Economics 456 - Faculty of Artsfaculty.arts.ubc.ca/gdunbar/Econ_456_files/Intfin_s6.pdf · longer sustainable then there is typically a large adjustment to a new oating rate. This

Economics 456International Macroeconomics and Finance: Section 6: Crises

Geoffrey Dunbar

UBC, Winter 2013

March 27, 2013

Geoffrey Dunbar (UBC, Winter 2013) Economics 456 March 27, 2013 1 / 74

The Three Crises

There are three types of crises that occur in international economics.Often they occur contemporaneously. The three types of crises are:

Exchange Rate Crises

Default Crises

Banking Crises


The Three Crises

We have examined models in which default crises can occur.We saw that rational lenders will consider the incentives of countries torepay debts when they decide on the level of lending to offer.We also saw that such models tend to feature debt increase limits ratherthan specific debt limit levels.I argued that although our simple model always leads to default, this wasbecause of our unrealistic assumption regarding the income process. Whennational incomes are subject to uncertainty, then backward inductionarguments fail and default is no longer a certainty but rather aprobabilistic event.


The Three Crises

But what about exchange rate crises and banking crises. And why wouldthe three be related?We usually think that an exchange rate crisis is the failure of a fixedexchange rate mechanism to hold. When a fixed exchange rate is nolonger sustainable then there is typically a large adjustment to a newfloating rate. This readjustment can be costly.While we usually think that exchange rate crises are phenoma related tofixed regimes, this is a matter of subjective opinion. For example, duringthe 1990’s the Canadian dollar fell from roughly 90 cents US to 63 centsUS. This is a dramatic change in the value of the dollar. But because itwas not ‘sudden’ we typically do not call it a crisis.


The Three Crises

But what is the linkage between these three types of crises?Central Banks.The reason is that central banks usually perform a number of differentroles in an economy.

1 They are usually the lender of last resort.

2 They usually manage exchange rate mechanisms.

3 They sometimes finance government deficits (though we usually hopethey won’t).


The Three Crises

In times of crises, these three roles can come together in unfortunate ways.Consider the following situation. Suppose Canada had a fixed exchangerate with the U.S. (it doesn’t anymore although it did during theBretton-Woods period). The Bank of Canada must then be ready to buyor sell U.S. dollars at the fixed rate. Central banks usually have reserves todo just that.But, and this is a key point, while the Bank of Canada can print Canadiandollars, it cannot print US dollars. Thus, it has a limited amount of USdollars to ‘defend’ the fixed rate.


The Three Crises

Now suppose that the Canadian banking sector has a crisis and the Bankof Canada is required to increase the money supply to prevent banks frombecoming insolvent. This leads to an increase in the money supply.We know from our exchange rate studies that the increase in the moneysupply will cause the exchange rate to fall. Recall our exchange rateequation:

EH/F = MH − MF − [YH − YF ]

Thus the increase in Canadian money supply will cause the exchange rateto rise (thus more Canadian dollars are need to buy US dollars).In order for the nominal exchange to remain fixed, the Bank of Canadamust therefore now sell US dollars at the fixed rate. This is sustainable foronly as long as the Bank of Canada has US dollars. If it runs out of USdollars, the exchange rate must float and thus fall in value.


The Three Crises

I could have done pretty much the same example with the followingchange.Suppose instead of a banking crisis that the Canadian government hassuddenly a large deficit. Ordinarily this would simply lead the governmentto borrow internationally via the CA.But let’s suppose that Canada has been running persistent deficits (bothCA and fiscal) and that it is no longer able to borrow internationally.Instead let’s imagine that it turns to the Bank of Canada to help financethe fiscal deficit via money supply increases. This is a so-called fiscaldominance viewpoint.This has the same effect as if the Bank of Canada increased money supplybecause of a banking crisis.


The Three Crises

Let’s consider current account interactions. Since the world is fixed, it isimpossible for the aggregation of current accounts across all countries tobe non-zero. If the sum of all nations’ current account were non-zero thenthis would imply that the Earth is trading in space. Most people think weare quite a ways from being able to do that.Current account dynamics may therefore also reflect supply factors andnot just demand factors.For instance, the US ran a large current account deficit during the 1980’s.Was this because other countries wanted to lend to the US? Or becausethe US wanted to borrow from them?


The Three Crises


The Three Crises


The Three Crises

Fortunately we can use price movements to discriminate between thesetwo factors. If the CA decrease is due to supply factors then the price ofUS borrowing should fall.If, however, the CA decrease is due to demand factors (i.e. the US wishesto borrow more) then the price of US borrowing should rise.We can therefore discriminate between these two scenarios using data onreal borrowing costs for the US.


The Three Crises


The Three Crises

The evidence suggests that for the US demand factors were the cause ofthe CA deficits in the 1980s.Thus, either US savings decreased or investment rose to shift the UScurrent account to the left.From examining the data from that period, one can make the case thatmuch of the US deficit was financed by international borrowing to fundbudget deficits. During this era, President Reagan presided over tax cutsand also increases in military spending which led the US government torun deficits. (That this would cause the CA to fall would seem to requirethat Ricardian Equivalence does not hold.)


The Three Crises


The Three Crises


The Three Crises


A Quantity Theory of Money Model

The idea is therefore that persistent current account deficits requireforeign investors to be willing to increase their holdings of domestic assets.It is not clear that they wish to do this at any price.A rise in the exchange rate reduces the price of investment for foreigninvestors and leads to higher demand for US assets.


8. Financial Intermediation

A financial intermediary is an agent that

borrows from one group to lend to another

transforms assets such that the characteristics of its assets aredifferent from its liabilities

process and keeps information.



Generally, financial intermediaries interact with broad groups. Examples ofintermediaries are banks, trust companies, insurance companies, mutualfunds and pension funds.It is important to consider how intermediaries differ from markets.Markets bring groups together at single points in time. So far in thiscourse, we have imagined that there is a Walrasian auctioneer whodetermines the price.An intermediary is potentially different. An intermediary need not have toclear a market at one point in time.



For example, consider ticketmaster. Suppose you are dying to see JackJohnson in concert and you purchase a ticket to a show. You pay cashnow but receive the payoff (the show) in a few months time. Ticketmasteris intermediating between you and Jack Johnson.



Intermediaries can also play two beneficial roles:

Diversify risk across a pool of agents

Provide a service specific to the market it serves (i.e. creditappraisals, matching)



While it might be possible in theory to replace an intermediary with adirect lender, there are in practice six problems with this approach:

Matching between borrowers and lenders is costly

Lenders may not be skilled at evaluating credit risk

Multiple costs because many lenders may be required

Lenders will minimize information costs (and risks) by lending to asmall pool of borrowers (may not be efficient)

Loans will usually be illiquid

There may be a maturity mismatch



Some of these problems are obvious. The last two may not be. Withdirect lending, loans will usually be illiquid because one lender cannot sella loan (asset) to another lender easily because of the information costsand credit risks. Hence lenders will not be able to efficiently optimize theirportfolios. Second, there may be a maturity mismatch between the loan(e.g. a mortgage) and how long the lender wants to lend the money.Intermediaries can avoid both problems either by their size or byreputational enforcement.BUT these benefits can also expose a bank to a risk of insolvency...


8. Diamond-Dybvig Model

The Diamond-Dybvig (DD) model is a stylized model that captures someof the important features of banks. There are three periods, 0, 1, 2. Thereare N consumers.Each consumer is endowed with 1 unit of a good in period 0 which canserve as an imput to production.Production takes one unit of the input good in period 0 and converts thisinto R > 1 units of the consumption good in period 2.Production can be interrupted in period 1. If interrupted then the payoff isr ≤ 1 in period 1 and nothing is produced in period 2. For simplicity, wewill assume r = 1.



Consumers are ex-ante identical. In period 1 consumers learn their type,where types indicate in which period the consumer wishes to consume.Consumers have a probability λ of being an early consumer (period 1) or alate consumer (period 2). The type is intended to reflect a consumptionshock representing an unexpected demand for one’s deposit.Thus, there are λN consumers who learn that they wish to withdraw theircash and (1− λ)N who learn that they wish to withdraw late, in period 2.



Notice that I wrote ‘wish.’Notice as well that the production technology is intended to captureliquidity in a simple way, like a mortgage or a long bond. That is, inessence, the point of the DD model. Banks have a mismatch betweendemand deposits (redeemable in the short-term) and their loan assets(payoff in the long-term).Banks therefore need to estimate its short-run withdrawls. This might notbe such a simple thing to do.In the past, banking rules required banks to maintain a certain fraction ofdeposits in reserve. These rules have been relaxed.



Consumers receive utility U(c) where U is a utility function and c isconsumption.Utility has the usual properties: it is concave – i.e. marginal utility ofconsumption declines as consumption increases. A consumer’s expectedutility, EU is:

EU = λU(c1) + (1− λ)U(c2) (1)

The marginal rate of subsitution between early consumption and lateconsumption is:

MRSc1,c2 =λEUc1

(1− λ)EUc2

(2)

where MRSc1,c2 is the negative of the slope of the indifference curve.



If early consumption and late consumption are the same (i.e. c1 = c2)then EUc1 = EUc2 . In this case,

MRSc1,c2 =λ

(1− λ)(3)



If we suppose a world where consumers do not intermediate (contract)with each other then the best each can do is to invest in the project inperiod 0. Then when period 1 occurs and she learns whether she is an earlyor late consumer, she re-optimizes. If she is an early consumer then sheliquidates the project and consumes c1 = 1. If she is a late consumer, sheremains invested and earns R in period 2 when the investment matures.



One question posed by this model is: Can a bank lead to a Pareto-superioroutcome?We imagine that the bank can offer a deposit contract which is anallocation of consumption in both periods, i.e. a set (c1, c2).The contract allows a consumer to withdraw c1 in period 1 and c2 inperiod 2.



We make two meaningful assumptions:

The bank serves clients sequentially. In other words, consumers lineup and the bank deals with each one in turn.

The bank cannot tell a consumer’s true type.



No early consumer will want to pose as a late consumer because she willonly be worse off.However, a late consumer may wish to pose as an early consumer if she canstore her withdrawl until the second period. We will assume that she can.



We will focus on the competitive equilibrium in which there is one bankwhich behaves competitively. In other words, we can suppose that there isfree-entry into banking which implies that banks earn zero profits but offerthe (constrained) optimal contract to each consumer.Because all consumers deposit in period 0 then the bank has N units toinvest in the production technology. The bank must choose a fraction x tointerrupt (or equivalently hold in reserve) to satisfy the demands of theearly consumers in period 1. If we imagine that only early consumerswithdraw in period 1 then the bank must determine x such that:

Nλc1 = Nx

λc1 = x(4)



In period 2 the bank receives the payoff from the previous period’scontract and pays off the remaining consumers so that:

N(1− λ)c2 = (1− x)N(R)

(1− λ)c2 = (1− x)(R)(5)

We can substitute for x from our equation for the early types to find:

λc1 +(1− λ)c2

R= 1 (6)



We can represent the bank’s contact in a couple of useful ways. Considerit in terms of the bank’s budget constraint. Rewriting the equation above:

c2 =R

1− λ− λ(R)

1− λc1 (7)

The slope of the budget constraint is therefore: −λ(R)1−λ which is steeper

than the slope of the consumers indifference curve at equal consumption(which was λ

(1−λ) ).This means that the optimal contract offered by the bank will give moreconsumption to late consumers. Indeed, the solution to the optimalcontract with be:

MRSc1,c2 =λ(R)

1− λ>

λ

(1− λ)(8)



In other words, the bank will give relatively less consumption to earlywithdrawers than to late withdrawers. But ex-ante both consumers preferthe deposit contract because the bank’s contract provides moreconsumption in period 1 then the consumer could earn on her own. I.e.c1 > 1.The cost of the insurance is less consumption in period 2 so that c2 < R.Essentially, the bank contract provides insurance to consumers against thepossibility that they will be an early type.



The fact that the bank offers insurance to consumers also leaves it open tobank runs. Bank runs in this environment will be entirely determined bythe beliefs of the late type of consumer.We have constructed above a good equilibrium where each early consumerlines up at the bank to withdraw her deposit and no late consumers do sobecause they believe that waiting and received c2 is better than receivingc1.But this belief is only true if every other late consumer believes the samething.



Suppose instead that some late consumers believe that other lateconsumers are going to withdraw early. Imagine an extreme example wherelate consumers believe that every other late consumer will withdraw early.Then the total amount of withdrawls in period 1 is:

(N − 1)c1 (9)

The bank can only receive 1 unit for liquidating early so the total amountit can repay is N. As long as c1 > 1 (which we know it is) and N is largethen:

(N − 1)c1 > N (10)

and the bank is insolvent.



Indeed, depending on c1, the liquidation value of interrupting the project(here it is 1) and the number of people withdrawing early there is someN∗ where all remaining agents in line receive no money from their deposit.Thus, if late consumers believe that there are enough other late typeswithdrawing early then they should line-up to withdraw early as well. Ifthey all do so, then there is a bank run and the bank is insolvent.As well, if more people withdraw early then the bank expects, then itmight not be able to pay off all of the late consumers in period 2 as well.



This bank run story relies on multiple equilibria to generate bank runs.Indeed, it is in some respects a sunspot theory.But it seems to capture the spirit of bank runs pretty well. Think ofNorthern Rock (in the UK) as an example.


Deposit Insurance

The Diamond-Dybvig model provides a role for deposit insurance. If thegovernment can credibly commit to each late consumer that they willreceive c2 no matter what then they have no reason to line up in period 1.Thus, credible deposit insurance can prevent bank runs. (Again, think ofthe UK gov’ts response to the Northern Rock crisis).In Canada, the CDIC insurances deposits up to 100, 000 and has roughly 2billion in assets. This is much less than the total amount of depositsoutstanding but there are two reasons not to worry about this. The first isthat most loans are collateralized so that the loss a bank incurs byforeclosing on a loan is reasonably small and it is only these costs thatdeposit insurance needs to cover. The second is that the government canalways levy a tax to raise the funds.


Deposit Insurance

The problem with deposit insurance is that it creates a moral hazardproblem in two ways.

Banks have more reason to try to ‘earn’ profits by taking on more riskbecause they are protected if they fail.

Depositors have less reason to scrutinize banks because they areinsured from risk.

As a result, bank loans might be more risky than otherwise would be thecase. (Perhaps one can think of the sub-prime problem here, or theSavings and Loan crisis of the 1980s).Second, the tax costs might be borne in an inefficient way. I.e. thoseconsumers than benefited from the higher risk may not bear all theconsequences for the costs.


An International Model

So now that we have a model of bank runs, we will embed this model intoa small-open economy following Chang and Velasco (JET 2000).We will keep much of the same machinery but will now need to add in theinternational bits.To do this, we shall assume that the consumption good is freely traded inworld markets and has a fixed world price in a foreign currency. Call thiscurrency Dollars.In contrast, the domestic economy issues Pesos.



Assume that there is a large number of agents with an endowment eDollars at time 0.They can invest b in the world market and earn return rw = 1. Thus, onedollar invested at time 0 is worth 1 dollar in either t = 1 or t = 2. For themajority of our analysis we shall assume that domestic agents (includingthe Central Bank) can only invest and not borrow. This assumption is forsimplicity but it is not crucial to the results.Alternatively, they can invest k in the illiquid technology and earn r < 1 attime t = 1 or R > 1 at time t = 2.



Agents are of two possible types: patient and impatient. They learn theirtype at t = 1. With probability λ the agent is impatient and derives utilityonly from consumption in period t = 1, c1. With probability 1− λ theagent is patient and derives utility from holding Pesos in period t = 1 andfrom consumption in period t = 2, c2.There will be no aggregate uncertainty.



The agent’s expected utility is then:

λu(c1) + (1− λ)u(g(M/E2) + c2) F

where M is the quantity of pesos acquired in t = 1 and E2 is the exchangerate in period t = 2. The function g(M/E2) converts real money balancesinto consumption equivalents. We assume g ′(m) = 0 gives a satiationlevel of pesos m.We shall assume that pesos are costlessly created or destroyed by thedomestic Central Bank.These type of preferences are called money in the utility functionpreferences. They are a crude way to motivate money demand but makethe analysis tractable.



As you might have guessed, the results from this model depend on theexchange rate E2. In particular, they depend on the exchange rate regime.In our analysis which follows, we shall consider three: currency boards,fixed exchange rates and flexible exchange rates.


Currency Board

With a currency board, the Central Bank issues base money (Pesos) thatare fully backed by foreign reserves of dollars. Thus there cannot be abalance of payments crisis.Because there is no aggregate uncertainty, ex-ante domestic agents are allthe same and so like in the Diamond-Dybvig set-up it is optimal for themto form a commercial bank.We will assume that the commercial bank can observe domestictransactions but not world transactions. It can also not observeconsumption.


Currency Board

The commercial bank’s problem is to promise consumptions to agents thatlead agents to reveal their true type. These types of mechanisms are calledRevelation Mechanisms. Basically, these mechanism induce agents totruthfully reveal their type.


Currency Board

Since the exchange rate is fixed, for simplicity assume E2 = 1. Thecommercial bank’s problem is then:

k + b ≤ e

λc1 + (1− λ)M ≤ b + rl

(1− λ)c2 ≤ (1− λ)M + R(k − l)

g(M) + c2 ≥ c1

kgeql

k , b, c1, c2,M, l ≥ 0

where l is the domestic investment liquated early. All these amounts on inper-depositor terms.


Currency Board

Although this problem might seem difficult, it is really pretty simple.Note that the equation

λc1 + (1− λ)M ≤ b + rl

embeds the assumption that banks get M pesos from the Central Bank atan exchange rate of 1 : 1. Then equation

(1− λ)c2 ≤ (1− λ)M + R(k − l)

implies that the bank requires the type 2 agents to return the pesos whichthe bank then sells back to the Central Bank to finance consumption.


Currency Board

The commercial bank clearly wants to set l = 0 because it is better offwith a return of 1 than r .Next, notice that for type 2 agents, the optimal choice of M and k mustsatisfy an equality of marginal returns. The marginal return to holding Mis:

g ′(M)

and the marginal return to holding one extra unit of k is:

R − 1

Thus, in an equilibrium:

g ′(M) = R − 1 > 0

This equation pins down an optimal M.


Currency Board

Now consider the consumptions that can be offered by the commercialbank. The commercial bank has resources:

eR − (R − 1)(1− λ)M

to share net of Peso purchases. What it must finance is:

λRc1 + (1− λ)c2

Note that the Rc1 is the price of the current consumption in period 2units. I.e., the bank must give up R units of c2 to purchase 1 unit of c1.We shall assume eR − (R − 1)(1− λ)M > 0 always.


Currency Board

The final optimality condition is that the optimal expected marginal utilityratio must be tangent to the transformation curve. This is the basicMRS = MRT condition for efficiency. The commercial bank’s problem is:

L = λu(c1)+(1−λ)u(g(M)+c2)+µ[eR−(R−1)(1−λ)M−λRc1−(1−λ)c2]

The first-order conditions yield

λu′(c1) = µλR

and(1− λ)u′(g(M)− c2) = µ(1− λ)

Thus, at the optimum

λu′(c1)

(1− λ)u′(g(M + c2)


Currency Board

This clearly simplifies to:

u′(c1) = Ru′(g(M + c2)

As long as u() is concave and R > 1 then this implies that the incentiveconstraint for type 2’s:

g(M) + c2 ≥ c1

does not bind. These equations then pin down the optimal contract undera currency board.


Currency Board

As in the Diamond-Dybvig model, we assume that this is implemented viademand deposits with sequential service.We shall also assume that the commercial bank can only pay depositorsusing pesos. But all agents can visit the CB to buy dollars.So the game unfolds as in Diamond-Dybvig. The agents report randomlyto the commercial bank in period t = 1 and report their type. Type 1’swithdraw c1 units of pesos for consumption. Type 2’s withdraw M. Thecommercial bank services depositors until it runs out of assets.After the commercial bank closes, type 1 agents report to the CentralBank and exchange their pesos for dollars and then buy consumption.


Currency Board

In this scheme there is an honest equilibrium in which all agents truthfullyreport and agents consume c1 or c2 according to their type.That this equilibrium exists is pretty clear from the contract above. Sincetype 2’s have no incentive to misreport then the optimal contractestablished above can exists as a solution.Type 2’s get M in period t = 1 and then in period t = 2 they receivec2 − M from the bank. They then consume M + c2 − M = c2.The Central Bank is also solvent. It ends period t = 1 with (1− λ)Mdollars and it uses these dollars to redeem the (1− λ)M in period t = 2.


Currency Board

Thus, this currency board solution can have a no run equilibrium.It can also have a run equilibrium. If

c1 > b + r k

then if all agents report as type 1’s the commercial bank will be insolvent.But, the Central Bank does not fail. It simply redeems b + r k pesos andthen closes. Since this is the total amount which can be withdrawn fromthe commercial bank then the CB’s assets and liabilities perfectly coincide.Note that in this world pesos in time t = 2 are worthless and so themisreporting by type 2’s is incentive compatible.


Currency Board

So currency boards can have both types of equilibria. But, there is nopossibility of a balance of payments crisis.Let’s reflect for a moment on the Euro-zone economies. The Euro-zone issimilar to the currency board arrangement we studied above. No singlecountry in the Euro-zone can print Euro’s and so their central banks arerestricted by the supply of Euro they have available. If we considerdeposits to be the issuance of private, domestic, credit then it is clear thatthe lessons from the currency board above are similar to what is beingexperienced currently in some European countries, e.g. Cyprus, Greece andpossibly Italy, Spain and Portugal. That is, a banking crisis can occur butnot a balance of payments crisis. And the national central banks cannotbe the lenders of last resort.


Fixed Exchange Rates

The currency board example is interesting but it is pretty obvious thatalthough bank runs can exist there is no difficulty for the exchange rate.The currency board in the example is fully backed and so there are noconvertibility concerns.This is not true in a world with fixed exchange rates because the centralbank does not have enough foreign currency to redeem all domesticcurrency at that rate.The currency board is also inefficient for two reasons. One, the centralbank cannot help a bank in distress. Two, the marginal cost of a peso isthe opportunity cost of a foreign dollar to back the peso but the cost ofmaking a peso is zero. Thus, marginal costs are not equated.



With a fixed exchange rate regime, banks runs and balance of paymentscrises are possible.This is the theoretical link betweent the twin crises.We shall assume for simplicity that E2 = 1 in the fixed exchange ratesystem.The question we need to ask is what sort of allocation is possible if thecommercial bank and the Central Bank act optimally?



If both act optimally, then this is a social planner’s problem. A socialplanner wants to maximize:

λu(c1) + (1− λ)u(g(M/E2) + c2) F

subject to feasibility (what is possible)

k + b ≤ e

λc1 ≤ b

(1− λ)c2 ≤ Rk

c1, c2,M, k, b ≥ 0

Here pesos are provided costlessly.



The solution to this problem will feature M = m –¿ the Central Bank willprovide the satiation levels of pesos since creating pesos is costless.Second, the transformation curve is:

Rλc1 + (1− λ)c2 = eR

Notice the difference between this transformation curve and the currencyboard transformation curve which was:

eR = (R − 1)(1− λ)M + λRc1 + (1− λ)c2

The difference is the (R − 1)(1− λ)M. This is the opportunity cost for theCentral Bank to provide credit to the patient types in a currency boardwhere all pesos are explicitly backed. Here the pesos are not backed. Thefinal optimality condition says that:

u′(c1) = Ru′(g(M) + c2)



To implement this allocation in a decentralized world requires that thecommercial bank act to maximize F subject to E2 = 1 and:

λc1 + (1− λ)M ≤ b + h

(1− λ)c2 ≤ (1− λ)M + Rk − h

c1, c2,M, k , b, h ≥ 0

and the incentive compatibility condition:

g(M) + c2 ≥ c1

Here h is the commercial banks borrowing from the Central Bank.


Fixed Exchange RatesNow let’s think about this for a minute. What would a commercial bankwant to do? Invest e in only the long-term asset and borrow h from theCentral Bank. So to make this interesting, we need another restriction onhow much the bank can borrow from the Central Bank. In other words, dowe really want a model in which a bank can sell mortgages to CentralBanks?So let’s assume that the commercial bank must have liquid assets toborrow pesos:

λc1 ≤ b

This implies that

h ≥ (1− λ)M

and

Rk ≥ (1− λ)c2

This is the same problem as the social planners above.Geoffrey Dunbar (UBC, Winter 2013) Economics 456 March 27, 2013 66 / 74


With a fixed exchange rate regime, the transformation curve is furtherfrom the origin. Hence both c1 and c2 can be higher than in a currencyboard. So it is true that currency boards are inefficient.The first-order condition for an optimum is:

u′(c1) = Ru′(g(M) + c2)

so c1 > c1. Whether M > M and/or c2 > c1 depends on g(). Given c1,then h = (1− λ)MBut the main point is that the fixed exchange rate regime with a reserverequirement implements the social optimum.



There are two cases to examine with fixed exchange rates.

Case 1 The Central Bank is not a lender of last resort (LLR)

Case 2 The Central Bank is a LLR

Continue to assume sequential service and demand deposits.


Fixed Exchange Rates: Case 1

In Case 1, there can be bank runs but no balance of payments crisis.As is usual in this model, there is an honest equilibrium in which all agentsreport their type truthfully and there is no bank run.There is also a bank run if

c1 > b + r k

. In this case the commercial bank cannot service all the deposits at t = 1and the commercial bank fails.But in this case, the Central Bank receives demand for b + r k. But sincethis is what it received from the bank it can service the demand. So nobalance of payments crisis.I also note that if c1 > b + r k then it follows that c1 > b + r k but theconverse is not true.



In Case 2, there is also a honest equilibrium.But in this case, if there is a bank run in period there can also be abalance of payments crisis.To model this case, we need to describe what happens in the event of abank run. Let’s assume that if the bank needs to borrow more than h thatit is insolvent and all it’s assets are turned over to the Central Bank.To see this, assume that all impatient types claim to be patient andwithdraw c1. But as long as c1 > b + r k then the Central Bank cannotredeem all pesos!Now the bank run leads to a balance of payments crisis because E2 mustfall for all depositors after c1 = b + r k. An alternative, in anticipation isthat E2 falls before.


Flexible Exchange Rates

Although we don’t have time to model a flexible exchange rate system, I’lljust mention briefly the outcome.In a flexible exchange rate world neither bank runs nor exchange rate crisesare possible. The absence of bank runs is due to the assumptions madeand arises because the Central Bank can punish early withdrawers bydevaluing the exchange rate if too many agents withdraw. This howeverdepends crucially on the Central Bank knowing the fraction λ withcertainty.Exchange rates crises also do not occur because in the absence of bankruns there is no excess demand for dollars from the Central Bank (becauseof the devaluation above).So in this world, flexible exchange rates are best.








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Economics 456 - Faculty of Artsfaculty.arts.ubc.ca/gdunbar/Econ_456_files/Intfin_s6.pdf · longer sustainable then there is typically a large adjustment to a new oating rate. This