + bβti.Montht

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Parametric Results
Pass-Through Estimate (IQR effects)
0.4

Pass-Through Estimate (All Controls)

NBER Recessions
Level of Pass-through

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0

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Pass-Through Estimate (All Controls Except IQR)
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Non-Parametric Results
Estimate MRPT in rolling 12-month windows

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Section 3

Understanding Our Empirical Relationship

Berger & Vavra(NWU and Booth)

PassthroughMay 25, 2014

Organizing framework: ‡exible prices

Optimal price is:pi = µi + mci (e, η i )gross markup (µi )common dollar marginal cost (mc (e ))idiosyncratic cost (mc (η i ))Taking total derivative gives:∆pi =with ΓinBerger & Vavra∂µiand αi∂(∆p i ∆p )(NWU and Booth)Γi (∆pi∆p ) + αi ∆e + ∆η i

∂mci
∂e

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Organizing framework: pass-through and variance

Exchange rate pass-through
∆pi
αi
=
∆e
1 + Γi
Variance of pricesvar (∆pi ) =αi
1 + Γi2var (∆ei ) +1
1 + Γi2var (∆η i )Theory implies positive relationship between PT and variance: factors
which increase pass-through (α " and Γ #) also increase varianceFurthermore, will show α channel doesn’t explain our results

Berger & Vavra(NWU and Booth)

PassthroughMay 25, 2014

Quantitative Models

As pure empirical statement, micro data on price dispersion isimportant for predicting pass-through, but...
What explains the positive relationship between pass-through andprice dispersion?
Estimate a model to assess di¤erent possibilities. Heterogeneity in:
Menu costs?
Volatility?
Import intensity?
Responsiveness?
Exchange rate volatility?
"Common-ness" of shocks

Berger & Vavra(NWU and Booth)

PassthroughMay 25, 2014

Modeling Exchange Rate Pass-throughAssess Calvo and Menu cost version of model in Gopinath and
Itshkhoki (2010)
Dynamic price-setting model of import prices
Firms set prices to maximize discounted pro…ts
Firms face Kimball demand with elasticity σ and super-elasticity εhCj = 1

Berger & Vavra(NWU and Booth)

ε ln

σ Pj
σ 1 P

iσ/ε

;

PassthroughΓ=ε
σ 1 +ε ln

σxj
σ 1

May 25, 2014

Firm Pro…ts

Firm j’s marginal cost depends on idiosyncratic productivity Aj ,foreign wages W and domestic wages Wih
W 1 α (W ) α
Cj
Firm pro…ts given by Πj = Pj
Aj
Domestic …rms have α = 0 foreign …rms have α > 0

Cost shocks:
W follows a random walkReal exchange rate E
W
log Aj = ρA log Aj 1 + σA ej

Firms face menu costs of price adjustment κ

Berger & Vavra(NWU and Booth)

PassthroughMay 25, 2014

Calibration

β = .961/12
Foreign share of sector = 16.5%
Demand elasticity = 5
Std dev of erate = .025
ρA = 0.85
Sensitivity to exchange rates, markup elasticity, menu cost andstandard deviation of shocks set to match ave:
MRPT, R 2 of MRPT, std dev of price changes, and frequency

Berger & Vavra(NWU and Booth)

PassthroughMay 25, 2014

What A¤ects Pass-through?

∆pi ,t = β∆e + e implies:cov (∆p, ∆e )cov ( β∆e + e, ∆e )cov (e, ∆e )
b
β=
=
= β+
var (∆e )var (∆e )var (∆e )With ‡ex prices:

β=

α
1+Γ

To increase pass-through
Increase α or lower ε (and thus Γ).
Increase κ or lower σA since increases cov (e, ∆e )Berger & Vavra(NWU and Booth)

PassthroughMay 25, 2014

Matching the Cross-Item Dispersion Results

Holding other parameters at baseline, vary menu costs, volatility andsuper elasticity and look at e¤ects on MRPT, XSD and freq

Berger & Vavra(NWU and Booth)

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Figure: Menu Cost Comparative Statics

κ (Menu Cost)
0.3

0.25

0.25
pass-throughpass-throughε (Markup Elasticity)
0.3

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0
0

data
model

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0.05

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0.2
std dev of price changes

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0

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pass-throughpass-through

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σA (Idiosyncratic Volatility)α (Import Intensity)

0
0

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0.2
std dev of price changes

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std dev of price changes(NWU and Booth)

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Passthrough

0
0

0.05

0.1
0.15
0.2
std dev of price changes

May 25, 2014

Cross-Item dispersion results conclusion

Variation in either ε or κ can match relationship between XSD and
MRPT
Only variation in ε generates (the empirically correct)
corr (freq, XSD ) > 0
Qualitatively, responsiveness is best able to match cross-sectional facts
Can we make more formal statements?

Berger & Vavra(NWU and Booth)

PassthroughMay 25, 2014

Indirect Inference Estimation

Let …rms simultaneously di¤er in responsiveness, idiosyncratic
volatility and menu costs
For tractability use binary distribution for each

Formally estimate importance of each using indirect inference:
Match MRPT, XSD and Freq by 5 XSD bins
Gives us 15 auxiliary moments and 3 parameters to estimate

Berger & Vavra(NWU and Booth)

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Heterogeneity Estimates

Estimate how much each parameter varies from mean:
Parameterε∆σ∆κ∆

Estimated Variation
10
.03
.014

CI Estimated Variation(8.14,11.86)(.0035,.0565)(-.0125,.0405)

Can also compute goodness of …tFormally reject models without ε
But easier to see all this visually

Berger & Vavra(NWU and Booth)

PassthroughMay 25, 2014

Estimated Fit to 15 Moments
Relative PT by XSD bins

Relative XSD by XSD bins

Best Fit

2

1.5

2
1

1
1

No ε variation2

No κ variation

2

No σ variation0
1

2

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Relative Freq by XSD bins

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(NWU and Booth)

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Passthrough

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May 25, 2014

Aggregate shocks

In the paper we add aggregate shocks to ε, α, κ, σA to try to match
time-series regressions
Don’t have strong guidance for modeling the shocks so try di¤erent
thingsAgain …nd only ε consistent with the data
Note: what matters is variation in Γ = σ ε 1=> time-variation in elasticity of substitution also works

Berger & Vavra(NWU and Booth)

PassthroughMay 25, 2014

Aggregate Shocks Continued

In addition, also explored whether time-varying exchange rate
volatility or "commonness" of aggregate shocks can exlain
month-level dispersion pass-through relationshipTo make shocks more common, change the fraction of …rms whose
costs depend on exchange rate
Neither shock works:
Exchange rate volatility
Commonality of shocks

Berger & Vavra(NWU and Booth)

PassthroughMay 25, 2014

Model Implications
Uncertainty shocks vs time-varying responsiveness
Existing literature on countercyclical dispersion (e.g. Bloom et al;
Vavra; Arellano et al) has implicitly embraced σA " as way to explain
time series variation in dispersion
However, variation in Γ also generates time variation in pricedispersion
Our model results suggest only variation in Γ can explain thetime-series relationship between MRPT and XSD
Our exchange rate shock let’s us identify time-varying responsivenessvs. heteroscedastic shocks
Model supports time-varying responsiveness: recessions are time ofincreased competitiveness (σ ") which leads to larger price changes andmore pass-throughBerger & Vavra(NWU and Booth)

PassthroughMay 25, 2014

What Drives Responsiveness?

Our model results tell us in a reduced form sense we should look forthings that a¤ect responsivenessBut lots of mechanisms deliver imperfect responsiveness as reduced
form
Kimball Demand (This paper)
Market share (Atkeson and Burstein 2008)
Customer concerns (Paciello, Pozzi and Trachter 2013)
Reduced form variation in quadratic adjustment costs

Hard to disentangle with our data but not hopeless with other datasets
Our results suggest variation in something like market structure or
demand is important for aggregate dynamics

Berger & Vavra(NWU and Booth)

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Conclusions

Empirically, aggregate pass-through moves strongly across time withmicroeconomic price change dispersion
Provides "model-free" evidence that distributions matter for importprice IRF to exchange rate shock

Show that this arises naturally through if there is variation in"responsiveness"
Other channels like volatility shocks don’t work in estimated model

Future work:
Thinking about what could drive "responsiveness" shocks
Thinking about ways to apply empirical strategy to alternativeenvironments

Berger & Vavra(NWU and Booth)

PassthroughMay 25, 2014

A Mechanical Relationship?

Flex price benchmark:∆pi ,tvar (∆pi ,t )= βj ∆ei ,t + ei ,t
)
=

βj

2

var (∆ei ,t ) + var (ei ,t )What if only β (e.g. import intensity) varies across …rms?
Can run this experiment and show it explains <0.1% of our results (seepaper)
Will show also in quantitative model

Berger & Vavra(NWU and Booth)

PassthroughMay 25, 2014

Section 5

Measurement Error?

Berger & Vavra(NWU and Booth)

PassthroughMay 25, 2014

Various Forms of Measurement Error in Data

Various forms of measurement and sampling error might a¤ect bothmeasured pass-through and dispersion:
Sampling Error
Size of price changes reported incorrectly
Inertia so not all price changes reported
Shipping lags

Simulate these things in model to try to assess importance

Berger & Vavra(NWU and Booth)

PassthroughMay 25, 2014

Modeling Measurement Error

Modeling sampling error:
We already sample simulated data in previous experiments in same way
as BLS, so all our results account for thisModeling errors in price change size:
Assume that ∆preported = ∆ptrue + e

Missing price changes
Assume that ∆preported = Ireportvariable that takes value 0 and 1∆ptrue where Ireport is a random

Shipping lags:∆preported ,t = ∆ptrue,tBerger & Vavra(NWU and Booth)L with L

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Classical ME

0.2
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std of price changes

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Timing Error

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std of price changes

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tto
Bu

el
ab

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Non-reporting Error
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pass-throughpass-throughpass-through

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std of price changes

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Data
Model

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Classical ME

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pass-through

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Menu Cost Model

Non-reporting Error

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pass-throughpass-throughCalvo Model

Timing Error
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Data
Model

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0.2
std of price changes

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0
0

0.1
0.2
std of price changes

0.3

Even really big measurement or non-reporting error don’t a¤ect
measured passthrough much
Time-varying shipping lags might be more important but even there
would need big variation and would need to be correlated withsomething a¤ecting volatility
Berger & Vavra(NWU and Booth)

PassthroughMay 25, 2014

.5

.55

shr_vessel

.6

.65

Can try to proxy for errors induced by shipping lags indirectly in data
since more likely important for goods imported by boat:

2004m1

2006m1

2008m1

2010m1

2012m1

2014m1mdate

Berger & Vavra(NWU and Booth)

PassthroughMay 25, 2014

Items shipped by boat more likely to have long lags, attenuation bias
and thus understated passthroughBut there is a positive correlation (0.13) between fraction of tradeshipped by boat and IQR
So would work against our result
Have also controlled directly for shipping composition to the extent
possible in both month-level and item-level results

Other reason shipping lags have a hard time explaining our result:
Our results are strongest for …rms with highest frequency of adjustment
Timing can be o¤ by at most one month if prices adjust every month

Berger & Vavra(NWU and Booth)

PassthroughMay 25, 2014

Other Exchange Rate Passthrough Speci…cations
May still have concerns about MRPT, measurement error, timing etc
and prefer LRPT
Can’t use LRPT since …xed for each item across time
But can do …xed horizon PT regressions. Theory)Same relationships
Instead of life-long, do 1-month, 3-month, 6-month, 12-month,24-month PT. All results go throughOne price change not enough to re‡ect full passthroughPrices respond to exchange rate movements before previous pricechangeTheory: If item more responsive, should also be more responsive tolagged changes
Redo all regressions interacting passthrough of current and lagged
exchange rate movement with dispersion
Find same result

Berger & Vavra(NWU and Booth)

PassthroughMay 25, 2014

More Structure and Additional Controls∆pi ,tBerger & Vavra= βave ∆c ei ,t+ βVol (Voli ∆c ei ,t ) + δVoli+ βIQR IQRt ∆c ei ,t + λIQRt+ βother Othert ∆c ei ,t + χOthert+Zi0,t γ + ei ,t(NWU and Booth)

PassthroughMay 25, 2014

DI Results with Item-Level Controls
Ave PT

Volatility

Frequency

βavg

βVol

βfreq

All countries, all items ex petroleum- Cross-sectional std

0.14

0.05***

0.14

0.05***

0.18

0.09***

0.19

0.08***

0.02*

OECD countries, all items ex petroleum- Cross-sectional std

0.07***All countries, all manufacturing items- Cross-sectional std

Berger & Vavra(NWU and Booth)

Passthrough0.14

0.06***

0.13

0.06***

0.03***

May 25, 2014

DM Results with Controls

Ave PT

Volatility

Frequency/Subs

avg

Vol

βfreq

β

β

- Time trend + Month.135***.058***- Frequency.14***.063***.011- Product subs

.143***.062***.0004- Time tr + Mth + Freq

.122***.057***.012- Time tr + Mth + Prd sub.134***.058***-.006

Berger & Vavra(NWU and Booth)

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DM vs DI

Ave PT

DI E¤ects

DM E¤ects

βavg

βXSD

βIQR

.141***.139***.137***.137***.125***.043***.041***.041***.042***.042***.060***.060***.060***.055***.055***All countries, all items ex petroleum- No additional controls- Item level frequency- Aggregate frequency- Time trend + Month- All above controls
ReturnBerger & Vavra(NWU and Booth)

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Additional Robustness Results
Average PT

Volatility

Freq

βavg

βVol

βfreq

0.15***

0.05***

0.15***

0.05***

0.41***

0.26***

0.44***

0.21***

0.28***

0.21***

0.29***

0.18***

Placebo num changes

0.15***

0.00

0.15***-0.00

Placebo num obs

0.15***-0.00

0.15***-0.00

Median regression

0.16***

0.07***

0.16***

0.07***At least 3 price changes
Using trade-weighted broad xrate
Using trade-weighted major country xrate

0.01
0.27***
0.15***
0.02*
0.02*
0.01***

ReturnBerger & Vavra(NWU and Booth)

PassthroughMay 25, 2014