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Export Decision under Risk

Export Decision under Risk∗
José De Sousa, Anne-Célia Disdier and Carl Gaigné†
March 2, 2015
Very preliminary and incomplete
Abstract
Does demand volatility matter for exports? How do exporting firms deal with
skewed demand? A simple model of downside risk aversion shows that on average
exporters increase export prices and reduce export volumes when demand volatility
in destination markets increases. They behave the opposite way when demand
skewness rises. We find that the moments of the demand distribution also affect
the number of exporting firms and the industry supply. These adjustments may
lead some firms to increase their exports when demand volatility increases. These
theoretical predictions are put to the test by using French firm-level exports across
destination markets with different levels of demand volatility and skewness. The
firm-level results, over the period 2000-2009, are consistent with our predictions.
JEL classification: D81, F12, L25
Keywords: Uncertainty, Demand volatility, Firm exports, Skewness
1
Introduction
Does demand volatility matter for exporters supply decisions? According to the Capgemini 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 production levels or input procurements before the output is marketed or the market price
∗
We thank Holger Breinlich, Maggie Chen, Gabriel Felbermayr, James Harrigan, Keith Head, Nuno
Limão, Gianmarco Ottaviano, John McLaren, John Morrow, Denis Novy, Mathieu Parenti, Ariell Reshef,
Veronica Rappoport, Daniel Sturm and seminar and conference participants at U; of Virginia, U. of George
Washington, CEPII, U. of Caen, London School of Economics, U. of Munich (ETSG), U. of Strathclyde,
and U. of Tours for their helpful comments. This work is supported by the French National Research
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
for output is known. Demand cannot be known for certain at the time the contracts with
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 certainty 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 demand volatility in destination markets. This point is illustrated in Figure (1) from data
on world sectoral-level data.
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Log of Apparent Consumption (Mean) - 3 digit
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Figure 1: Demand (apparent consumption) level and demand volatility
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MAC
-4
-2
0
2
Log 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 exposure. 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 volatil2
ity should import less. Using the same database of world sectoral-level data, we find
prima facie evidence of a negative relationship between demand volatility and imports,
as depicted in Figure (2).1
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E as c y= 1 19 s e = 02
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Log o Sec o mpo s 3 d g
5
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Figure 2: Relationship between imports and demand volatility
53
33
13
Log o Appa en Consump on Vo a
7
y sd
3dg
No e 100 coun es 63 sec o s 2000 09
However, risk-averse firms react differently to uncertainty according to their characteristics. 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 varieties 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.
1
Th s ev dence s supported by an adjusted part a res dua p ot contro ng for year and country
fixed effects The correspond ng e ast c ty of demand vo at ty s −0 17 (p<0 01) suggest ng that an 1%
ncrease n vo at ty n a dest nat on country s assoc ated w th a 0 17% decrease n sectora mports
3
Yet, the variance does not distinguish between upside risk versus downside risk. Skewness
(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
2
3
However, the converse is not necessarily true (Menezes, Geiss, and Tressler, 1980).
A similar example can be found in Eeckhoudt, Gollier, and Schlesinger (2005) in a different context.
4
market raises the unit prices set by firms in this market through a change in their markup.
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 outcomes (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 particular, 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
5
foreign countries or importing from different countries depend less on the domestic shocks
(Giovanni and Levchenko 2009). On the one side, the industries exporting (or importing) 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 uncertainty. He finds that when multinational sales are priced in the local currency while
exports are priced in the producer currency, destination volatility benefits exporters: during 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
6
volatility of production costs in the destination country.
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 under 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 industry 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 climatic 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
7
is therefore uncertain, and can be either higher or lower than the average expenditures,
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 variety 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) =
τij qij (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,
8
this is no longer the case under uncertainty. The firm has two options: (i) set quantity
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) −
wi τij
qij (v) − wi fij ,
ϕ
(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 countries, 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 to9
tal exporting sales Σj πij , such that πi = πii + Σj πij . Throughout, we assume that the
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 Π0 (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
1 000
1 00
0
Π(πi ) ≈ Π(E(πi )) + Π [πi − E(πi )] + Π [πi − E(πi )]2 + Π [πi − E(πi )]3 .
2
6
Taking the expectation and assuming that the moments exist lead to
1 00
1 000
EΠ(πi ) ≈ Π[E(πi )] + Π E[πi − E(πi )]2 + Π E[πi − E(πi )]3 .
2
6
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 )] − ΓΠ0 , we have
00
000
1Π
1Π
Γ≈−
S(πi ),
0 V(πi ) −
2Π
6 Π0
00
0
000
(2)
0
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.
00
0
The term −Π /2Π is known as the so-called Arrow–Pratt absolute risk aversion coef000
0
000
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 skewness to the left (S(π) < 0) is associated with “downside risk” exposure, while skewness to
10
the right (S(π) > 0) is associated with “upside risk” exposure.
Two remarks are in order. First, risk aversion can decrease with wealth of the individuals. Under this configuration, decision makers exhibit decreasing absolute risk aversion
(DARA preferences) implying Π000 > 0. This entails that the risk aversion of the exporter
decreases with its level of domestic sales. Second, Π000 > 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 decisionmaker can always be approximated by
Πv (πi ) ≈ E(πi ) − ρv V(πi ) + ηv S(πi ),
00
0
000
(3)
0
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 identical
4
We 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 matters
for most of our results is that export prices (1) decrease in export quantities (∂pij /∂qij < 0), (2) increase
in destination demand (∂pij /∂Rj > 0), (3) with a diminishing marginal effect as export quantities increase
∂ 2 pij /(∂Rij ∂qij ) < 0.
11
and the utility of the consumption of the differentiated good is given by
Uj =
Z
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 (.) = θv qj (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 ∂ 2 u(v)/∂q(v)2 < 0, consumers exhibit a
preference for variety.
The budget constraint faced by a consumer is given by
Z
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) =
−1
θv
qij (v) 2 ,
2λ
(6)
where λ is the Lagrange multiplier. Plugging (6) into (5) implies λ = Ψj /2Rj with
Ψj ≡
Z
Ωj
1
θv qkj (v) 2 dv.
(7)
The expression Ψj can be interpreted as a measure of industry supply. As a consequence,
5
Note 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) = Rj θv qij (v)
−1
2
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 introduction 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). Profitmaximizing quantity is given by
1
qij (v) 2 =
Rj ϕθv −1
Ψ ,
2 wi τij j
(9)
so that
pij (v) = 2
wi τij
.
ϕ
Thus, under certainty, the equilibrium price is equal to the marginal cost wi τij /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 )θv qij (v)
13
−1
2
Ψ−1
j .
(10)
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 ) − ρv V(πi ) =
X
j
E(πij ) − ρv
X
j
V(πij ),
where E(πij ) is given by (1) and Σj V(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 )θv2 qij (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
−1
wi τij
1
E(Rj )θv qij (v) 2 Ψ−1
− ρv V(Rj )θv2 Ψ−2
j −
j = 0,
2
ϕ
(12)
and it is readily to check that ∂ 2 Πv /∂qij2 < 0. As a result, Payoff -maximizing quantity is
given by
"
θv2 ϕ
E(Rj )θv ϕ −1
qij (v) =
Ψj 1 + ρv V(Rj )Ψ−2
j
2wi τij
wi τij
1
2
#−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 ∂ 2 qij /∂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 ∂ 2 qij /∂τij2 > 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 industry supply (Ψ), the negative effect of demand volatility on export quantities is strengthened when firm productivity increases and trade costs decrease.
As a simple proof, we can establish from equation (13)
∂ 2 qij
∂ 2 qij
<0<
,
∂ϕ∂V(Rj )
∂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:
"
θv2 ϕ −2
wi τij Rj
2
1 + ρv V(Rj )
pij (v) =
Ψ
ϕ E(Rj )
wi τij j
#
(14)
The equilibrium price is equal to the marginal cost (wi τij /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 information, 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 variable 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 industrial 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 destinations 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 of
6
An 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 ) − ρv V(πij ) > wi fij .
It is straightforward to check that Πv = sij /2 where sij ≡ E(pij )qij with
#−1
"
E(Rj )2 wi τij 2
Ψ + ρv V(Rj )
sij =
2
θv2 ϕ j
(15)
.
As a result, Πv = 0 when ϕ = 0 and ∂Πv /∂ϕ > 0. Hence, there exists a quality-adjusted
productivity cutoff θv2 ϕ above which a firm serves country j. As expected, the probability
of exporting decreases with V(Rj ). In addition, we have ∂ 2 Πv /∂ϕ∂V(Rj ) < 0 so the
payoffs of large firms are more impacted by a rise in demand volatility than the small
n
2
firms. Notice also that ∂Πv /∂Ψj < 0 and sign{∂ 2 Πv /∂ϕ∂Ψj } = sign ρv V(Rj ) wθivτϕij − Ψ2j
o
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 quantities through Ψj . In what follows,
we determine the relationship between Ψj and V(Rj ) and the total effect of V(Rj ). Let
ξ ≡ 1/(θv2 ϕ) ≥ 0 be an inverse measure of quality-adjusted productivity and µ(ξ) is the
distribution of ξ. The cutoff for exporting ξbij is such that Πv (ξbij ) = wi fij or, equivalently,
Ψ−2
E(Rj )2
j
b
− ρv V(Rj )
.
ξij ≡
4wi fij
wi τij
"
#
(16)
It follows that a firm exports as long as ξ < ξbij . 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 zeropayoff cutoff conditions ξbij 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
Ψj ≡ −
V(Rj ) ∂Ψj
> 0,
Ψj ∂V(Rj )
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)
∂sij (v)
∂sij (v) ∂Ψj
sij 2wi τij ξΨj − ρv V(Rj )Ψ−2
j
=
+
=
,
−2
dV(Rj )
∂V(Rj )
∂Ψj ∂V(Rj )
V(Rj ) wi τij ξ + ρv V(Rj )Ψj
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 productivity 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
Export Sales (sij /2)
A
sij (ξ, V + )
sij (ξ, V − )
Production costs (ξij )
Note: V − and V + mean low and high volatility, respectively.
ambiguous. Some standard calculations reveal that
"
1
dξbij
∂ ξbij
∂ ξbij ∂Ψj
E(Rj )2
− ρv V(Rj ) 1 +
=
+
=
dV(Rj )
∂V(Rj ) ∂Ψj ∂V(Rj )
4wi fij
2Ψj
!#
2Ψj Ψ−2
j
V(Rj )wi τij
where ∂ ξbij /∂V(Rj ) < 0 while ∂ ξbij /∂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
qij (v) wi τij ξ − ρv V(Rj )Ψ−2
dqij (v)
j (1 + Ψj )
=
dV(Rj )
V(Rj )
wi τij ξ + ρv V(Rj )Ψ−2
j
and
d2 qij
d2 qij
<0<
dϕ∂V(Rj )
dτ dV(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
Payoff (Πij )
Payoff (Πij )
Πij (ξ, V − )
wi fij
Πij (ξ, V + )
A
A
Πij (ξ, V + )
wi fij
Πij (ξ, V − )
ξˆij (V − ) ξˆij (V + )
ξij
(a) Low export fixed costs wi fij
ξˆij (V + ) ξˆij (V − )
ξij
(b) High export fixed costs wi fij
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 direction 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
3
S(πij ) = S(Rj )θv3 qij2 (v)Ψ−3
j .
(17)
and the Payoff -maximizing quantity is implicitly given by ∂Πo /∂qij = 0, or, equivalently,
3S(Rj )θv3 Ψ−3
1
E(Rj )
τij
j
2 −2
2 + η
θv Ψ−1
−
w
+
ρ
V(R
)θ
Ψ
q
(v)
qij (v) = 0.
i
v
j
ij
v
j
v j
2
ϕ
2
!
(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 predictions 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 straightforward to verify that ∂qij /∂S(Rj ) > 0 whereas ∂pij /∂S(Rj ) < 0 when the second order
condition holds (E(Rj )Ψ2j − ηv 3S(Rj )θv2 qij (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
∂ 2 qij
∂ 2 qij
>0>
∂ϕ∂S(Rj )
∂τ ∂S(Rj )
and
∂pij
∂pij (v)
>0>
∂τ ∂S(Rj )
∂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
4.1
Empirical Analysis
Identification strategy
According to our theoretical predictions exporters react in response to volatility by decreasing volumes
∂qij
<
∂V(Rj )
0 and increasing prices
21
∂pij
>
∂V(Rj )
0 , while in response to
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
K
K
) and the skewness
) , the volatility V(Rjt
tion j: the lagged expected value E(Rj,t−1
K
S(Rjt
) 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: aK
jt =
K
K
ProductionK
jt + Importsjt − Exportsjt , 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:
K
1. The mean demand or absorption E(Rj,t−1
) computed in year t as the log of the
lagged value of mean absorption over the 5 previous years;
K
2. The volatility of demand V(Rjt
) computed as the standard deviation of the yearly
growth rates of aK
jt 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.
K
3. The unbiased skewness of demand S(Rjt
) computed as the skewness of the yearly
growth rates of aK
jt over 6 years and the sub-sectors k.
Figure 5: Demand level and demand volatility of a given 3-digit sector
USA
16
JPN
DEU
CHN
GBR
ESP
MEX
CAN
14
POL
ITA
TUR
NLD
PRT
GRC
FRA
AUS
BLXKOR
UKR
IND
COL
NOR
ROM
HUN
12
PER
MYS
CYP
FIN
IDN
ECU
SVK
PAN
KAZ
MAR
IRN
LTU
EGY
OMN
LVA
TTO
URY
MLT
DNK
JOR
EST
ETH
MDA
MWI
10
Log of Apparent Consumption (Mean) - 3 digit
18
Manufacture of beverages in 2005
SVNSEN
MKD
GEO
AZE
ARM
KGZ
ERI
8
TJK
-2.7
-.7
Log Volatility (standard deviation) of destination county - 3 digit
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 included
7
The 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
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
Note: 119
Nb. destinations
79151
77115
76509
74304
72021
70871
71207
68400
65803
47011
4-digit sectors per
80
80
81
86
85
83
88
86
79
66
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 (multidestinations 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 multisectors 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-sector
(1)
Mono-dest.
Multi-dest.
& Multi-sector & Mono-sector
(2)
(3)
2000
35.8
2001
36.1
2002
36.1
2003
35.5
2004
34.5
2005
33.3
2006
33.5
2007
32.7
2008
32.9
2009
37.7
Dest. means destination.
8.2
7.9
7.9
7.5
7.5
7.8
7.5
7.6
7.6
8.2
Multi-dest.
& Multi-sector
(4)
19.3
18.9
18.6
19.1
19.4
19.7
19.7
20.1
20.5
17.7
36.7
37.1
37.4
37.9
38.6
39.2
39.3
39.5
39.0
36.4
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
Volatility, by industry
Rubber and plastics
Paper
Tobacco
Other mineral products
Food & beverages
Textiles
Office, accounting
Wearing apparel
Wood
Leather
Chemicals
Motor vehicles
Basic metals
Electrical machinery
Furniture, manufacturing n.e.c
Fabricated metal products
Medical, optical instruments
Publishing, printing
coke, petroleum, nuclear fuel
Machinery and equipment
Radio, tv, comm. equipment
Other transport equipment
Skewness, by industry
Tobacco
Office, accounting
Rubber and plastics
Paper
Electrical machinery
Radio, tv, comm. equipment
Medical, optical instruments
Wood
Motor vehicles
Fabricated metal products
coke, petroleum, nuclear fuel
Leather
Basic metals
Wearing apparel
Chemicals
Textiles
Other mineral products
Food & beverages
Publishing, printing
Furniture, manufacturing n.e.c
Other transport equipment
Machinery and equipment
−4 −3 −2 −1 0
1
−4
Outside values excluded
−2
0
2
4
Outside values excluded
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
Volatility (median), 20 main partners
01−DEU
02−ESP
03−GBR
04−ITA
05−BLX
06−USA
07−NLD
08−JPN
09−CHN
10−POL
11−PRT
12−SWE
13−TUR
14−AUT
15−MAR
16−CAN
17−SGP
18−DNK
19−HUN
20−IRL
Volatility (median), 20 minor partners
01−BOL
02−ERI
03−KGZ
04−MWI
05−TTO
06−ARM
07−MDA
08−MKD
09−GEO
10−URY
11−VNM
12−ETH
13−QAT
14−PHL
15−ECU
16−AZE
17−PER
18−KWT
19−ARG
20−LVA
−2.5
−2
−1.5
−1
−.5
0
−2
Outside values excluded
−1.5
−1
−.5
0
Outside values excluded
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) skewness 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 between 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
20 least volatile countries
20 most volatile countries
USA
GBR
CAN
CHN
ESP
DNK
PRT
PER
DEU
JPN
NOR
BLX
POL
FIN
GRC
AUT
IRL
ITA
ISR
NLD
LTU
SVK
MYS
SEN
UKR
MLT
TUR
KAZ
ECU
IRN
OMN
ETH
KWT
AZE
MDA
ARM
GEO
KGZ
IDN
ERI
−2.5
−2
−1.5
−1
median volat.
−.5
0
−1.5
−1
−.5
median volat.
0
Figure 9: Most and least demand skewed countries
20 least skewed countries
20 most skewed countries
RUS
CHN
USA
CAN
IRN
BRA
JPN
BLX
ESP
PRT
COL
MKD
GBR
CYP
URY
KOR
LVA
ARG
ROM
POL
SWE
EGY
SVN
ECU
MYS
BGR
AZE
HUN
MDA
ETH
SVK
UKR
OMN
KAZ
KGZ
ARM
ERI
GEO
MLT
IDN
−.1
4.3
0
.1
.2
median skewness
.3
0
.2
.4
.6
median skewness
.8
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:
K
K
K
) + FE + εkf jt ,
) + ηS(Rjt
) + ρV(Rjt
ln qfkjt = ln E(Rjt
(19)
where qfkjt 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 qfkjt
(1)
(2)
(3)
Ln Mean Demand3K
j,t−1
0.250a
0.075a
0.060a
(0.028)
(0.025)
(0.21)
b
-0.017
b
-0.029
-0.022b
(0.008)
(0.014)
(0.011)
b
0.007
b
0.012
0.009b
(0.003)
(0.006)
(0.004)
0.814
0.377
0.635
Yes
Yes
-
Yes
Yes
-
Yes
Yes
Ln
Volatility3K
jt
Skewness3K
jt
AdjustedR2
Fixed Effects:
Firm.Destination.Sectorf jk
Timet
Firm.Destination.Timef jt
Sector (4-digit)k
Firm.Sector.Timef kt
Destinationj
Note: Robust and industry-destination clustered standard errors in
parentheses. 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:
K
Rj,t−1
K
K
+ ρV(Rjt
) + ηS(Rjt
) + FE + εkf jt ,
= ln
K
)
E(Rj,t−1
!
ln pkf jt
(20)
where pkf jt 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 pkf jt
(1)
(2)
(3)
Ln Demand3K
j,t−1
0.022b
0.001
0.001
(0.011)
(0.017)
(0.006)
-0.038c
-0.003
-0.004
(0.021)
(0.020)
(0.008)
Ln Mean Demand3K
j,t−1
Ln Volatility3K
jt
Skewness3K
jt
R2
Fixed Effects:
Firm.Destination.Sectorf jk
Timet
Firm.Destination.Timef jt
Sector (4-digit)k
Firm.Sector.Timef kt
Destinationj
0.014b
0.004
0.002
(0.007)
(0.007)
(0.003)
-0.005b
-0.003
-0.001
(0.002)
(0.003)
(0.001)
0.844
0.658
0.811
Yes
Yes
-
Yes
Yes
-
Yes
Yes
Note: Robust and industry-destination clustered standard errors in
parentheses. 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
Predicted Mean Trade Volume (logs)
-.4
-1.2 -1
-.8
-.6
-.2
Predictive Margins with 95% CIs
-2.69
-2.45
-2.27 -2.11 -1.96 -1.8
-1.62
Deciles of Demand Volatility
-1.4
-1.01
Distance (km) < 440
440 <= Distance < 1110
1110 <= Distance < 1875
Distance >= 1875
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: ∂ 2 qij /∂τij ∂V(Rj ) > 0.
To capture the non-linear effect of firm productivity and volatility on export volumes
(∂ 2 qij /∂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
Predicted Mean Trade Volume (logs)
-.85 -.8 -.75 -.7 -.65 -.6
Predictive Margins with 95% CIs
-2.69
-2.45
-2.27 -2.11 -1.96 -1.8
-1.62
Deciles of Demand Volatility
-1.4
-1.01
Log Productivity < P(25)
P(25) <= Log Productivity < P(50)
P(50) <= Log Productivity < P(75)
Log Productivity >= P(75)
4.3.2
Extensive trade margin
Entry and exit
We now explore the impact of uncertainty on the extensive margin of trade. We distinguish 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 ∗ f jkt 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:




1 if yf∗jkt > 0


0 if yf∗jkt ≤ 0
P r(yf jk,t |yf jk,t−1 = 0) = 
(21)
with
K
K
K
) + FE + εkf jt .
) + ηS(Rjt
) + ρV(Rjt
yf∗jkt = ln E(Rjt
K
K
K
As previously, E(Rjt
), V(Rjt
) and S(Rjt
) 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. Explanatory 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 international
market
Dep. Var.:
Firm’s entry:
Firm’s exit:
P rob(yf jk,t = 1|yf jk,t−1 = 0) P rob(yf jk,t = 0|yf jk,t−1 = 1)
(1)
(2)
(3)
(4)
(5)
(6)
Ln Mean Demand3K
j,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)
a
a
a
c
a
Ln
Volatility3K
jt
Skewness3K
jt
R2
Fixed Effects:
Firm.Destination.Sectorf jk
Timet
Firm.Destination.Timef jt
Sector (4-digit)k
Firm.Sector.Timef kt
Destinationj
-0.029
-0.019
-0.009
0.020
0.043
0.008
(0.002)
(0.001)
(0.002)
(0.011)
(0.009)
(0.010)
0.0003a
0.0002b
0.0002b
-0.0009
-0.001b
-0.001
(0.0001)
(0.0001)
(0.0001)
(0.0007)
(0.0006)
(0.0005)
0.205
0.144
0.066
0.374
0.279
0.259
Yes
Yes
-
Yes
Yes
-
Yes
Yes
Yes
Yes
-
Yes
Yes
-
Yes
Yes
Note: 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 the
international market
Dep. Var.:
Firm’s entry:
P rob(yf jk,t = 1|yf jk,t−1 = 0)
(1)
(2)
(3)
Firm’s exit:
P rob(yf jk,t = 0|yf jk,t−1 = 1)
(4)
(5)
(6)
Ln Mean Demand3K
j,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)
a
a
a
c
a
Ln
Volatility3K
jt
Ln Volatility3K
jt × Ln Distancej
Skewness3K
jt
R2
Fixed Effects:
Firm.Destination.Sectorf jk
Timet
Firm.Destination.Timef jt
Sector (4-digit)k
Firm.Sector.Timef kt
Destinationj
-0.029
-0.019
-0.009
0.020
0.043
0.008
(0.002)
(0.001)
(0.002)
(0.011)
(0.009)
(0.010)
0.004a
0.002a
0.001a
-0.003c
-0.005a
-0.0002
(0.0002)
(0.0002)
(0.0002)
(0.001)
(0.001)
(0.001)
a
b
b
b
0.0003
0.0002
0.0002
-0.0009
-0.001
-0.001
(0.0001)
(0.0001)
(0.0001)
(0.0007)
(0.0006)
(0.0005)
0.205
0.145
0.066
0.374
0.279
0.259
Yes
Yes
-
Yes
Yes
-
Yes
Yes
Yes
Yes
-
Yes
Yes
-
Yes
Yes
Note: 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!
References
Baldwin, R., and P. Krugman (1989): “Persistent Trade Effects of Large Exchange
Rate Shocks,” Quarterly Journal of Economics, 104(4), 635–654.
Bloom, N. (2014): “Fluctuations in Uncertainty,” Journal of Economic Perspectives,
28(2), 153–175.
Dixit, A. K., and R. S. Pindyck (1994): Investment under Uncertainty. Princeton
University Press.
Dixit, A. K., and J. E. Stiglitz (1977): “Monopolistic Competition and Optimum
Product Diversity,” American Economic Review, 67(3), 297–308.
34
Eeckhoudt, L., C. Gollier, and H. Schlesinger (2005): Economic and Financial
Decisions under Risk. Princeton University Press.
Gabaix, X. (2011): “The Granular Origins of Aggregate Fluctuations,” Econometrica,
79(3), 733–772.
Giovanni, J. d., and A. A. Levchenko (2009): “Trade openness and volatility,”
Review of Economics and Statistics, 91(3), 558–585.
Handley, K., and N. Limao (2013): “Policy Uncertainty, Trade and Welfare: Theory
and Evidence for China and the US,” Discussion Paper 19376, National Bureau of
Economic Research.
Helpman, E., and A. Razin (1978): “A theory of international trade under uncertainty,” Discussion paper, Academic Press, Harcourt Brace Jovanovitch.
Klemperer, P., and M. Meyer (1986): “Price competition vs. quantity competition:
the role of uncertainty,” RAND Journal of Economics, 17(4), 618–638.
Krugman, P. R. (1979): “Increasing returns, monopolistic competition, and international trade,” Journal of international Economics, 9(4), 469–479.
Leland, H. E. (1972): “Theory of the firm facing uncertain demand,” American Economic Review, 62(3), 278–291.
Lewis, T. L. (2014): “Exports versus Multinational Production under Nominal Uncertainty,” Journal of International Economics, forthcoming.
Melitz, M. J. (2003): “The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity,” Econometrica, 71(6), 1695–1725.
Menezes, C., C. Geiss, and J. Tressler (1980): “Increasing Downside Risk,” American Economic Review, 70(5), 921–932.
Popov, A. A. (2011): “Output Growth and Fluctuations: The Role of Financial Openness,” Discussion paper, ECB Working Paper.
35
Ramondo, N., V. Rappoport, and K. J. Ruhl (2013):
“The Proximity-
Concentration Tradeoff under Uncertainty,” Review of Economic Studies, 80(4), 1582–
1621.
Zhelobodko, E., S. Kokovin, M. Parenti, and J.-F. Thisse (2012): “Monopolistic competition: Beyond the constant elasticity of substitution,” Econometrica, 80(6),
2765–2784.
Appendices
A
Price setting
The demand for a variety v is
−2
qij (v) = Rj2 θv2 Ψ−2
j pij (v)
so that
pij qij (v)
−1
= Rj θv2 Ψ−2
j pij (v)
Rj
Summing this expression over each variety consumed in country j yields
Ψ−2
j
=
Rj−1
#−1
"Z
Ωj
θv2 pij (v)−1 dv
implying the demand for a variety can be rewritten as follows
qij (v) =
Rj θv2
"Z
Ωj
#−1
θv2 pij (v)−1 dv
pij (v)−2 = Rj θv2 Pj p−2
ij
with
Pj ≡
"Z
Ωj
#−1
θv2 pij (v)−1 dv
36
.
Hence, the export profit is
πij = Rj θv2 Pj /pij − cij Rj θv2 Pj p−2
ij − wi fij
with cij ≡ wi τij /ϕ. The payoff of each firm is as follows:
Πo (v) = E(πi ) − ρv V(πi ),
Given the demand of consumers, we have
E(πij ) = E(Rj )θv2
Pj
Pj
− cij E(Rj )θv2 2 − wi fi ,
pij
pij
and
2 4
V(πij ) = p2ij − c2ij p−4
ij Pj θv V(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
2
Φ(pij ) ≡ − (pij − 2cij ) E(Rj ) + ρv p2ij − 2c2ij 2p−2
ij Pj θv V(Rj )
(22)
while the second order condition implies
2
E(Rj ) − ρv 8c2ij p−3
ij Pj θv V(Rj ) > 0
or, evaluated at Φ(pij ) = 0,
p2ij − 2c2ij pij − 4c2ij (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
E(Rj )
pij − 2cij
=
>0
∂V(Rj )
V(Rj ) E(Rj ) − 8ρv c2ij Pj θv2 V(Rj )p−3
ij
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 −
X
Mk
k
Z ξbkj
0
i−1
E(Rj ) −1 h
µ(ξ)dξ,
Ψj wk τkj ξ + ρv V(Rj )Ψ−2
j
2
1/2
where ∂Λj /∂V(Rj ) > 0 because both θv qij
and ξbij decrease with V(Rj ). The envelop
theorem implies
sign
∂Ψj
∂ 2Λ
= −sign
,
∂V(Rj )
∂Ψj
as ∂Λ/∂V(Rj ) > 0. Standard calculations show that
1 − Ψ−1
j
∂Λ
=
∂Ψj
P
k
Mk
R ξbkj
0
1
θv [qkj (ξ)] 2
∂ ξb
− ∂Ψkjj θv
h
qkj
ρv V(Rj )Ψ−2
j −wk τkj ξ
ρv V(Rj )Ψ−2
j +wk τkj ξ
(ξb
kj )
i1
2
µ(ξ)dξ
(23)
,
where ∂Λ/∂Ψj > 0 as the second term on the RHS of (23) is inferior to 1 and ∂ ξbkj /∂Ψj < 0.
As a result,
Ψj ≡ −
V(Rj ) ∂Ψj
> 0.
Ψj ∂V(Rj )
38
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