econ modification
strength
eci3-solution.docx
1 Capital Controls, Monetary Autonomy and
Exchange Rate Stability
this policy makes the Uncovered Interest Parity condition break down.
Uncovered interest rate parity (UIP) predicts that high interest rate currencies will depreciate relative to their low interest rate counterparts. This relationship between interest rate differentials and spot exchange rate depreciation is at the heart of many theoretical models in finance. A simple example can illustrate these dynamics. Suppose foreign interest rates were higher over a one week horizon than their domestic counterparts. Risk neutral investors with rational expectations (two key assumptions of the model) would buy the foreign currency to invest abroad at the one week maturity and capture these excess returns. This would continue up to the point that the foreign currency depreciates sufficiently to account for the initial interest rate differential. This simple uncovered arbitrage argument dictates that in equilibrium, there are zero attainable excess returns from such a strategy. If we are to believe that such a process holds for all currency pairs over all time horizons, UIP will hold. Given the depth of liquidity in markets for foreign exchange, efficiency of this type is not an unreasonable assumption.
2 Balance-of-Payments Crisis
Uncovered Interest Parity and Purchasing Power Parity to express the shadow exchange rate as a function of the monetary base.
an attack on the currency will occur when the shadow exchange rate hits the exchange rate peg
the government forces its monetary authorities to monetize new debt at an even faster rate
3 Self-fulfilling Currency Attack
4 Speculation against the European Monetary
System
"the British government's critics" have thought it possible to lower interest rates after taking Sterling out of the ER
The Economist think the opposite would occur soon after Britain exited the ER
British nominal interest rates relative to German rates have suggested an expectation of high future British ination.
purchase of the German stock is a debit in the U.S. financial account. There is a
corresponding credit in the U.S. financial account when the American pays with a
check on his Swiss bank account because his claims on Switzerland fall by the amount
of the check. This is a case in which an American trades one foreign asset for another.
there is a U.S. financial account debit as a result of the purchase of a German
stock by an American. The corresponding credit in this case occurs when the German
seller deposits the U.S. check in its German bank and that bank lends the money to a
German importer (in which case the credit will be in the U.S. current account) or to an
individual or corporation that purchases a U.S. asset (in which case the credit will be
in the U.S. financial account). Ultimately, there will be some action taken by the bank
which results in a credit in the U.S. balance of payments.
5 Bank Run
in the case of withdrawals by all investors, the central
bank serves as a lender of last resort, prints money and pays r in cash to every
investor. Of course, rational investors know that these 3r money units only buy
3 units of real goods under the storage technology so that the real payo_s in
this crisis case are 1 to each investor.
6 Debt Sustainability
This structure allows for heterogeneity, generates a yield curve and some interesting dynamics
and, at the same time, is quite tractable. If D is the measure of agents that holds debtor’s
bonds, then the amount of debt with maturity at this period is DλΔt, regardless of history –
it does not matter how we got to the present state.
Each lender can buy one bond that pays 1 (infinitesimal) unit at maturity (if there is no
default) and costs 1 − r when it is bought – bonds will be offered with several different
maturities and interest rates, r is the main endogenous variable of the model.
The outside option of the lender is a safe technology that yields zero return for sure. Lenders
have to pay a small transaction cost every time they have to make a decision and invest.
The debtor at a given period has own resources equal to θ. In addition, it can borrow from the
lenders by issuing bonds (i.e., promises to pay 1 at a given maturity date) that cost 1 − r. At
a given period, the debtor has debt D and its available resources are θ + D. The debtor goes
bankrupt if its own resources plus the debt become negative (that is, if it runs out of money).
The amout of its own resources, θ, follows a random walk and is also affected by the total
amount of interest paid (R(t)). Thus:
1. At the beginning of each period, the debtor has debt D, and own resources θ and so,
D + θ resources available.
2. The debtor repays the lenders that are leaving the economy and may issue debt. The
lenders that are just arriving choose whether they buy one bond or not.
3. The random term ΔX is revealed.
The debtor may go bankrupt at either step 2 or 3. If that doesn’t happen, another period
starts.
with maturity in 1 period for (λΔt) (λΔt) lenders with discount factor r = Φ(Δt),
• with maturity in 2 periods for (λΔt) (λΔt) (1 − λΔt) lenders with discount factor r =
Φ (2Δt),
• with maturity in 3 periods for (λΔt) (λΔt) (1 − λΔt)2 lenders with discount factor r =
Φ (3Δt),
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