Download Twin Crises in Emerging Markets:

Twin Crises in Emerging Markets:
The Role of Liability Dollarization and Imperfect Competition in Banking∗
Alina C. Luca and Marı́a Pı́a Olivero†
Department of Economics, LeBow College of Business, Drexel University
February 2008
Abstract
Recent currency crises in emerging markets have been accompanied by banking
crises, with concentration in the market for bank credit increasing after large devaluations. In this paper we study the role of imperfect competition and liability dollarization in banking in shaping the real effects of twin crises. We do so by introducing currency mismatches in a modified version of the Schargrodsky and Sturzenegger (2000)
model of imperfect competition in the banking industry with endogenous product differentiation. We then embed it in an otherwise standard general equilibrium model
of a small open economy. We show that both imperfections-currency mismatches and
imperfect competition in banking-can generate a banking crisis in the presence of an
exogenous currency crisis. We then discuss the contribution of each distortion to the
magnitude of crises.
Keywords: Devaluation, twin crises, balance sheet effects, liability dollarization,
imperfect competition, product differentiation. JEL codes: E4, F3, F4.
∗
We are grateful to Roger Aliaga-Dı́az, Cristopher Ball, Christopher Laincz, Vibhas Madan, Pietro
Peretto, Sangeeta Pratap, Constantinos Syropoulos, and participants at the 2006 Annual Meetings of
LACEA, the 2007 Midwest Theory Meeting and the 2007 Latin American Meetings of the Econometric
Society for helpful suggestions.
†
Corresponding author: Marı́a Olivero, Matheson Hall, Suite 503-A, 3141 Chestnut Street, Philadelphia,
PA, 19104. Tel: (215) 895-4908. Fax: (215) 895-6975. [email protected]
1
A pegged exchange-rate regime and liability dollarization are a deadly combination that
leaves emerging market countries highly vulnerable to financial crises (Mishkin, 2006).
1
Introduction
Substantial empirical evidence points to the existence of twin crises in emerging markets.
Kaminsky and Reinhart (1999) state that many of the countries that have had currency
crises have also had fully-fledged domestic banking crises around the time when they were
experiencing mayhem in their foreign exchange market. Also, Burnside et al. (2001) state
that in the post-Bretton Woods era currency crises have been accompanied by banking
crises, and many banks have gone bankrupt after a currency devaluation.
A common explanation for the twin crises phenomenon provided in the literature is to
assume an imperfection such that a currency devaluation reduces the profitability of bank
debtors, who are then unable to repay their debt. Good loans turn bad and the banking
industry collapses.
Our goal in this paper is to study an alternative channel for the occurrence of twin
crises. In our framework, banking crises are unrelated to borrowers defaulting on their
loans. Alternatively, the roots of crises can be traced to two other imperfections: currency
mismatches on the balance sheets of banks themselves and imperfect competition in the
banking industry.
With this goal in mind we build a dynamic stochastic general equilibrium (DSGE)
model by introducing currency mismatches in a modified version of the Schargrodsky and
Sturzenegger (2000) model of an imperfectly competitive banking industry with endoge-
2
nous product differentiation1 . We then embed this framework into an otherwise standard
dynamic general equilibrium model of a small open economy.
Only a few theoretical papers consider liability dollarization2 in the banking sector as
a determinant of twin crises. They do so in the presence of perfectly competitive banks.
Despite the substantial empirical evidence on the non-competitive behavior of banks in
emerging markets and the negative effects of devaluations on the structure of the banking
industry, there is no work modeling these effects.
Burnside et al. (2001) model currency crises that coincide with banking crises because
banks are subject to both currency and default risk3 . The presence of government guarantees induces banks not to hedge against exchange rate risk, but rather to increase their
exposure in the foreign exchange derivatives market. Then, after a currency devaluation,
banks go bankrupt, the domestic interest rate rises, and output falls. In Disyatat (2004)
1
By banks competing in the product differentiation dimension, we refer to the fact that banks can target
the financial services that they provide together with a loan towards particular sectors of economic activity,
and build expertise in the provision of these services only for these sectors. Examples of these services
are firm monitoring, valuation of collateral and investment project evaluation. Following the industrial
organization literature (e.g., von Ungern-Sternberg (1988)), a bank that specializes in many sectors of
economic activity follows a generalist strategy and offers a “general purposeness” product, while a bank
specializing in one (or few) sectors follows a specialist strategy and offers a more focused product.
2
As it is standard in the literature, by “dollarization” we refer to the use of any foreign currency, not
necessarily the dollar.
3
Banks are exposed to exchange rate risk both directly and indirectly. Directly, because they borrow in
foreign currency and lend in local currency. Indirectly, exchange rate risk arises from the fact that banks
also lend in foreign currency to finance the production of non-traded goods. Borrowers are hurt when
a currency devaluation lowers the relative price of these goods, and this leaves banks exposed to higher
default rates on loans.
3
firms depend on bank credit to finance working capital needs, and banks finance loans by
borrowing from foreign investors and are subject to default risk. A currency depreciation
leaves the value of assets unchanged and increases the debt burden of banks. Their net
worth falls as a result and they cannot guarantee firms funding as before. This is translated
into higher interest rates and lower employment. In Choi and Cook (2004) banks also have
a mismatch in the currency denomination of their assets and liabilities, and a currency depreciation lowers banks’ net worth. Due to asymmetric information between the bank and
foreign investors à la Bernanke and Gertler (1989), the country’s risk premium increases
and drives up the cost of external borrowing4 .
All these papers assume perfectly competitive banking sectors. However, there are
three reasons why we consider that studying the role of imperfect competition in banking
is crucial. First, the banking literature seems to have reached a consensus on the fact
that banking is not perfectly competitive, particularly in emerging markets. Second, we
want to be able to explain both the market structure changes that occur in the banking
sector after a crisis, as well as the increase observed in domestic real interest rates, even
with banks’ marginal cost of funds not being affected. Third, we show that with perfectly
competitive banks, devaluations have no real effects in our framework, which is consistent
with the empirical evidence we present for motivation in Section 2.
Moreover, recent papers highlight the relevance of banks product differentiation strategies on their returns and risk (Winton (1999) and Acharya et al. (2002)) and performance
during currency crises (Bebczuk and Galindo (2005)). Also, Degryse and Ongena (2005)
provide comprehensive evidence on the existence of spatial price discrimination in bank
4
Somewhat related to our paper is the work by Daniel and Bailey Jones (2007), in which banking crises
arise as a result of financial liberalization and banks’ incentives to take on risk over time.
4
lending, caused by product differentiation.
Thus, we depart from the previous work on twin crises by modeling imperfect competition in banking, where banks compete in two dimensions: price of loans and product
differentiation.
What role do liability dollarization and imperfect competition in banking play in shaping the real effects of twin crises? We provide the following answer: With currency mismatches on banks’ balance sheets (i.e. banks’ assets are denominated in domestic currency,
while their liabilities are denominated in foreign currency), banks’ net worth falls after a
devaluation. Some banks, which are now illiquid, exit the industry, and we reproduce a
banking crisis. Further, the resulting increase in market concentration lowers competitive
pressures and induces the banks that stay in business to increase the degree of their products generality (i.e. make their financial services less focused). By producing more general
purpose services, they can increase the size of the market they serve and their profits.
Therefore, there are two opposing forces on the price-cost margins that banks charge: The
increase in concentration drives them up (“concentration effect”), while the increase in
product generality drives them down (“product differentiation effect”).
Ultimately, the net effect of a devaluation on the total cost of credit and thus, on
employment and production depends on whether the “concentration” or the “product differentiation” effect dominates5 .
Our simulation results indicate that crises become deeper as the size of the devaluation
5
A theoretical appeal of our model is that it can explain how concentration in the banking sector is not
necessarily positively related to market power as measured by price-cost margins. It is well known that in
banking, high market concentration alone does not necessarily provide a good indication of non-competitive
behavior (See Northcott (2004) and Berger et al. (2004), for a detailed discussion).
5
increases, and as the devaluation is less expected by agents in the economy. We also show
that devaluations are in general more contractionary when banks change their strategy
(focus of their financial services) in the aftermath of crises.
Our paper is also related to the literature that considers the role played by currency
mismatches on firms’ balance sheets in shaping the real effects of devaluations. Christiano
et al. (2002) study how a nominal exchange rate depreciation lowers firms’ net worth,
when firms have a mismatch in the currency denomination of assets and liabilities. As
a result, the firms’ collateral constraint is tightened, the amount of borrowing that they
can obtain is limited, and both output and employment fall. Aghion et al. (2004) also
study the effects of currency depreciations in the presence of balance sheet mismatches. In
particular, they look at multiple equilibria; currency crises can occur in their model when
an expectational shock pushes the economy into the “bad” equilibrium, with low output
and a high nominal exchange rate. Céspedes et al. (2004) model a small open economy in
which firms have dollarized liabilities and a depreciation of the domestic currency lowers
their net worth. Due to informational asymmetries à la Bernanke and Gertler (1989), the
firms’ cost of borrowing increases after a real currency depreciation and induces a fall in net
worth. This creates the contractionary effects of a currency depreciation. Cook (2004) also
introduces currency mismatches at the firm level and monitoring costs à la Carlstrom and
Fuerst (1997) and Bernanke and Gertler (1989). After a devaluation, the cost of borrowing
increases and both capital spending and output fall. This literature, however, does not
consider twin crises, nor does it examine the behavior of banks in the aftermath of crises.
The rest of the paper is organized as follows. Section 2 contains some empirical and
anecdotal evidence on the importance of the transmission channels we emphasize in this
paper. Section 3 presents the model. Section 4 studies the effects of a currency crisis.
6
Section 5 concludes and discusses some directions for further research.
2
Motivation
In this paper we study an alternative mechanism for the occurrence of twin crises. Thus, it
is crucial to provide thorough evidence on the new transmission channels that we emphasize
here.
To do so we use bank-level balance sheet and income statement data for a sample of
commercial banks in several Latin American and Asian countries for the period 1996-2003.
We focus on these two regions because they have experienced either currency crises or
significant devaluations during this period. To provide information on the coverage of our
dataset, Table 1 shows the number of banks covered in each country-year.
Table 2 presents the results of an econometric analysis where we regress the growth
rate of real GDP on the first difference in the net interest margins (NIMs) charged by
commercial banks, the currency devaluation rate and an interaction term. We use margins
as a measure of market power in the banking industry, arguing that they are a better and
more general measure of competitiveness than concentration indicators6 .
A negative and significant coefficient on the interaction term provides empirical support
to our claim that currency devaluations become contractionary (or less expansionary) in
the presence of imperfect competition in the banking sector. Two more results arise from
6
The banking industry is particular in the sense that high market concentration is not necessarily
synonymous of high market power. Two other main sources of market power in the financial sector are
product differentiation in financial services and informational asymmetries among competitor banks (which
generate customer lock-in effects and switching costs for borrowers).
7
this analysis. First, devaluations could be expansionary in the absence of margin changes.
Second, margins have a negative effect on output through devaluations, and no other direct
effect. These observations suggest that the mechanism at work in our model is realistic.
The first subplot in Figure 1 presents a scatter diagram for a regression of currency
devaluation rates on the NIMs. It shows the positive correlation between the two. Therefore, this chart motivates our theoretical mechanism that banks’ margins are larger in the
presence of devaluations. The second subplot shows the negative correlation between margins and GDP growth. It supports our result that the larger the margins, the larger the
contraction in aggregate economic activity.
In figures 2 and 3 we include the plots of both GDP growth and devaluation rates against
margins for the Latin American and Asian countries that experienced large devaluations
over the period considered. The correlations observed in the scatter diagrams are also
evident from these charts for each individual country. Some data points are worthy of
note. In Argentina, the 230% devaluation of the peso in 2002 was accompanied by an 8%
reduction in real GDP, while NIMs almost doubled from 3.6 percentage points in 2001 to
6.05 in 2002. In Uruguay, an 84% devaluation of the peso in 2002 caused a 7% decrease
in output and a 128% increase in NIMs. In Venezuela, the 84% devaluation of the bolivar
in 2002 was accompanied by a 1% reduction in real GDP in 2002, followed by a 5% fall in
2003. Bank margins increased from 16.4 percentage points in 2001 to 18.7 in 2002. The
rupiah was devalued in Indonesia by 95% and 73% in 1997 and 1998, respectively. As a
result, the growth rate of real GDP amounted to a negative 4% for two consecutive years.
NIMs rose from 3 to 8 percentage points between 1997 and 1998. The 84% devaluation of
the baht in 1997 in Thailand triggered a 3% fall in output and a slight increase in bank
margins.
8
Also illustrative is some anecdotal evidence on recent crises. During these crises the
banking system seems to have been affected indirectly by increased borrowers default risk,
but also directly because either their liabilities were more highly dollarized than their assets, or their dollarized liabilities were of shorter maturities than their dollarized assets.
Moreover, the banking sector seems to have been far from perfectly competitive in all these
episodes. The Mexican banking system had gone through an important process of privatization and restriction of competition prior to the 1994-1995 crisis. Banks’ balance sheets
were also highly exposed to currency risk. As a result, and even with the Mexican government stepping in to avoid a bigger banking collapse, only 22 out of 32 banks survived
after the crisis. The South Korean crisis of 1997-1998 can also be used to support our
theoretical claims. With a widespread exposure to exchange rate risk for chaebols (familyowned conglomerates), many of them declared bankruptcy throughout 1997, after the won
depreciation. The government stepped in and prevented a bank panic. Still, the number
of banks fell from 33 in January 1998 to 20 in December 20027 . The pre-crisis Russian
banking sector can be characterized as highly non-competitive, mostly dominated by one
state-owned savings institution, and a few large private banks, all with a high exposure to
currency forward contracts. Most of the big banks failed after the 1998 currency devaluation. The Argentine banking sector can also be characterized as highly non-competitive
at the time of the 2001-02 crisis, mainly due to previous substantial consolidation and
privatization processes. A large number of banks were driven out of business after the peso
was devalued in January 20028 .
7
Chue and Cook (2004) show that agents with relatively larger exposure to short-term foreign debt
performed worse and had a higher probability of bankruptcy.
8
Lacoste (2005) presents data on the value of banks net worth during a two year period after a crisis.
9
Regarding liability dollarization, Levy-Yeyati (2006) provides empirical evidence on the
extent of financial dollarization for a sample of 122 developed and developing countries,
for the period 1975-2002. He shows that financially dollarized economies display higher
propensity to banking crises, and slower and more volatile GDP growth. Burnside et
al. (2001) use data for countries that have experienced twin crises, and present evidence
that banks had significant net foreign debt at the time of these crises. They also provide
qualitative evidence that these positions were unhedged.
To conclude, all these empirical observations provide strong support to the story that
we tell in this paper.
3
The Model
This is an infinite-period DSGE model of a small open economy 9 . Households are composed
of workers that consume and provide their services in a competitive labor market. Firms
operate in a perfectly competitive market and produce a tradable good using labor. They
need to borrow from domestic banks to finance working capital needs.
The banking sector is imperfectly competitive, with imperfect competition modeled
using a circular road model à la Salop (1979). Banks compete in two dimensions: price
and degree of differentiation of their financial services. Banks intermediate funds between
After the Tequila crisis, banks net worth fell by 64% and 6% in Mexico and Venezuela, respectively. After
the Asian crisis in 1997, net worth fell by 15%, 183% and 58% in South Korea, Indonesia and Thailand,
respectively. Ecuadorian banks saw their net worth drop by 59% in the period 1998-2001. After the 2001
crisis, banks in Argentina saw a 37% fall in their net worth.
9
We do not specify the monetary side of the model. Specific monetary policy rules allow for the study
of monetary issues in cashless economies (See Woodford (2003) and Céspedes at al. (2004)).
10
the small open economy and the rest of world by borrowing from foreign investors in
foreign currency and lending to local firms in domestic currency10 . Therefore, banks face
a currency mismatch between the asset and liability sides of their balance sheets.
To model the banking sector we build on Schargrodsky and Sturzenegger (2000) and
extend their framework to allow for currency mismatches for banks, which then allows us to
study twin crises. Another important way in which our paper deviates from Schargrodsky
and Sturzenegger (2000) is that we allow the demand for credit faced by banks to change
after a currency devaluation.
We want to abstract from the effects of hedging and thus, one important assumption of
our framework is that banks do not hedge currency risk. This assumption can be justified
in several ways. First, this could be a product of the presence of government guarantees as
in Burnside et al. (2001). Second, the costs of hedging could be high enough to make this
insurance device actually unavailable to banks in emerging economies. Last, this could be
endogenously obtained as a result of deposit insurance as in Broda and Levy-Yeyati (2006).
We model a currency crisis as an unexpected large currency devaluation taking place
after banks and firms have decided on their portfolio allocations. We assume devaluations
are exogenous events. Moreover, as in Burnside et al. (2001), there is no exchange rate
uncertainty once a devaluation occurs: the currency then depreciates at a constant rate Ω
per period. Thus, the exchange rate S (expressed in units of domestic currency per unit of
foreign currency) follows a Markov chain: The economy starts with a fixed exchange rate
10
We do not model the need for banks. Rather, we assume that all external finance has to be channeled
by banks, as perhaps they have more information on domestic firms than the foreign investors. Also, all
distortions in our model are in the banking sector. Therefore, currency devaluations have no real effects
in the absence of liability dollarization in the banking sector.
11
regime
St
St−1
= 1 with St = S I and it can switch to a devaluation regime where
St
St−1
= Ω,
which is an absorbing state. The probability transition matrix is:


 (1 − p) p 

where p = P r
St+1
St
0
1

(1)
t
= Ω| SSt−1
= 1 . S D is the level of the exchange rate in the first
period of the devaluation regime, such that S D = ΩS I . This Markov specification implies
that, before a devaluation takes place, Et (St+1 ) = [pΩ + (1 − p)] St and after, Et (St+1 ) =
St+1 = ΩSt .
3.1
The Production Sector
There is a continuum of mass 1 of identical firms indexed by k. They operate in a competitive market and use labor to produce a final tradable consumption good, using a decreasing
returns to scale technology:
Ykt = Ahαkt
(2)
where 0 < α < 1, Yk denotes firm k’s output, hk denotes firm k’s employment and A is a
constant representing total factor productivity11
12
.
We denote the international price of the tradable good, which the small open economy
takes as given, by P ∗ and the nominal exchange rate by S. Without any restrictions to
international trade, purchasing power parity holds and the domestic currency price of the
11
There is no capital in this economy. Alternatively, this assumption can be interpreted as the capital
stock being constant, with investment flows being equal to capital depreciation in every period.
12
The assumption of decreasing returns to scale is crucial. Without it, the firms that bear the lowest
cost of credit (i.e. the ones that are closest to the bank from which they borrow) could increase their
production levels, eventually driving all other businesses out of the market.
12
good is Pt = St Pt∗ . The tradable good is the numeraire in this economy (Pt∗ ≡ 1), and by
perfect pass-through from exchange rates to prices, Pt = St at every point in time.
Firms need to borrow from domestic banks to finance their working capital needs. They
borrow from the banking sector in domestic currency and their sales revenue and wage bill
are both denominated in domestic currency. However, it is worth noting that by perfect
exchange rate pass-through, sales revenues are actually affected by changes to the value
of the currency. Firms effectively face a currency mismatch between the denomination of
their assets and liabilities. However, this mismatch is the opposite from that studied by
Christiano et al. (2002), Aghion et al. (2004), Céspedes et al. (2004) and Cook (2004)13 .
Firm k chooses from which bank (i) to borrow, the amount of credit from bank i (Likt )
and employment (hikt ) to maximize the expected present discounted value of its lifetime
real profits. Thus, firm k’s optimization problem is given by:
max E0
Likt ,hikt
ΠFikt = Yikt −
∞
X
1
ΠF
∗ )t ikt
(1
+
r
t=0
s.t.
wt
Likt
Likt−1
hikt +
− (1 + Rit−1 )
− θit xikt
Pt
Pt
Pt
Yikt = Ahαikt
13
(3)
(4)
(5)
A related issue is that we are modeling bank lending in domestic currency to firms that have their
sales revenues in foreign currency. One could argue that banks would prefer to lend in foreign currency
in such an economy. There are two alternative ways to justify this assumption. First, regulations might
not allow for lending in foreign currency in domestic markets. Second, international financial markets may
be liberalized before domestic markets, so that banks that can access the former can start borrowing in
foreign currency before firms can. We do this to place all frictions in the banking sector, keeping in mind
our goal of modeling a transmission channel where banking crises can be traced to mismatches on the
balance sheets of banks themselves.
13
Likt ≥ φwt hikt
(6)
it = {1, ......, Nt }
where r∗ denotes the constant interest rate on foreign deposits, given by the world interest
rate that the small open economy takes as given, Rit−1 is the net interest rate on loans
contracted in period t − 1 with bank i charged in period t14 , and θit is the degree of product
differentiation chosen in period t by bank i.
Equation (4) defines the cash flow for firm k in period t when borrowing from bank i.
This is denoted by ΠFikt and the superscript F is used to denote firms. This is in turn given
by sales revenue minus the wage bill plus loans obtained in period t minus repayment of
loans contracted in period t − 1 minus the costs of purchasing differentiated services from
bank i (i.e. cost of getting to the bank of its choice)15 .
The costs of purchasing differentiated products are given by the last term in the profit
function. A standard assumption in circular road models à la Salop (1979) is that these
costs are linear in the “distance” to the bank x and the degree of differentiation θ. xik is
the distance between borrower k and the bank i that she decides to borrow from. Given
that we give this framework a sectorial interpretation as opposed to a purely geographical
one, xik can be thought of as how different the sector in which bank i specializes is from
the sector in which the borrower operates. Therefore, loans are more costly as the distance
to the bank of choice increases16 . With these costs given by θi xik , the parameter θ can
14
Therefore, the interest rate on loans is risk-free.
Notice that a firm can borrow from different banks in different periods.
16
If a bank is targeting sector A and therefore building expertise in valuation of collateral, evaluation
15
of projects, monitoring, etc. in that sector, x is smaller for borrowers in that sector than for borrowers in
other sectors. This makes borrowing from that bank cheaper for the former.
14
be interpreted as the per-unit distance transport cost of “traveling” the distance to bank
i. Thus, the more general purpose the services offered by bank i (i.e. the lower θi ), the
lower the costs of borrowing from bank i for all firms. Therefore, these services will better
accommodate the needs of borrowers. In subsection 3.2 we elaborate more on the structure
of the banking industry and discuss product differentiation strategies in more detail.
Equation (6) states that at least a fraction φ of firm k’s wage bill needs to be financed
by bank credit17 .
One implicit assumption here is that firms repay their loans regardless of whether the
bank from which they borrow goes bankrupt. Another assumption is that banks cannot
discriminate by price or product characteristics, so that we have already imposed the
condition that Rikt and θikt are the same for all firms and we have dropped the k subscript.
Therefore, the value of a firm k when borrowing from bank i is given by the value
function:
F
Vikt
(Rit−1 , Likt−1 , ikt−1 , St ) = ΠFikt +
h
i
1
F
E
V
(R
,
L
,
i
,
S
)
t
it
ikt
kt
t+1
ikt+1
(1 + r∗ )
(7)
Firm k’s discrete choice of which bank to borrow from can be expressed as:
F
i∗kt = argmaxVikt
(8)
We solve for a non-cooperative Nash equilibrium with N banks. Denoting by R̄ and θ̄
the interest rate and the degree of differentiation chosen by the (N -1) competitors of bank
i, a borrower k at a distance xik from bank i (with 0 ≤ xik ≤
17
1
)
N
will borrow from bank i
This constraint always binds in equilibrium because the firms’ discount factor (1 + r∗ ) is smaller than
the gross interest rate on loans.
15
if and only if:18
F
F
Vikt
(Rit−1 , Likt−1 , ikt−1 , St ) ≥ V(N
−1)kt (R̄t−1 , L̄kt−1 , (N − 1)kt−1 , St )
Yikt −
wt
Likt
hikt − θit xikt +
+
Pt
Pt
F
Et Vikt+1
(1 + r∗ )
≥ Ȳkt −
1
wt
L̄kt
h̄kt − θ̄t
− xikt +
+
Pt
Nt
Pt
(9)
F
Et V(N
−1)kt+1
(1 + r∗ )
(10)
i.e. if and only if xikt ≤ x̂it where x̂it is given by:
A(hαikt
−
h̄αkt )
− (1 −
φ) wPtt (hikt
− h̄kt ) −
x̂it =
w
t
w
t
[(1+Rit )φ P t hikt −(1+R̄t )φ P t h̄kt ]
(1+r ∗ )
Et (St+1 )
St
+
θ̄t
Nt
(11)
(θit + θ̄t )
Assuming symmetry, the demand faced by each bank is the same across borrowers (i.e.
Lik = Li for all k), and we can drop the k subscript. Thus, bank i will provide loans to all
firms positioned from its location through x̂it on each side of the circle. The total demand
faced by bank i will be:
lit = 2
Z
x̂it
φwt hit dx
0
(12)
Using equations (11) and (12):
lit (θit , θ̄t , Rit , R̄t ) = 2φwt hit x̂it
(13)
The firms’ FOC for the optimal choice of employment when borrowing from bank i is:

α−1
Aαhikt

wt 
(1 + Rit ) 
=
(1 − φ) + φ
Pt
(1 + r∗ ) Et (SSt+1 )
(14)
t
and it indicates that the marginal productivity of labor in a firm that borrows from bank
i has to equal the real wage rate times a weighted average of 1 and
18
(1+Rit )
(1+r ∗ )
Et (St+1 )
St
, with the
Notice that the term (1 + Rit−1 )Likt−1 appears on both sides of the equation and cancels out. Thus,
the choice of bank in the previous period does not affect the current period’s choice.
16
weights given by (1 − φ) and φ (i.e. the share of the wage bill financed with firms’ own
earnings and the share financed by bank loans, respectively).
3.2
The Banking System
Consider a Salop circular city with a perimeter equal to one, and a unitary density of
entrepreneurs located uniformly around the circle. Each borrower is identified by a point
on the circle (and x is the distance between the borrower and its preferred bank). Banks
are located symmetrically around the circle, and each bank is allowed to choose only one
location. As discussed in Schargrodsky and Sturzenegger (2000), we interpret this model
as one of sectorial product differentiation, so that a particular bank’s location on the circle
implies a particular sector towards which the bank targets its financial services. There is
a continuum of activities around the circle19 .
As a simplification, we assume perfect competition in the market for foreign deposits.
This assumption is justified by the evidence that domestic banks in small open economies
exercise no market power when obtaining deposits from the rest of the world. Banks face
a currency mismatch: They lend in domestic currency but borrow in foreign currency.
In the first period of operation each bank i is subject to an idiosyncratic cost shock
(ci ), which then enters their profit function in an additive way in every period of operation.
Therefore, there is no uncertainty regarding these operation costs after period 1. These can
19
This interpretation is particularly relevant for our purposes. It will become clear later that the en-
dogenous number of banks will change after a shock to the value of the currency. Therefore, banks will
“reposition” themselves on the circle. With this interpretation in mind, changing position does not imply
a change in geographical location, but a change in the sector of economic activity towards which banks
target their financial services.
17
be thought of as operation costs or, as in Schargrodsky and Sturzenegger (2000), shocks
that turn some of the banks’ assets non-performing and that differ across banks. These
shocks follow a discrete uniform distribution U [0, c̄]. For simplicity, we assume that they
are independent of the degree of product differentiation.
This is a model of competition for horizontally differentiated products (“circular-roadmodel” of monopolistic competition à la Salop (1979)). It makes sense to think that banks
compete not only in price and sectorial location (horizontal dimension), but also in the
degree of product differentiation (vertical dimension). Degryse and Ongena (2005) provide
comprehensive evidence on the existence of spatial price discrimination in bank lending
caused by transportation costs20 .
When banks choose a high degree of product differentiation (i.e. a high θ), they focus
or target their services towards a few specific sectors.
Following von Ungern-Sternberg (1988), in our model banks face a trade-off when deciding how specialized they want to become. On the one hand, lowering θ implies following
a generalist strategy (i.e. one through which banks offer “general purpose” financial services). When a bank lowers θ it is reducing “transportation costs” or trying to cater its
services to a broader consumer base, and that increases the size of the market they serve.
On the other hand, the operation costs for banks increase in the general purposeness of their
financial services, as banks spend more resources to target more sectors. Thus, banks pay
a fixed operation cost F (θ) of producing financial services, where F 0 (θ) < 0 and F 00 (θ) > 0.
We think of these costs as operation costs that banks need to incur to provide differentiated
services, regardless of the magnitude of loans made in each period. In equilibrium, these
20
Using Belgian data, they show that loan rates decrease with the distance between the bank and the
borrowing firm, and increase with the distance between the firm and competing banks.
18
two forces work together to determine the optimal degree of differentiation of financial
services offered by each bank.
An example will be useful to further clarify how product differentiation should be
interpreted in our framework. As a bank decides where to locate in the product space, it
is choosing its focus target. For example, when building expertise in investment project
evaluation, valuation of borrowers’ assets, firms’ monitoring, etc. (all financial services that
it provides together with a loan), any particular bank might be choosing among focusing
on the agricultural sector, on industrial producers, or the service sector. Once it has chosen
a location on the circle, the bank has to choose the degree of focus. For example, it must
decide whether to specialize in advising and project evaluation just for car producers, or
whether to choose more general purpose products and build expertise also on advising and
project evaluation for the auto parts industry. If going for the second alternative, the bank
is deciding to lower θ. This increases its demand because now it faces the demand from
both car and auto parts producers, as the cost of borrowing for auto parts producers goes
down. To do that, banks’ fixed costs of production F (θ) will rise, because it needs to
accumulate expertise to provide services to both subsectors of the economy21 .
Bank i’s optimization problem is to choose deposits (dit ), the interest rate on loans (Rit )
and the degree of product differentiation (θit ) to maximize the expected present discounted
value of its lifetime real profits.
21
Notice that all the bank’s customers benefit from this (i.e. they all pay a lower cost) because by
expanding the set of subsectors that it is able to target, the bank also becomes more efficient at supplying
services for their old customers (in this case the car producers, which also benefit from banks’ acquired
expertise in the auto parts industry).
19
max E0
dit ,Rit ,θit
∞
X
1
ΠB
∗ )t it
(1
+
r
t=0
(15)
s.t.
ΠB
it = (dit −
lit−1
lit
) + (1 + Rit−1 )
− (1 + r∗ )dit−1 − ci − F (θit )
St
St
(16)
lit
St
= 2φwt hit x̂it
dit =
(17)
lit
(18)
ΠB
it ≥ 0
∀t
(19)
Equation (16) shows the cash flow for bank i expressed in real terms, equation (17) is
the balance sheet condition for banks22 , and equation (18) denotes the demand for loans
that banks internalize.
The value function for bank i is therefore:
h
i
1
B
E
V
(z
,
S
)
it
t+1
t
it+1
(1 + r∗ )
≡ (Rit−1 , lit−1 , dit−1 )
VitB (zit−1 , St ) = ΠB
it +
zit−1
(20)
(21)
Taking into account the probability of a currency devaluation p, and the fact that bank i
may go bankrupt if ci is large enough so that the bank is unable to repay foreign depositors
after an unexpected devaluation, the value function can be rewritten as:
1
(1 − p)ΠB
it+1 (zit , St ) +
∗
(1 + r )
"∞
#
h
i
X
1
1
B
(1 − p)Et Vit+2
(zit+1 , St+2 ) + pνit
ΠB (z
, Ωn S t )
∗ )n it+n it+(n−1)
(1 + r∗ )2
(1
+
r
n=1
(22)
VitB (zit−1 , St ) = ΠB
it (zit−1 , St ) +
22
Notice that this equation implies no reserve requirements on deposits.
20
where νit is the probability of bank i staying in business during period t+1 after a currency
devaluation in period t.
Before the devaluation, bank i’s FOC for the choice of Rit is:
1
(1 + Rit )
= 1−
∗
(1 + r )
it
−1
[(1 − p) + pνit ]
h
(1 − p) + p νΩit
(23)
i
After the devaluation, the markup becomes:
1
(1 + Rit )
= 1−
∗
(1 + r )
it
−1
Ω
(24)
where:
(1 + Rit )
∂lit
∂(1 + Rit )
lit
∂ x̂it
(1 + Rit )
= −
∂(1 + Rit )
x̂it
Nt (1 + Rit ) φwt hit
=
θt (1 + r∗ ) Et−1 (St )
it = −
(25)
Equations (23) and (24) show that the price-cost margin charged by bank i is inversely
related to the interest rate elasticity of the demand for loans. The pre-devaluation markup
also depends on the likelihood of crises and banks’ probability of survival (see equation
(23)). Equation (25) shows the interest rate elasticity of loan demand, which equals the
interest rate elasticity of each bank’s market share (2x̂). This elasticity is larger when the
competition is more intense, that is, the number of banks N is large and the degree of
product differentiation θ is small. It is also directly related to the real amount of the loan
φwt hit
.
Et−1 (St )
An expression for bank i’s pre-devaluation markup can be obtained by plugging equation (25) into equation (23). The markup becomes:
[(1 − p) + pνit ]
θt
(1 + Rit )
i+
=h
∗
ν
(1 + r )
Nt
(1 − p) + p Ωit
21
φwt hit
[pΩ + (1 − p)] St−1
!−1
(26)
pre-devaluation and
(1 + Rit )
θt
=Ω+
∗
(1 + r )
Nt
φwt hit
ΩSt−1
!−1
(27)
post-devaluation.
νit is a function of Rit itself, and therefore, we cannot obtain a closed form analytical
expression for the price-cost markup charged by bank i. Equation (26) shows that predevaluation markups are affected by four key forces. First, they are positively related to
market concentration (i.e. a fall in N raises markups). Second, they are positively related
to θi as product differentiation provides a source of market power for bank i. Third,
they increase with the probability of bank i staying in business. Fourth, they depend
negatively on the amount financed. The latter effect comes from the fact that in this
general equilibrium model, the demand faced by banks is not fixed as in the benchmark
partial equilibrium model à la Salop (1979). Schargrodsky and Sturzenegger (2000) also
obtain the first and second effects, but their model is static and partial equilibrium. Thus,
the demand for loans is fixed and normalized at 1.
The bank’s FOC for the choice of θit is:
∂lit (1 + Rit ) 1
pνit
∂F (θit )
=
(1 − p) +
∗
∂θit
∂θit (1 + r ) it
Ω
Pt
(28)
pre-devaluation, and
Pt
∂F (θit )
∂lit (1 + Rit ) 1 1
=
∂θit
∂θit (1 + r∗ ) it Ω
(29)
post-devaluation, where:
∂lit
φwt hit
=−
∂θit
2θit Nt
(30)
The intuition underlying equations (28) and (29) is the following. The left hand side
represents the marginal benefit a bank gets from increasing θ, in terms of reducing its
22
fixed costs of producing differentiated financial services. The right hand side represents
the marginal cost of an increased θ. These costs are given by the fall in the quantity
∂lit
demanded of loans faced by the individual bank ( ∂θ
) multiplied by the per-unit profits
it
and the change in the quantity demanded of loans when the interest rate changes as a
result of the change in θ. A bank’s optimal choice of θ is given by the point where this
marginal cost equals this marginal benefit.
3.3
Households
Households choose consumption (C) and work effort (h) to maximize the expected present
discounted value of lifetime utility subject to their budget constraint. For simplicity, but
without loss of generality, households are not allowed to access capital markets. Firms and
banks profits are distributed to households in a lump-sum fashion23 .
The representative household’s optimization problem is given by:
max
Ct ,ht
(1−σ)
Ct − ωκ hωt
1
E0
∗ t
(1 − σ)
t=0 (1 + r )
(31)
Z 1
N
X
wt
ΠFkt dk +
ΠB
ht +
it
Pt
0
i=1
(32)
∞
X
s.t.
Ct =
The labor supply equation is given by:
κhω−1
=
t
wt
Pt
(33)
and shows that there are no wealth effects on labor supply.
23
This justifies our choice of (1 + r∗ ) as the households’ discount factor, the same used for firms and
banks.
23
3.4
Timing
The timing of the model within any period is as follows:
• The aggregate exchange rate shock is realized.
• When the actual exchange rate differs from the expected rate, some banks are liquidated, which determines a new equilibrium number of banks and the degree of
product differentiation that they choose.
• The firms choose their demand for labor and loans. The households choose their
supply of labor.
• Banks determine the supply of loans and intermediate funds from abroad to finance
them. They face an infinitely elastic supply of funds at the world interest rate r∗ .
• The equilibrium interest rate on loans is determined as a function of the expected
depreciation rate for the next period.
• Firms use labor to produce the tradable good.
• Output is sold and firms repay loans.
• Banks, if liquid, repay foreign deposits.
• Firms and banks profits are distributed to households, and consumption is realized.
3.5
The Economy’s Equilibrium
The equilibrium concept used is the non-cooperative Nash equilibrium in interest rates Rt
and degree of focus θt . We restrict attention to symmetric equilibria with free-entry in the
24
banking sector. Each bank i takes as given the rate and the degree of differentiation chosen
by all other banks, and chooses Rit and θit to maximize the expected present discounted
value of lifetime profits.
The economy’s symmetric equilibrium is defined by a set of prices {wt , Rt , Pt , St , Pt∗ },
a set of allocations {Ct , ht , Yt , dt , Lt , lt , θt } and an endogenous number of banks Nt , such
that all agents FOCs are met, the households’ budget constraint holds, the labor and loans
markets clear at all times, and the economy’s resource constraint holds.
The economy’s resource constraint is given by:
Yt = Ct +
N
X
(F (θit ) + ci ) +
Z
i=1
1
0
θt xkt dk − Dt + (1 + r∗ )Dt−1
(34)
where Dt = dt Nt , and the term − (Dt − Dt−1 ) measures the current account.
Market clearing in the market for loans requires Lt = lt Nt .
The liquidity constraint that requires banks’ profits to be non-negative allows us to find
the idiosyncratic costs for the bank that breaks even in period t.
ĉit =
(1 + Rit−1 )lit−1
− (1 + r∗ )dit−1 − F (θit )
St
(35)
where î is used to index the marginal bank.
Considering that ci is a uniformly distributed discrete random variable in [0, c̄], and
using G(c) to denote its cumulative density function, the mass of banks that stay in business
after the aggregate exchange rate shock is realized is:
G(ĉit ) =
ĉit
ĉit−1
(36)
By the law of large numbers, G(ĉit ) equals the probability of bank i staying in business
during period t + 1 after a currency devaluation in period t (i.e. G(ĉit ) = νit ).
25
Thus, ignoring the integer constraint, the endogenous equilibrium number of banks (Nt )
is:
Nt = G(ĉit )Nt−1
(37)
It is worth noting that before the devaluation Nt−1 = N0 , i.e. the equilibrium number of
banks does not change before the devaluation takes place and it equals the predetermined
N0 . There is no entry of banks in equilibrium. This is a result of our assumption on the
timing of financial contracts: in the first period of its lifetime a new bank borrows from
international investors and lends to domestic firms, but gets no income to cover operation
costs.
Obtaining the equilibrium number of banks in this way implies that whenever a bank
cannot repay its depositors in period t, it goes bankrupt and exits the market. We are
not allowing for any inter-bank borrowing by banks so that these temporary illiquid banks
could stay in business if they expected positive future profits. We believe this is a compelling assumption given that we are thinking about big shocks and currency crises, when
liquidity in the inter-bank market dries (see Rajan (2004)), and governments have insufficient reserves to bail out banks. Within this context, especially for emerging markets, it
would be difficult to argue that all banks severely affected by a currency devaluation are
able to survive the crisis24 .
24
Note that our model does not consider the financial amplifier role of the external risk premium discussed
by other papers. The world interest rate in our model is constant and exogenous.
26
4
The Effects of a Currency Crisis
4.1
A Discussion of the Model’s Transmission Mechanisms
In this subsection we discuss the intuition on each of the model’s transmission mechanisms
after the economy experiences a currency devaluation.
If the banking sector is perfectly competitive and the only friction is given by the
presence of dollarized liabilities and mismatches on banks’ balance sheets, then the interest
rate on loans equals the exchange-rate adjusted marginal cost of funds for banks (i.e.
(1 + Rit ) = (1 + r∗ ) Et (SStt+1 ) ). Given the Markov structure assumed for the exchange rate
shock, the term
Et St+1
St
increases from pΩ + (1 − p) to Ω after a currency devaluation. The
exchange-rate adjusted marginal cost of funds is higher after the devaluation, and this
raises the interest rate on loans. We call this effect the “balance sheet effect”.
However, with equilibrium employment given by equation (14), when banks are competitive and with no nominal rigidities such that real wages stay constant after the shock,
employment and output are not affected in this case. Therefore, in this setup (with no
frictions related to either borrowers defaulting on their loans or any other change to banks’
marginal cost of funds), imperfect competition in banking is crucial and needed to reproduce contractionary effects of devaluations as well as twin crises.
We next look at the case where imperfectly competitive banks internalize the demand
for loans that they face when choosing the interest rate on loans, but they cannot affect
the degree of general purposeness of their services (i.e. the case of exogenous θ).
Due to the presence of balance sheet mismatches, a devaluation increases the value of
banks’ liabilities relative to that of their assets, lowers banks’ net worth and drives some
27
banks out of business. We label this effect the “concentration effect” 25 .
Notice that a large enough exchange rate shock can drive some banks out of business,
but not firms. In this paper we focus only on negative shocks to the value of the currency
and firms might benefit from them, given that they borrow in domestic currency but have
implicitly dollar-denominated returns.
With this increase in concentration, it is clear from equations (26) and (27) that the
markup charged by banks increases. This has a negative impact on employment and
production, and leads to contractionary devaluations.
An additional effect arises when banks compete not only in price but also in product
differentiation, by choosing the degree of focus of their financial services (i.e. the case
of endogenous θ). As N falls and concentration rises following an unexpected currency
devaluation, competitive pressures fall and banks find it optimal to lower their degree of
product specialization to attract customers located farther away on the circle and increase
their market share (even if this increases their fixed operation costs). In other words, they
lower θ to increase the general purposeness of their loans. This drives down the cost of
credit for firms, and employment and output are positively affected. We label this effect
the “product differentiation effect”.
The “concentration effect” and the “product differentiation effect” acting jointly form
what we label the “market structure effect”.
It is important to notice that we obtain real effects of devaluations in this setup, even
without assuming any price or wage rigidities. This is a result of the dynamic nature of
loan contracts in the credit market. In each period t, bank i sets its interest rate Rit based
25
It is clear from equation (35) that an unexpected shock to St lowers ĉit and drives some banks out of
business, such that Nt < Nt−1 .
28
on the expected exchange rate for the next period, when it will get loan repayments and
use them to repay foreign depositors. After a partially unexpected devaluation, the realized
exchange rate is different from the expected rate, and the interest rate set in period t might
be too low for bank i to stay in business. As a result, some banks exit the industry and
the remaining banks lower their optimal degree of product differentiation. Therefore, real
interest rates increase, which affects the cost of the wage bill for firms, employment and
output.
All the papers that study liability dollarization in the banking sector as a determinant of
twin crises consider the “balance sheet effect”. Choi and Cook (2004) and Disyatat (2004)
also obtain an endogenous price-cost margin charged by banks. However, in these papers
the margin is given by a country-risk default premium, which increases after a devaluation
as banks’ net worth falls. There are neither changes in market concentration nor are banks
offering differentiated products (i.e. no market structure effects). In Burnside et al. (2001)
the devaluation causes a change in concentration as the number of banks falls, but their
transmission mechanism is different from ours. In their setup, the combination of higher
costs of funds for banks and the existence of government guarantees generates an increase
in the interest rate on loans after a devaluation. Thus, real wages fall, leading to lower
aggregate employment, a lower number of firms and, as a result, a lower number of banks.
Although their framework generates an aggregate contraction, per firm employment and
output are not affected by a currency devaluation. None of these previous studies consider
the role of product differentiation in generating twin crises.
Schargrodsky and Sturzenegger (2000) study product differentiation, but they do so in
a partial equilibrium, static model, with a fixed demand for credit. Also, they use this
setup to address a different question, namely the effects of capital requirements on the
29
solvency and competitiveness of the banking sector.
4.2
Simulation Results
We cannot obtain analytical solutions due to the non-linearity of the system. Therefore,
in this subsection we present the results for numerical simulations of the model. Table 3
shows the parameter values used for the benchmark case.
Table 4 presents the model simulation results. It also shows the implied costs of product
differentiation in banking expressed as a percentage of GDP and firms’ and banks’ profits.
In the benchmark parametrization of the model, and when θ is endogenously determined
in the model, a 15% currency devaluation to which banks attach a 95% chance of realization,
induces a fall of approximately 1.5% in output and 2% in employment. This is a result of a
significant reduction in the equilibrium number of banks (33% of the banks are driven out
of the market), which causes real markups in the banking industry to rise by 3%, and the
real interest rate on loans by 25%. This increase in the cost of borrowing is driven by an
increase in the ratio
θ
,
N
which causes a decline in the interest rate elasticity of the demand
for credit. Both the number of banks and the degree of product differentiation fall, but
the decline in N is larger than that in θ.
The contraction in employment and output happens even with real wages falling after
the shock, because the increase in interest rates more than offsets the fall in wages and
generates an increase in firms’ total cost of labor.
Worthy of note is that aggregate loans fall by approximately 4%, but loans per bank
increase by more than 40%, so that the remaining banks benefit from the currency devaluation.
30
The effects of a devaluation on households consumption are almost nil for our benchmark set of parameter values. Conceptually, aggregate consumption could increase or
decrease depending on the effects of devaluations on banks’ and firms’ profits, which are
both rebated to households in a lump-sum fashion. It is not our goal to study any welfare
effects and therefore, we do not focus on the behavior of consumption in this paper.
Figures 4-10 present the real effects of devaluations for a wide range of all the relevant
parameters in the model. In each figure, the subplots show the growth rates of real GDP,
the interest rate on loans, markups charged by the banking industry, the degree of product
differentiation θ and the equilibrium number of banks N . It can be seen there that our
results are robust to all parameter values.
Figure 4 shows that, intuitively, devaluations become more contractionary as Ω rises.
The contraction can be explained by the fact that both the markup and the interest rate on
loans always go up after a devaluation (with the variation being monotonically increasing
in Ω). Both N and θ always fall after a currency devaluation, and the reductions are
increasing in the rate of devaluation.
Figure 5 shows that devaluations are more contractionary as they become more unexpected for economic agents (i.e. as p falls). When p is low, banks set a lower interest rate,
which increases the probability of bankruptcy after the shock hits. Thus, the smaller p,
the larger the reduction in N , and the larger the percentage increase in markups and R.
In our model the parameter φ measures the economy’s dependence on an imperfectly
competitive and liability dollarized financial sector. The results presented in Figure 6 show
that devaluations become more contractionary as this dependence increases, and a higher
share of total labor costs is negatively affected by a devaluation of the currency. Also, the
reduction in N and θ are both monotonically increasing in φ.
31
To study the role played in our model by the initial degree of competitiveness in the
banking industry, we look at how the real effects of devaluations change with the initial
number of banks N0 . In Figure 7 the fall in output is diminishing in N0 . Devaluations are
less contractionary in economies that start with a more competitive banking sector. This
finding is consistent with the empirical evidence presented in section 2 according to which
NIMs (our measure of market power) are negatively correlated with GDP growth.
We also conducted a sensitivity analysis on the value of τ . This parameter denotes
the elasticity of the banks cost function F (θ). Our results are quantitatively not sensitive
to this parameter for large enough values of τ , which produce realistic interest rates and
costs as a share of GDP and profits. Qualitatively, the increase in R after a devaluation
is monotonically increasing in τ , the contraction in θ is monotonically decreasing in τ and
the fall in N is monotonically increasing in τ (see Figure 8).
Figure 9 shows that the adverse effects of devaluations are monotonically increasing in
the labor share of output α, both in terms of the increase in the cost of credit and the
fall in output. This is a result of the fact that the fall in employment and output after an
increase in the interest rate is increasing in α.
Last, Figure 10 shows the sensitivity of our simulation results to the elasticity of labor
supply, which is pinned down by the parameter ω 26 . The contraction in output is monotonically decreasing in ω. This result is intuitive. A devaluation of the currency raises the
cost of credit to finance the wage bill. Labor demand falls as a result. The more elastic
labor supply (i.e. the smaller ω), the larger the effect of the devaluation on equilibrium
employment and GDP for a given reduction in labor demand.
26
The elasticity of labor supply is given by
1
(ω−1) .
32
4.2.1
The “Product Differentiation Effect”
There are two ways in which allowing banks to choose the degree of differentiation of the
financial services they offer might change these results. On the one hand, with endogenous
product differentiation, θ falls after the currency is devalued. This tends to lower pricecost margins and ceteris paribus, the cost of credit, which should raise employment and
output. However, on the other hand, as margins tend to fall, banks face further incentives
to exit coming from this channel and therefore, the equilibrium number of banks could
end up falling by more in the endogenous product differentiation case. This second effect
tends to raise margins, and negatively affects economic activity. Two potential outcomes
arise depending on which of these two effects dominates. In the first case, endogenous
differentiation may act as a buffer for banks, such that they do not need to raise interest
rates on loans that much, which would result in crises with milder real effects, or even
in expansionary devaluations if this effect is large enough to offset that of bank exit. In
the second case, endogenous differentiation may work as an amplifier, resulting in deeper
banking crises and larger contractions in employment and output27 .
Thus, what we do next is to close the endogenous product differentiation channel to
assess how much of the real effects of a currency devaluation are due to banks competing
only in the price dimension. For comparability, the value chosen for the parameter θ is the
equilibrium value obtained in the case of endogenous product differentiation.
When the degree of product differentiation θ is exogenous, aggregate output and employment fall by 1.5% and 1.9%, respectively, approximately the same change as when θ
27
By “buffer” and “amplifier”, we mean relative to the real effects of devaluations observed for the case
of exogenous θ.
33
is endogenous. In this case, the equilibrium number of banks falls by 32% (see Table 5).
Therefore, it seems that the two opposite forces discussed before offset each other after a
devaluation. This renders in the real effects being the same regardless of whether banks
are allowed to vary the degree of differentiation. Thus, allowing banks to compete in the
degree of differentiation is not a necessary assumption to generate our results.
For devaluation rates above 50% endogenous product differentiation acts as an amplifier,
and results in crises that are deeper than in the case where θ is exogenous. In other words,
in the simulated economies devaluations are less contractionary when banks cannot adjust
the degree of general purposeness of their products (see Figure 4).
Regarding the effect of the expectation of devaluation p, the reduction in the degree of
product differentiation that arises after a devaluation is not a function of this expectation.
θ does not seem to act as either a buffer or an amplifier for any value of p (see Figure 5).
Figure 6 shows that, for large enough values of φ, the reduction in the degree of product
differentiation lowers margins and drives more banks out of business than in the case
where banks cannot compete in this dimension. The effect of N dominates and causes
an increase in the cost of credit larger than for the case of exogenous θ, and a more
significant contraction in real GDP. Endogenous product differentiation acts as an amplifier
in economies where firms are heavily dependent on bank credit to finance production. This
might well be the case in the economies of emerging countries.
Also, for large enough values of N0 , endogenous θ acts as an amplifier, with the increase in markups and interest rates on loans being larger than in the case of exogenous
θ. However, it is evident from Figure 7 that this amplification effect is quantitatively very
small.
Worthy of note is that endogenous differentiation acts as a buffer for small values of τ ,
34
with the contraction generated by a devaluation being smaller than in the case of exogenous
θ (see Figure 8). The reduction in the degree of product differentiation is large enough to
dominate the effect of a reduction in N .
The real effects of devaluations across a sensible range of values for α are quantitatively
the same regardless of whether banks are allowed to compete in the product differentiation
dimension (see Figure 9).
4.2.2
The “Market Concentration Effect”
If the number of banks was assumed constant in the model28 , then a currency devaluation would not have any real effects on aggregate economic activity (even with liability
dollarization and mismatched balance sheets in the banking industry).
If this is the case, an unexpected shock to the value of the currency affects only expost markups. If this does not trigger any exit from the banking industry, then there is
no change in the optimal degree of product differentiation. Therefore, only ex-ante real
markups are relevant for real allocations. Moreover, changes in market concentration are
necessary to explain contractionary devaluations.
28
This implies assuming that the distribution of the idiosyncratic costs ci is such that no devaluation is
large enough to drive even the most inefficient bank out of business.
35
5
Conclusions
In this paper we study a novel channel that generates twin crises and explains their contractionary effects. In our framework banking crises are unrelated to borrowers defaulting
on their loans. Conversely, the roots of crises can be traced to two other imperfections
mainly ignored by the existing literature: currency mismatches on the balance sheets of
banks themselves and imperfect competition in the banking industry.
With this goal in mind we build a DSGE model by introducing currency mismatches in
a modified version of the Schargrodsky and Sturzenegger (2000) model of an imperfectly
competitive banking industry. We then embed this framework into an otherwise standard
dynamic general equilibrium model of a small open economy.
In our model banks compete in two dimensions: price of credit and product differentiation of the financial services they provide together with loans. By modeling the endogenous
choice of product differentiation by banks, our model provides a good framework to study
market power in banking, even when it is not directly related to market concentration.
To our knowledge, this is the first attempt to study the effects of currency mismatches
in the context of an imperfectly competitive banking sector. This is important for at least
two reasons. First, previous findings in the banking literature seem to indicate that this
is an accurate description of banking in emerging markets. Second, we are able to show
that in our setup (with no frictions related to either borrowers defaulting on their loans
or any other change to banks’ marginal cost of funds), devaluations have no real effects
under perfect competition. Thus, imperfect competition in banking is crucial to reproduce
contractionary effects of devaluations and twin crises.
Our results show that currency devaluations result in deeper crises in economies that
36
have higher rates of devaluation, where devaluations are less expected by economic agents,
and producers are more dependent on bank credit. Last, devaluations are less contractionary the more competitive the banking sector is prior to the devaluation. We also show
that allowing banks to choose the degree of product differentiation of their financial services
tends to amplify the contractionary effects of financial crises.
A natural extension of this work would be to study the effects of prudential regulations,
such as capital adequacy regulations and limits on banks’ foreign exchange open positions.
Our model could be used to analyze the role played by these regulations on the effects of
devaluations. Moreover, we have assumed that devaluations are exogenous events. It would
be interesting to endogenize the likelihood of a currency crisis in emerging economies.
37
References
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[12] Chue, T. and D. Cook (2004), “Sudden Stops and Liability Dollarization: Evidence
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39
[24] Schargrodsky, E. and F. Sturzenegger (2000), “Banking Regulation and Competition
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Specialization in Lending”, working paper University of Minnesota.
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Policy, Princeton, NJ: Princeton University Press.
40
0
100
200
Regression Fit of Devaluation Rate on NIM
-100
Devaluation Rate
300
Figure 1: Empirical Evidence on the Real Effects of Currency Crises
0
5
10
15
20
25
NIM
10
0
-10
GDP growth
20
Regression Fit of GDP growth on NIM
0
5
10
NIM
41
15
20
25
Figure 2: Empirical Evidence on the Real Effects of Currency Crises
Latin American Countries
Argentina
Argentina
7
6
5
250
7
200
6
8
6
4
5
150
4
2
4
0
3
-2
100
3
50
2
1
0
1996
1997
1998
1999
2000
NIM
2001
2002
-4
2
-6
0
1
-50
0
2003
-8
-10
1996
1997
1998
Devaluation Rate
1999
NIM
9
8
50
8
7
40
7
6
30
6
5
20
5
4
10
4
3
0
3
2
-10
2
1
-20
1
0
-30
0
1998
1999
NIM
2000
2002
2003
Brazil
60
1997
2001
GDP growth
Brazil
9
1996
2000
2001
2002
2003
6
5
4
3
2
1
0
1996
1997
1998
Devaluation Rate
1999
NIM
2000
2001
2002
2003
GDP growth
Mexico
Mexico
8
25
8
7
20
7
6
8
6
15
5
10
6
5
10
4
4
5
3
0
2
1
1
0
-10
0
1997
1998
1999
NIM
2000
2001
2002
2
2
-5
1996
4
3
2003
0
-2
1996
1997
Devaluation Rate
1998
1999
NIM
Note: NIM measured on left axis, devaluation rate and GDP growth on right axis.
42
2000
2001
GDP growth
2002
2003
Figure 2 (ctd.): Empirical Evidence on the Real Effects of Currency Crises
Latin American Countries
Paraguay
Paraguay
14
60
14
12
50
12
40
10
30
8
8
7
6
10
5
8
4
3
20
6
10
4
0
6
2
4
1
0
2
-10
2
0
-20
0
1996
1997
1998
1999
NIM
2000
2001
2002
2003
-1
-2
1996
1997
1998
Devaluation Rate
1999
NIM
Uruguay
2000
2001
2002
2003
GDP growth
Uruguay
9
90
9
8
80
8
7
70
7
6
60
6
5
50
5
0
4
40
4
-2
3
30
3
2
20
2
1
10
1
0
0
0
1996
1997
1998
1999
NIM
2000
2001
2002
2003
6
4
2
-4
-6
-8
1996
1997
1998
Devaluation Rate
1999
NIM
Venezuela
2000
2001
2002
2003
GDP growth
Venezuela
30
90
30
20
25
15
80
25
70
20
60
10
20
5
50
15
40
10
30
15
0
10
-5
20
5
10
0
0
1996
1997
1998
1999
NIM
2000
2001
2002
5
-10
-15
0
2003
1996
1997
Devaluation Rate
1998
1999
NIM
Note: NIM measured on left axis, devaluation rate and GDP growth on right axis.
43
2000
2001
GDP growth
2002
2003
Figure 3: Empirical Evidence on the Real Effects of Currency Crises
Asian Countries
Indonesia
Indonesia
10
120
10
25
8
100
8
20
6
80
6
15
4
60
4
10
2
40
2
5
0
20
0
-2
0
-2
-4
-20
-4
1996
1997
1998
1999
NIM
2000
2001
2002
2003
0
1996
1997
1998
1999
2000
2001
2002
2003
-5
-10
Devaluation Rate
NIM
GDP growth
Korea
Korea
3.5
120
3.5
3
100
3
80
2.5
60
2
10
8
6
2.5
4
2
2
0
40
1.5
20
1
0
1.5
-2
1
-4
0.5
-20
0.5
0
-40
0
1996
1997
1998
1999
NIM
2000
2001
2002
2003
-6
-8
-10
1996
1997
1998
Devaluation Rate
1999
NIM
Malaysia
2000
2001
2002
2003
GDP growth
Malaysia
14
3.5
60
3.5
3
50
3
2.5
40
2.5
8
2
30
2
6
1.5
20
1.5
2
1
10
1
0
12
10
4
0.5
-2
0
0
0.5
-10
1996
1997
1998
1999
NIM
2000
2001
2002
-4
-6
0
2003
1996
Devaluation Rate
1997
1998
1999
NIM
Note: NIM measured on left axis, devaluation rate and GDP growth on right axis.
44
2000
2001
GDP growth
2002
2003
Figure 3 (ctd.): Empirical Evidence on the Real Effects of Currency Crises
Asian Countries
Philippines
Philippines
6
60
6
5
50
5
40
4
9
8
7
4
6
30
3
5
3
4
20
2
2
10
1
0
1
0
-10
0
1996
1997
1998
1999
NIM
2000
2001
2002
3
2
1
0
2003
1996
1997
1998
Devaluation Rate
1999
NIM
Singapore
2000
2001
2002
2003
GDP growth
Singapore
2.5
25
14
2.5
12
20
2
10
2
15
1.5
8
6
1.5
10
4
5
1
2
1
0
0
0.5
0
-4
-10
1996
1997
1998
1999
NIM
2000
2001
2002
-2
0.5
-5
0
2003
-6
1996
1997
1998
Devaluation Rate
NIM
4
100
3.5
80
3
2
20
1.5
0
1
8
6
0
-2
-4
-6
1
-40
0
2002
2
1.5
0
2001
4
2
0.5
NIM
GDP growth
4
-20
2000
2003
3.5
0.5
1999
2002
2.5
40
1998
2001
3
60
2.5
1997
2000
Thailand
Thailand
1996
1999
-8
-10
-12
1996
2003
1997
1998
1999
NIM
Devaluation Rate
Note: NIM measured on left axis, devaluation rate and GDP growth on right axis.
45
2000
2001
GDP growth
2002
2003
Figure 4: Simulation Results: Sensitivity of Real Effects of Currency Crises to
Rate of Devaluation
Output
Real Interest Rate on Loans
180
0
1
-2
05
1.
5
1
1. 1.1
5
2
1. 1.2
5
3
1. 1.3
1
5
5
5
1. 1.5 1.6 1.6
5
4
1. 1.4
5
7
1. 1.7
160
140
120
-4
100
-6
80
60
-8
40
-10
20
0
-12
1
-14
05
1.
5
1
1. 1.1
5
2
1. 1.2
5
3
1. 1.3
5
4
1. 1.4
1
5
5
5
1. 1.5 1.6 1.6
5
7
1. 1.7
Ω
Ω
Endogenous product differentiation
Endogenous product differentiation
Exogenous product differentiation
Real Markup
Exogenous product differentiation
θ
0
80
-0.5
60
1
05
1.
5
1
1. 1.1
5
2
1. 1.2
5
3
1. 1.3
5
4
1. 1.4
5
1
5
5
1. 1.5 1.6 1.6
5
7
1. 1.7
-1
-1.5
40
-2
-2.5
20
-3
-3.5
0
-4
1
05
1.
5
1
1. 1.1
25
1.
2
1.
3
1.
35
1.
4
1.
45
1.
5
1.
55 .61 .65
1.
1
1
5
7
1. 1.7
-4.5
Ω
Endogenous product differentiation
Ω
Exogenous product differentiation
Endogenous product differentiation
Number of Banks
0
1
05
1.
1
1.
15
1.
2
1.
25
1.
5
3
1. 1.3
5
4
1. 1.4
5
1.
55 .61 .65
1
1
1.
5
7
1. 1.7
-20
-40
-60
-80
Ω
Endogenous product differentiation
Exogenous product differentiation
46
Exogenous product differentiation
Figure 5: Simulation Results: Sensitivity of Real Effects of Currency Crises to
Expectation of Devaluation
Output
Real Interest Rate on Loans
120
-1.1 0
06 .12 .18 .24
0.
0
0
0
6
4
2
8
3
0. 0.3 0.4 0.4 0.5
4
8
2
6
6
0. 0.6 0.7 0.7 0.8
6
9
0. 0.9
100
-1.3
80
-1.5
60
-1.7
40
-1.9
20
0
-2.1
06 .12 .18 .24
0
0
0
0.
4
8
2
6
3
0. 0.3 0.4 0.4 0.5
Endogenous product differentiation
8
4
2
6
6
0. 0.6 0.7 0.7 0.8
6
9
0. 0.9
p
p
Exogenous product differentiation
Endogenous product differentiation
Real Markup
Exogenous product differentiation
θ
30
0
25
-0.2
0
20
06 .12 .18 .24
0
0
0
0.
4
8
2
6
3
0. 0.3 0.4 0.4 0.5
4
8
6
2
6
0. 0.6 0.7 0.7 0.8
6
9
0. 0.9
-0.4
15
-0.6
10
-0.8
5
-1
0
0 06 12 18 24
0.
0.
0.
0.
4
8
2
6
3
0. 0.3 0.4 0.4 0.5
4
8
2
6
6
0. 0.6 0.7 0.7 0.8
6
9
0. 0.9
-1.2
p
Endogenous product differentiation
p
Exogenous product differentiation
Endogenous product differentiation
Number of Banks
-30
0
-32
06 .12 .18 .24
0
0.
0
0
4
8
2
6
3
0. 0.3 0.4 0.4 0.5
4
8
2
6
6
0. 0.6 0.7 0.7 0.8
6
9
0. 0.9
-34
-36
-38
-40
-42
-44
p
Endogenous product differentiation
Exogenous product differentiation
47
Exogenous product differentiation
Figure 6: Simulation Results: Sensitivity of Real Effects of Currency Crises to
Need for External Credit
Output
Real Interest Rate on Loans
250
0.
01
0.
04
0.
07
0.
1
0.
13
0.
16
0.
19
0.
22
0.
25
0.
28
0.
31
0.
34
0.
37
0.
4
0.
43
0.
46
0.
49
0.
52
0.
55
0
-2
200
-4
150
-6
100
-8
50
-10
0.
01
0.
04
0.
07
0.
1
0.
13
0.
16
0.
19
0.
22
0.
25
0.
28
0.
31
0.
34
0.
37
0.
4
0.
43
0.
46
0.
49
0.
52
0.
55
0
-12
phi
phi
Endogenous product differentiation
Endogenous product differentiation
Exogenous product differentiation
Real Markup
Exogenous product differentiation
θ
25
0.
01
0.
04
0.
07
0.
1
0.
13
0.
16
0.
19
0.
22
0.
25
0.
28
0.
31
0.
34
0.
37
0.
4
0.
43
0.
46
0.
49
0.
52
0.
55
0
-0.5
20
-1
15
-1.5
-2
10
-2.5
-3
5
-3.5
0
0.
01
0.
04
0.
07
0.
1
0.
13
0.
16
0.
19
0.
22
0.
25
0.
28
0.
31
0.
34
0.
37
0.
4
0.
43
0.
46
0.
49
0.
52
0.
55
-4
-4.5
phi
Endogenous product differentiation
phi
Exogenous product differentiation
Endogenous product differentiation
Number of Banks
0.
01
0.
04
0.
07
0.
1
0.
13
0.
16
0.
19
0.
22
0.
25
0.
28
0.
31
0.
34
0.
37
0.
4
0.
43
0.
46
0.
49
0.
52
0.
55
0
-20
-40
-60
-80
phi
Endogenous product differentiation
Exogenous product differentiation
48
Exogenous product differentiation
Figure 7: Simulation Results: Sensitivity of Real Effects of Currency Crises to
Initial Degree of Competitiveness in Banking
Output
Real Interest Rate on Loans
130
56
53
47
50
44
41
38
35
32
29
26
20
23
14
17
8
11
-1.5
5
2
-1
-2
110
-2.5
90
-3
70
-3.5
N0
56
53
50
47
44
41
38
35
N0
Exogenous product differentiation
Endogenous product differentiation
Real Markup
Exogenous product differentiation
56
53
50
47
44
41
38
35
32
26
23
20
17
14
11
-0.5
8
0
12
2
14
5
θ
29
Endogenous product differentiation
32
29
26
23
20
17
14
2
8
10
-5.5
11
30
-5
5
50
-4
-4.5
-1
10
-1.5
8
-2
-2.5
6
-3
4
-3.5
56
53
50
47
44
41
38
35
32
29
26
23
20
17
14
11
8
-4
5
2
2
-4.5
N0
Endogenous product differentiation
N0
Exogenous product differentiation
Endogenous product differentiation
Number of Banks
53
56
50
47
44
41
38
35
32
26
29
20
23
14
17
11
8
2
-20
5
-10
-30
-40
-50
-60
-70
-80
N0
Endogenous product differentiation
Exogenous product differentiation
49
Exogenous product differentiation
Figure 8: Simulation Results: Sensitivity of Real Effects of Currency Crises to
Costs of Product Differentiation in Banking
Output
Real Interest Rate on Loans
27
91
99
10
7
11
5
12
3
13
1
13
9
14
7
75
83
59
67
43
51
27
19
11
-1.1
35
-1
25
-1.2
23
-1.3
-1.4
21
-1.5
19
-1.6
-1.7
17
-1.8
tau
91
99
10
7
11
5
12
3
13
1
13
9
14
7
75
83
59
67
43
51
27
35
11
-2
19
15
-1.9
tau
Endogenous product differentiation
Exogenous product differentiation
Endogenous product differentiation
Real Markup
Exogenous product differentiation
θ
99
10
7
11
5
12
3
13
1
13
9
14
7
91
75
83
59
67
43
51
27
35
11
-1
19
0
4.5
4
-2
3.5
-3
3
-4
-5
2.5
-6
2
91
99
10
7
11
5
12
3
13
1
13
9
14
7
75
83
59
67
51
43
35
27
19
11
-7
-8
tau
tau
Endogenous product differentiation
Exogenous product differentiation
Endogenous product differentiation
Number of Banks
13
9
14
7
13
1
11
5
12
3
99
10
7
91
83
75
67
59
51
43
35
27
19
11
-25
-27.5
-30
-32.5
-35
tau
Endogenous product differentiation
Exogenous product differentiation
50
Exogenous product differentiation
Figure 9: Simulation Results: Sensitivity of Real Effects of Currency Crises to
Labor Share
Output
Real Interest Rate on Loans
-1
-1.2
0.
8
0.
83
0.
86
0.
89
0.
92
0.
95
0.
98
0.
5
0.
53
0.
56
0.
59
0.
62
0.
65
0.
68
0.
71
0.
74
0.
77
80
70
60
-1.4
50
-1.6
40
-1.8
10
0.
5
0.
53
0.
56
0.
59
0.
62
0.
65
0.
68
0.
71
0.
74
0.
77
20
-2.2
-2.4
0.
8
0.
83
0.
86
0.
89
0.
92
0.
95
0.
98
30
-2
α
α
Endogenous product differentiation
Endogenous product differentiation
Exogenous product differentiation
Real Markup
Exogenous product differentiation
θ
6
-0.5
5
0.
8
0.
83
0.
86
0.
89
0.
92
0.
95
0.
98
0.
5
0.
53
0.
56
0.
59
0.
62
0.
65
0.
68
0.
71
0.
74
0.
77
0
-1
4
-1.5
3
-2
-2.5
0.
8
0.
83
0.
86
0.
89
0.
92
0.
95
0.
98
0.
5
0.
53
0.
56
0.
59
0.
62
0.
65
0.
68
0.
71
0.
74
0.
77
2
-3
α
α
Endogenous product differentiation
Endogenous product differentiation
Exogenous product differentiation
Number of Banks
0.
8
0.
83
0.
86
0.
89
0.
92
0.
95
0.
98
0.
5
0.
53
0.
56
0.
59
0.
62
0.
65
0.
68
0.
71
0.
74
0.
77
0
-10
-20
-30
-40
-50
-60
-70
α
Endogenous product differentiation
Exogenous product differentiation
51
Exogenous product differentiation
Figure 10: Simulation Results: Sensitivity of Real Effects of Currency Crises
to Elasticity of Labor Supply
Output
Real Interest Rate on Loans
4.
9
4.
7
4.
5
4.
3
4.
1
3.
9
3.
7
3.
5
3.
1
3.
3
2.
9
2.
7
2.
5
2.
3
2.
1
1.
9
100
1.
7
-1
1.
5
1.
3
-0.5
80
-1.5
60
-2
40
-2.5
20
-3
-3.5
ω
4.
9
4.
5
4.
7
4.
1
4.
3
3.
7
3.
9
3.
3
3.
5
2.
9
3.
1
2.
5
2.
7
2.
1
2.
3
1.
7
1.
9
1.
3
1.
5
0
-4
ω
Endogenous product differentiation
Exogenous product differentiation
Endogenous product differentiation
Real Markup
Exogenous product differentiation
θ
10
8
4.
9
4.
7
4.
5
4.
3
4.
1
3.
9
3.
7
3.
5
3.
3
3.
1
2.
9
2.
7
2.
5
2.
3
2.
1
1.
9
1.
7
1.
5
1.
3
0
-0.5
-1
-1.5
6
-2
-2.5
4
-3
-3.5
4.
9
4.
7
4.
5
4.
3
4.
1
3.
9
3.
7
3.
5
3.
3
3.
1
2.
9
2.
7
2.
5
2.
3
2.
1
1.
9
1.
7
1.
3
1.
5
2
-4
ω
ω
Endogenous product differentiation
Exogenous product differentiation
Endogenous product differentiation
Number of Banks
4.
9
4.
7
4.
5
4.
3
4.
1
3.
9
3.
7
3.
5
3.
3
3.
1
2.
9
2.
7
2.
5
2.
3
2.
1
1.
9
1.
7
1.
5
1.
3
-20
-30
-40
-50
-60
-70
ω
Endogenous product differentiation
Exogenous product differentiation
52
Exogenous product differentiation
Table 1: Number of Banks
1996
1997
1998
1999
2000
2001
2002
2003
Argentina
60
75
79
74
67
67
59
51
Bolivia
3
14
11
11
11
11
11
11
Brazil
96
113
115
111
105
110
103
75
Chile
9
29
28
26
25
24
22
22
Colombia
13
30
26
23
25
24
26
26
Hong Kong
29
35
36
36
36
33
34
31
India
58
62
63
64
62
57
55
50
Indonesia
55
53
40
54
51
49
48
40
Korea
19
29
19
19
16
17
17
16
Malaysia
30
30
31
28
24
25
24
22
Mexico
33
30
34
34
32
28
29
24
Paraguay
5
13
23
22
22
19
17
14
Peru
11
23
23
17
18
15
15
14
Philippines
22
26
26
26
23
25
32
32
Singapore
13
16
15
14
17
13
11
10
Thailand
6
12
12
12
12
13
14
14
Uruguay
10
16
19
18
33
31
24
23
Venezuela
6
23
23
43
37
33
31
27
Source: Bankscope from Bureau Van Dijk.
53
Table 2: The Real Effects of Currency Crises: Regression Analysis
Dependent Variable: Growth Rate of Real GDP
N IMt − N IMt−1
Devaluation rate
-0.0332*
-0.0015
-0.0327*
0.0015
(0.0164)
(0.0195)
(0.0180)
(0.0225)
-0.0058
0.0358
0.0026
0.0421*
(0.0223)
(0.0248)
(0.0234)
(0.0241)
Interaction term
Constant
-0.0012***
-0.0012**
(0.0004)
(0.0004)
2.3849***
2.3007***
2.2824***
2.2357***
(0.4005)
(0.3976)
(0.2925)
(0.1967)
Country effects
No
No
Yes
Yes
N
126
126
126
126
R2
0.0667
0.1700
0.2077
0.3025
Adj. R2
0.0515
0.1496
0.0657
0.1696
Note: Standard errors shown in parentheses.
*Significant at 10%, ** Significant at 5%, *** Significant at 1%
54
Table 3: Benchmark Parameter Values
α = 0.75
ω=2
σ=2
κ = 0.1
A=1
φ=0.1
r∗ = 0.01
N0 = 10
p = 0.95
Ω = 1.15
F (θ) = θ−τ
τ =100
55
Table 4: Simulation Results: Endogenous Product Differentiation
Pre-Devaluation
Post-Devaluation
% Variation
Macroeconomic Aggregates
Y
3.26
3.21
-1.44%
h
4.83
4.74
-1.91%
C
3.04
3.05
0.18%
L
P
0.23
0.22
-3.78%
l
P
0.02
0.03
43.26%
w
P
0.48
0.47
-1.91%
Variables Determining the Cost of Credit
R
0.6962
1.0041
44.23%
N
10.00
6.72
-32.84%
θ
1.11
1.09
-1.15%
θ
N
0.11
0.16
47.19%
R
P
0.6962
0.8731
25.42%
(1+R)
P (1+r ∗ )
1.68
1.73
2.74%
3.10
2.38
-23.27%
Implied Costs of Product Differentiation
θx
ΠF
7.27
9.63
32.52%
F (θ)
ΠB
0.24
1.12
368.07%
θx
Y
1.70
2.54
49.33%
F (θ)
Y
0.01
0.03
116.11%
F (θ)+ci
Y
4.92
2.27
-53.83%
Values correspond to a devaluation rate of 15%.
56
Table 5: Simulation Results: Exogenous Product Differentiation
Pre-Devaluation
Post-Devaluation
% Variation
Macroeconomic Aggregates
Y
3.26
3.21
-1.45
h
4.83
4.74
-1.93
C
3.04
3.05
0.13
L
P
0.23
0.22
-3.83
l
P
0.02
0.03
42.09
w
P
0.48
0.47
-1.93
Variables Determining the Cost of Credit
R
0.6963
1.0077
44.72
N
10.00
6.77
-32.32
θ
1.11
1.11
0.00
θ
N
0.11
0.16
47.75
R
P
0.6963
0.8763
25.85
(1+R)
P (1+r ∗ )
1.68
1.73
2.92
3.10
2.37
-23.46
Implied Costs of Product Differentiation
θx
ΠF
7.27
9.66
32.96
F (θ)
ΠB
0.24
0.35
47.58
θx
Y
1.70
2.55
49.92
F (θ)
Y
0.01
0.01
-31.32
F (θ)+ci
Y
4.92
2.29
-53.46
Values correspond to a devaluation rate of 15%.
57