Economics 103 — Spring 2007International Monetary RelationsProblem Set 3May 29, 2007Due: Thu, June 7, 1:55pmInstructor: Marc-Andreas MuendlerE-mail: [email protected] Capital Controls, Monetary Autonomy andExchange Rate StabilitySuppose a country has strict capital controls in place and restricts capital flowsunless approved by the government. Argue that this policy makes the UncoveredInterest Parity condition break down. Use a diagram showing the exchange rate,expected currency returns and real money holdings to verify that the centralbank can reduce the domestic interest R to a level of its choice without an effecton the exchange rate.Now suppose that capital is completely free to flow in and out of the coun-try. However, investors assess the risk of the country’s securities as very differentfrom other countries assets. Show how the central bank can reduce the inter-est rate R without affecting the exchange rate level. [Hint: Engineer a partlysterilized intervention that moves the risk premium to the right extent.]2 Debt SustainabilityWe speak of a Ponzi scheme when an agent’s debt grows at a rate α suchthat interest payments on existing debt fall short of new borrowing relative toexisting debt. What does a Ponzi scheme imply for the relationship betweenα and the real interest rate r∗? Explain why a Ponzi scheme would leave theborrower with unlimited resources as time passes. Will lenders be willing totolerate this?Now suppose that, at some date T in the future, the interest on the debtcontracts is anticipated to permanently increase to some r∗0so that α < r∗0from T on forever. Can the borrower start to accumulate new debt at a rate αfrom today on? Would your answer change if the interest rate were anticipatedto fall back to r∗at some time T0> T ?3 Currency UnionThe incentives to join a currency union depend on the likely sources of economicshocks and how they would be absorbed when the country joins the monetary1union. Consider two sources of shocks:• Candidate country M anticipates to suffer large and frequent sho cks tomoney demand. All other things equal, will country M be more likely tojoin the monetary union than a country with smaller and less frequentshocks?• Candidate country L has a population that is historically reluctant tomove. All other things equal, will country L be more likely to join themonetary union than a country with a more mobile labor force? Whatwould your answer be if the education system in country L awarded manydegrees that are little comparable to other countries’ degrees in the mon-etary union?4 Balance-of-Payments CrisisA small open economy pegs its exchange rate to a foreign currency at the level¯E.The government expands its debt steadily and forces its monetary authorities tobuy (monetize) the new debt. The government also requires the monetary au-thorities to maintain the exchange rate peg as long as they have foreign reserves.Once foreign reserves are depleted monetary authorities float the exchange ratefreely.• In this scenario, government debt and therefore the monetary base expandat a rate µ. Depict the time path of foreign reserves of the monetaryauthorities. Is the peg sustainable indefinitely?• Define the shadow exchange rate. Use Uncovered Interest Parity and Pur-chasing Power Parity to express the shadow exchange rate as a functionof the monetary base. Depict the time path of the shadow exchange rate.• Explain why an attack on the currency will occur when the shadow ex-change rate hits the exchange rate peg¯E. Depict the immediate responseof the domestic interest rate and the domestic price level to the attack.• Are there features of this model that capture elements of the Asian Fi-nancial Crisis in 1997? What elements of the Asian Financial Crisis doesthe model ignore?5 Self-fulfilling Currency AttackConsider the following attack game (with foreign and domestic asset holdingssuch that WCB<BCB). There is a number J of small investors who all own oneunit of currency, and one big investor who owns K units of currency. In thecase of a defense, the central bank incurs losses of R per unit of foreign reservesthat it has to use for the intervention.2Central BankInvestor iDefend (∆E = 0) Devalue (∆E > 0)Attack−c ∆E − c−R(J + K) ∆E(WCB− BCB)Hold0 −∆E0 ∆E(WCB− BCB)• State the condition for a self-fulfilling attack to be an equilibrium.• Explain under what condition a successful attack becomes a best responsefor any small investor (among the J investors) when he or she observesthe big investor in a fire sale of K units of the currency but the J − 1other small investors holding on to the currency.• Suppose K = 0. Investor i and the central bank anticipate that J − 1other investors will attempt to attack. Show that a successful attack is anequilibrium for every investor i if there is a large number I of other at-tacking investors. Also show that a no-attack-no-devaluation equilibriumexists.• Why is a discrete foreseeable devaluation ∆E > 0 possible in a self-fulfilling crisis but not in a fundamentals-driven crisis?• Evaluate the following statement.One way to reduce the chance of a self-fulfilling attack is toraise the transaction cost c so that investors are more reluctantto run.Is this statement correct in the strategic framework above? Why or whynot?6 Speculation against the European MonetarySystemShort before the British government gave in to speculative pressure on theBritish Pound against the German Deutschemark and abandoned the Euro-pean Exchange Rate Mechanism (ERM) in September 1992, The Economistmagazine wrote (“Crisis? What Crisis?”, in The Economist, August 29, 1992):The [British] government’s critics want lower interest rates, andthink this would be possible if Britain devalued Sterling, leavingthe ERM if necessary. They are wrong. Quitting the ERM would3soon lead to higher, not lower, interest rates, as British economicmanagement lost the degree of credibility already won through ERMmembership. Two years ago British government bonds yielded threepercentage points more than German ones. Today the gap is half apoint, reflecting investors’ belief that British inflation is on its waydown—permanently.Evaluate this statement.• Why might “the British government’s critics” have thought it possibleto lower interest rates after taking Sterling out of the ERM? Britain’seconomy was in a recession in fall 1992.• Why did The Economist think the