Endogenous Financial Dollarization ¤ Christian Broda y Massachusetts Institute of Technology Eduardo Levy Yeyati z Universidad Torcuato Di Tella This Version: October 2001 Abstract This paper provides a simple dynamic framework to study the relation between the banking sector’s safety nets and the share of deposit dollariza- tion. It incorporates exchange rate risk in a model of …nancial intermedi- ation in a two-currency economy where banks have to choose the optimal currency composition of deposits to …nance their investments. We identify two sources of endogenous dollarization. First, common deposit and bank insurance schemes, by not discriminating between currencies, introduce a cross-transfer from local currency to foreign currency (dollar) deposits that favors deposit dollarization and results in an increased currency exposure of banks. Second, the presence of a lender of last resort, by reducing the cost of risk to banks, stimulates dollar …nancing. These results suggest that in most of the highly dollarized countries where banks are sensitive to devaluations, by simply measuring currency risk using the peso-dollar deposit spread we under-estimate the true currency risk. ¤ We are grateful to Miguel Broda, Rudi Dornbusch and Roberto Rigobon for their helpful comments. We also bene…ted from suggestions of participants at the International breakfast at MIT, the Conference on Exchange Rate Regimes at Universidad Di Tella and LACEA (2000) meeting . All remaining errors are our own. y Email: [email protected]z Email: [email protected]
Transcript
Endogenous Financial Dollarization¤
Christian Broday
Massachusetts Institute of Technology
Eduardo Levy Yeyatiz
Universidad Torcuato Di Tella
This Version: October 2001
Abstract
This paper provides a simple dynamic framework to study the relationbetween the banking sector’s safety nets and the share of deposit dollariza-tion. It incorporates exchange rate risk in a model of …nancial intermedi-ation in a two-currency economy where banks have to choose the optimalcurrency composition of deposits to …nance their investments. We identifytwo sources of endogenous dollarization. First, common deposit and bankinsurance schemes, by not discriminating between currencies, introduce across-transfer from local currency to foreign currency (dollar) deposits thatfavors deposit dollarization and results in an increased currency exposure ofbanks. Second, the presence of a lender of last resort, by reducing the cost ofrisk to banks, stimulates dollar …nancing. These results suggest that in mostof the highly dollarized countries where banks are sensitive to devaluations,by simply measuring currency risk using the peso-dollar deposit spread weunder-estimate the true currency risk.
¤We are grateful to Miguel Broda, Rudi Dornbusch and Roberto Rigobon for their helpfulcomments. We also bene…ted from suggestions of participants at the International breakfast atMIT, the Conference on Exchange Rate Regimes at Universidad Di Tella and LACEA (2000)meeting . All remaining errors are our own.
Financial dollarization1 is a widespread phenomenon among developing economies.In countries like Argentina, Bolivia, Latvia and Lithuania among others the shareof foreign currency deposits exceeds 40%.2 In many of these countries, this prac-tice began as unexpected in‡ation increased and domestic residents turned toforeign money as a store of value to avoid the domestic currency’s rapid depreci-ation rate. This can be readily seen in the large increase in the share of foreigncurrency deposits in these countries in periods of high in‡ation. However, despitethe local currencies being successfully stabilized and …nancial markets deepening,time-deposits are still largely denominated in foreign currency.
Much of the literature that has tried to explain the process of dollarizationhas focused on currency substitution even though the bulk of dollarization hasoccurred in the savings component of broad money.3,4 On the other hand, thestrand of the literature that has focused on asset substitution has concentrated ona dollarization process driven by the depositors’ optimal portfolio choice.5 Sahayand Vegh (1996) and Balino et al. (1999) show that interest rate di¤erentialshelp explain swings in deposit dollarization in Eastern Europe, but have muchless success in explaining dollarization patterns in Latin America. By constrast,Ize and Levy Yeyati (1998) derive minimun variance portfolio (MVP) allocationsfor risk averse borrowers and lenders, and …nd that MVP dollarization closelyresembles actual dollarization for a broad sample of countries.6 However, thesepapers do not model …nancial intemediation explicitly and thus abstract fromimportant aspect such as currency mismatch and default risk.
1The term “dollarization” is applied generically to the use of foreign currency assets andliabilites, although in some cases the dollar is not the main foreign currency of choice of domesticresidents.
2Balino et al. (1999) de…ne a country as highly “dollarized” when Foreign Currency De-posits (FCD) exceed 30% of deposits. They …nd eighteen developing countries that satisfy thiscriterium.
3See Guidotti and Rodriguez (1992) and Sturzennegger (1997) for “hysteresis” models ofcurrency substitution. As noted by Calvo and Vegh (1992), among others, much of the empiricalliterature is plagued by a de…nitional prolbem, as interest bearing deposits are used to estimatemoney demand equations due to lack of adequate data.
4Moreover, in only some cases, notably in Latin America in the midst of a hyperin‡ation,domestic currencies were substituted as a medium of exchange. However, once the hyperin‡ationwas over, the local currency was quickly reestablished as the main medium of exchange.
5See Thomas (1985) for an early example.6For an application of a CAPM model to explain the patterns of dollarization in Bolivia and
Peru, see McNellis and Rojas-Suárez (1996) . Since income is positively correlated with thedepreciation of the local currency, agents will want to demand dollar assets to escape from thepositive correlation between income and return of peso assets.
This paper attempts to remedy these shortcomings. Building on the assetsubstitution approach, we present a model of …nancial intermediation in a two-currency economy where banks have to choose the optimal currency compositionof deposits to …nance their investments. In the event of a sudden devaluation, theerosion of the dollar value of peso-denominated assets impinges on the debtors’capacity to repay, either of dollar indebted …rms or of currency imbalanced banks.7
In this context, dollar depositors are protected againts exchange rate ‡uctuationswhenever the devaluation does not precipitate a default, while they share thelosses with peso depositors in the case of default. Using this setup we study theconnection between safety nets8 and the banks’ …nancing (or hedging) strategies.
The model identi…es two alternative sources of endogenous dollarization. Onthe one hand, common banking system safety nets, by not discriminating betweencurrencies, induce a cross-transfer from local (pesos) to foreign currency (dollar)deposits that favors dollarization and results in an increased currency exposureof banks.9 The intuition behind this result is straightforward. In the event of abank default, depositors are (partially) reimbursed according to some distribu-tion scheme. If this scheme treats deposits of di¤erent currencies symetrically(say, it returns ± pesos (dollars) for every 1 peso (dollar) deposit), since bankdefaults are associated with exchange rate depreciations, it extends the exchangerate insurance of dollar deposits to the default scenario. As a result, depositorsdemand a high peso-dollar spread to compensate for this additional insurancecoverage. Since banks do not face the higher costs of dollar deposits in the eventof default, this high peso-dollar spread reduces the e¤ective cost of dollar relativeto peso borrowing, creating an incentive for banks to raise the share of dollar de-posits. Interestingly, an explicit deposit insurance scheme is not needed to attainthis result: for example, if the residual asset value of a failed bank is distributed
7Even if banks are currency balanced, this risk still exists insofar as the level of …nancialdollarization exceeds the fraction of the real economy e¤ectively dollarized. Gavin and Hausmann(1996) recognize this has played an important role in the Chilean banking crisis of 1982, “in adollarized economy where the exchange rate has been credibly …xed, the strutcture of assets andliabiities will re‡ect the expectations of exchange rate stability, which will cause an accumulationof dollar-denominated debt in both the notradable and household sector. This will make anexchange rate adjustmnet particularly devastating for bank solvency since ther will be sign…cantexchange rate risk hidden in the form of credit risk, as in the Chilean crisis of 1982.”
8By safety nets we understand two aspects in particular: the recovery value of bank depositsin case of default (through the liquidation of the residual value of the failed bank’s assets, orthrough a deposit insurance scheme) and bank insurance (speci…cally, the presence of a lenderof last resort that bails out banks in distress).
9 In general, a di¤erent treatment of foreign currency deposits from local currency depositsis more often the exception than the rule. For instance, Garcia (1999) presents an extensivesurvey on deposit insurance and shows that out of a sample of 72 countries only 20 discriminateagainst foreign currency deposits by not being included in the insurance coverage.
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in proportion of the current value of the bank’s liabilities,10 dollar deposits stillbene…t from partial exchange rate insurance at the expense of peso deposits.11
The second source of …nancial dollarization mentioned above arises directlyfrom the presence of bank insurance. For example, a lender of last resort thatprovides limited liquidity insurance to the bank in the event of a large devaluation,reduces the costs of risk-taking, which in the previous context entails a higherdollar share of deposits.12 Therefore, banks will be willing to increase their level ofdollarization as part of the cost of this action is transferred to the provider of thebank insurance services, or to the other insured banks. This result is analogousto that in Kareken and Wallace (1978) and Burnside et al. (1999). These authors…nd that, in the presence of government guarantees, it is optimal for limitedliability banks to hold as risky a portfolio as permissible to maximize the value ofthe guarantee. In our model, however, full dollarization is mitigated because ofan additional intertemporal e¤ect that reduces the incentive to dollarize as riskincreases.13
Driving both sources of endogenous dollarization is the equal treatment ofpeso and dollar deposits in the event of a bank default despite dollar depositsbeing the source of risk in the model. This treatment is not unusual in practice.Bankruptcy laws do not adjust creditors’ assets for their currency of denomina-tion.14 Similarly, deposit insurance schemes tend to cover both local and foreigncurrency deposits in the same terms15. The case of a lender of last resort is evenclearer, since central banks are not known to base their assistance to particularbanks on the currency composition of their portfolios above and beyond what itis required by prudential regulations.16
10We show that this is equivalent to the symmetric scheme mentioned above.11Demirguc-Kunt and Detragiache (2000) present evidence that a deposit insurance that in-
cludes covers foreign-currency assets increases the probability of a bank run. They suggest thatthe underlying reason is no di¤erent from the moral hazard typically associated with depositinsurance, that is, that banks’ ability to attract deposits no longer re‡ects the risk of their assetportfolio, thereby inducing excessive risk-taking (on this, see also Freixas and Rochet (1997)Ch.9). In this paper, we provide an alternative intepretation of their …ndings.12 In a separate but related literature, Mishkin (1996) and Obstfeld (1998) argue that in many
cases a government’s promise to maintain the exchange rate …xed is seen as providing an implicitgovernment guarantee for dollar bank deposits against a possible devaluation. In this paper, wedo not allow the government to avoid default by preventing the exchange rate to devalue.13Blum (1999) describes a similar e¤ect when assessing the e¤ect of capital adequacy rules in
the banks’ riskiness. Suarez (1993) …nds bang-bang solutions analogous to those in our paper.14For a summary of how prudential regulation deal with the measurement of foreign exchange
risk, see Abrams and Beato (1998).15For an overview of deposit insurance in both developed and developing countries, see Kyei
(1995) and Garcia (1999).16However, we show that it is easy to conceive (although possibly di¢cult to implement)
An important, and often overlooked, consequence of the previous discussionis the fact that the peso-dollar premium, as measured from the market rates ofreturn in each currency, is not independent of the existence of either deposit orbank insurance. We show that as long as there is a probability of default thepeso-dollar spread will underestimate the true currency risk. Moreover, givendevaluation expectations, di¤erent degrees of insurance across countries shouldbe associated with di¤erent measured currency risks even though the underlyingtrue risk may be identical.
The paper proceeds as follows. In section 2 we present the basic model,and describe the centralized and decentralized equilibria with no safety nets. Insection 3 we analyze, in turn, how a DIS and a LLR can a¤ect the peso-dollardeposit spread and the level of dollarization in the economy. In section 4 wediscuss the implications of the results for the measure of currency risk based onmarket rates. In section 5 we extend the model to include liquidity services ondeposits. In section 6 we present some …nal remarks and suggest some empiricaland normative applications of the theory presented.
2. The Model
This section examines a simple dynamic framework to study the relation betweenthe …nancial sector’s safety nets and the currency composition of banks’ depositportfolio in a two-currency banking system. We introduce how the banks, depos-itors and Central Bank behave in an economy with exchange rate risk as the onlysource of risk.
Consider limited liability banks that are endowed with a technology that con-verts 1 dollar (or 1=e pesos, where e is the dollar/peso exchange rate) into Rpesos. R denotes (gross) returns on bank assets, assumed to be …xed in pesoterms. This assumption tries to capture the fact that whenever the degree of…nancial dollarization exceeds the fraction of the real economy e¤ectively dollar-ized, there is a currency mismatch somewhere in the economy. In the event ofa sudden devaluation, the erosion of the dollar value of peso-denominated assetsimpinges on the debtors’ capacity to repay, either of dollar indebted …rms or ofcurrency imbalanced banks. For simplicity, we model this currency mismatch inthe bank’s balance sheet.17 Each bank has to decide the optimal currency com-
LLR rules that condition its assistance on the degree of dollarization, eliminating the source ofdistortion.17An alternative would be to eliminate the bank’s currency mismatch by imposing some cur-
rency mismatch regulation and introducing …rms which have to borrow from the bank to invest.Since for every dollar deposit the bank receives it has to give a dollar loan, some of the …rmswill be indebted in dollars but still receive all their income in pesos. In other words, loans are
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position of its liability portfolio (or hedging strategy). Assuming the nature ofthe problem is recursive and expressing values in dollar terms, we can representit as:
V = max¸
1Xi=0
½iP (¸i) ¼ (¸i) = max¸
¼ (¸)
1 ¡ ½P (¸); (2.1)
¼ (¸) =
Z 1
0max [0; e(R ¡ (1 ¡ ¸)rp) ¡ ¸rd)] f(e)de (2.2)
where ¸ is the share of dollar deposits, rp and rd are the (gross) returns of pesoand dollar deposits respectively, P (¸) is the probability that the bank does notdefault18, f(e) is the p.d.f. of the exchange rate at the end of the period (withsupport [0; 1] and mean equal to em), and the current exchange rate is normalizedto e0 = 1: We can think of e as driven by an exogenous shock, with low values(large depreciations) corresponding to bad states of nature. Finally, for simplicity,we assume that the distribution of end-of-period devaluation rates is identical ineach period (ie., does not depend on history).
The pro…t function can be restated as:
¼ =
Z 1
ec(¸)[e(R¡(1¡¸)rp)¡¸rd]f(e)de = P (¸)[e(¸) (R ¡ (1 ¡ ¸)rp)+¸rd] (2.3)
where ec denotes the critical value of end-of period exchange rate below whichbank liabilities exceed bank assets, and e(¸) is the average exchange rate condi-tional on the bank’s not defaulting, that is,
ec (¸) ´ ¸rd
R ¡ (1 ¡ ¸) rp;
P (¸) =
Z 1
ec(¸)f(e)de; (2.4)
e(¸) =
R 1ec(¸) ef(e)de
P (¸):
In case the bank defaults and in the absence of both deposit and bank insur-ance, it is liquidated at a discount 0 < µ · 1: We will discuss below how the value
in dollars but not in dollar producing sectors. The currency mismatch is simply shifted to the…rms. With the assumption in the main text we are simply merging the bank and the …rms.18For future reference note that P 0 < 0 since e0
c > 0.
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of the liquidated bank (µR) is divided among peso and dollar depositors. Finally,we assume that R is such that, for any degree of dollarization, ec < em.19
To make our argument as plain as possible, we focus on the e¤ect of the banks’behavior on the share of dollar deposits and make the depositor’s portfolio decisionproblem simple.20 We assume that depositors are risk neutral and they can eitherinvest in dollar deposits, peso deposits or an outside risk-free asset with returnrf > 1. This implies that depositors are indi¤erent to the currency denominationof the deposits as long as:
rep =
Z 1
0eerpf(e)de = rf =
Z 1
0erdf(e)de = re
d (2.5)
where eri equals ri if the bank does not default, and whatever return they receivefrom the CB (or the insurer) in case of default. Depositors do not observe thebank’s dollarization share. Thus, we implicitly assume that the bank cannotcommit to a posted interest rate, re‡ecting the fact that rates are customarilypacted with each client on a personal basis.
2.1. Centralized equilibrium
As a useful benchmark, we present the solution for the optimal dollarizationshare in a centralized equilibrium. A risk neutral central planner maximizes theexpected return of the investment minus expected funding and liquidation coststaking into account the e¤ect the composition of liabilities has on the depositsinterest rates. Replacing (2.5) into (2.1) before computing the FOC of the bank,we obtain:
max¸
1Xi=0
½i
·ZeRf (e) de ¡ rf
¸=max
¸
emR ¡ rf ¡ [1 ¡ P (¸)] (1 ¡ µ) eR
1 ¡ ½: (2.6)
Proposition 1. When µ < 1; the optimal share of dollar deposits is ¸¤ = 0.When µ = 1 the central planner is indi¤erent between the composition of fund-ing.21
19A su¢cient condition for this to happen is:
(1 ¡ F (em)) emR ¸ rf :
20For a more complete discussion of this portfolio decision see Ize-Levy Yeyati (1998)).21 It follows from the condition on R of the previous footnote that R is big enough for invest-
ment to be optimal.
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P roof. mmediately from 2.6.
In other words, when there are liquidation costs it is optimal for banks tofully hedge exchange rate risk by demanding no dollar deposits. This propositionis analogous to the results in the paper by Kareken and Wallace (1978).22 Theintuition is straightforward: since the central planner internalizes the e¤ect ¸ hason rp(¸) and rd(¸) dollarization does not entail any gain in terms of cheaperfunding costs, while on the other hand generates a potential risk of default withthe associated loss in terms of liquidation costs.
2.2. Decentralized equilibrium
In the absence of a deposit or bank insurance scheme, interest rates depend cru-cially on the way the CB distributes the remaining bank’s assets among depositorsin case of failure. They are several ways in which the residual valueof the bankcan be distributed among creditors (depositors) in the event of bankruptcy. Forexample, it can realistically be assumed that, in the absence of seniority of anyparticular depositor, this value is distributed in proportion to the value (includingprincipal and interest) of each deposit. Thus, for every 1 peso (dollar) deposited,depositors receive a fraction ±rp pesos (±rd dollars) back, where23
± (¸; e) =eµR
e(1 ¡ ¸)rp + ¸rd: (2.7)
Then, de…ning Si as the expected recovery rate (expressed in dollar terms)for deposits denominated in currency i, conditional to the event of default,
Sd =
Z ec
0± (¸; e) f (e) de
Sp =
Z ec
0e £ ± (¸; e) f (e) de: (2.8)
It is inmediate to see that this scheme implies Sd > Sp.24 In other words, sincethe scheme distributes the residual value of the bank in proportion to the ex-post22They show that with no government guarantees (in their case, deposit insurance) the pres-
ence of bankruptcy costs induce banks to avoid bankruptcy states which implies fully hedgingagainst the existing risk. It also closely resembles Proposition 4.1 in Burnside et al. (1999).23Note that, for any ex-post exchange rate e < ec such that the bank defaults, the distribution
has to satisfy:± [(1 ¡ ¸)erp + ¸rd] = eµR:
24 It can be shown that this is the case for any scheme that recognizes (at least part of) theinsurance value of dollar deposits in the case of default.
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value of deposits, it preserves (part of) the currency risk insurance implicit indollar assets. Moreover, the larger the recovery rate ±, the larger the bene…ts ofdollar deposits.25
In turn, depositors’ expected returns (and deposit rates) must satisfy thefollowing arbitrage conditions:
rep = rp [P (¸)e + Sp(¸)] = re
d = rd [P (¸) + Sd (¸)] = rf ; (2.9)
it follows that the peso-dollar spread is given by:
rp
rd=
1
e£ s (¸) ; (2.10)
where
s (¸) =P (¸) +
R ec
0 ± (¸; e) f (e) de
P (¸) +R ec
0 ± (¸; e) eef (e) de
> 1 (2.11)
is a measure of the expected cross-transfer from peso deposits to dollar deposits inthe event of a default, and is strictly positive for any deposit dollarization ratio.Note that s > 1 implies a positive di¤erence in the salvage value of depositsin each of the two currencies (Sdrd ¡ Sprp) : This, in turn, is the case with anyliquidation scheme that at least partially recognizes the insurance value of dollardeposits in case of bank default.
A Nash equilibrium equilibrium is de…ned as the triplet (¸D; rp;rd) such thatthe bank maximizes (2.1), condition 2.9 hold, and ¸D = ¸e.
Di¤erentiating (2.1) with respect to the dollarization ratio, we obtain thefollowing FOC:
@V
@¸=
1
1 ¡ ½P (¸)
¡¼0 + ½P 0V
¢(2.12)
In turn, using e0 = ¡e0c(¸)f(ec)ec
P ¡ P 0eP = P 0
P (ec ¡ e), we get
¼0 =¡P 0e + Pe0¢ (R ¡ (1 ¡ ¸)rp) ¡ P 0¸rd + P (erp ¡ rd)
= Sdrd ¡ Sprp = rdP (s (¸) ¡ 1) > 0
25Among the many alternative distribution schemes we can think of, a useful benchmark isprovided by an scheme ensures depositors the same (dollar) …xed return per unit of deposit(independent of its currency of denomination), so that:
Sp = Sd = µR
Z ec
0
± (¸; e) f (e) de = [1 ¡ P (¸)] µeR;
where e is the expected exchange rate conditional to e < ec.
9
and¼00 = P 0 (ecrp ¡ rd) ¸ 0: (2.13)
Then, the reader can easily see that:i) In the presence of the cross-transfer s > 1 the solution to the static problem
(maximization of current pro…ts) is always at the corner ¸ = 1,26
ii) There is an intertemporal e¤ect that reduces the incentive to dollarize, asthe bank’s expected future value falls by the term ½P 0V when the share of dollardeposits increases.
If the latter is small enough, the stimulus to dollarize prevails, eventuallyleading to full dollarization, as the following proposition formally states:
Proposition 2. For P 00 ¸ 0 (alternatively, for ½ su¢ciently small), s > 1 impliesfull dollarization (¸D = 1) in the decentralized equilibrium. When s · 1 instead,¸D = 0 as in the centralized equilibium (complete exchange rate risk hedging).
P roof. See appendix.To understand the intuition behind this proposition take the case where s >
1. This implies a higher salvage value for dollar relative to pesos deposits andtherefore depositors demand a high peso-dollar spread to compensate for thisadditional insurance coverage. However, since the way depositors are reimbursedin the event of default does not a¤ect the e¤ective relative funding costs of thebank (given by 1
e ); this high peso-dollar spread understates the e¤ective relativecost of dollar funding to the bank, creating an incentive to dollarize. It is thisincentive, typical of bimonetary economies, that induces endogenous dollarization.More generally, proposition 2 implies that when depositors perceive that the CBwil not discriminate across currencies in case of default, it is in the banks’ interestto increase the share of dollar deposits.
A di¤erent way to examine the above proposition is by comparing the hy-pothetical case of banks specialized by currency with a bank that has liabilitiesin both currencies. In the case of specialized banks, risk is assigned accordingto their sources: only the dollar rate is adjusted for default risk, while the pesorate continues to be a¤ected by devaluation expectations. From r0
d (¸) > 0 andr0
p (¸) > 0 27 we can directly infer that for any given ¸, the peso dollar spread
26The problem is convex, and ¼0 ¸ 0 for all ¸:27Fully di¤erentiating (2.5) and (2.6) and rearranging:
r0d = e0
c
[rd ¡ ± (¸; ec)] f (ec) ¡ R ec
0±0 (¸; e) f (e) deR 1
ecf (e) de
> 0 (2.14)
10
narrows in this case, since:
rpj¸=0 =rf ¡ Sp (0)
e (0) P (0)=
rf
em<
rf ¡ Sp (¸)
eP (¸);
rdj¸=1 =rf ¡ Sd(1)
P (1)¸ rf ¡ Sd
P (¸): (2.16)
Thus, dual-currency banks, by aggregating both portfolios, transfer part ofthe devaluation-related exchange rate risk to peso depositors, bene…tting dollarholders by reducing the set of default events (e0
c (¸) > 0) and enhancing the bank’sprobability of survival in the process. Then, in the absence of a cross-transfer(s = 1), the peso-dollar spread simply re‡ects exchange rate risk considerations,as default risk a¤ects deposits in both currencies in the same way and correctlycapture the relative cost of borrowing in di¤erent currencies for the bank. How-ever, when the CB recognizes part of the insurance value of dollar deposits in theevent of a default (Sd > Sp), it widens of the peso-dollar spread and thereforeinduces an incentive to increase the share of dollar deposits.
Indeed, banks would be better o¤ if they could commit not dollarize at all.This can be easily veri…ed by noting that specialized dollar banks would be lesspro…table than peso ones;28 hence, they would not exist in equilibrium. However,given this automatic transfer implicit in the distribution of the residual bankvalue, it is optimal for banks to pro…t from the wide peso premium by increasingtheir dollar funding. Then, in this simple example, dollarization is solely due tothe cross-transfers implicit in the distribution mechanism.
3. Insurance
In the previous section we showed how the loss sharing implicit in default eventsresulted in endogenous dollarization. Now we introduce deposit and bank in-surance and show how either or both safety nets may introduce incentives todollarize.
3.1. Deposit insurance
The argument of the previous example can be applied to analyze the e¤ect ofan implicit or explicit DIS on the share of dollar deposits. Assume for simplicity
r0p = e0
c
[rp ¡ ± (¸; ec)] ecf (ec) ¡ R ec
0e±0 (¸; e) f (e) deR 1
ecef (e) de
> 0 (2.15)
28This can be readily seen from: ¼D = [P (1)e(1) + (1 ¡ P (1))e(1)µ]R ¡ rf < emR ¡ rf
11
that a full DIS is …nanced through lump sum taxes on depositors.29
The …rst thing to note is that, as long as the insurance scheme covers bothpeso and dollar deposits,30 the peso-dollar spread now depends on the expecteddevaluation em. That is,
rp
rd=
1
em· 1
¹e(3.1)
while both deposit rates are default risk-free and, in particular, rd = rf . Thus,the DIS enhances the insurance properties of the dollar by enlarging the set ofevents under which dollar depositors are fully protected, in contrast with theprevious case in which this insurance was only partial.
Proposition 1. With a full DIS, the equilibium share of dollarization is weaklyhigher than in the centralized equilibrium,
¸D ¸ ¸¤ = 0
P roof. ows directly from (2.14).
It is useful to illustrate the incremental e¤ect of the DIS by looking at thecross tranfer in (2.11). In this context, a full DIS simply makes the recovery rate± (¸; e) = 1 for any realization of the exchange rate.
In turn, it is immediate to verify that s (¸) depends positively on the recoveryrate:
s (¸) =P (¸) + ±
R ec
0 f (e) de
P (¸) + ±R ec
0eef (e) de
: (3.2)
Thus, any partial insurance that reimburses a fraction of deposits ± = max f± (¸; e) ; kg,where k 2 (0; 1), increases the cross-transfer and, in turn, the peso-dollar spread,for a given level of dollarization.31
Note that, as in Proposition 2, this result is driven by the e¤ect the DIS hason the current relative pricing of deposits and not from the well known moralhazard consequences of DIS.32 It is also interesting to note that whenever the29We will return to this issue in subsection 3.3. The analysis can be easily generalized to a
partial DIS.30Garcia (1999) shows that this is the case in most developing countries.31Naturally, the result is ambiguous when the …xed DIS coverage ± can be either above or
below the recovery rate in the absence of default. However, ± < ± (¸; e) would imply thatdepositors are given less than the residual value of the bank, with the di¤erence accruing to theDIS agency, an arguably unrealistic situation.32See Freixas and Rochet (1997) and Suarez (1993) for a discussion of this in a setup where
banks choose their risky asset portfolios.
12
cost of the DIS is sustained by the government, the mechanism is no di¤erentthan a tax on peso depositors which proceeds are transferred to dollar depositorsin case of bank default. Peso (dollar) depositors react by demanding a higher(lower) rate, which in turn fuels dollarization. However, the result still holdswhen the DIS is funded through bank contributions (e.g., a tax on pro…ts), aslong as the insurance premium does not depend on risk (i.e., the currency ofdenomination).33
3.2. Bank insurance (lender of last resort)
In the absence of deposit insurance, a LLR policy (or any other bank insurancepolicy) has the same e¤ect as a DIS inasmuch as it enlarges the range of end-of-period exchange rates over which dollar depositors are insulated from exchangerate risk.34 However, as opposed to deposit insurance, the LLR introduces anew incentive to dollarize beyond and above the channel analyzed in the previousexamples. To distinguish between these two di¤erent channels, we assume in hatfollows that depositors are already covered by a full DIS.
For the moment, we make the (realistic) assumption that the LLR policy isblind to the degree of dollarization of the failed institution. The blanket LLRpolicy that we have in mind is the following: whenever the exchange rate at theend of the period falls below ec, with a probability ¯ the central bank coversthe gap between bank assets and liabilities at no cost. The bank’s probability ofsurvival is then given by
b (¸) = (1 ¡ ¯)P (¸) + ¯; (3.3)
where b (¸) > P (¸) and 0 > b0 (¸) = (1 ¡ ¯)P 0 (¸) > P 0 (¸) : The bank’s problemthen becomes:
VLLR = max¸
P (¸) [e (¸) R ¡ C (¸)]
1 ¡ ½b (¸); (3.4)
Proposition 2. Under a blanket LLR policy, the equilibrium level of dollariza-tion is weakly higher than otherwise,
¸LLR ¸ ¸D: (3.5)
33 In this case, VDIS = (1 ¡ ¿) max¸¼(¸)
1¡±P (¸)
and the tax ¿ = (1 ¡ P (¸e)) [(1 ¡ ¸e) e (¸e) rp + ¸erd] is computed ex-ante based on rationalexpectations, so that the expected net outlays of the DIS are fully funded by banks.34For bank insurance we understand any policy that, in the event of a devaluations that
renders banks insolvent, provides the needed funds to cover banks liabilities and avoid default.
13
P roof. It follows directly from:
@VLLR
@¸=
1
1 ¡ ½b (¸)
¡¼0 + ½b0VLLR
¢;
b (¸) > P (¸) and b0 (¸) > P 0 (¸) :Thus, a LLR policy results in a reduction in the cost of risk to the banks
(the loss of future rents) that induces risk-taking incentives, which in the contextof our model can only take the form of engaging in less costly (although riskier)dollar funding. It should be clear to the reader that these results rely on the (quiterealistic) assumption that the LLR facility is available to banks irrespective oftheir dollarization ratio, so that the chances of preserving the insurance bene…tsin the event of a devaluation are enhanced, without any increase in the e¤ectivecost of dollar funding to the bank. In other words, the bank bene…ts from lowerdollar rates, transferring the cost to the LLR.35
However, it is easy to conceive a LLR rule contingent on the degree of dol-larization of the bank, such that ¯ (¸), ¯0 (¸) < 0, which can readily undo thedistortion associated with the insurance policy. In this case,
b0 (¸) = (1 ¡ ¯)P 0 + (1 ¡ P )¯0; (3.6)
which can be set to the desired level of dollarization by making ¯ (¸) arbitrarilysteeper.
Proposition 4 is analogous to results in Kareken and Wallace (1978) and Burn-side et al (1999). The nature of the government guarantee is, however, di¤erentin this paper and this result does not depend on the existence of bankruptcy costsas in the mentioned papers. Furthermore, in this context the banks’ portfolio de-cision is the currency compostion of liabilities instead of choosing their portfolioof assets.
4. Empirical measurement of currency risk
Currency risk is typically (albeit incorrectly) used to denote both the currency riskpremium as directly measured from di¤erential returns on assets denominated inlocal and foreing currency, and exchange rate (devaluation) expectations. On theother hand, deposit and lending rate di¤erentialials are usually used to computedevaluation expectations. In what follows, we adopt the second use of the term35Again, the results remains true even if the LLR facility is fully funded through a tax on
to study how currency risk is re‡ected in interest rate spreads. More precisely,in this section we exploit an important, and often overlooked, consequence ofthe previous discussion is the fact that the peso-dollar premium, as measuredfrom the market rates of return in each currency, is not independent from eitherthe …nancial dollarization ratio or the existence of deposit or bank insurance.36
Moreover, tis mismeasurement is itself correlated with the true level of currencyrisk.
4.1. Currency risk and currency premium
In the abscence of insurance, the arbitrage condition (2.9) can be written as:
rp
rd=
1 ¡ R ec
0 (1 ¡ ± (¸; e)) f (e) de
em ¡ R ec
0 (1 ¡ ± (¸; e)) ef (e) de=
1
em£ t (¸)
where (using ec < em):
t (¸) =1 ¡ R ec
0 (1 ¡ ± (¸; e)) f (e) de
1 ¡ R ec
0 (1 ¡ ± (¸; e)) eem f (e) de
< 1
Hence, inasmuch as there is some risk of default, the peso-dollar spread un-derestimates the true currency risk. Moreover, it is easy to check that the higherthe bankruptcy cost (the smaller µ), the smaller the peso-dollar spread and thehigher its di¤erence with the true currency risk.37
It can also be shown that this di¤erence is higher for low levels of dollarization.TO see this, …rst note that, form (2:4) and (2:7), we know that the maximalrecovery rate ± (¸; e) < µ: In turn, using P 0 < 0;
±1 (¸; e)0 = eµRerp ¡ rd ¡ e (1 ¡ ¸) r0
p ¡ ¸r0d
[e (1 ¡ ¸) rp + ¸rd]2< 0:
Finally, using (4:1), dtd¸ < 0 follows from :·
1 ¡Z ec
0[1 ¡ ± (¸; e)]
e
emf (e) de
¸ ·e0
c [1 ¡ ± (¸; ec)] f (ec) ¡Z ec
0±1 (¸; e)0 f (e) de
¸>
ec
em
·1 ¡
Z ec
0[1 ¡ ± (¸; e)] f (e) de
¸ ·e0
c [1 ¡ ± (¸; ec)] f (ec) ¡Z ec
0± (¸; e)0 e
ecf (e) de
¸36There are other asset-speci…c factors that may in‡uence the currency risk premium, such as
counterparty risk. See Schmukler and Serven (2001).37Trivially, for su¢ciently high bankruptcy costs, the recovery value of depositors falls to cero
and the exchange rate insurance is limited to those states of nature in which the bank does notdefault
15
The intuition behind the result is simple. As dollarization increases, both therecovery rate and the range of exchange rate realizations for which exchange raterisk is perfectly insured by dollar depoists decline, making dollar deposits rela-tively less attractive. Conversely, the peso-dollar spread declines as we approachzero dollarization, converginf to currency risk in the limit.38
4.2. The impact of deposit insurance
In this case, since a full DIS completely assures the depositors that they will berepayed no matter what the exchange rate turns out to be, the spread is solelydetermined by the depositors’ behavior, namely
rp
rd=
1
em
Hence, the currency risk is correctly measured. However, when the DIS is notfull (that is, ± = max (±(¸; e); k) where k ² (0; 1)) the equilibrium peso premiumis always weakly smaller than the true currency risk. The following Propositionsummarizes these results:
Proposition 1. For all ±, the peso-dollar spread (weakly) under-estimates thetrue currency risk.:
P roof. De…ne ± =
8<:¸¤ = 0 if ± < ±
¸¤² [0; 1] if ± = ±
¸¤ = 1 if ± > ±
Then,
i) For 0 < ± < ±; it follows immediately from ¸¤ = 0:that rp
rd= 1
em :
ii) For ± = ±; the equilibrium peso-dollar spread is unde…ned in the rangehs(1)e(1) ; 1
em
iiii) For 1 > ± > ±; the equilibrium spread, rp
rd; increases monotonically to 1
em
.This follows from the result of full dollarization combined with ds(¸)d± > 0 and the
full DIS above result.In general, then, the peso premium will be the highest in assets that are ex-
pected to be covered by government guarantees, though still smaller than the truecurrency risk. We can easily extend the argument to other …nancial instruments:for example, a haircut on the accruances of bondholders in both currencies39.
38Note that with zero dollarization, default risk disappears, as does the inuence of theimplicit cross-transfer in the default states.39See Neumeyer and Nicolini (2000) for an application to bonds.
16
5. Conclusions
This paper presents a simple framework for understanding the e¤ect of …nancialsector safety nets on the share of deposit dollarization. It incorporates exchangerate risk in a model of a two-currency banking sector where banks choose thecurrency composition of their deposit portfolio with a given asset structure. Theexistence of safety nets has an e¤ect on the pricing of deposits that depends onthe compositional coverage of the scheme and on the circumstances under whichthe bank defaults.
We …nd general results relating the characteristics of the safety net schemeand the composition of deposits. In particular, the most common and feasiblecharacteristics of safety nets are found to induce a bias towards increasing theshare of dollar deposits and the currency exposure of the economy. That is,when safety nets do not discriminate between currencies, part of the exchangerate insurance of dollar deposits is extended to the default scenario. Depositorsdemand a higher peso-dollar spread accordingly but banks must only pay for thedeposits in case of no default. Hence these types of safety nets introduce a costadvantage that induce banks to rely more heavily on dollar deposits for their…nancing.
In addition, the paper shows that in the presence of a lender of last resort, thecosts of risk taking are reduced since the bank will be bailed out with a certainprobability. The moral hazard created by the presence of bank insurance inducesbanks to have a more risky behavior. In the context of the model, this implies thatbanks will increase their share of dollar deposits and introduce a larger currencyexposure to the economy as a whole.
In the model, the interaction between the optimal share of dollar depositsand the characteristics of the safety nets determine the peso-dollar spread. Weshow that as long as there is a probability of default the peso-dollar spread willunderestimate the true currency risk. Moreover, given devaluation expectations,di¤erent degrees of insurance across countries should be associated with di¤erentmeasured currency risks even though the underlying true risk may be identical.In future work we intend to test some of the positive implications of this modelin the data.
17
References
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[3] Blum, J (1999), ”Do Capital Adequatcy Requirements reduce risk in bank-ing?,” Journal of Banking & Finance,23, 755-771.
[4] Burnside, C., M. Eichenbaum and S.Rebelo (1999), Hedging and FinancialFragility in Fixed Exchange Rate Regimes,” NBER Working Paper No.7143.
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[7] Freixas and Rochet (1997), Microeconomics of Banking, MIT Press.
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[9] Gavin, M.and R.Hausmann (1996), ”The roots of Banking Crises: TheMacroeconoimc Context,” in Hausmann and Rojas Suarez eds., BankingCrises in Latin America. Washington, DC: Inter-American DevelopmentBank.
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[12] Kareken, J. and N.Wallace (1978), ”Deposit Insurance and Bank Regulation:A Partial Equillibrium Exposition,” Journal of Business, 51,413-438.
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Suppose that b̧ 2 (0; 1) is an interior equilibrium (FOC = 0). Then,
SOC =1
1 ¡ ±P (¸)
£¼00 + ±P 00V
¤> 0:
and, by contradiction, the equilibrium can only be at a corner.We can compute a ±c such that for ± ¸ ±c, ¸ = 1. Assuming that ¸e = 1, and
denoting by the subindex the value of ¸ (alt., the corner), the condition to satisfyis:
¢1 ´ V1 ¡ V0 =P1
1 ¡ ±P1
µe1R ¡ rf
P1
¶¡ 1
1 ¡ ±
µemR ¡ rf
P1£ em (1 + s1)
e1
¶> 0;
(6.4)so that a bank does not deviate from the full dollarization equilibrium. Rear-ranging (2.8), we obtain:
± · ±c1 ´ 1
P1£
em
e1£ rf
P1s1 ¡ (em ¡ P1e1)
³R ¡ rf
P1e1
´em
e1£ rf
P1s1 + (e1 ¡ em)
³R ¡ rf
P1e1
´ :
6.1. Financing
As was mentioned in the main text, one can think of several inobstrusive waysof …nancing either the DIS or a LLR. For the purpose of the model, the easiestway is an up-front tax on pro…ts that does not interfere with the bank’s problem,or an ex-post lump-sum tax on depositors (including the issuance of public debtto distribute this tax over a longer time period). Whenever the …nancing needscannot be resolved through taxes (or, similarly, when projected …scal de…citsinduce current in‡ation), there is still an in‡ation tax such that holders of pesos(consumers in general) and peso assets cross-subsidize dollar asset holders. In
20
this case, however, the injection of peso liquidity that drives up prices may havea feed-back e¤ect the exchange rate.40
An interesting aspect of the problem, and one that we implicitly assumed,is that, as long as dollar deposits do not require repayment in hard currency(alternatively, as long as banks are allowed to convert dollar deposits at theattendant exchange rate) there is always a tax that redistributes resources frompeso to dollar holders without the need to resort to dollar reserves. Note that inprinciple, since the dollar in our model is used as store of value, the banks (or thecentral bank) could always o¤er to pay an amount of domestic currency equal tothe current dollar value of the deposit. As long as dollar deposits are used fortransaction purposes but rather to protect the purchasing power of savings, ourdeposits are equivalent to dollar-indexed instruments, hence we can ignore thedollar liquidity problem usually associated with dollarized economies, and reduceeverything to a …scal issue.
40On the other hand, dollar deposits are not legally dollar-indexed deposits, so they can beconverted at an arbitrary rate in a way quite close to a con…scation. Of course, rational dollardepositors anticipate this demanding higher rates, so that the desired reduction in …nancingcosts will not materialize while, the peso-dollar spread narrows, and dollarization is reduced.
