export decision under risk - university of virginiapeople.virginia.edu/~jh4xd/workshop...

Export Decision under Risk∗

José De Sousa, Anne-Célia Disdier and Carl Gaigné†

February 19, 2015

Very preliminary and incomplete

Abstract

Does demand volatility matter for exports? How do exporting firms deal withskewed demand? A simple model of risk aversion shows that exporters react toan increase in demand volatility in destination markets by increasing their exportprices and decreasing their export volumes. In sharp contrast, exporters decreaseprices and increase volumes when demand skewness rises. We also show that themoments of the demand distribution affect the extensive margin of trade. Thesetheoretical predictions are put to the test by using French firm-level exports acrossdestination markets with different levels of demand volatility and skewness. Thefirm-level results, over the period 2000-2009, are consistent with our predictions.

JEL classification: D81, F12, L25Keywords: Uncertainty, Demand volatility, Firm exports, Skewness

1 Introduction

Does demand volatility matter for exporters supply decisions? According to the Capgem-

ini 2011 survey of large companies, 40% of respondents say that demand volatility is their

number one business driver. Indeed, in numerous industries, sellers need to decide pro-

duction levels or input procurements before the output is marketed or the market price

for output is known. Demand cannot be known for certain at the time the contracts with∗We thank Holger Breinlich, Gabriel Felbermayr, Keith Head, Nuno Limão, Gianmarco Ottaviano,

John Morrow, Denis Novy, Mathieu Parenti, Veronica Rappoport, Daniel Sturm and seminar and con-ference participants at CEPII, U. of Caen, London School of Economics, U. of Munich (ETSG), U. ofStrathclyde, and U. of Tours for their helpful comments. This work is supported by the French NationalResearch Agency, through the program Investissements d’Avenir, ANR-10-LBX-93-01.†José De Sousa: Université Paris-Sud, RITM and Sciences-Po Paris, LIEPP, [email protected].

Anne-Célia Disdier: Paris School of Economics-INRA, [email protected]. Carl Gaigné: INRA,UMR1302 SMART, Rennes (France) and Université Laval, CREATE, Québec (Canada). Email:[email protected].

1

the importers are signed as expenditures for an industry are subject to random shocks. In

this paper, we analyze how demand volatility affect the export decision at the firm level.

In most of the trade literature, the firm knows the state of demand function with cer-

tainty and only the level of foreign market size plays a key role in firm export performance.

However, for a same level of demand (apparent absorption), we observe a significant de-

mand volatility in destination markets. This point is illustrated in Figure (1) from data

on world sectoral-level data.

Figure 1: Demand (apparent consumption) level and demand volatility

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05

1015

20Lo

g of

App

aren

t Con

sum

ptio

n (M

ean)

- 3

dig

it

-4 -2 0 2Log of Apparent Consumption Volatility (sd) - 3 digit

Note: 82 countries, 62 sectors, 2005.

Under demand or price uncertainty, risk-averse firms have to manage their risk expo-

sure. Indeed, there exists some delay between the time an export decision is made and the

time the corresponding output reaches the market. Hence, during this delay, the foreign

demand or market price can change so that there is an uncertainty that the decision-maker

has to handle. The literature on production decision under risk shows that an increase

in risk (as measured by a higher volatility) has a negative effect on output size when the

decision maker is averse to risk.

As a result, if firms are risk-averse, they should export less to a country with more

volatile demand, ceteris paribus. In other words, a country with higher demand volatil-

ity should import less. Using the same database of world sectoral-level data, we find

2

prima facie evidence of a negative relationship between demand volatility and imports,

as depicted in Figure (2).1

Figure 2: Relationship between imports and demand volatility

AFGAFG

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KORKORKORKORKORKORKORKOR KOR

KORKORKORKORKORKORKOR

KORKORKORKORKORKOR

KOR KORKOR KORKORKORKORKORKORKORKOR

KOR


KOR KOR

KORKORKOR

KORKOR

KORKOR

KORKORKORKORKORKORKORKORKOR

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KOR KORKORKORKORKORKORKORKORKOR

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KORKOR


KORKORKOR

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KORKORKORKORKORKOR KOR





KORKORKOR

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KOR

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KORKORKORKORKORKORKORKORKOR KORKORKORKOR

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KORKORKORKORKORKOR

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KORKORKORKORKORKOR KORKORKOR

KORKORKORKOR

KORKORKOR

KORKORKORKOR

KORKORKOR

KORKORKORKOR

KORKORKOR

KORKOR

KORKORKORKORKORKORKORKOR KOR

KORKORKORKORKORKORKOR KORKOR

KORKORKOR

KORKORKORKOR

KORKOR


KORKORKORKOR



KORKORKORKORKOR

KORKOR KORKORKORKORKORKORKOR

KORKORKORKORKORKOR

KORKORKOR

KORKOR

KORKORKOR


KORKORKOR

KORKORKOR

KOR KORKORKORKORKORKORKORKORKORKOR

KORKORKORKORKOR

KORKORKORKOR

KOR


KORKOR

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KOR

KORKORKOR

KORKORKOR

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KORKORKORKOR

KORKORKOR

KOR

KOR

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KORKORKOR KORKOR

KORKOR

KORKOR

KORKOR

KOR

KORKORKORKOR

KORKORKOR

KORKORKORKOR

KORKORKOR

KORKOR KORKOR


KWT

KWTKWT

KWT

KWT

KWTKWTKWTKWT

KWTKWT

KWTKWT

KWT

KWT

KWT

KWT

KWT

KWT

KWT

KWT

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KWT KWT

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KWTKWTKWTKWTKWT

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KWT

KWT

KWTKWT

KWTKWTKWTKWTKWT

KWT

KWT

KWTKWT

KWTKWT

KWTKWT

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KWTLKA

LKA

LKA

LKA

LKA

LKALKA

LKA

LKALKA

LKA LKA

LKA

LKA

LTULTULTULTULTU

LTULTULTU

LTULTU

LTULTU

LTU LTULTU

LTULTU

LTULTU

LTULTULTULTU

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LTULTULTULTULTULTU

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LTULTU LTULTULTULTULTULTULTULTU

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LTULTU LTULTU LTULTU

LTULTU LTU LTULTULTULTULTU

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LTULTULTULTULTULTULTULTU LTU LTU

LTULTULTULTU LTU LTULTULTULTU

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LTU LTULTULTU

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LTULTULTULTULTULTU

LTULTULTULTU

LVALVALVALVALVA

LVALVALVA

LVA LVA

LVA LVALVALVALVALVA

LVALVA

LVALVALVALVA

LVALVALVALVA

LVA LVALVALVALVALVALVALVA

LVALVA

LVA LVA

LVA

LVALVALVA

LVALVA

LVALVA LVA

LVALVALVALVA

LVALVALVALVALVA

LVALVA

LVALVALVALVA

LVALVALVALVALVA

LVA

LVALVA LVALVA

LVALVALVALVALVA

LVALVA

LVALVA

LVALVA

LVA

LVALVALVA LVA

LVALVALVALVA

LVALVALVALVA LVALVALVA

LVA

LVALVALVA

LVALVA

LVALVA

LVA

LVALVA

LVALVALVALVALVALVALVALVA

LVALVA

LVA

LVA LVALVALVALVA

LVALVA

LVALVALVALVALVA LVALVA

LVALVALVA

LVA

LVALVALVALVALVA

LVALVA

LVALVA

LVALVALVA

LVALVALVALVA

LVA

LVALVALVA

LVALVALVALVALVALVA

LVALVALVA

LVA

LVALVALVALVA

LVALVA

LVALVALVA

LVALVALVALVALVALVALVA

LVALVA

LVALVALVA

LVALVA

LVALVA

LVA


LVALVA

LVA

LVALVALVALVALVA

LVALVA

LVALVA

LVALVA


LVALVA

LVA LVALVALVALVALVALVA

LVALVA

LVALVALVALVALVALVA

LVALVA

LVALVA

LVA

LVALVALVA

LVALVA


LVA

LVA

LVALVALVA

LVALVALVA

LVA

LVALVALVALVALVA

LVALVALVA

LVA LVALVA

LVALVALVALVALVA

LVALVALVALVALVALVA

LVALVALVALVALVALVA

LVALVALVA

LVA

LVALVALVA

LVALVA

LVALVA LVA

LVALVALVALVALVALVA

LVALVALVA

LVA

LVALVALVALVALVALVA

LVALVA

LVA LVALVALVA

LVALVA

LVA

LVALVA

LVALVALVALVALVALVA

LVALVA

LVA

LVA

LVALVA

LVA

LVALVA

LVA

LVA LVA

LVA

LVA

LVALVA

LVA

LVA

LVA

LVA

LVA

LVALVA

LVALVA

LVALVA LVA

LVA

LVALVALVALVALVA

LVALVALVA

LVALVALVALVALVA

LVALVALVALVA

LVA

MACMAC

MAC

MACMAC

MACMAC

MACMACMAC

MACMAC

MACMACMACMAC

MACMAC

MACMAC

MAR MARMARMARMARMAR

MARMARMAR

MARMARMARMAR

MARMAR

MAR

MARMARMARMARMARMAR

MARMAR MAR

MAR

MAR MARMARMARMARMAR MAR

MAR

MAR MARMARMARMARMAR

MARMARMAR

MAR MARMARMAR MARMAR

MAR

MAR MARMARMARMARMAR MARMAR

MARMARMARMARMARMAR

MARMARMAR

MARMARMAR MAR MARMARMARMARMARMARMAR MARMARMAR MAR

MARMAR

MARMARMARMARMARMARMAR

MARMARMARMARMARMAR

MARMARMAR

MARMAR

MARMARMARMAR

MARMARMAR

MARMAR

MARMARMARMAR

MARMAR

MARMAR

MARMARMAR

MAR

MAR

MAR MARMAR

MARMAR

MARMAR

MAR MARMARMAR MAR

MARMARMAR

MARMARMARMAR

MARMARMARMARMAR

MARMARMARMARMARMAR MAR

MARMAR

MARMAR

MARMAR

MARMARMARMARMARMARMARMAR MAR

MAR MARMARMARMAR

MAR MAR

MARMARMARMARMAR

MARMARMARMAR

MARMARMARMAR

MARMAR

MAR

MARMAR

MARMARMAR MAR

MAR

MARMAR

MAR

MARMARMAR

MARMAR

MARMAR

MARMARMARMARMAR

MARMARMARMARMAR

MARMARMARMAR

MARMARMAR

MARMARMAR MARMARMARMARMARMAR

MARMARMARMAR

MARMARMARMARMARMARMARMARMAR MAR

MARMARMAR

MARMAR

MAR

MARMARMARMARMARMARMARMAR

MARMAR MARMARMAR

MARMARMARMARMARMAR

MARMARMARMAR MARMARMAR

MARMAR

MARMARMARMAR

MARMARMAR

MARMARMARMARMARMARMAR

MARMARMARMARMARMAR

MARMAR

MARMARMARMAR MAR

MAR

MARMAR

MARMARMAR

MARMAR

MAR

MARMAR MARMAR

MARMAR

MAR MAR MARMARMAR

MARMAR

MARMAR

MARMARMAR

MARMAR

MAR

MAR

MARMARMAR

MARMAR

MARMARMARMAR

MAR MARMARMARMARMAR

MARMAR

MARMARMARMARMAR

MARMARMAR

MAR MAR MARMARMAR MAR

MARMARMAR

MDAMDA

MDAMDA

MDAMDA

MDAMDA

MDA

MDA

MDAMDA

MDAMDA

MDAMDAMDA

MDAMDA MDA

MDA MDAMDA

MDAMDA

MDA

MDA

MDA

MDA

MDAMDA

MDAMDAMDAMDA

MDAMDAMDA

MDAMDAMDA

MDAMDAMDA MDA

MDAMDA

MDAMDAMDA

MDA

MDAMDAMDA

MDAMDAMDAMDA

MDAMDAMDAMDAMDAMDAMDA MDA MDAMDA

MDAMDAMDAMDAMDAMDAMDA

MDAMDAMDA

MDAMDAMDAMDA

MDA

MDAMDA

MDA

MDAMDA

MDAMDAMDAMDA

MDAMDA

MDAMDA

MDA

MDAMDA

MDAMDAMDA

MDAMDAMDAMDA

MDAMDA

MDAMDAMDAMDA

MDAMDA MDA

MDAMDA

MDAMDAMDAMDAMDA

MDAMDAMDAMDAMDAMDAMDAMDAMDA

MDA

MDAMDAMDAMDA

MDAMDA

MDAMDAMDAMDA

MDAMDAMDAMDA

MDAMDAMDAMDA

MDAMDA

MDAMDA

MDA

MDAMDAMDA

MDA

MDA

MDA

MDA

MDA MDAMDA

MDAMDAMDAMDA

MDA MDAMDAMDAMDAMDA

MDAMDAMDA

MDAMDA

MDAMDAMDAMDAMDAMDA

MDAMDAMDA

MDA

MDAMDA

MDAMDA

MDAMDA

MDA

MDAMDA

MDA

MDAMDAMDA

MDAMDA

MDAMDAMDAMDA

MDA

MDA

MDAMDA

MDAMDA

MDAMDAMDA MDA

MDA

MDAMDAMDAMDAMDA

MDAMDAMDAMDA

MDA

MDAMDA

MDA

MDAMDA

MDAMDA

MDAMDAMDA

MDAMDA

MDA

MDAMDAMDA

MDAMDA

MDAMDAMDAMDAMDA

MDA

MDAMDAMDAMDAMDA

MDAMDA

MDA

MDA

MDAMDAMDA

MDAMDAMDAMDA

MDAMDA

MDA

MDAMDAMDA

MDAMDAMDAMDA

MDAMDAMDA

MDA

MDAMDAMDA

MDAMDAMDAMDA

MDAMDA

MDAMDAMDA

MDAMDA

MDAMDA

MDA

MDAMDAMDA

MDAMDAMDA

MDAMDA

MDA MDA

MDAMDA

MDA

MDA

MDA

MDA

MDA MDA MDA

MDAMDAMDA

MDA

MDAMDAMDA

MDA

MDAMDAMDAMDAMDA

MDA MDAMDA MDAMDAMDA

MDAMDAMDA

MDAMDA

MDA

MDAMDA

MDAMDAMDA

MDAMDAMDA

MDAMDA

MDA

MDAMDA

MDAMDAMDAMDA

MDAMDA

MDAMDA

MDAMDA

MDA MDAMDA

MDA

MDA

MDA

MDAMDAMDA

MDAMDA

MDAMDAMDA

MDAMDA

MDA

MDAMDAMDA

MDAMDAMDA

MDAMDA

MDAMDAMDA

MDA

MDAMDAMDAMDA

MDAMDAMDA

MDAMDA MDA

MDGMDGMDG

MDGMDGMDG

MDGMDGMDG

MDGMDGMDG

MDGMDGMDG

MDGMDGMDG

MDGMDGMDGMDGMDG

MDG

MEXMEXMEXMEXMEXMEXMEXMEXMEXMEX

MEXMEX MEXMEXMEX

MEXMEXMEX

MEXMEXMEX MEXMEX

MEX

MEXMEX

MEXMEXMEXMEXMEX MEX

MEXMEXMEXMEX

MEXMEX

MEXMEX MEX MEXMEXMEXMEX

MEXMEXMEX

MEXMEXMEX MEXMEXMEX

MEXMEX

MEXMEX

MEXMEXMEX MEXMEXMEXMEXMEX MEXMEXMEXMEXMEXMEXMEXMEXMEXMEX

MEXMEX

MEX MEX MEXMEXMEXMEXMEX

MEX MEXMEXMEXMEXMEXMEXMEX

MEXMEXMEX MEXMEXMEXMEXMEXMEXMEX

MEX

MEXMEXMEXMEXMEXMEX MEXMEXMEXMEXMEX

MEXMEX

MEX MEXMEX MEX MEXMEXMEXMEXMEXMEX

MEXMEXMEX

MEX

MEXMEXMEX MEXMEXMEXMEXMEX

MEXMEXMEX

MEX

MEXMEXMEX MEX

MEX

MEXMEXMEXMEX

MEXMEXMEXMEX MEXMEXMEXMEXMEX

MEX

MEX

MEXMEXMEX MEXMEXMEXMEXMEXMEXMEX

MEXMEXMEX MEX MEXMEXMEXMEX MEX

MEX

MEXMEXMEXMEX

MEXMEXMEXMEX

MEXMEX

MEX MEXMEX MEXMEXMEXMEXMEXMEXMEX

MEXMEXMEX MEX MEXMEXMEXMEXMEX

MEXMEX MEXMEX

MEX MEXMEXMEXMEXMEXMEX

MEXMEXMEXMEXMEXMEXMEXMEXMEX

MEX

MEX MEXMEXMEXMEXMEX

MEXMEXMEXMEX

MEXMEX MEX MEXMEXMEXMEXMEXMEX

MEX

MEXMEXMEX MEXMEXMEXMEXMEXMEXMEXMEXMEX MEX

MEXMEXMEX MEXMEXMEX

MEXMEXMEXMEXMEX MEXMEXMEXMEX

MEXMEX

MEXMEXMEX MEXMEX MEX

MEXMEX

MEXMEXMEXMEXMEX

MEXMEX

MEXMEX MEXMEX

MEXMEXMEXMEX MEXMEX MEX MEX MEXMEX

MEXMEXMEXMEXMEXMEXMEXMEX

MEX MEXMEXMEXMEXMEXMEX

MEXMEXMEX

MEXMEXMEXMEXMEXMEX

MEXMEXMEXMEX

MEXMEX

MEXMEXMEX

MEX

MEXMEXMEXMEXMEXMEXMEXMEX MEX

MEX

MEXMEXMEXMEXMEX

MEXMEXMEXMEXMEX

MEXMEXMEX MEXMEXMEXMEXMEX MEXMEX

MEX

MEX

MEX

MEX

MEXMEX

MEXMEX

MEXMEXMEX

MEX

MEXMEXMEX

MEX

MEXMEXMEXMEXMEX

MEX

MEXMEXMEX

MEXMEXMEXMEX

MEXMEXMEX

MKDMKD MKDMKDMKDMKD

MKDMKD MKDMKD

MKDMKD

MKDMKDMKD

MKDMKDMKDMKDMKDMKD

MKD MKD

MKDMKD

MKD MKD

MKDMKDMKDMKD

MKDMKDMKDMKDMKD

MKDMKD MKD

MKDMKDMKDMKDMKD

MKD

MKDMKDMKD

MKDMKDMKDMKDMKD

MKD MKD MKD MKDMKDMKDMKD

MKDMKDMKD

MKDMKDMKDMKDMKD MKD

MKDMKDMKD

MKDMKDMKD

MKD MKDMKDMKDMKD

MKDMKD

MKD

MKD MKD MKD MKDMKDMKDMKD

MKDMKDMKDMKDMKD MKD MKDMKDMKD

MKDMKDMKDMKDMKD

MKDMKD

MKD MKD

MKDMKDMKDMKD

MKD MKDMKDMKDMKDMKD MKDMKD MKD

MKD

MKDMKDMKDMKD

MKDMKDMKDMKDMKD

MKDMKDMKD MKDMKDMKD

MKD

MKDMKD

MKDMKDMKD

MKDMKDMKD

MKDMKDMKD MKDMKD

MKDMKDMKD

MKD

MKD

MKD

MKDMKD

MKDMKD MKD

MKDMKDMKDMKD

MKDMKD

MKDMKDMKDMKD

MKD MKDMKDMKD MKDMKD

MKD

MKDMKD

MKDMKD

MKDMKDMKD

MKD MKDMKDMKDMKD MKD MKD

MKDMKDMKD

MKDMKD

MKD

MKD

MKDMKDMKD

MKDMKD

MKDMKD

MKD

MKDMKDMKDMKDMKD

MKD

MKD

MKD

MKDMKDMKD

MKDMKD

MKDMKD

MKDMKD

MKD MKD

MKD

MKDMKDMKD

MKDMKDMLTMLTMLT MLTMLTMLTMLTMLT

MLT

MLT MLTMLTMLTMLTMLTMLT

MLTMLT MLTMLT MLTMLTMLTMLTMLT

MLTMLTMLTMLTMLTMLTMLTMLTMLT

MLT

MLTMLTMLT

MLTMLT

MLTMLT

MLT

MLTMLTMLT MLT

MLTMLTMLTMLT

MLTMLTMLT

MLTMLT

MLTMLTMLT

MLTMLTMLTMLT

MLT

MLTMLT

MLT

MLT

MLTMLT

MLT

MLTMLT

MLTMLTMLTMLTMLTMLTMLTMLT MLT

MLT MLTMLTMLTMLTMLTMLTMLTMLTMLTMLTMLTMLT

MLTMLTMLT

MLTMLT

MLTMLT MLT MLT

MLTMLTMLT



MLT

MLTMLTMLTMLT

MLT

MLTMLTMLTMLTMLTMLT MLTMLT MLT

MLTMLTMLT MLTMLT MLTMLTMLTMLT

MLTMLTMLTMLTMLTMLTMLTMLTMLT MLTMLTMLT MLTMLTMLTMLTMLTMLTMLTMLTMLTMLT

MLTMLT

MLT

MLTMLTMLTMLT

MLT

MLTMLTMLTMLTMLTMLTMLTMLTMLT MLTMLTMLTMLTMLT

MLTMLTMLTMLTMLT

MLTMLTMLTMLTMLTMLTMLTMLT

MLTMLTMLTMLT MLTMLT

MLT MLT MLTMLTMLTMLTMLTMLTMLT

MLTMLTMLTMLT MLTMLT

MLT

MLT

MLTMLTMLTMLT

MLTMLTMLTMLT


MLTMLT

MLT

MLTMLT MLTMLT

MLT

MLTMLT

MLTMLT MLT


MLT

MLTMLTMLTMLTMLT

MLTMLTMLT

MLTMLTMLT MLT MLTMLTMLT

MLTMLT

MLT MLT MLTMLT

MLT

MLTMLTMLTMLT

MLT

MLT

MLTMLTMLT

MLTMLTMLTMLTMLTMLTMLT MLTMLT

MLT

MLTMLTMLT

MLTMLTMLT MLT

MLT

MLT

MLT

MLT

MLT

MLT

MLTMLTMLT

MLT MLTMLTMLTMLTMLT

MLTMLT

MLT

MLTMLTMLT

MLTMLT MLT

MNGMNG

MNGMNGMNG MNG

MNGMNG

MNGMNG

MNGMNG

MNGMNGMNG

MNGMNGMNG

MNG

MNG

MNG

MNGMNG

MNGMNG MNG

MNG

MNG

MNG

MNG

MNG

MNG

MNG

MNG

MNG

MNG

MNG

MNGMNG

MNG

MNG

MNG

MNG

MNG

MNGMNGMNG

MNGMNGMNG

MNG

MNG

MNG

MNG

MNG

MNG

MNG

MNG

MNG

MNG

MNG

MNGMNG

MNG

MNG

MNGMNG

MNG

MNG

MNGMNGMNGMNGMNG

MNG

MNG

MNG

MNG

MUSMUSMUSMUSMUSMUSMUS MUSMUSMUS

MUSMUS

MUSMUSMUS

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MUS

MWIMWI

MWIMWIMWIMWIMWI MWI

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MWI

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MYS MYSMYSMYSMYSMYS MYS

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MYS MYSMYSMYSMYSMYSMYSMYSMYS

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MYSMYSMYSMYS MYS

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MYSMYSMYSMYSMYSMYSMYSMYSMYSMYS

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MYSMYSMYSMYSMYSMYS

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MYS MYS MYSMYSMYSMYS

MYSMYS MYS MYSMYS MYS

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NGA

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NGANGANGANGA

NGANGA

NGA

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NGA

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NGA

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NGANGA

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NGANGA

NGANGA

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NGA NGANGA

NGA

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NLDNLDNLDNLDNLD

NLD

NLDNLDNLD

NLD NLDNLDNLDNLDNLDNLD

NLDNLD

NLD NLDNLD

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NLDNLD

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NLDNLDNLDNLDNLDNLDNLDNLDNLD

NLDNLDNLD

NLDNLDNLDNLD

NLDNLDNLD NLDNLDNLD NLDNLDNLDNLDNLDNLDNLDNLDNLD

NLDNLDNLD

NLDNLDNLD NLDNLDNLD NLDNLD

NLDNLDNLD

NLDNLDNLD NLDNLDNLD

NLD

NLDNLDNLDNLDNLD NLDNLD NLDNLDNLDNLD

NLDNLDNLDNLDNLDNLD

NLD

NLDNLDNLD

NLDNLDNLDNLDNLD

NLDNLD

NLD

NLDNLDNLDNLDNLDNLDNLDNLD

NLD

NLDNLDNLDNLD NLDNLDNLD NLD

NLD

NLDNLDNLDNLDNLDNLDNLD

NLDNLD


NLD

NLDNLDNLDNLDNLDNLD

NLDNLD NLD

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NLDNLDNLDNLD NLD

NLDNLDNLD

NLDNLDNLDNLD NLDNLDNLDNLDNLDNLDNLD

NLDNLDNLDNLDNLDNLD NLDNLDNLDNLD

NLDNLDNLDNLDNLD NLDNLD NLD

NLD NLDNLDNLD

NLD NLDNLDNLDNLDNLDNLDNLDNLD

NLDNLD NLDNLDNLDNLDNLDNLDNLD NLDNLDNLDNLDNLDNLDNLD

NLDNLD

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NLDNLDNLD NLD NLDNLDNLDNLDNLD

NLDNLDNLDNLDNLDNLD

NLDNLDNLD

NLDNLDNLDNLDNLD NLDNLD

NLDNLD NLDNLDNLDNLDNLDNLD

NLDNLDNLDNLDNLDNLD

NLDNLDNLDNLDNLD

NLD NLDNLDNLD

NLD NLD NLD

NLDNLD

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NLDNLD NLDNLDNLDNLDNLDNLDNLD NLD

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NLDNLDNLD

NLD NLDNLDNLDNLD

NLD

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NLDNLDNLD

NLDNLDNLD

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NLDNLDNLDNLDNLDNLDNLD NLDNLDNLDNLD

NLD

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NLD

NORNOR NORNOR

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NOR

NORNORNORNORNORNORNORNORNOR

NORNORNORNOR NOR NOR

NOR

NORNORNORNORNORNOR

NORNORNOR

NORNOR

NOR

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NORNOR NORNORNORNORNORNOR

NORNOR NOR

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NORNORNOR

NORNOR NOR NORNORNORNORNORNOR

NORNORNORNORNORNOR

NORNORNOR

NORNORNORNORNORNORNOR NORNORNOR NORNORNOR

NORNORNORNOR NORNORNORNORNOR

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NORNORNORNORNORNORNORNOR NOR

NORNORNORNOR

NOR

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NORNORNORNOR

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NORNORNORNORNORNORNORNOR NOR



NORNOR

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NOR NOR

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NOR NORNORNORNORNOR

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NZLNZL

NZLNZL

NZL NZLNZLOMNOMNOMN OMN OMNOMNOMN

OMNOMNOMN

OMNOMN OMN

OMN OMNOMNOMNOMN

OMNOMN

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OMNOMNOMNOMN

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OMNPAN PAN

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POL POLPRTPRTPRTPRTPRTPRTPRTPRT

PRTPRT

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PRTPRTPRTPRTPRT

PRTPRT

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PRT PRTPRTPRTPRT PRT

PRT

PRT

PRTPRT

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PRTPRT

PRTPRT

PRTPRTPRTPRT

PRT PRTPRTPRT

PRT PRTPRT PRTPRTPRTPRT

PRT PRTPRT

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PRTPRT PRTPRTPRTPRT

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PRTPRT PRTPRTPRT

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ROMROMROMROM

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Note: 100 countries, 63 sectors, 2000-09.

However, risk-averse firms react differently to uncertainty according to their charac-

teristics. Indeed, demand fluctuation may force some producers to not enter the export

market or to cease exporting and, in turn, the demand for the incumbent exporting firms

may rise. Additionally, change in uncertainty may modify the relative prices among vari-

eties supplied leading to a reallocation of market shares among the incumbent exporters.

Hence, the effects of industry-specific uncertain demand on export performance at the

firm level are not a priori clear.

Further, managers can be sensitive to downside losses, relatively to upside gains. It

has been shown that macroeconomic fluctuations are skewed rather than symmetric (see

e.g., Popov 2011). Ceteris paribus, managers might prefer to serve a country exhibiting

a high probability of an extreme event associated with a high level of demand than a

country with a high probability of an extreme event associated with a very low demand.

Yet, the variance does not distinguish between upside risk versus downside risk. Skewness1This evidence is supported by an adjusted partial residual plot, controlling for year and country

fixed effects. The corresponding elasticity of demand volatility is −0.17 (p<0.01) suggesting that an 1%increase in volatility in a destination country is associated with a 0.17% decrease in sectoral imports.

3

(the third central moment of a distribution) can be used as a measure of downside risk.

Indeed, the sign of the skewness provides information on the asymmetry of the demand

distribution, and thus on downside risk exposure. For a same mean and variance, countries

with a demand distribution which is more skewed to the right can be viewed as providing

better downside protection or smaller downside risk. A basic intuition is that an increase in

skewness involves a smaller probability for low (or large negative) returns. A distribution

exhibiting more downside risk than another is less skewed to the right.2 For a same mean

and variance, a decision-maker therefore prefer a distribution with the highest skewness.

To illustrate our point, consider the demand pattern of two hypothetical countries A

and B. Each country exhibits a demand distribution with the same mean (6000 ke) and

same variance ((6000)2/3 ke). Assume that, in country A, the level of demand is either

4000 ke with a probability 3/4 or 12000 ke with a probability 1/4 while, in country B,

the level of demand is either 0 ke with a probability 1/4 or 8000 ke with a probability

3/4.3 Despite an equal demand variance in each country, the manager may prefer to

serve the country with a higher skewness (country A) because of a lower exposure to

downside risk. In this case, the decision-maker is averse to downside risk. As a result,

a manager prefers to serve a country with a large mean demand, a small variance and a

large (unweighted) skewness.

In this paper, we study theoretically and empirically how firms adjust their intensive

and extensive margins to a change in the variance and skewness of foreign demand. To

achieve our goal, we first build a trade model where heterogeneous firms producing under

imperfect competition face same industry-wide uncertainty over foreign demand. We

adopt a mean-variance-skewness analysis so that firms are assumed to be averse both to

risk and to downside losses. A comment is in order. By adopting this decomposition

analysis, we consider a “small” risk. Indeed, export sales in a foreign country represent a

low share in total sales of firms.

Our theory leads to the following predictions. A higher variance of foreign demand in a

market raises the unit prices set by firms in this market through a change in their markup.2However, the converse is not necessarily true (Menezes, Geiss, and Tressler, 1980).3A similar example can be found in Eeckhoudt, Gollier, and Schlesinger (2005) in a different context.

4

The magnitude of this effect increases with the productivity of firms but decreases with

trade costs. We also show that, even though a higher foreign demand volatility reduces

the volume of industry export sales, its effect on the probability of exporting (extensive

margin) and on the level of export sales at the firm level (intensive margin) is ambiguous.

Indeed, a rise in demand volatility induces a reallocation of market share from most

productive (and largest) firms to smaller firms. As a result, the probability of exporting

may increase when fixed trade costs are not too high. Under this configuration, the export

sales of medium-sized firms (or the smallest exporters) may grow. However, this effect is

weakened when the skewness of foreign income increases.

To test our predictions, we use firm-level data from the French customs over the period

2000-2009. This database reports the volume (in tons) and value (in euros) of exports

for each product (combined nomenclature) and destination, for each firm located on the

French metropolitan territory. Our different estimations confirm our main predictions.

Hence, decision-makers seem to act as if they were risk-averse and averse to downside

losses. Our results are robust over different sized panels and to the inclusion of a plethora

of fixed effects, and additional controls.

Our paper proceeds as follows. We present the related literature in Section 2. We

then develop our multi-country model of trade with heteregeneous firms under imperfect

competition in Section 3. Section 4 exposes the empirical strategy and the results. We

conclude in Section 5.

2 Related literature

Although macroeconomic volatility plays a key role in a wide variety of economic out-

comes (in long-run growth, investment and production decisions, welfare), rather little

consideration has been given to its impact on export decision.

The determinants of macroeconomic volatility has received much attention. In partic-

ular, it has been argued that freer trade increases volatility at the country level. Industries

more open to international trade are more volatile even though the industries exporting in

foreign countries or importing from different countries depend less on the domestic shocks

5

(Giovanni and Levchenko 2009). On the one side, the industries exporting (or import-

ing) a large fraction of their production (or their intermediate products) are vulnerable

to world demand shocks (or supply shocks). On the other side, trade openness leads

to a less diversified production structure, implying a greater specialization and, in turn,

an increase in volatility. In addition, trade openness can exacerbate domestic volatility

through a decline in the number of firms (Gabaix, 2011). Indeed, since lowering trade

barriers induces an exit of small firms and boosts the size of large firms (Melitz, 2003),

the economy becomes more and more dependent on the shocks at the firm level.

Besides, the macroeconomic volatility is a source of uncertainty which potentially

influences the export decision. Indeed, trade decision are often made before the resolution

of uncertainty. When an export commitment is made, the price received is unknown. The

expected utility theory has been used to analyze international trade under risk and perfect

competition (see Helpman and Razin 1978). More recently, the framework supplied by

real option theory (Dixit and Pindyck 1994) has been introduced in trade model under

imperfect competition. Given export sunk costs, the decision whether and when to export

is very similar to an investment decision. For example, Baldwin and Krugman (1989)

explain trade hysteresis despite large exchange rate fluctuations. In addition, Handley

and Limao (2013) model trade policy uncertainty as a rare event to explain world trade

patterns. A standard assumption in new trade theory is that firms are risk-neutral.

A recent literature emphasizes that uncertainty shocks may affect the choice to serve

a foreign market through exports or affiliate sales. Lewis (2014) considers nominal un-

certainty. He finds that when multinational sales are priced in the local currency while

exports are priced in the producer currency, destination volatility benefits exporters: dur-

ing a foreign nominal contraction, the foreign exchange rate appreciates, causing exports

to be relatively cheaper. Exporters gain non-linearly through demand, making profit

convex in prices. Ramondo, Rappoport, and Ruhl (2013) consider real uncertainty and

changes in relative costs between exporters and multinationals. Exporters hire labor

at home compared to affiliates. Exporters’ expected profits are thus increasing in the

volatility of production costs in the destination country.

6

Our approach contributes to the trade literature in a number ways. First, we consider

that when a firm chooses a certain quantity to serve a foreign market, the price that will

obtain in the market is uncertain. The real value taken by foreign demand for each product

is not known ahead of time. Second, we consider that firms are averse to risk and more

particularly to downside risk. Third, we develop a model where firms are heterogeneous in

productivity supplying a differentiated product (horizontal and vertical differentiation).

Our approach differs from the current trade literature since we consider that managers

know the productivity of their firm but do not have perfect information about the level

of foreign demand.

3 Theory

In this section, we develop a multi-country model of trade with heterogeneous firms un-

der imperfect competition. Firms differ in productivity, but unlike Melitz (2003), they

know with certainty their production technology. Firms face instead an industry-wide

uncertainty over foreign demand. Industry-specific demand is uncertain because indus-

try level expenditures in destination country j, denoted by Rj, are subject to random

shocks. Factors beyond the firm’s control that influence the demand realization are cli-

matic conditions, changes in consumer tastes, opinion leaders’ attitudes, popularity of

competing products, etc. We assume that Rj is independently distributed with a mean, a

variance, and a skewness given by E(Rj), V(Rj), and S(Rj) respectively. Note that E(Rj)

and V(Rj) are always positive while S(Rj) can be positive or negative. The economic

interpretation of these three moments of Rj distribution is discussed below.

Hence, each firm located in country i and producing a variety v faces a downward

sloping demand curve in destination country j given by pij(v) = f [qij(v), Rj, .], where

pij(v) and qij(v) are the price and the quantity of variety v respectively. We assume that

the demand is not known for certain at the time the contracts with the importers are

signed. As above-mentioned Rj is subject to random shocks that cannot be observed

at the time strategic variables (pij or qij) are chosen. The actual demand realization

is therefore uncertain, and can be either higher or lower than the average expenditures,

7

E(Rj). As a result, the dependence of price on quantity (and vice-versa) is given for every

state of nature. In other words, the marginal revenue of each firm is volatile and not

known with certainty at the time the contracts are signed.

Our objective is to analyze how risk-averse firms react to industry-level uncertainty

in export decisions (both at the intensive and extensive margins), according to their

characteristics and the features of destination country. On the one hand, the level of

output may decrease for all firms due to demand fluctuations in accordance with the

standard theory of production under uncertainty. On the other hand, some producers

may not enter the export market or cease to export because of these fluctuations so that

the demand for the remaining exporters may rise (due to a reallocation of demand). In

addition, even if the demand shocks are common for all firms within an industry, it may

modify the relative prices among varieties supplied by the surviving firms in this industry,

leading to a reallocation of market shares. Hence, the effects of industry-specific uncertain

demand on export performance at the firm level are not a priori clear.

Market structure, technology, and firm behavior

Varieties are provided by heterogeneous monopolistically competitive firms. Each vari-

ety is produced by a single firm and each firm supplies a single variety. This means that

producers are negligible to the market, behave as monopolists on their market and their

decisions do not account for the impact of their choice on aggregate statistics.

Labor is the only production factor and is assumed to be supplied inelastically. The

production of qij(v) units of variety v requires a quantity of labor equals to `ij(v) =

τijqij(v)/ϕ, where ϕ is the labor productivity and τij > 1 is an iceberg trade cost. We

assume that the labor productivity is known a priori but differs among firms. Thus, the

marginal requirement in labor is specific to each firm and to each destination, but does

not vary with production.

Under imperfect competition, the choice of the action variables (quantity or price)

merits a discussion. We know from Leland (1972) and Klemperer and Meyer (1986) that,

if the choice of behavioral mode by a monopolistic firm is unimportant under certainty,

this is no longer the case under uncertainty. The firm has two options: (i) set quantity

8

before demand is known and thereafter the actual demand curve yields the market clearing

price or (ii) set price before demand is known and thereafter the actual demand curve

yields the market clearing quantity. Ideally, we would determine endogenously if firms

choose either a quantity to produce or a price to charge, as in Klemperer and Meyer

(1986). In this section, we consider that firms set quantity first, before demand is known.

In Appendix (A), we report the case where price is the strategic variable. We show that

this configuration yields the same predictions than the case where firms set quantity even

if the level of prices and quantities differ according to the behavioral mode.

Hence, without loss of generality, we assume that firms determine quantity, qij, for

each destination j before knowing the value of Rj. Equilibrium prices pij are determined

ex post in accord with realized demand. We assume that firms cannot adjust ex post

quantity with respect to the demand shock. The decision to produce for exports has been

taken ex ante and thus ex post adjustments of quantity are not feasible. The producer

cannot refuse the deal ex post once the price is realized. This implies that products cannot

be sent back. They are sold once exported.

As the shocks to market demand are unobservable, the impact of quantity on price is

uncertain. The expected export profit in a given market is

E [πij(v)] = E [pij(v)] qij(v)− wiτijϕ

qij(v)− wifij, (1)

where wi is the wage rate prevailing in the exporting country i. Firms located in country

i serving the destination country j have to pay a fixed cost fij to serve foreign markets,

which are the costs to maintain a presence, (i.e., maintaining a distribution and service

network, minimum freight and insurance charges, costs of monitoring foreign customs

procedures and product standards, etc.).

We assume that markets are segmented and that shocks are not correlated across coun-

tries, such that the covariance between πij and πik, with k 6= j, is zero as Cov(Rk, Rj) = 0.

The uncertain terminal profit of a firm producing variety v and located in country i, πi,

can be decomposed into two parts: the profit of domestic sales πii and the profit of to-

tal exporting sales Σjπij, such that πi = πii + Σjπij. Throughout, we assume that the

9

domestic profit πii is known with certainty.

Uncertainty and firm behavior

We consider an utility function of a manager Π(πi) representing his/her risk preferences

with Π′(πi) > 0. The manager is made better off by an increase in his/her terminal profit.

Assume that the utility function Π(πi) is continuously differentiable up to order 3. We

follow the methodology developed in Eeckhoudt, Gollier, and Schlesinger (2005). A third

order Taylor series expansion of Π(πi) evaluated at E(πi) gives

Π(πi) ≈ Π(E(πi)) + Π′ [πi − E(πi)] + 12Π′′ [πi − E(πi)]2 + 1

6Π′′′ [πi − E(πi)]3 .

Taking the expectation and assuming that the moments exist lead to

EΠ(πi) ≈ Π[E(πi)] + 12Π′′E[πi − E(πi)]2 + 1

6Π′′′E[πi − E(πi)]3.

According to the expected utility theory, in the neighborhood of E(x) where x is

a random variable, we have EΠ(x) = Π(E(x) − Γ) where Γ is the risk premium. In

our case, the risk premium Γ is defined as the sure amount of money a manager would

be willing to receive to become indifferent between receiving the risky return πi versus

receiving the sure amount E(πi)−Γ. Because EΠ(πi) can also be approximated as follows

EΠ(πi) = Π[E(πi)]− ΓΠ′, we have

Γ ≈ −12

Π′′

Π′ V(πi)−16

Π′′′

Π′ S(πi), (2)

where −Π′′/2Π′ and −Π′′′/6Π′ are the marginal contributions of variance (V(πi) = E[πi−

E(πi)]2) and skewness (S(πi) = E[πi − E(πi)]3) of πi to the risk premium Γ, respectively.

The term −Π′′/2Π′ is known as the so-called Arrow–Pratt absolute risk aversion coef-

ficient. The term −Π′′′/6Π′ captures a preference for positive skewness when Π′′′ > 0,

because it implies a low probability of obtaining a large negative return. Note that skew-

ness to the left (S(π) < 0) is associated with “downside risk” exposure, while skewness to

the right (S(π) > 0) is associated with “upside risk” exposure.

10

Two remarks are in order. First, risk aversion can decrease with wealth of the individ-

uals. Under this configuration, decision makers exhibit decreasing absolute risk aversion

(DARA preferences) implying Π′′′ > 0. This entails that the risk aversion of the exporter

decreases with its level of domestic sales. Second, Π′′′ > 0 corresponds to “downside risk

aversion”, implying that a rise in downside risk (a decrease in S(π)) would tend to increase

the willingness to pay to avoid risk (Menezes, Geiss, and Tressler, 1980).

Finally, we know from expected utility theory that maximizing EΠ(x) is equivalent

to maximizing the certainty equivalent E(x) − Γ. Since expression (2) provides a local

approximation to the risk premium Γ, it follows that the objective function of a decision-

maker can always be approximated by

Πv(πi) ≈ E(πi)− ρvV(πi) + ηvS(πi), (3)

with ρv ≡ −Π′′/2Π′ and ηv ≡ Π′′′/6Π′ . Remember that ρv > 0 expresses the absolute

degree of the firm’s risk aversion. If ρv = 0, firms are risk neutral. This general formulation

does not require a full specification of the utility function Πv(π) and it allows us going

beyond a simple mean-variance analysis in the investigation of export decision under

demand uncertainty. This may be particularly useful in the analysis of “downside risk”

exposure. However, the reader should keep in mind that expression Πv(π) is valid only in

the neighborhood of the point E(πi). In other words, we only consider small risk. Given

that the share of export sales in one country to total sales is low, this assumption is not

too restrictive.

Preferences and demand

To study the effect of uncertainty on export decision, we use a simple and tractable

utility function yielding a specific demand curve.4 The consumer preferences are identical4We could use the general setting in which the demand curve is pij = f(qij , Rj). However, this

increases the complexity of the formal developments while the gains in results are limited. What mattersfor most of our results is that export prices (1) decrease in export quantities (∂pij/∂qij < 0), (2) increasein destination demand (∂pij/∂Rj > 0), (3) with a diminishing marginal effect as export quantities increase∂2pij/(∂Rij∂qij) < 0.

11

and the utility of the consumption of the differentiated good is given by

Uj =∫v∈Ωj

uj(v)dv, (4)

where Ωj is the set of available varieties v in country j. Hence, as in Dixit and Stiglitz

(1977), Krugman (1979) and Zhelobodko et al. (2012), we assume that preferences over

the differentiated product are additively separable across varieties. To keep things simple,

we consider uj(.) = θvqj(v)1/2 where θv is the quality of variety v and q(v) is the quantity

consumed. Given that ∂u(v)/∂q(v) > 0 and ∂2u(v)/∂q(v)2 < 0, consumers exhibit a

preference for variety.

The budget constraint faced by a consumer is given by

∫Ωj

pkj(v)qkj(v)dv = Rj, (5)

where Rj represents the income of the consumer and its total expenses, while pkj(v) is

the price of variety v produced in country k with k = i, j, ..K.5 Notice that deviations

from expected demand in individual foreign markets, due to random shocks, may lead to

potential gains and losses. By neglecting their effect on total income, which may cancel

out, we adopt a partial equilibrium approach.

Maximizing (4) under the budget constraint (5) leads to the inverse demand:

pij(v) = θv2λqij(v)

−12 , (6)

where λ is the Lagrange multiplier. Plugging (6) into (5) implies λ = Ψj/2Rj with

Ψj ≡∫

Ωj

θvqkj(v) 12 dv. (7)

The expression Ψj can be interpreted as a measure of industry supply. As a consequence,5Note that we could extend easily this framework by considering the case where U is embodied in a

Cobb-Douglas upper-tier utility.

12

the inverse demand for each variety is now

pij(v) = Rjθvqij(v)−12 Ψ−1

j . (8)

As expected, the price of a variety increases with its quality (θv) and the market size (Rj)

but decreases with its quantity (qij) and rivals’ quantity and quality of products (Ψj).

Intensive margin of exports with no uncertainty

We start by analyzing briefly the export decision with no uncertainty before introduc-

tion uncertainty. Each firm maximizes its profit (1) by setting its output qij(v) to serve

market j and by taking into account its impact on prices pij(v) given in (8). Profit-

maximizing quantity is given by

qij(v) 12 = Rj

2ϕθvwiτij

Ψ−1j , (9)

so that

pij(v) = 2wiτijϕ

.

Thus, under certainty, the equilibrium price is equal to the marginal cost wiτij/ϕ times

a constant (equals to 2), while exports (in value and quantity) increase with productivity,

quality and demand.

In what follows, we analyze how uncertain demand curve affect equilibrium prices and

quantities at the firm level.

Intensive margin of exports with uncertainty

Under uncertainty, remember that exporting firms face a downward sloping demand

curve characterized by a random shift parameter Rj (common to all firms in a given

industry). Rj is not known for certain at the time the contracts with the importers are

signed. The expected price prevailing for each firm in the foreign market is therefore given

by

E [pij(v)] = E(Rj)θvqij(v)−12 Ψ−1

j . (10)

13

For the sake of clarity, we first consider a mean-variance utility function such that

ηv = 0 (i.e., downside and upside risks are not accounted for). Then, we will consider the

role of skewness with ηv 6= 0. The payoff of each firm when ηv = 0 is as follows:

Πv(πi) = E(πi)− ρvV(πi) =∑

jE(πij)− ρv

∑jV(πij),

where E(πij) is given by (1) and ΣjV(πij) = V(πi) because Cov(Rk, Rj) = 0 for all

k 6= j. Hence, the marginal revenue is uncertain while the marginal cost is known with

certainty. The expected export sales E [pij(v)] qij(v) increases with qij but decreases with

the industry’s output size (captured through Ψj). The profit variance is

V(πij) = V(Rj)θ2vqij(v)Ψ−2

j , (11)

which increases with the firm’s output size qij and decreases with the industry’s output

size. Hence, the mass of rivals serving the same market has an ambiguous effect on the

export performance at the firm level. Indeed, a rise in Ψj decreases the marginal revenue

of the firm but reduces the variance of profits.

First order condition ∂Πv/∂qij = 0 implies

12E(Rj)θvqij(v)

−12 Ψ−1

j −wiτijϕ− ρvV(Rj)θ2

vΨ−2j = 0, (12)

and it is readily to check that ∂2Πv/∂q2ij < 0. As a result, Payoff -maximizing quantity is

given by

qij(v) 12 = E(Rj)θvϕ

2wiτijΨ−1j

[1 + ρvV(Rj)Ψ−2

j

θ2vϕ

wiτij

]−1

. (13)

In accordance with the standard literature related to producer theory under uncertainty,

the risk averse firms produce less than they would under certainty (because ρv > 0 so

that ∂qij/∂V(Rj) < 0), for a given mass of exporters. Further, we can readily check that

quantities are concave in productivity (∂qij/∂ϕ > 0 and ∂2qij/∂ϕ2 < 0). Thus, the most

productive firms are the largest in terms of labor and quantity produced. Another result

standard in the trade theory literature is that quantities are convex in trade costs, such

14

that ∂qij/∂τij < 0 and ∂2qij/∂τ2ij > 0). Hence, export sales decrease with trade costs,

while they increase with productivity. New and more original is the following proposition:

Proposition 3.1 For a given positive degree of the firm’s risk aversion (ρv > 0) and in-

dustry supply (Ψ), the negative effect of demand volatility on export quantities is strength-

ened when firm productivity increases and trade costs decrease.

As a simple proof, we can establish from equation (13)

∂2qij∂ϕ∂V(Rj)

< 0 < ∂2qij∂τ∂V(Rj)

,

when ρv > 0. Remember that the variance of profits in a given foreign market is equal

to the variance of foreign demand times the output size dedicated to that foreign country

(see equation 11). Stated differently, the variance of profits of a firm increases with its

productivity and decreases with trade costs for a given mass of firms.

Using (8) and (13), we can now determine the ex post equilibrium price of variety v

prevailing in country j:

pij(v) = wiτijϕ

2 Rj

E(Rj)

[1 + ρvV(Rj)

θ2vϕ

wiτijΨ−2j

](14)

The equilibrium price is equal to the marginal cost (wiτij/ϕ) times a markup. Remember

that, under demand certainty, the markup is equal to 2 (because of E[Rj/E(Rj)] = 1

and V(Rj) = 0). With uncertain demand and risk-averse firms, the markup is higher

on average than the markup prevailing under certain demand due to the fluctuations of

income. Hence, uncertain demand curve tends to increase prices through a higher markup.

It is worth stressing that, unlike models of monopolistic competition with perfect in-

formation, the markup is not a constant. Firms charge variable markups even under

CES preferences. In other words, demand uncertainty and risk-averse firms allow for vari-

able markups even though demand curve is iso-elastic. Markup depends on the demand

volatility, firm’s productivity and features of origin and destination countries. Note also

that the markup increases with the firm’s productivity (ϕ) and decreases with trade costs

15

(τij) and the mass of rivals (captured by Ψj). Those findings are in accordance with in-

dustrial organization theory. However, the mechanisms at work are different. Our results

are related to the existence of demand fluctuations and risk aversion. The variance of

profits being high for the most productive firms, they charge greater markups. Similarly,

low market size induces low variance of profits so that the markup is lower for destina-

tions with a low potential market. Hence, even though preferences exhibit an iso-elastic

demand, markups vary according to destinations and firms.

In addition, under demand uncertainty, the markup captures two opposite effects

associated with the destination income (Rj). On the one side, higher income raises the

markup and, in turn, prices (demand effect). On the other side, higher expected foreign

demand increases the competition across firms (which have an incentive to reduce their

level of production) and, in turn, decreases the markup. However, on average, both effects

cancel each other out (E[Rj/E(Rj)] = 1). The next proposition sums up our results on

destination prices:

Proposition 3.2 For a given positive degree of the firm’s risk aversion (ρv > 0) and

industry supply (Ψ), the markup increases more with foreign demand uncertainty, the

higher the firm productivity and the lower the trade costs.

Propositions (3.1) and (3.2) are related to the intensive margin of trade, i.e., variation

in trade of existing trade relationships. They are established without accounting for the

adjustment in the industry supply (Ψ). However, uncertainty leads to an adjustment in

the quantities produced by the competitors. This adjustment reinforces proposition (3.2)

on export prices but renders proposition (3.1) on exported quantities more ambiguous.

Before presenting the effect of the industry adjustment, we study the role of uncertainty

on the extensive margin of trade, i.e., on the emergence of new trade relationships and/or

the death of existing ones.

Extensive margin of exports with uncertainty

The mass of domestic firms in each country is exogenously given,6 while the mass of6An endogenous mass of domestic firms can be incorporated in the analysis without qualitatively

changing any of the main results.

16

exporting firms is treated as endogenous. There is a large supply of potential entrants in

the international market. However, firms located in country i serving destination country

j have to pay a fixed cost fij to serve foreign markets (see equation 1). The decision to

exit or enter a foreign market is taken on the basis of the expected payoff. A firm exports

to destination j if and only if ex ante payoff Πv is positive, i.e., E(πij)− ρvV(πij) > wifij.

It is straightforward to check that Πv = sij/2 where sij ≡ E(pij)qij with

sij = E(Rj)2

2

[wiτijθ2vϕ

Ψ2j + ρvV(Rj)

]−1

. (15)

As a result, Πv = 0 when ϕ = 0 and ∂Πv/∂ϕ > 0. Hence, there exists a quality-adjusted

productivity cutoff θ2vϕ above which a firm serves country j. As expected, the probability

of exporting decreases with V(Rj). In addition, we have ∂2Πv/∂ϕ∂V(Rj) < 0 so the

payoffs of large firms are more impacted by a rise in demand volatility than the small

firms. Notice also that ∂Πv/∂Ψj < 0 and sign∂2Πv/∂ϕ∂Ψj = signρvV(Rj) θ2

vϕwiτij−Ψ2

j

so that a higher total supply decreases the ex ante payoff of each incumbent firm. However,

the high productivity firms are less affected by a rise in Ψj.

Until now, we have studied the impact of V(Rj) on exports and prices for a given Ψj.

However, Ψj adjusts when V(Rj) changes. Therefore, we have to take into account the

indirect effect of demand volatility on prices and quantity through Ψj. In what follows,

we determine the relationship between Ψj and V(Rj) and the total effect of V(Rj). Let

ξ ≡ 1/(θ2vϕ) ≥ 0 be an inverse measure of quality-adjusted productivity and µ(ξ) is the

distribution of ξ. The cutoff for exporting ξij is such that Πv(ξij) = wifij or, equivalently,

ξij ≡[E(Rj)2

4wifij− ρvV(Rj)

]Ψ−2j

wiτij. (16)

It follows that a firm exports as long as ξ < ξij. As expected, high productivity firms are

more likely to be exporters while high fixed and variable trade costs reduce the probability

of exporting. However, unlike trade models with heterogeneous firms, the exporting zero-

payoff cutoff conditions ξij can be non positive. No firm finds a priori profitable to serve

country j if the expected income E(Rj) is not sufficiently high relatively to its variance

17

V(Rj). Hence, we provide a rationale for the prevalence of zeros in bilateral trade without

making an ad hoc assumption on the distribution of productivity across firms. Helpman

et al. (2008) allow also for zero bilateral trade volumes as the authors assume that the

most productive firms exhibit a level of productivity which is below than the exporting

threshold.

Uncertainty and industry adjustment

Although our modeling strategy gives our framework a partial equilibrium flavor, it

does not remove the interdependence among firms within industries. We can show that

εΨj≡ −V(Rj)

Ψj

∂Ψj

∂V(Rj)> 0,

or, equivalently, ∂Ψj/∂V(Rj) < 0 (see Appendix (B)). As expected, an increase in the

variance of income reduces the aggregate supply for destination market j and, in turn,

the equilibrium prices. Hence, equilibrium prices (14) increase with demand fluctuations

through two effects: (i) a direct effect due to risk aversion (as explained above) and (ii)

an indirect effect via the exit of firms relaxing competition among surviving firms. In

contrast, the effect of demand volatility on the export sales (or profits) is ambiguous

when Ψj adjusts to a change in V(Rj). Indeed, we have

dsij(v)dV(Rj)

= ∂sij(v)∂V(Rj)

+ ∂sij(v)∂Ψj

∂Ψj

∂V(Rj)= sij

V(Rj)2wiτijξεΨj

− ρvV(Rj)Ψ−2j

wiτijξ + ρvV(Rj)Ψ−2j

,

where ∂sij(v)/∂V(Rj) < 0 while ∂sij/∂Ψj < 0 and ∂Ψj/∂V(Rj) < 0 (see above). It

follows that a rise in demand volatility induces a reallocation of market shares from larger

firms to smaller ones as dsij(v)/dV(Rj) increases with ξ. Hence, the aggregate productiv-

ity of exporters can decrease ceteris paribus with a higher uncertainty, in accordance with

empirical facts (see Bloom, 2014). In addition, as the larger firms reduce their export

sales in high proportion when demand fluctuations increase, the export sales of smaller

exporters may expand at their expense (see Figure 3).

As a result, the effect of demand volatility on the probability of exporting is also

18

Figure 3: Productivity and reallocation of export sales when demand volatility increases

Production costs (ξij)

Export Sales (sij/2)

sij(ξ, V −)

sij(ξ, V +)A

Note: V − and V + mean low and high volatility, respectively.

ambiguous. Some standard calculations reveal that

dξijdV(Rj)

= ∂ξij∂V(Rj)

+ ∂ξij∂Ψj

∂Ψj

∂V(Rj)=[E(Rj)2

4wifij− ρvV(Rj)

(1 + 1

2εΨj

)]2εΨj

Ψ−2j

V(Rj)wiτij

where ∂ξij/∂V(Rj) < 0 while ∂ξij/∂Ψj < 0 and ∂Ψj/∂V(Rj) < 0 (see above). Hence,

the probability of serving a country decreases with the volatility of its demand provided

that fixed trade costs or demand volatility are not too high. If fixed trade costs are low

enough, more medium sized firms can export when demand fluctuations rise as the export

sales of large firms decrease (see Figure 4).

When we focus the total effect of demand fluctuation on quantity, it appears

dqij(v)dV(Rj)

= qij(v)V(Rj)

wiτijξ − ρvV(Rj)Ψ−2j (1 + εΨj

)wiτijξ + ρvV(Rj)Ψ−2

j

and d2qijdϕ∂V(Rj)

< 0 < d2qijdτdV(Rj)

so that the effects of V(Rj) on qij(v) when Ψj reacts to a change in demand volatility are

qualitatively similar to the effects on export sales. It also be noted that higher uncertainty

can make trade policy (lowering trade costs) or innovation policy (rising productivity) less

effective, in accordance with Bloom (2014).

To summarize:

19

Figure 4: The impact of higher demand volatility on exporting cutoff

ξij

Payoff (Πij)

Πij(ξ, V −)

Πij(ξ, V +)

A

wifij

ξij(V −) ξij(V +)

(a) Low export fixed costs wifij

ξij

Payoff (Πij)

Πij(ξ, V −)

Πij(ξ, V +)

A

wifij

ξij(V +) ξij(V −)

(b) High export fixed costs wifij

Notes: V − and V + mean low and high volatility, respectively. ξij : production costs.

Proposition 3.3 A rise in industry-level foreign demand uncertainty decreases industry

export sales but

(i) decreases the export sales of large firms and increases the market share of medium

sized firms;

(ii) increases the probability of exporting and the export sales of medium-sized firms

when trade costs are not too high.

The bad and the good variance: the role of skewness

We have considered a mean-variance analysis. The basic intuition is that the exporters

prefer higher expected returns and lower risk. However, we should consider that, ceteris

paribus, entrepreneurs prefer a high probability of an extreme event in the positive direc-

tion over a high probability of an extreme event in the negative direction. In order to take

into account the fact that the marginal willingness of exporter to accept a risk increases

when the distribution of the risk becomes more skewed to the right, we now consider the

mean-variance-skewness utility function where ηv > 0. The payoff of each firm is given

20

by (3). Given the inverse demand of consumers, we have

S(πij) = S(Rj)θ3vq

32ij(v)Ψ−3

j . (17)

and the Payoff -maximizing quantity is implicitly given by ∂Πo/∂qij = 0, or, equivalently,

E(Rj)2 θvΨ−1

j −(wiτijϕ

+ ρvV(Rj)θ2vΨ−2

j

)qij(v) 1

2 + ηv3S(Rj)θ3

vΨ−3j

2 qij(v) = 0. (18)

Clearly, if the income distribution is positively (resp., negatively) skewed, each exporter

has an incentive to increase (resp., decrease) its level of output for a given V(Rj). The

degree of skewness modifies the desirability of risk. It is readily to check that our pre-

dictions related to the impact of V(Rj) on quantity and prices according to the level of

productivity and trade costs hold when S(Rj) 6= 0. Using envelop theorem, it is straight-

forward to verify that ∂qij/∂S(Rj) > 0 whereas ∂pij/∂S(Rj) < 0 when the second order

condition holds (E(Rj)Ψ2j − ηv3S(Rj)θ2

vqij(v) > 0). Regardless of the sign of S(Rj), an

income distribution that is more skewed to the right induces higher level of output. More

interesting, standard calculations show that

∂2qij∂ϕ∂S(Rj)

> 0 > ∂2qij∂τ∂S(Rj)

and ∂pij∂τ∂S(Rj)

> 0 > ∂pij(v)∂ϕ∂S(Rj)

as ∂qij/∂ϕ > 0 and ∂qij/∂τ > 0. The magnitude of the positive impact of a higher S(Rj)

on production is stronger for firms exhibiting a higher productivity and for destination

implying lower trade costs. The prices move in the opposite direction.

4 Empirical Analysis

4.1 Identification strategy

According to our theoretical predictions exporters react in response to volatility by de-

creasing volumes(

∂qij

∂V(Rj)< 0)

and increasing prices(

∂pij

∂V(Rj)> 0), while in response to

21

upside gains exporters increase volumes(

∂qij

∂S(Rj)> 0)and reduce prices

(∂pij

∂S(Rj)< 0).

The estimations of these predictions may be plagued by potential endogeneity at the

aggregate level between trade openness and demand volatility. To mitigate this potential

bias we exploit the following strategy of identification. We use French firm exports at the

4-digit level k in a given year as our dependent variable. Then, we regress disaggregated

French exports on three different moments of the distribution of demand R in destina-

tion j: the lagged expected value(E(RK

j,t−1)), the volatility

(V(RK

jt))and the skewness(

S(RKjt))of demand at the 3-digit sector level. We expect variation in French 4-digit

exports to be explained by 3-digit demand shifters in destination countries. However, in

turn, it is unlikely that a particular 4-digit export in a destination affects substantially

a 3-digit sector demand in that destination. The 3-digit demand in a country is made

of imports from all sources (including itself) and all 4-digit sub-sectors. To reinforce this

strategy of identification, we remove French flows to compute countries’ demand and its

moments. Moreover, we exploit the different sources of variation of our panel and use

various combinations of fixed effects to control for unobservables: firm f , destination j,

4-digit sector k and time (year) t fixed effects.

4.2 Data

Demand R in destination country j is proxied with apparent consumption such as: aKjt =

ProductionKjt + ImportsKjt − ExportsKjt , where K is 3-digit sector and t year. Our sectoral

data on production, exports and imports come from COMTRADE and UNIDO and covers

the period 1995 to 2009. Using the absorption formula and the sector data, we construct

three important regressors at the industry 3-digit level K in the destination country j.

They correspond to three different moments of apparent consumption:

1. The mean demand or absorption(E(RK

j,t−1))computed in year t as the log of the

lagged value of mean absorption over the 5 previous years;

2. The volatility of demand(V(RK

jt))computed as the standard deviation of the yearly

growth rates of aKjt over 6 years and the sub-sectors k. As an example, consider

22

the manufacture of beverages (K=155) in the United Kingdom in 2000. We first

compute the yearly growth rates of the UK’s apparent consumption over 1995 to

2000, and over the 4 sub-sectors of 155.7 Then, we compute the standard deviation of

the 20 growth rates. Figure (5) reports the volatility of demand in the manufacture

of beverages in 2005. For a same level of mean demand for beverages in 2005, we

observe different levels of demand volatility.

3. The unbiased skewness of demand(S(RK

jt))computed as the skewness of the yearly

growth rates of aKjt over 6 years and the sub-sectors k.

Figure 5: Demand level and demand volatility of a given 3-digit sector

IRNLVA

MEX ITA

SVK PAN

ERI

NLD

MDA

ETH

JPN

SVN

ROMPRT

JOR

MAR

UKR

TJK

URY

IDN

DNK

KAZ

EGY

AUS

TTO

GEO

CHN

MWI

GRC

KGZ

CAN

TUR

OMN

ARM

ECU

EST

NOR

MYS

MLT

BLX

HUNPER

COL

IND

USA

FRA

CYP

DEU

LTU

AZE

SEN

KORPOL

MKD

GBRESP

FIN

810

1214

1618

Log

of A

ppar

ent C

onsu

mpt

ion

(Mea

n) -

3 d

igit

-2.7 -.7Log Volatility (standard deviation) of destination county - 3 digit

Manufacture of beverages in 2005

To construct our dependent variable and test our theoretical predictions we use very

rich firm-destination specific export data from the French customs over the period 2000

to 2009. We observe volume (in tons) and value (in euros) of exports for each product

and destination, for each firm located on the French metropolitan territory. Unit values

are computed as the ratio of export value to export volume.

4.2.1 Descriptive Statistics

We present in this section some descriptive statistics on French exports and firms, and

on the volatility and skewness of demand in sectors and destination countries included7The 4 sub-sectors are: 1551 - Distilling, rectifying and blending of spirits; ethyl alcohol production

from fermented materials; 1552 - Manufacture of wines; 1553 - Manufacture of malt liquors and malt;1554 - Manufacture of soft drinks; production of mineral waters.

23

in our sample. In our empirical analysis, we focus on manufactured exports. French

manufactured export flows reach on average 258,062 millions USD and 94,072 millions of

tons per year. On average, our sample includes 70,239 firms per year, serving 81 countries

and 119 4-digit sectors. Table (1) provides the annual statistics. All sectors are served

every year. By contrast, we observe some changes in the number of destinations, with an

increase over the 2000-2006 period and a significant decrease during the 2008-2009 crisis.

The number of exporting firms is decreasing over time (except in 2006).

Table 1: Number of French firms and destinations per year

Year Nb. exporters Nb. destinations2000 79151 802001 77115 802002 76509 812003 74304 862004 72021 852005 70871 832006 71207 882007 68400 862008 65803 792009 47011 66Note: 119 4-digit sectors per year.

The turnover of firms in sectors and destinations is rather high in our sample over

the period 2000-2009. On average, a firm is present 2.77 years in one destination-sector

(4-digit). Firms serve on average 1.96 sectors per destination-year and 3.14 destinations

per sector-year.

Each year, exporting firms may export to one sector (4-digit) and one destination

(mono-destination and mono-sector firms), to various sectors but to one destination

(mono-destination and multi-sectors firms), to various destinations and to one sector

(multi-destinations and mono-sector firms) or to multi destinations and sectors (multi-

destinations and multi-sectors firms). Table (2) presents the share of each of the four

categories in the total of exporting firms. The two main categories of firms in our sample

are mono-destination and mono-sector firms (col. 1), and multi-destinations and multi-

sectors firms (col. 4). The shares are fairly stable over time. However, the share of

multi-destinations firms has slightly decreased in 2009. Some firms, which were present

in several destinations, seem to have reduced their international exposure in 2009 because

24

of the world crisis.

Table 2: Share of the four categories (mono- vs. multi-destinations/sectors) of firms

Year Mono-dest. Mono-dest. Multi-dest. Multi-dest.& Mono-sector & Multi-sector & Mono-sector & Multi-sector

(1) (2) (3) (4)2000 35.8 8.2 19.3 36.72001 36.1 7.9 18.9 37.12002 36.1 7.9 18.6 37.42003 35.5 7.5 19.1 37.92004 34.5 7.5 19.4 38.62005 33.3 7.8 19.7 39.22006 33.5 7.5 19.7 39.32007 32.7 7.6 20.1 39.52008 32.9 7.6 20.5 39.02009 37.7 8.2 17.7 36.4Dest. means destination.

Figure (6) reports the distribution of demand volatility (in logs) and demand skewness

across 2-digit sectors. The ranking of sectors is not similar for both moments and only

one sector (Tobacco) has a negative median skewness.

Figure 6: Distribution of volatility and skewness demand

−4 −3 −2 −1 0 1

Other transport equipmentRadio, tv, comm. equipment

Machinery and equipmentcoke, petroleum, nuclear fuel

Publishing, printingMedical, optical instruments

Fabricated metal productsFurniture, manufacturing n.e.c

Electrical machineryBasic metals

Motor vehiclesChemicals

LeatherWood

Wearing apparelOffice, accounting

TextilesFood & beverages

Other mineral productsTobacco

PaperRubber and plastics

Outside values excluded

Volatility, by industry

−4 −2 0 2 4

Machinery and equipmentOther transport equipment

Furniture, manufacturing n.e.cPublishing, printingFood & beverages

Other mineral productsTextiles

ChemicalsWearing apparel

Basic metalsLeather

coke, petroleum, nuclear fuelFabricated metal products

Motor vehiclesWood

Medical, optical instrumentsRadio, tv, comm. equipment

Electrical machineryPaper

Rubber and plasticsOffice, accounting

Tobacco


Skewness, by industry

Figure (7) presents the distribution volatility across the destinations of French exports.

For clarity, we select the 20 top main destinations and the 20 minor destinations over the

2000-2009 period. The figure reports the median (log) volatility for each of these partners.

For each country, the median is computed using all 3-digit sectors and years for which

25

we are able to compute the absorption (at most we have 10 years * 57 three-digit sectors

= 570 observations). We can observe that the main destinations of French exports have

lower median volatilities that minor destinations. Note that there is also a composition

effect: main partners are often developed countries, which are less volatile than developing

ones. This pattern is confirmed in Figure (8), where we try to answer to the question:

which are the most/least volatile countries? The United States has very low volatility,

as well as the United Kingdom and Canada. By contrast, the most volatile countries (in

the left panel) tend to be developing countries. On average, developed countries are less

volatile than developing ones.

Figure 7: Volatility of demand across destinations

−2.5 −2 −1.5 −1 −.5 0

20−IRL19−HUN18−DNK17−SGP16−CAN15−MAR14−AUT13−TUR12−SWE11−PRT10−POL09−CHN08−JPN07−NLD06−USA05−BLX04−ITA

03−GBR02−ESP01−DEU


Volatility (median), 20 main partners

−2 −1.5 −1 −.5 0

20−LVA19−ARG18−KWT17−PER16−AZE15−ECU14−PHL13−QAT12−ETH11−VNM10−URY09−GEO08−MKD07−MDA06−ARM05−TTO04−MWI03−KGZ02−ERI

01−BOL


Volatility (median), 20 minor partners

Which are the more/least skewed countries? Results are reported in Figure (9). As

previously done, each sub-figure presents 20 countries and reports the median (log) skew-

ness for each of these countries over 2000-2009. We keep only countries for which we have

at least 10% of the 570 potential observations (we do the same for Figure 8). We can

notice that developed countries are often less skewed. The difference for skewness be-

tween developing and developed countries seems to be less pronounced than for volatility.

However, one limit of our approach is the number of observations per country: for some

(developing) countries, the number of sector-year for which we are able to compute the

volatility (and even more the skewness) is rather small and this restriction may of course

26

bias the median value that we obtain.

Figure 8: Most and least demand volatile countries

−2.5 −2 −1.5 −1 −.5 0median volat.

NLDISRITAIRL

AUTGRC

FINPOLBLX

NORJPNDEUPERPRTDNKESPCHNCANGBRUSA

20 least volatile countries

−1.5 −1 −.5 0median volat.

ERIIDN

KGZGEOARMMDAAZEKWTETH

OMNIRN

ECUKAZTURMLTUKRSENMYSSVKLTU

20 most volatile countries

Figure 9: Most and least demand skewed countries

−.1 0 .1 .2 .3median skewness

POLROMARGLVAKORURYCYPGBRMKDCOLPRTESPBLXJPNBRAIRN

CANUSACHNRUS

20 least skewed countries

0 .2 .4 .6 .8median skewness

IDNMLTGEO

ERIARMKGZKAZ

OMNUKRSVKETHMDAHUNAZEBGRMYSECUSVNEGYSWE

20 most skewed countries

4.3 Empirical results

We now present our empirical results on the intensive and the extensive margin of trade.

27

4.3.1 Intensive trade margin

Export volumes

The estimated equation for the export volumes comes directly from the theoretical

model:

ln qkfjt = lnE(RKjt) + ρV(RK

jt) + ηS(RKjt) + FE + εkfjt, (19)

where qkfjt is French firm f export volumes to j in 4-digit k in year t. This variable is

regressed on different moments of demand defined in the data section (4.2). FE represents

a vector of different combinations of fixed effects. The estimations of equation (19) is

reported in Table (3). The sample covers the period 2000 to 2009.

Table 3: Firm level estimations: export volumes

Dep. Var.: Firm export volumes: ln qkfjt(1) (2) (3)

Ln Mean Demand3Kj,t−1 0.250a 0.075a 0.060a

(0.028) (0.025) (0.21)

Ln Volatility3Kjt -0.017b -0.029b -0.022b

(0.008) (0.014) (0.011)

Skewness3Kjt 0.007b 0.012b 0.009b

(0.003) (0.006) (0.004)AdjustedR2 0.814 0.377 0.635Fixed Effects:Firm.Destination.Sectorfjk Yes - -Timet Yes - -Firm.Destination.Timefjt - Yes -Sector (4-digit)k - Yes -Firm.Sector.Timefkt - - YesDestinationj - - YesNote: Robust and industry-destination clustered standard errors inparentheses. a : p < 0.01, b : p < 0.05, c : p < 0.1. N=5,668,638.

The results are in line with our theoretical predictions. An increase in demand level

and demand skewness in destination markets increases export volumes. In contrast, an

increase in volatility reduces exports. How economically meaningful are the estimates

of volatility and skewness? Based on the first column within estimates, we find that in

2005 a one standard deviation increase in the average of volatility of Belgium, reduces

aggregate French exports to Belgium by 1.2%, while a one standard deviation increase in

the average of volatility of China, reduces aggregate French exports to China by 1.3%.

Moreover, if the United Kingdom market would be as volatile as Vietnam, French exports

28

to the UK would decrease by 2.5%. On the other hand, if the UK would be as skewed

as Vietnam, French exports to the UK would increase by 0.5%. This implies that both

absolute and downside risk matter for exporters.

Export prices

The estimated equation for the export prices comes from the theoretical model as well:

ln pkfjt = ln(

RKj,t−1

E(RKj,t−1)

)+ ρV(RK

jt) + ηS(RKjt) + FE + εkfjt, (20)

where pkfjt is French firm f export unit values to destination j in 4-digit sector k in

year t. Table (4) reports the estimates of equation (20) with the same sets of fixed effects

as for the export volumes.

Table 4: Firm level estimations: export prices

Dep. Var.: Firm export unit values: ln pkfjt(1) (2) (3)

Ln Demand3Kj,t−1 0.022b 0.001 0.001

(0.011) (0.017) (0.006)

Ln Mean Demand3Kj,t−1 -0.038c -0.003 -0.004

(0.021) (0.020) (0.008)

Ln Volatility3Kjt 0.014b 0.004 0.002

(0.007) (0.007) (0.003)

Skewness3Kjt -0.005b -0.003 -0.001

(0.002) (0.003) (0.001)R2 0.844 0.658 0.811Fixed Effects:Firm.Destination.Sectorfjk Yes - -Timet Yes - -Firm.Destination.Timefjt - Yes -Sector (4-digit)k - Yes -Firm.Sector.Timefkt - - YesDestinationj - - YesNote: Robust and industry-destination clustered standard errors inparentheses. a : p < 0.01, b : p < 0.05, c : p < 0.1. N=5,668,638.

Results on export prices are in line with our predictions but are not robust across all

specifications. The within estimates, reported in column (1), highlight the two opposite

effects associated with demand in the destination market. On the one side, higher lagged

demand raises export prices (demand effect). On the other side, higher expected foreign

demand, captured by the mean demand variable, increases the competition across firms

(which have an incentive to reduce their level of production) and, in turn, decreases prices.

29

As expected, the volatility and skewness estimates have an opposite effect compared with

their influence on export volumes.

Interaction effects of uncertainty

Proposition (3.1) establishes that the negative effect of demand volatility on export

quantities is strengthened when firm productivity increases and trade costs decrease.

Remember that the variance of profits in a given foreign market is equal to the volatility

(variance) of foreign demand times the output size dedicated to that foreign country.

Given that the most productive firms export more, they are at the margin more affected

by the increase in demand volatility. With the same logic, the lower the trade costs, the

higher the quantities sold and the larger the effect of demand volatility at the margin.

To capture the non-linearity of demand volatility related to trade costs, we use the

distance variable to destination markets, which is a usual proxy for trade costs. More

precisely, we split the distance variable into quartiles. The four distance intervals (in km)

are: [0, 440); [440, 1110); [1110, 1875); and [1875, maximum]. Then, we interact the four

categories with the volatility of demand and compute the predicted mean trade volumes

(in logs) for the deciles of volatility. Results are presented in Figure (10).

Figure 10: Volatility, distance and export volumes

-1.2

-1-.

8-.

6-.

4-.

2P

redi

cted

Mea

n T

rade

Vol

ume

(logs

)

-2.69 -2.45 -2.27 -2.11 -1.96 -1.8 -1.62 -1.4 -1.01Deciles of Demand Volatility

Distance (km) < 440440 <= Distance < 11101110 <= Distance < 1875Distance >= 1875

Predictive Margins with 95% CIs

As expected and depicted in Figure (10), the lower the distance to a destination, the

higher the exports, ceteris paribus. However, the increase in demand volatility affects

differently the quartiles of distance. In particular, export volumes to the more distant

30

markets are line with our theoretical prediction: ∂2qij/∂τij∂V(Rj) > 0.

To capture the non-linear effect of firm productivity and volatility on export volumes

(∂2qij/∂ϕ∂V(Rj) < 0), we use a similar strategy: we split the log of productivity into

quartiles and interact the four categories with demand volatility. Then, we compute the

predicted mean trade volumes (in logs) for the deciles of volatility and the quartiles of

productivity. The different predictions of trade are plotted in Figure (11). This plot shows

three interesting results: (1) the most productive firms export more than the others; (2)

the larger the demand volatility, the lower the export volumes for all levels of productivity;

and (3) the marginal decrease in exports is larger for the most productive firms as the

volatility increases.

Figure 11: Volatility, productivity and export volumes

-.85

-.8

-.75

-.7

-.65

-.6

Pre

dict

ed M

ean

Tra

de V

olum

e (lo

gs)

-2.69 -2.45 -2.27 -2.11 -1.96 -1.8 -1.62 -1.4 -1.01Deciles of Demand Volatility

Log Productivity < P(25)P(25) <= Log Productivity < P(50)P(50) <= Log Productivity < P(75)Log Productivity >= P(75)

Predictive Margins with 95% CIs

4.3.2 Extensive trade margin

Entry and exit

We now explore the impact of uncertainty on the extensive margin of trade. We dis-

tinguish between the entry of new firms on the international market and the exit of the

incumbents from that market. For the entry, our dependent variable is the probability

for a firm f to start exporting to destination j in 4-digit sector k in year t. This choice

model can be written in the latent variable representation, with y∗fjkt the latent variable

that determines whether or not a strictly positive export flow is observed from firm f to

31

destination j on sector k in year t. Our estimated equation is therefore as follows:

Pr(yfjk,t|yfjk,t−1 = 0) =

1 if y∗fjkt > 0

0 if y∗fjkt ≤ 0(21)

with

y∗fjkt = lnE(RKjt) + ρV(RK

jt) + ηS(RKjt) + FE + εkfjt.

As previously, E(RKjt), V(RK

jt) and S(RKjt) represent different moments of demand (see

section 4.2). This equation is estimated using a linear probability model. The inclusion

of fixed effects (FE) in a probit would give rise to the incidental parameter problem. The

linear probability model avoids this issue. In all regressions, we account for correlation of

errors by clustering at country-4-digit sector level. Results are reported in the first three

columns of Table (5). Estimations cover the entry on the international market over the

2000-2009 period.

In addition to the probability of entry, one can also study the exit transition. Higher

volatility or lower upside gains may indeed increase exit of firms from the export market.

In that case, our dependent variable is the probability that firm f in destination j and

sector k in year t − 1 stop exporting to this destination that product k in year t. Ex-

planatory variables are the same as for the entry estimations and results are reported in

the last three columns of Table (5)

Results are again in line with the theoretical model. The probability for a firm to enter

the export market is positively and significantly influenced by an increase in demand and

in potential upside gains (skewness) in the destination markets, while an increase in

volatility reduces the firm’s entry. Opposite effects are observed for the probability of

exit: a higher demand and skewness lower the probability of exit, while a higher volatility

increases it.

Interaction effects of uncertainty

We now investigate whether the impact of volatility on the probability of entry and

exit from the export market is affected by trade costs. To do so, we interact the volatility

32

Table 5: Firm level estimations: probability of entry and exit from the internationalmarket

Dep. Var.: Firm’s entry Firm’s exit:Prob(yfjk,t = 1|yfjk,t−1 = 0) Prob(yfjk,t = 0|yfjk,t−1 = 1)(1) (2) (3) (4) (5) (6)

Ln Mean Demand3Kj,t−1 0.005a 0.004a 0.002a -0.019a -0.003 -0.012a

(0.0002) (0.0001) (0.0002) (0.002) (0.002) (0.002)

Ln Volatility3Kjt -0.029a -0.019a -0.009a 0.020c 0.043a 0.008

(0.002) (0.001) (0.002) (0.011) (0.009) (0.010)

Skewness3Kjt 0.0003a 0.0002b 0.0002b -0.0009 -0.001b -0.001

(0.0001) (0.0001) (0.0001) (0.0007) (0.0006) (0.0005)R2 0.205 0.144 0.066 0.374 0.279 0.259Fixed Effects:Firm.Destination.Sectorfjk Yes - - Yes - -Timet Yes - - Yes - -Firm.Destination.Timefjt - Yes - - Yes -Sector (4-digit)k - Yes - - Yes -Firm.Sector.Timefkt - - Yes - - YesDestinationj - - Yes - - YesNote: Robust and clustered standard errors in parentheses.a : p < 0.01, b : p < 0.05, c : p < 0.1. N= 52,752,877 for entry and N = 4,308,691 for exit.

variable with the distance between France and the destination market j. Results are

presented in Table (6). According to our theoretical predictions, we expect a positive

estimated coefficient on the interaction term for the probability of entry and a negative

one for the probability of exit: trade costs tend to lower the impact of volatility.

Empirical estimations are in line with these theoretical predictions. The interaction

term is positive and highly significant for the probability of entry, and to a lesser extent for

the probability of exit. Furthermore, following the inclusion of the interaction term, the

coefficients on the volatility variable remain very similar to the ones obtained in Table (5).

33

Table 6: Interaction of volatility with distance: probability of entry and exit from theinternational market

Dep. Var.: Firm’s entry Firm’s exit:Prob(yfjk,t = 1|yfjk,t−1 = 0) Prob(yfjk,t = 0|yfjk,t−1 = 1)(1) (2) (3) (4) (5) (6)

Ln Mean Demand3Kj,t−1 0.005a 0.004a 0.002a -0.019a -0.003 -0.012a

(0.0002) (0.0001) (0.0002) (0.002) (0.002) (0.002)

Ln Volatility3Kjt -0.029a -0.019a -0.009a 0.020c 0.043a 0.008

(0.002) (0.001) (0.002) (0.011) (0.009) (0.010)

Ln Volatility3Kjt × Ln Distancej 0.004a 0.002a 0.001a -0.003c -0.005a -0.0002

(0.0002) (0.0002) (0.0002) (0.001) (0.001) (0.001)

Skewness3Kjt 0.0003a 0.0002b 0.0002b -0.0009 -0.001b -0.001

(0.0001) (0.0001) (0.0001) (0.0007) (0.0006) (0.0005)R2 0.205 0.145 0.066 0.374 0.279 0.259Fixed Effects:Firm.Destination.Sectorfjk Yes - - Yes - -Timet Yes - - Yes - -Firm.Destination.Timefjt - Yes - - Yes -Sector (4-digit)k - Yes - - Yes -Firm.Sector.Timefkt - - Yes - - YesDestinationj - - Yes - - YesNote: Robust and clustered standard errors in parentheses.a : p < 0.01, b : p < 0.05, c : p < 0.1. N= 52,752,877 for entry and N = 4,308,691 for exit.

5 Preliminary conclusion

Does demand volatility matter for exports? Yes and skewness as well!

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Appendices

A Price setting

The demand for a variety v is

qij(v) = R2jθ

2vΨ−2

j pij(v)−2

so thatpijqij(v)Rj

= Rjθ2vΨ−2

j pij(v)−1

Summing this expression over each variety consumed in country j yields

Ψ−2j = R−1

j

[∫Ωj

θ2vpij(v)−1dv

]−1

implying the demand for a variety can be rewritten as follows

qij(v) = Rjθ2v

[∫Ωj

θ2vpij(v)−1dv

]−1

pij(v)−2 = Rjθ2vPjp

−2ij

with

Pj ≡[∫

Ωj

θ2vpij(v)−1dv

]−1

.

36

Hence, the export profit is

πij = Rjθ2vPj/pij − cijRjθ

2vPjp

−2ij − wifij

with cij ≡ wiτij/ϕ. The payoff of each firm is as follows:

Πo(v) = E(πi)− ρvV(πi),

Given the demand of consumers, we have

E(πij) = E(Rj)θ2v

Pjpij− cijE(Rj)θ2

v

Pjp2ij

− wifi,

and

V(πij) =(p2ij − c2

ij

)p−4ij P

2j θ

4vV(Rj)

It appears that the expected profit is maximized when the price is equal 2 times the

marginal cost cij while the variance is minimized whens the price is equal to the marginal

cost.

The first order condition implies that the equilibrium price is implicitly given by

Φ(pij) = 0 with

Φ(pij) ≡ − (pij − 2cij)E(Rj) + ρv(p2ij − 2c2

ij

)2p−2

ij Pjθ2vV(Rj) (22)

while the second order condition implies

E(Rj)− ρv8c2ijp−3ij Pjθ

2vV(Rj) > 0

or, evaluated at Φ(pij) = 0,

(p2ij − 2c2

ij

)pij − 4c2

ij (pij − 2cij) > 0

Without uncertainty, the equilibrium price would be pij = 2cij, which is identical to the

37

price prevailing when firms determine strategically the level of quantity. However, under

uncertainty, pij = 2cij is not an equilibrium as long as ρv > 0. Introducing pij = 2cij into

(22) implies Φ(pij) > 0 so that the equilibrium price under uncertainty is higher than

2cij. Using the envelop theorem:

∂pij∂V(Rj)

= E(Rj)V(Rj)

pij − 2cijE(Rj)− 8ρvc2

ijPjθ2vV(Rj)p−3

ij

> 0

B Industry supply and income volatility

In this Appendix, we show that ∂Ψj/∂V(Rj) < 0. According to (7) and (13), we have

Λ[Ψj,V(Rj)] = 0 with

Λ ≡ Ψj −∑

kMk

∫ ξkj

0

E(Rj)2 Ψ−1

j

[wkτkjξ + ρvV(Rj)Ψ−2

j

]−1µ(ξ)dξ,

where ∂Λj/∂V(Rj) > 0 because both θvq1/2ij and ξij decrease with V(Rj). The envelop

theorem implies

sign ∂Ψj

∂V(Rj)= −sign∂

2Λ∂Ψj

,

as ∂Λ/∂V(Rj) > 0. Standard calculations show that

∂Λ∂Ψj

=1−Ψ−1

j

∑kMk

∫ ξkj

0 θv [qkj(ξ)]12ρvV(Rj)Ψ−2

j −wkτkjξ

ρvV(Rj)Ψ−2j +wkτkjξ

µ(ξ)dξ

−∂ξkj

∂Ψjθv[qkj(ξkj)

] 12 ,

(23)

where ∂Λ/∂Ψj > 0 as the second term on the RHS of (23) is inferior to 1 and ∂ξkj/∂Ψj < 0.

As a result,

εΨj≡ −V(Rj)

Ψj

∂Ψj

∂V(Rj)> 0.

38

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