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Exchange rate volatility and trade: The role of credit constraints

Shu Lin, Kang Shi, Haichun Ye

PII:
DOI:
Reference:

S1094-2025(18)30186-8
/>YREDY 871

To appear in:

Review of Economic Dynamics

Received date:
Revised date:

16 August 2016
25 April 2018

Please cite this article in press as: Lin, S., et al. Exchange rate volatility and trade: The role of credit constraints. Review of Economic
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Highlights

• The role of credit constraints play an important role in determining the trade effect of exchange rate volatility.
• A theoretical model is developed to show how constrained firms and unconstrained firms respond to the changes of exchange rate
volatility.
• Financially more constrained sectors have a more negative exposure of their trade volumes to exchange rate volatility both theoretically
and empirically.
• The estimated trade effects of exchange rate volatility vary substantially across sectors.


Exchange rate volatility and trade: The role of credit constraints
Shu Lin
Chinese University of Hong Kong
Kang Shi*
Chinese University of Hong Kong
Haichun Ye
Hong Kong Monetary Authority
Abstract
This study examines the role of credit constraints in determining the trade effect
of exchange rate volatility. We first develop a small open economy general equilibrium
model with credit constraints. In our model, constrained firms respond to real
depreciations and appreciations in an asymmetric way, and exchange rate volatility
reduces their exports on average. The effect of exchange rate volatility on unconstrained
firms' exports, however, is ambiguous. Overall, exchange rate volatility has a more
negative impact on constrained firms. In a large sector-level bilateral trade dataset, we
find robust empirical evidence supporting the predictions of the model. We show that
financially more constrained sectors have a more negative exposure of their trade
volumes to exchange rate volatility. Moreover, the estimated trade effects of exchange
rate volatility vary substantially across sectors and can be either positive or negative
depending on the degree of credit constraints.
Keywords: exchange rate volatility; trade; credit constraints; sectoral heterogeneity
JEL classification: F14, F31, G20

Acknowledgements: The authors would like to thank Editor Matthias Doepke, an associate editor,
and two anonymous referees for valuable comments. Any views expressed are those of the
authors only and should not be attributed to Hong Kong Monetary Authority.
*Corresponding author. Address: Department of Economics, Chinese University of Hong Kong,
ELB931, Shatin, N.T., Hong Kong. Email: Phone: (852)93272680.


1. Introduction
The effect of exchange rate volatility on trade is not only an important academic
research topic but also a question of high policy relevance. The supposedly beneficial
effect on trade flows of limiting exchange rate volatility has been one of the major
pro-arguments for currency unions or other types of fixed exchange rate arrangements.
Numerous studies have empirically examined this issue. Early empirical work in the
literature (e.g., Hooper and Kohlhagen, 1978; Cushman, 1983; IMF, 1984) often study a
small set of rich countries and report no consistent trade effects of exchange rate
volatility. More recent studies typically apply a gravity model approach to large bilateral
trade data to estimate the effect of real exchange rate volatility (e.g., Frankel and Wei,
1993; Dell’Ariccia, 1999; Wei, 1999; Rose, 2000; IMF, 2004). Some studies in this group
find a statistically significant but quantitatively small negative effect, but others argue
that even this small negative effect is not robust.1 Another group of studies in this
literature focus on the unpredictable variation in the real exchange rate and employ
ARCH/GARCH type of time-series methods to examine the effects of real exchange rate
uncertainty on trade (e.g. Baum et al., 2004; Grier and Smallwood, 2007). The results
obtained in these studies are also mixed.2
To sum up, despite many efforts, the existing empirical evidence on the trade
effect of exchange rate volatility still remains inconclusive, a common conclusion drawn
in two comprehensive surveys of the literature, McKenzie (1999) and IMF (2004). For
example, in their 2004 study, a group of IMF researchers led by Peter Clark and
Shang-Jin Wei reach the following conclusion,
1

See McKenzie (1999) and IMF (2004) for detailed survey of this large literature.
For example, Grier and Smallwood (2007) show that exchange rate uncertainty has no effect in developed countries
but a significantly negative effect in 6 of the 9 emerging countries in their sample.
2

1


"... Overall, if exchange rate volatility has a negative effect on trade, this effect
would appear to be fairly small and is by no means a robust, universal finding." (IMF
2004, p.6)
The mixed empirical findings perhaps should not be surprising as it merely
reflects the fact that there are no clear-cut theoretical predictions on the effect of
exchange rate volatility on aggregate (bilateral) trade flows. Under different assumptions,
partial equilibrium models can generate either a negative or a positive effect. For example,
Clark (1973) and Hooper and Kohlhagen (1978) focus on the role of risk aversion and
show that an increase in exchange rate variations causes fluctuations in firms' profits and
results in a drop in trade volumes if firms are highly risk averse. On the other hand,
Pindyck (1982) and Canzoneri et al. (1984) consider adjustment costs and show that,
given an increase in exchange rate variability, a risk-averse firm may increase output if it
is able to adjust factor inputs, and the expected profitability from this adjustment
outweighs the aversion to the increased risk. More recently, in a general equilibrium
framework, Bacchetta and van Wincoop (2000) show that there is no clear relationship
between exchange rate volatility and trade either.
In this study, we argue that a weak and inconclusive average effect of exchange
rate volatility on aggregate (bilateral) trade volumes masks a large sectoral heterogeneity.
More specifically, we combine the exchange rate volatility literature and the
recently-emerged credit constraints and trade literature (e.g., Amiti and Weinstein, 2008;
Cheney, 2005; Chor and Manova, 2012; Manova, 2013; Manova, Wei, and Zhang, 2015;

Minetti and Zhu, 2010) and show both theoretically and empirically that financially more
vulnerable sectors have a more negative exposure of their trade volumes to exchange rate

2


volatility. Quantitatively, exchange rate volatility has an effect on trade that is negative in
some sectors but positive in other sectors depending on the financial vulnerability of the
sector.
We first present a simple small open economy general equilibrium model to
examine the role of credit constraints in determining the trade effects of exchange rate
volatility. In our simple model, households consume, invest, supply labor, and hold
foreign assets while firms in non-traded and traded goods sectors produce goods and sell
them to domestic and foreign markets, respectively. To investigate how credit constraints
affect the trade effect of exchange rate volatility, we assume that a fraction of firms in the
traded goods sector are subject to credit constraints. In an open economy, a real
appreciation reduces firms' exports while a real depreciation increases firms' exports.
Without credit constraints or firm heterogeneity, firms respond to depreciations and
appreciations symmetrically. Hence, on average, it is difficult to find a clear relationship
between exchange rate volatility and trade as these responses cancel each other out.
However, if credit constraints and firm heterogeneity are considered, the trade effects of
exchange rate volatility will be different for constrained and unconstrained firms.
Constrained firms are directly affected by their own credit constraints. When the
real exchange rate appreciates, constrained firms reduce exports as the demand for
domestic tradable goods declines; however, when the real exchange rate depreciates,
constrained firms are not able to increase exports fully since their capacity is limited by
credit constraints. This implies that appreciations and depreciations will affect
constrained firms in an asymmetric way. Due to the asymmetric responses, constrained
firms' exports decline with exchange rate volatility.

3


The effect of exchange rate volatility on unconstrained firms, however, is
ambiguous. While unconstrained firms are not directly subject to credit constraints, they
are indirectly affected in a general equilibrium setting. Compared with constrained firms,
unconstrained firms can expand or shrink freely in face of exchange rate changes. When
the real exchange rate depreciates, due to the expenditure switching effect, the demand
for domestically produced traded-goods increases. Consequently, the export of
unconstrained firms will increase. Meanwhile, since constrained firms cannot expand
fully, unconstrained firms will also benefit from the substitution between goods produced
by constrained and unconstrained firms. However, when the real exchange rate
appreciates, both constrained and unconstrained firms are hurt, and unconstrained firms
cannot benefit more from their advantage in credit market. Hence, the trade effect of
exchange rate volatility on unconstrained firms is ambiguous.
Overall, our model predicts that exchange rate volatility hurts constrained firms
more, and the effect on unconstrained firms’ (and total) exports depends on some key
parameters, including the degree of credit constraints, the share of unconstrained firms in
the traded goods sector, and the substitutability of goods produced by constrained and
unconstrained firms. This ambiguity thus can help explain why previous empirical work
often finds a small and insignificant effect on aggregate (bilateral) trade.
We then provide empirical evidence to support the predictions of the model.
Using a large disaggregate sector-level bilateral trade data of 132 countries for the years
1970-2000 and an augmented gravity model estimation strategy suggested by Anderson
and van Wincoop (2003), we find that the estimated interaction effect of exchange rate
volatility and sector level financial vulnerability is negative and highly significant.

4

Quantitatively, the estimated trade effects of exchange rate volatility vary substantially
across sectors and can be either positive or negative depending on the degree of credit
constraints. The implied overall effect on total bilateral trade is thus ambiguous, which is
consistent with the weak effect on aggregate (bilateral) trade documented in previous
studies.
Our empirical results are robust to alternative samples, measures of exchange rate
volatility, and model specifications. We also make efforts to address the potential
endogeneity and zero-trade flows issues. Using an instrumental variable (IV) regression
approach and a two-stage method developed by Helpman, Melitz, and Rubinstein (2008),
we show that controlling for endogeneity and the inclusion of zero-trade flow
observations do not alter our findings. Moreover, in Helpman, Melitz, and Rubinstein's
(2008) first-stage Probit estimation, we also detect a significantly negative interaction
effect between exchange rate volatility and sectoral financial vulnerability even on the
probability of selection into trade partners.
Our work contributes to the relevant literature in the following ways. First, we
present a small open economy model to illustrate the role of credit constraints in
determining the trade effect of real exchange rate volatility. We also provide empirical
evidence to confirm the predictions of our model. Second, while our result is at
disaggregate level, it has important aggregate implications. Quantitatively, the sectoral
heterogeneity implies an ambiguous average effect on aggregate (bilateral) trade, which
helps explain why previous work often find a small and insignificant effect. Moreover,
our findings also suggest that the sectoral composition of a country's trade is important
for its exposure to exchange rate volatility. Finally, our study complements nicely with

5


the growing credit constraints and trade literature that documents a crucial role of credit
constraints in trade. It is also related to the broad literature that explores the
heterogeneous effects of exchange rate volatility. For example, Broda and Romalis (2011)

and Bryne, Darby, and MacDonald (2008) find exchange rate volatility has different
effects on homogeneous and differentiated goods. Grier and Smallwood (2007) show that
exchange rate uncertainty affects developed and emerging countries differently. Aghion,
Bacchetta, Rancière, and Rogoff (2009) examines how financial constraints influence the
effect of exchange rate volatility on productivity growth.
A recent study by Héricourt and Poncet (2013) finds a similar interaction effect in
Chinese firms for the years 2000-2006. Our study differs from theirs in several key
aspects. First, we present a theoretical model that illustrates how the interaction of credit
constraints and exchange rate volatility affects trade. Second, our empirical analysis
utilizes a comprehensive data of 138 countries for the years 1970-2000, which allows us
to draw much more general implications from our results with more confidence. The
longer sample period also enables us to examine the trade effects of the more relevant
long-run volatility measures. Further, while the bilateral nominal exchange rates between
China and the U.S., and many other countries that peg to the dollar remain strictly fixed
till mid-2005, our sample includes countries with various types of exchange rate
arrangements and levels of economic and financial development. Finally, we also take the
zero trade flow and endogeneity issues more seriously and make efforts to address them.
The remainder of this paper is organized as follows. In Section 2, we build a
simple small open economy general equilibrium model with credit constraints to provide
intuitions for the empirics. Section 3 discusses our empirical models and the data. Section

6


4 reports our main empirical results, and Section 5 conducts further sensitivity analyses.
Concluding remarks are offered in Section 6.
2. A small open economy model with credit constraints
In this section, we attempt to provide a theoretical model to demonstrate our main
ideas. For simplicity, we develop a two-sector small open economy general equilibrium
model with credit constraints. There are two sectors in the model: non-tradable and

tradable sectors. Firms in both sectors produce goods using labor and capital, and sell
goods to domestic and foreign markets, respectively. A key feature of our model is that a
fraction of firms in the tradable sector are subject to credit constraints.
2.1. Households
The representative household has preferences given by
∞

U = E0 ¦ β t [ln(Ct ) − η
t =0

L1t +ψ
]
1 +ψ

(2.1)

where Ct is consumption, and Lt is labor supply. Consumption is a Cobb-Douglas
aggregation of consumption of non-tradable goods and imported goods,

Ct =

1
1− a 3
. Hence, consumer price index is Pt = PNta PFt1− a , with PNt ( PFt )
C Nta C Ft
a (1 − a)1−a
a

defined as time t price of non-tradable (imported) goods.
Households have access to domestic and international bond markets. Trade in

international bonds is subject to small portfolio adjustment cost. If a household borrows
an amount Dt+1, then the portfolio adjustment cost is

3

ψD
2

( Dt +1 − D) 2 (denominated in the

This is a standard assumption in the literature; for example, see Devereux, Lane and Xu (2006). Our qualitative
results still hold if we add the domestic tradable goods into household consumption. Since our focus is on the impact of
exchange rate changes on exports, for simplicity, we make the household side as simple as possible.
7


composite good), where D is an exogenous steady state level of net foreign debt.4
Households can hold foreign debt (or asset) at a given interest rate it* , or domestic debt (or
asset) at an interest rate it. Households own traded-good firms (unconstrained) and
therefore receive their profits, Π t .
Households' revenue flow in any period thus comes from wage income, WtLt,
capital rental income from both traded goods sector (those firms that are not subject to
credit constraints) and non-traded goods sector, RtKt, less debt repayment from last period

(1 + it* ) Dt + (1 + it ) Bt , as well as portfolio adjustment costs. Bt is the stock of domestic
debt.5 A household then obtains new loans from the domestic and/or international capital
market, and uses these loans to consume, invest, and to pay portfolio adjustment costs.
Therefore, the budget constraint for the household is
Pt (Ct + I t +

ψD
2

( Dt +1 − D) 2 ) = Wt Lt + Rt K t + Dt +1 + Bt +1 − (1 + it* ) Dt − (1 + it ) Bt + Π t

(2.2)

The capital accumulation is given by Kt +1 = (1 − δ ) Kt + I t . The households' optimum can
be characterized by the following conditions:

ª CP º
1
ª1 −ψ D Pt ( Dt +1 − D ) º = β Et « t t »
* ¬
¼
1 + it +1
¬ Ct +1 Pt +1 ¼

(2.3)

§ CP ·
1
= β Et ¨ t t ¸
1 + it +1
© Ct +1 Pt +1 ¹

(2.4)

­° C ª
R º ½°

1 = Et ® β t «1 − δ + t +1 » ¾
Pt +1 ¼ ¿°
¯° Ct +1 ¬

(2.5)

4

Schmitt-Grohé and Uribe (2003) propose a few methods to solve the unit root problem of net foreign assets in small
open economies. The portfolio adjustment cost is one of these methods.
5
Note that, if Bt is positive (negative), then it implies that domestic household is borrowing debt (holding asset or
lending). This also applies to Dt.
8


Wt
= η Lψt Ct
Pt

(2.6)

Equations (2.3) and (2.4) represent the Euler equations for the purchase of
international and domestic bonds. The combination of these two equations gives the
representation of interest rate parity for this model. Equation (2.5) represents the Euler
equation for capital. The combination of Equations (2.4) and (2.5) gives the no-arbitrage
condition between capital investment and domestic lending. Equation (2.6) represents the
household’s labor supply function.

2.2. The Non-traded good sector

The non-traded goods sector is perfectly competitive. The production function of
αN

§ KN ·
a representative firm in the sector is given by YNt = ¨ t ¸
© αN ¹

1−α N

§ LNt ·
¨
¸
©1−αN ¹

, where K Nt and

LNt are capital and labor used this sector, respectively, and α N is the share of capital in

production. Cost minimizing then implies the following equation:

K Nt

§ R
= αN ¨ t
¨ MCN
t
©

−1

·
§ Wt
¸ YNt , LNt = (1 − α N ) ¨
¸
¨ MCN
t
¹
©

−1

·
¸ YNt
¸
¹

(2.7)

where MCNt = Rtα N Wt1−α N is the marginal cost of non-traded goods. Since the non-tradable
sector is perfectly competitive, we have PNt = MC Nt .

2.3. The Traded good sector
The traded good sector contains a unit interval [0,1] of firms indexed by j. Each
firm j produces a differentiated traded good, which is an imperfect substitute for each
other in the production of composite goods produced by a representative competitive firm.
We assume that a fraction of firms in the traded goods sector are subject to credit

9

constraints. So the production of composite goods, YX t , is given by
λ

λ −1
λ −1
ª κ
º λ −1
1
YX t = « ³ (YXct ( j )) λ dj + ³ (YXut ( j )) λ dj » , where λ is the elasticity of substitution
κ
0
¬
¼

between differentiated traded goods.6 YXct and YXut are goods produced by constrained and
unconstrained firms, respectively. κ is the weight of credit constraint goods in the
aggregation of tradable goods. In an equilibrium where the same type of firms
(constrained or unconstrained firms) set the same prices, the total demand for each type
of traded goods is given by

§ PXct
Y =κ ¨
¨ PX
© t
c
Xt

−λ

·

§ PXut
u
¸ YX t , YX t = (1 − κ ) ¨
¸
¨ PX
¹
© t

−λ

·
¸ YX t
¸
¹

( )

where aggregate price index PX t = ªκ PXct
«¬

(2.8)

1− λ

( )

+ (1 − κ ) P

u
Xt

1− λ

1

º 1-λ . For a small open
»¼

economy, we have PX t = PX*t , where PX*t is the world price of aggregate tradable goods.
We also assume that all firms in the traded goods sector have the same production

§ K Xj t
technology, Y = ¨
¨ αX
©
j
X

αX

·
¸¸
¹

§ LXj t
¨¨
© 1−α X

1−α X

·
¸¸
¹

, where α X is the share of capital in production,

and K Xj t and LXj t are capital and labor used by a subsector j, j = {c, u} , respectively.
Thus the optimization problem for firms in the unconstrained subsector is

K

u
Xt

§ R
= αX ¨ t
¨ MC X
t
©

−1

· u
§ W
u
¸ YX t , LX t = (1 − α X ) ¨ t
¸
¨ MC X
t
¹

©

6

−1

· u
¸ YX t
¸
¹

(2.9)

It should be noted that all the differentiated goods in traded good sector are domestically produced (in the same
country), so the elasticity of substitution here is not the trade elasticity or the elasticity of substitution between home
and foreign goods. Following Devereux, Lane and Xu (2006), we assume that all the imported goods are consumed by
households directly. Therefore, the substitution between home and foreign goods mainly affect households’
consumption allocation.
10


where MC Xu t = Rtα X Wt1−α X is the marginal cost, K Xu t and LuX t are capital and labor used in the
unconstrained subsector, respectively. Since each firm is monopolistically competitive,
we have PXut =

λ
λ −1

MC Xu t .

For the credit constrained subsector, there is an infinitely lived entrepreneur with
a mass of 1 who is seeking export opportunities. We assume that entrepreneurs face
financial constraints due to limited enforcement in the spirit of Kiyotaki and Moore
(1997). At the beginning of each period, an entrepreneur enters with predetermined
capital. After production, at the end of each period, the entrepreneur must decide how
much capital to purchase for the next period and how much loan to borrow from
households. When he borrows from households, an entrepreneur has a probability to
default on the loan, and the maximum amount a household can recover is a fraction φ of
c
the time t nominal value of the capital stock in the next period, PK
t X t +1 . Knowing that, an
c
entrepreneur will have no incentive to repay more than φ PK
t X t +1 . To make sure that the

entrepreneur has a need for external financing in the long run, we assume that for each
period, there is an exogenous probability ς that an entrepreneur will die and the same
probability that there is a newborn. Upon his death, the entrepreneur will transfer all of
his wealth to the newborn and will stop consumption.
At each period, an entrepreneur's problem is to maximize his utility subject to the
budget constraint and borrowing constraint.7 For simplicity, we drop the firm index j in
the subsequent analysis. Therefore, the entrepreneur j’s problem can be characterized as

7

We also consider an alternative specification of credit constraints, in which the limit of borrowing is subject to the
value of the firm. Two credit constraint specifications yield similar quantitative results, which are reported in an online
appendix.
11

the following dynamic problem:

V ( Btc , Ktc ) =

(

max

Cte , Btc+1 , K Xc t +1 , LcX t

(

ln Cte + β (1 − ξ ) EtV Btc+1 , K Xc t +1

)

(2.10)

c
c
Pt Cte + K Xc t +1 + (1 + it ) Btc = PXct YXct − Wt LcX t + (1 − δ ) PK
t
X t + Bt +1

)

(2.11)

c

Btc+1 ≤ φ PK
t X t +1

(2.12)

We solve the representative entrepreneur’s problem in the Appendix. As shown in
the Appendix, we have the following condition:
c
· ½°
·
1−φ
°­ 1 § Pt +1 § Rt +1
=
−
+ 1 − δ ¸ − φ (1 + it +1 ) ¸¸ ¾
E
β
1
ξ
(
)
¨
¨
t ®
e
e ¨
PC
t t
¹
¹ ¿°

¯° Pt +1Ct +1 © Pt © Pt +1

(2.13)

where Rtc is the nominal return to capital or the market value of marginal product of
capital. This equation describes the relationship between the return to capital in
constrained sector and domestic borrowing costs. Without credit constraints, in
equilibrium, the return of capital should be equal to the firm’s borrowing cost. However,
in the constrained sector, there is a wedge between them, and the constrained firms bear a
higher borrowing cost than unconstrained firms. Therefore, when the borrowing cost
changes, it will have asymmetric effects on constrained firms and unconstrained firms.
From Equation (2.13) and households’ no-arbitrage condition between capital and lending
(Equations (2.4) and (2.5)), we can also derive the no-arbitrage condition between
constrained capital and unconstrained capital. This implies that the credit constraint not
only affects the return to constrained capital but also affects the return to unconstrained
capital through general equilibrium effect, but of course the constrained sector is affected
more than the unconstrained one.
2.4. Shock

12


The shock considered in the model is a shock to terms of trade. We assume the log
of terms of trade, et =

PXt*
, follows a simple AR(1) process,
PFt*

()

ln ( et ) = (1 − ρ e ) ln e + ρe ln ( et −1 ) + ε t

(2.14)

where e is the steady state value of terms of trade, the persistence coefficient ρe ∈ [ 0,1] ,
and the innovations ε t is i.i.d. shock with zero mean and standard deviation σ . In general,
a positive terms of trade shock is equivalent to an income shock or a productivity shock
to the export sector, which leads to real exchange rate appreciation. Therefore, in this
simple model, the shock to terms of trade is also equivalent to a shock to the real
exchange rate.
2.5. Equilibrium

In equilibrium, the non-traded goods market clears. That is, YNt = a

PZ
t t
, where
PNt

Z t is the total demand for aggregate goods and is given by

(

)

Z t = Ct + I t + Cte + I Xc t +

ψD
2

(D

t +1

−D

)

2

(2.15)

In the model, the demand for aggregate goods comes mainly from household
consumption and investment. In addition, because portfolio adjustment costs are
represented in terms of the composite final good, part of these costs must be incurred in
terms of non-traded goods and imported goods. Labor is perfectly mobile across sectors,
so the labor market equilibrium condition implies that:

LNt + LcX t + LuX t = Lt

(2.16)

Meanwhile, we have K Nt + K Xu t = K t . In equilibrium, Bt + Btc = 0 , so the aggregate
13


budget constraint for the economy can be rewritten as
*
PZ

t t + (1 + it ) Dt = PY
t t + Dt +1

where Yt =

PNt YNt + PX t YX t
Pt

(2.17)

is the total output of this small open economy. Equation (2.17)

implies that total expenditures must be equal to total receipts, which are the output of
each sector, plus new net foreign borrowing.
The equilibrium now is defined as follows: given the stochastic process of terms
of trade shocks ( PXt* / PFt* ), an equilibrium is an allocation { Ct , Cte , Lt , LNt , LuXt , LcXt ,
YNt , YXt , YXtu , YXtc , K Nt , K Xtu , K Xtc , I t , I Xtc , Z t , Dt , Yt } and { Pt , PNt , PFt , PXt ,

PXtu , PXtc , MC Nt , M C Xtu , Rt , it , Wt } that satisfies households' and firms' optimization
conditions and market clearing conditions.
In our model, it is easy to see why positive and negative movements in the real
exchange rate affect credit constrained firms in an asymmetric way, and on average,
exchange rate volatility reduces their exports. The intuition is simple. When the real
exchange rate depreciates, constrained firms cannot expand fully due to the presence of
credit constraints. A real appreciation, however, hurts both constrained and unconstrained
firms. This implies that, for constrained firms, when the real exchange rate fluctuates,
their average exports decline. In other words, there is a negative effect of exchange rate
volatility on constrained firms’ exports.
For unconstrained firms, however, it is difficult to find a clear-cut relationship
between exchange rate volatility and trade. While they are not subject to credit

constraints, these firms can still be indirectly affected by constrained firms’ behavior in
general equilibrium. For example, during an expansion, constrained firms will push up
14


factor prices. Due to the households’ arbitrage between capital employed in the
constrained and unconstrained subsectors, credit constraints affect the rental cost of
capital in both subsectors, which indirectly increase marginal costs and prices of
unconstrained firms. Compared with constrained firms, unconstrained firms can expand
or shrink freely in face of exchange rate changes. When the real exchange rate
depreciates, due to the expenditure switching effect, the demand for domestically
produced traded-goods increases. Consequently, the export of unconstrained firms will
increase. Meanwhile, since constrained firms cannot expand fully, which gives
unconstrained firms a chance to export more as the goods produced by constrained and
unconstrained firms are substitutes. The magnitude of substitution effect is determined by
their relative price, which in turn depends on the difference in their rental cost of capital.
However, when the real exchange rate appreciates, both constrained and unconstrained
firms are hurt, and unconstrained firms cannot benefit more from their advantage in credit
market. Hence, the total trade effect of exchange rate volatility on unconstrained firms'
(and also total) exports is ambiguous, depending on some key parameters, such as the
substitutability of goods and the degree of credit constraints in the traded goods sector.
For a detailed analysis, we will resort to numerical simulations in the next subsection.
2.6. Results
2.6.1. Calibration

The period in the model is annual. We set β = 0.92 so that the steady-state annual
interest rate is 8.7%. We set η = 2.5 to ensure households allocate about 45% of their time
to market work. ψ is calibrated at 0.6 so that the labor-supply elasticity is 1 / ψ = 1.7 ,
which is common in the business cycle literature (e.g., Uribe, 2003, 2012; Mendoza,

15


1991).8 ξ is calibrated at 0.033 so that the average work time of an entrepreneur is 30
years. Following Schmitt-Grohé and Uribe (2003), we set the bond adjustment cost
parameterψ d = 0.001 . The annual depreciation rate is set to δ = 0.1 .We set α = 0.6 so that

the import to GDP ratio is 40%, which is the average of empirical estimation for small
open economies. The capital share α X and α N are set to 0.6 and 0.44, respectively, which
is consistent with the trade literature (e.g., di Giovanni, Levchenko, and Zhang, 2012). In
the benchmark case, we assume that half of the firms in the traded goods sector are
subject to credit constraints, ( κ = 0.5 ) and the entrepreneur in the constrained subsector
can borrow 20% of his capital expenditure ( φ = 0.2 ). The elasticity of substitution of
differentiated goods in the traded sector, λ , is calibrated to 11, which gives a 10%
markup. This value is commonly used in the open macro literature (e.g., Devereux, Lane,
and Xu, 2006; Betts and Devereux, 2000; Chari, Kehoe, and McGrattan 2002). In
addition, we also assume a balanced trade in the benchmark case ( tb / y = 0 ). Since these

parameters are important for the effect of exchange rate change on trade, we vary their
values and conduct sensitivity analysis. For the stochastic process, we normalize the
terms of trade in the steady state e = 1 and assume that the persistence of terms of trade
shock ρe = 0.5 and the standard deviation of shock σ =0.1, which is within the
estimation of the small open economy literature (Schmitt-Grohé and Uribe, 2017 and
Mendoza, 1995).
2.6.2. Quantitative results

The quantitative results are summarized in Table 1. Panel A shows our benchmark
8

Our results are not sensitive to the values of parameters that measure household’s preferences, such as the interest

rate, the time allocated to market activities and the labor supply elasticity. To save space, we omit the sensitivity
analysis of these variables.
16


results, and Panels B-F report the results under alternative parameter values of initial
trade balance, sector composition, elasticity of substitution, and credit constraints. In each
panel, we report the mean of output under a high exchange rate volatility regime (the
standard deviation of shock σ = 0.5 ) as a percentage of the mean of output under a low
exchange rate volatility regime ( σ = 0.1 ) for the constrained subsector, the unconstrained
subsector and the overall tradable sector, respectively. In the benchmark case, we find
that exchange rate volatility reduces trade in both subsectors and thus the overall trade
because the means of output in the high volatility regime are all smaller than those in the
low volatility regime. More interestingly, we find that the reduction in trade is much more
substantial for the constrained subsector. While the reduction in trade in the
unconstrained subsector is less than 6%, the trade-reducing effect of exchange rate
volatility is almost 20% in the constrained subsector. Intuitively, this is because the
constrained subsector cannot expand fully due to the presence of credit constraints when
the real exchange rate depreciates, but still shrinks when the real exchange rate
appreciates. This asymmetry leads to a negative trade effect of exchange rate volatility on
constrained firms. For unconstrained firms, the effect of exchange rate volatility on their
export is smaller as they are not directly affected by credit constraints. This result is
consistent with our main empirical finding that credit constraints amplify the
trade-reducing effect of exchange rate volatility.
Panels B and C consider alternative initial trade balances. Panel B assumes a 2%
initial trade surplus, and Panel C assumes a 2% trade deficit. Using alternative initial
trade balances does not affect our main results. Panels B and C suggest that, while
exchange rate volatility reduces trade in both subsectors, it lowers trade substantially

17

more in the constrained subsector. This result implies that initial trade balances do not
have much an impact on firms' exports.
In Panel D, we lower the elasticity of substitution to 6, which implies a 20%
markup. This change does not alter our finding that exchange rate volatility has a larger
harmful effect in the constrained subsector. Also, as expected, we find that now the
impacts of exchange rate volatility become smaller compared to the benchmark case in
which the elasticity of substitution within the traded good sector is larger. Intuitively, as
the elasticity of substitution approaches infinity, all the traded goods will become
homogenous and the traded good sector will become perfectly competitive. In such a
scenario, the constrained firms will be crowded out by unconstrained firms.
In Panel E, we now assume 75% of the firms in the traded-goods sector are
constrained.9 Qualitatively, our main finding is not affected. But, quantitatively, an
interesting result emerges. We now find that, exchange rate volatility reduces the mean of
output in the constrained subsector but increases it in the unconstrained subsector. In this
case, more firms are subject to credit constraints. Therefore, the total trade of constrained
firms declines more when exchange rate volatility increases, which naturally gives
unconstrained firms a chance to export more. This new result suggests that, quantitatively,
exchange rate volatility can possibly have a positive effect on exports in sectors with least
credit constraints.
9

This higher value reflects the fact that a large proportion of firms are financially constrained in some developing
countries. Here we offer two real illustrative examples. First, we compute the proportion of financially constrained
firms in Brazil using the firm-level survey data from the 2003 wave of World Banks' Enterprise Survey. In the survey,
firms were asked to rate the severity of their access to finance as an obstacle on a five-point scale: no obstacle (0),
minor obstacle (1), moderate obstacle (2), major obstacle (3), and very severe obstacle (4). We consider a firm as being
constrained if its rating is 2 or above. We find that 77% (75%) of the firms are constrained in the full sample
(exporting-firm subsample). Second, in the Chinese custom data for year 2000, we calculate the export volumes in

sectors whose degrees of external finance dependence are above the mean value of external finance dependence across
sectors as a percentage of total export volumes. The ratio is about 83%. We also calculate the average external finance
dependence weighted by export volumes, Ȉk(Fvk×exportsk /total exports), for each exporting firm. We then define a
firm as constrained if the weighted average external finance dependence of its exports is above the mean value of
external finance dependence across sectors. We find that about 72% of the firms are constrained.
18


In panel F, we reset the credit constraint parameter in Panel F to 0.9, which
implies that an entrepreneur in the constrained subsector can borrow 90% of his capital
expenditure. The increase in this parameter means that the two subsectors' difference in
financial vulnerability shrinks. As expected, we find that a looser credit constraint results
in smaller impacts of exchange rate volatility on trade. The trade-reducing effects of
exchange rate volatility now become much smaller compared to the benchmark case,
especially for the constrained subsector. The increase in exchange rate volatility results in
very little change in trade volume. Further, the differential effects of exchange rate
volatility in the two subsectors also become negligible in this case.
Finally, we increase the death rate ξ from 0.033 to 0.035. That is, the average
work time of entrepreneur will decrease by 1.5 years. This increase in the death rate
makes the entrepreneurs become more impatient than before and care more about current
consumption than future consumption. As a consequence, they have more incentives to
borrow and are more exposed to credit constraints. Hence, the effect of an increase in the
death rate is similar to that of a tighter credit constraint. The results in Panel G show that,
for the same increase in exchange rate volatility, trade in constrained and unconstrained
subsectors will decrease by 22% and 8%, respectively, which are larger than the negative
effects in benchmark case.

3. Econometric specifications and data
3.1. Empirical specifications and estimation issues

To empirically examine the role of credit constraints in determining the trade
effect of exchange rate volatility, we employ an augmented gravity model. This model

19


can be justified theoretically by alternative trade models (e.g., Anderson, 1979; Anderson
and van Wincoop 2003; Deardoff, 1998) and has been successfully used in empirical
studies on bilateral trade flows (e.g., Frankel and Wei, 1993; IMF, 2004; Manova, 2013;
Subramanian and Wei, 2007; Helpman, Melitz, and Rubinstein, 2008). Specifically, we
consider the following benchmark empirical specification based on the work of Anderson
and van Wincoop (2003):
log Exportsijkt = β 0 + β1Volijt + β 2Volijt * Fvk + Z (i, j )γ + ϕ it + ϕ jt + ϕ k + ε ijkt

(3.1)

The dependent variable in Equation (3.1) is log exports from country i to country j
in sector k in year t. Volijt is a measure of bilateral exchange rate volatility, and financial
vulnerability, Fvk, represents an empirical measure of credit constraints at the sector level.
Our main variable of interest is the interaction term between exchange rate volatility and
sector level financial vulnerability, Volijt* Fvk. Z(i,j) is a set of standard country-pair level
control variables commonly used in gravity model estimation. Following Helpman,
Melitz, and Rubinstein (2008), we include in Z(i,j) log distance and a group of bilateral
binary variables, same-legal-system, common-language, common-border, FTA,
colonial-ties, currency union, islands, landlocked countries, and WTO members.10 We
control for separate time-varying exporter and importer fixed effects, ϕit and ϕ jt , in the
regressions as proxy for "multilateral resistance". Finally, sector fixed effects, ϕ k , are also
included.11
In addition to the above benchmark models, we also consider a variety of
alternative specifications to ensure the robustness of our results. We also employ

Helpman, Melitz, and Rubinstein's (2008) two-stage method and other methods to correct
10
11

See the Data Appendix for detailed variable definitions.
Since sector financial vulnerability is time-invariant, it is submerged with the inclusion of sector fixed effects.
20


the biases associated with selection and the omission of the extensive margin due to
ignoring zero trade flows and use an IV regression approach to deal with endogeneity.
3.2. Sample coverage and data sources

Our sample consists of 132 countries with comprehensive trade and economic
data coverage. Country names are listed in the Appendix Table. We are interested in the
bilateral sector-level trade flows between each of the countries subject to data availability.
The full sample period covers the years 1970-2000.12 We obtain data from a variety of
sources. The bilateral sector level trade data at the SITC 4-digit level are obtained from
the NBER-United Nations trade dataset. Since our measures of sector financial
vulnerability are constructed at the ISIC 3-digit level, we aggregate the SITC 4-digit
product codes to those ISIC 3-digit categories. Exchange rates and other economic
variables are mainly drawn from the International Financial Statistics and the World
Bank's World Development Indicators. Log distance and bilateral binary variables are
from Helpman, Melitz, and Rubinstein (2008). We get our empirical measures of credit
constraints at the sector level from Kroszner, Laeven, and Klingebiel (2007). Detailed
variable definitions and data sources are listed in the Data Appendix.
3.3. Empirical measures of key variables

Estimating the above models requires us to find appropriate empirical measures of
exchange rate volatility and sector financial vulnerability. Previous studies in the

literature typically use the standard deviation of the first difference of logarithms of the
monthly bilateral real exchange rate over a certain period to measure real exchange rate
volatility. While most existing work focus on long-run real exchange rate variability and
12

The NBER-United Nations trade data starts from 1962. Since the long-run exchange rate volatility is measured in
every five-year period and we need five additional years to construct the first observation, we choose 1970 as the
starting year of our sample. The long-run exchange rate volatility in 1970 is calculated using data for years 1965-1969.
21


measure the standard deviation over a five-year period preceding the year in question (e.g,
Frankel and Wei, 1993; Rose, 2000), some studies also construct indicators of short-run
variability as the standard deviation over the current year.13
Our study follows the literature and uses the long-run real exchange rate volatility
measured over the five-year period preceding to the year in question as our benchmark
measure of exchange rate volatility. Besides, we also consider four alternative measures
constructed as the within-year, two-year, three-year, and four-year standard deviations to
ensure the robustness of our results. Subject to data availability, we calculate real
exchange rate volatility for the following years: 1970, 1975, 1980, 1985, 1990, 1995, and
2000. For the within-year measures, we regress log exports from country i to country j in
sector k in year t on contemporaneous exchange rate volatility.14 For other real exchange
rate volatility measures, we follow the literature to link exchange rate volatility in the
past years and current trade flows.15
The empirical measures of credit constraints at the sector level are fairly standard
in the literature. It is a common practice in both the credit constraints and growth
literature (e.g., Rajan and Zingales, 1998; Claessens and Laeven, 2003; Krosner, Laeven,
and Klingebiel, 2007) and the credit constraints and trade literature (e.g., Chor and
Manova, 2012; Manova, 2013; Manova, Wei, and Zhang, 2015) to use US firm level data
to construct sector level measures of financial vulnerability as proxy of credit constraints

at the sector level. These measures typically reflect technologically determined sector
characteristics that are inherent to the nature of the manufacturing process. Following
Krosner, Laeven, and Klingebiel (2007) and Manova, Wei, and Zhang (2015), here we
13

See IMF (2004) for detailed discussions on measures of exchange rate volatility.
We have also tried to use short-run exchange rate volatility measured at year t-1, and our results are not affected.
15
While exchange rate volatility measured in real term is preferred and more commonly used in previous studies, we
have also tried to use long-run and short-run nominal volatility. The results are similar.
14

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