Examples Questions With Guided Answers

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Franco Bruni

International Monetary Economics from Krugman-Obsfeld-Melitz, Chapters 13-19

EXAMPLES OF EXAM QUESTIONS WITH GUIDELINES FOR ANSWERS

Note that only “guidelines” are noted below: students’ answers are usually supposed to be more explicit , though in some parts more concise (when the guidelines written here go beyond the essential answer,

when they repeat the answer in different ways, when they help the student to place the question in the context of the relevant section of the program and thus recall certain explanations behind the answers). Students’ answers must normally contain the relevant formulas and graphs that are often avoided here (to show how much of the reasoning in the program can be conducted without algebra and geometry)

but that often can save words and allow quicker and more direct comments. Moreover answers can differ according to the ability of each student to go to the point with synthetic, clear but personal wording, to

be somewhat original in shaping the requested reasoning and, sometimes, to include personal comments.

February 2014

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AN INDEX

10 examples of exam texts are reported here, always consisting in 3 questions, often divided in

sub-questions. As in the real exams, in each example and to answer each question the material

of various chapters of the KOM textbook is required and somewhat mixed. To help students in

using this material to review the individual chapters, an index is provided where each chapter is

associated with the question or sub-question specifically referred to what is taught in that

chapter. Obviously to answer questions on a chapter, also previous ones have to be studied.

Questions are indicated in this index by specifying first the number of the example and then the

number of the question in the example: therefore, for instance: 5, 3a means question 3a in

example 5.

Chapter 13: 2, 1a; 3, 1a; 5, 1a&b; 7, 1a; 9, 2a&b; 10, 1c

Chapter 14: 1, 1a; 10, 1a&b; 10, 3a

Chapter 15: 1, 1b; 3, 3a; 4, 1a; 6, 1c; 7, 1b; 7, 3; 8, 1a

Chapter 16: 1, 2; 2, 1b; 2, 3; 3, 1b; 4, 2; 5, 3c; 6, 1a&b; 6, 2; 6, 3; 8, 1b; 9, 1b

Chapter 17: 1, 3; 2, 1c; 2, 2; 3, 2a&b; 4, 1c; 4, 3; 5, 2; 7, 2; 8, 2; 9, 1c; 10, 3b&c

Chapter 18: 3, 2c; 3, 3b; 4, 1b; 5, 3a; 7, 1c; 9, 1a; 9, 2c; 9, 3a

Chapter 19: 1, 1c; 3, 1c; 5, 1c; 5, 3b; 8, 1c; 8, 3; 9, 3b; 10, 2

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Example 1 - Closed books. One hour and 15 minutes, all the three questions have the same weight in the grading.

Question 1

Are the following three statements TRUE or FALSE? Motivate your answer in a brief way, but showing that

you are applying the right theory and/or using the correct and relevant information. It can happen that the

statement is neither totally true nor totally false: if you really think this is the case, clearly explain why.

(a) The forward exchange rate between two currencies can always be interpreted as a good estimator of

the future expected spot rate.

False. The crucial concept here (appendix to ch. 14, the only appendix which was part of the programme) is that F = Ee only if both the Open Interest Parity and the Covered Interest Parity are holding. The proof is immediate by writing OIP and CIP. Additional comments could list potential causes of deviation from OIP (imperfect asset substitutability) and/or CIP (imperfect capital mobility).

(b) A permanent monetary restriction does not cause overshooting of the exchange rate in case perfect

price flexibility prevails.

True. Overshooting is caused by price stickiness as the change in nominal money supply is not immediately matched by a proportional decrease in prices, thus resulting in a decrease of the real money supply. The short-run overshooting is what allows the interest rate to increase and the money demand to decrease, preserving money market equilibrium. [To avoid money market disequilibrium the real demand for money must change: as in the long run and in full employment Y cannot change, this can happen only if R changes. But R=R* if there are no expected changes in E. These expected changes must be such as to move R in the right direction. With monetary restriction real money demand must decrease, therefore R must increase: according to OIP this requires overshooting, i.e. E immediately stronger than its long run expected equilibrium value. Obviously all this path is not required in case P immediately adjusts to the changed Ms]. The type of comment written in parenthesis is not required for a fully satisfactory answer.

(c) Several reasons can justify the fact that macroeconomic policies try to avoid excessive and prolonged

current account deficits.

True. First of all the deficits can result from excessive private and/or public consumption, with no corresponding accumulation of productive assets to enable the country to reimburse, in the future, the debts incurred to finance the deficits. Sometimes it can even become difficult to pay the interest costs of those debts. The accumulation of debts can also cause a “sudden stop” in lending by international markets to the deficit country. Moreover, when deficits are financed running down official reserves of foreign currencies, reserves can be exhausted, it can become impossible to borrow more of them and the country can be troubled by the sudden need to let the exchange rate depreciate in an uncontrolled way, with undesired consequences on price and financial stability.

Question 2

Consider a long-run exchange rate model based on PPP and on money market equilibrium equations.

(a) Starting from a long-run equilibrium position, suppose a country increases its money supply. Will this policy move have consequences for the equilibrium level of its real interest rate?

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Here, as in the following (2b), the crucial point for answering is to pick the right model! The “long-run exchange rate model based on PPP and on Money market equilibrium equations” is the “monetary approach model” of Ch. 16. To answer part (a) it is sufficient to recall that, with PPP, the real interest rate cannot change if the foreign rate does not change (as PPP implies constant q and the real interest parity states that r=r*+Δe%q). Students that do not concentrate on the right model might try to answer with a “short-run” approach (the double graph reporting the forex and the money market) where it is difficult to show the path towards the long-term equilibrium with PPP.

(b) According to this model, what is the effect of a decrease in the domestic nominal interest rate on

the equilibrium nominal exchange rate? Can you give an intuitive explanation of the answer that

results from the analytical formulation of the model?

The domestic nominal interest rate enters the formula of E of the model in the denominator, as it influences negatively the domestic demand for money. Therefore a decrease in R, by increasing Md, decreases (appreciates) E. Which is counterintuitive as a lower yield on the domestic currency should make it less attractive thus causing a depreciation. The intuitive explanation is that, with PPP (one of the basis of the model), q is constant, therefore r is constant (according to the real interest parity): a change in R=r+ inflation (by definition) can be triggered only by a change in inflation. A decrease in R is therefore associated with a decrease in inflation, which, intuitively, is in accord with a strengthening value of the domestic currency. Students can “mention” the Fisher effect (that r is constant, so that R follows inflation levels) but this is not required and cannot substitute the correct reasoning based on the formula for E in the “monetary approach model”.

Question 3

Provide three synthetic definitions, each followed by a short explanation and comment, of the following

three expressions:

(a) J curve

The J curve describes the behaviour of the current account of the balance of payments over time following a change in the exchange rate. A depreciating (appreciating) E causes a negative (positive) “value-effect” *more (less) expensive imports and lower(higher)-unit-value exports] together with a positive (negative) “volume-effect” *more (less) exports and less (more) imports+. In the very short run the volume effect is weak, as export and import contracts must be changed and re-directed, while the value effect is immediate. Therefore in the short run a depreciation (appreciation) causes a worsening (improvement) of the current account, turning into an improvement (worsening) over time, thus describing a “J-shaped” time profile.

(b) Pass-though from the exchange rate to import prices

This is the ratio of the change in import prices (when expressed in domestic currency) caused by a change in the nominal exchange rate. The ratio stays between 0 and 1. When it is <1 the reason is the “strategic behaviour” of foreign importers that might decide, when for instance the domestic currency gets depreciated, to lower their selling prices in foreign currency to avoid losing market share in the devaluing country, thus giving up part of their profits to keep their clients. With lower (higher) P*, import prices will not fully reflect the higher (lower) E: which, by definition, is a pass-through “lower than 1”.

(c) Liquidity trap.

The liquidity trap is a situation where standard monetary policy (based on a “transmission mechanism” where interest rates changes are crucial) does not function, as the interest rate is so

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low that the demand for money is “infinite” and adding liquidity, for instance, results in larger money balances with lower velocity of circulation and no effect on interest rates and spending. This happens (often following economic crises with very low Y) when R is zero (and cannot become negative) or so low that nobody expects it to become lower. In the AA/DD graph the liquidity trap causes a flat segment in the AA line, when approaching the vertical axis. The nominal exchange rate cannot be further devalued because the nominal interest rate cannot be further lowered (and given the open interest parity: where the trap is at R=0, E cannot go higher than Ee=(1-R*) ). When the DD crosses the AA in the flat segment the system is in the liquidity trap: monetary expansion would simply lengthen the flat segment, with no effect on the equilibrium point: only a substantial shift in the DD (due, for instance, to an expansionary fiscal policy) can get the macro-equilibrium out of the trap. Note that, while expanding money in the trap is ineffective, restrictive monetary policy becomes effective when the flat segment of the AA is shortened enough, beyond the crossing point with the DD.

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Example 2 - Closed books. One hour and 15 minutes, all the three questions have the same weight in the grading

Question 1




(a) In an economy where private saving is 50, the public sector deficit is 30 and aggregate investment

is 20, 60 is the deficit of the current account of the balance of payments.

False. As CA = Sp+SG – I = Sp – (G-T) – I = 50 – 30 – 20 = 0 : the current account is in equilibrium.

(b) The validity of the law of one price for all goods and services is a necessary and sufficient condition

for absolute PPP to hold.

False. It can be considered a necessary condition (if, for instance, transport costs prevent equalizing individual prices in different currencies, no PPP will result in aggregate) but it is not sufficient. The main reason is that price indexes are calculated with baskets of goods and services that reflect consumption patterns, that can differ across countries, thus preventing aggregate PPP to hold. The issue of traded vs non-traded goods can also be cited: no arbitrage is possible with non traded goods in different countries, so that PPP can be violated for them also in the long run.

(c) If the sensitivity of the demand for money to an increase in output is small, the AA curve is rather flat (when drawn, as usual, with the exchange rate on the vertical axis). True. To answer it is crucial to show that the method to derive the AA line is well understood. In the usual double graph, where the money and the forex markets are represented, an increase in output shifts the money demand to the right thus increasing the interest rate and (in the upper part of the graph where the OIP is represented) strengthening the exchange rate. Therefore, when Y goes up, E goes down and this explains the slope of the AA line. But when the sensitivity of Md to Y is small, a given increase in Y will result in a small increase in R: therefore, for any given OIP curve, the corresponding decrease of E will also be small. This means that the AA line is flatter than when the sensitivity is higher.

Question 2

After a deep change in the political scenario, the level of aggregate private productive investment in a

country decreases substantially and the medium-long term expectations are such that the change is

considered “permanent”. The exchange rate is freely floating.

(a) Suppose first that there are no monetary and fiscal policy reactions. Use the AA-DD model to show

the short and long term effects of this abrupt event on the nominal and real exchange rate as well

as on the levels of economic activity and prices. What happens to the real interest rate?

The answer is exactly like in the case of a permanent fiscal restriction. The DD line shifts to the left but also the AA line shifts up and to the right, given the depreciation of Ee , due to the expected permanent nature of the decrease in investment. The latter shift will be such as to avoid any change in the price level, a change that would prevent the long term re-equilibrium of the

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money market: this means that also Y will not change in the short run (otherwise it would differ from the full employment level and prices would change) and that the new short-term equilibrium will be also a long-term equilibrium, with both lines shifted up and a resulting nominal and real depreciation. The latter plays a crucial role in re-equilibrating the macro-economy as it triggers an increase in net exports to substitute the lower level of investment while keeping the full employment level of aggregate demand. As far as the real interest rate is concerned: R=R* (unchanged by hypothesis) will keep holding in the new equilibrium where, obviously, inflation will be absent : therefore both the nominal and real interest rates will be unchanged.

(b) Is it possible for monetary and/or fiscal policies to reproduce the original equilibrium in the short

and/or in the long run?

The most obvious, short, and elegant answer - exploiting the idea that the consequences of the shock to investment can be dealt with like those of fiscal policy - is that YES, it is possible to immediately restore the initial equilibrium with a permanent fiscal expansion that compensates the shrinking private investment pushing back both the DD and the AA lines towards their original positions. DD shifts as new aggregate demand originates from the government budget, while the AA shift follows the return of Ee to its original level in view of the permanent nature of the fiscal expansion.

Question 3

Provide three synthetic definitions, each followed by a short explanation and comment, of the following

three expressions:

(a) Fisher effect

It is the effect of a change in inflation (expectations) on the nominal interest rate when, by hypothesis, the real interest rate is constant (for instance because PPP holds). The increase in R will be exactly equal to the increase in (expected) inflation.

(b) Relative PPP

It is PPP expressed with dlogs, % changes, stating that the change in the nominal exchange rate equals the difference between inflation rates of two countries.

(c) Real international interest rate parity.

States that the difference between the domestic and the foreign real interest rates equals the expected depreciation of the real exchange rate. This parity can be obtained combining the OIP with relative PPP.

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Question 1




(a) The current account of the balance of payments does not include only exports and imports of

goods and services.

True. Besides exports and imports the main items included in the current account are incomes from factors (like interest and dividends earned on foreign financial assets owned by domestic citizens, as well as interest and dividends paid to foreigner owners of domestic assets) and unilateral transfers (like international development aid received or transferred abroad).

(b) The ‘real interest parity condition’ implies that, if the foreign real interest rate is constant, also

the domestic real rate cannot change.

False. The condition equates the difference between the domestic and the foreign real interest rate to the expected change of the real exchange rate of the domestic economy. Therefore, if the latter changes (depreciates/appreciates), the domestic real rate changes (increases/decreases) also if the foreign real rate remains constant.

(c) Fixed exchange rates are worse (than floating) for macro-stability when the main shocks come from

the goods and services market (i.e. from DD shifts).

True. It can easily be proved showing on a AA-DD graph the extent of the change in Y caused by a shift in the DD when AA does not move, which implies a change in E, and then showing that a fixed exchange rate policy would imply a contemporaneous shift of the AA as well, which amplifies the change in Y. The question does not require (but … allows) to complete the answer by showing that, on the contrary, when the shock to the initial equilibrium is caused by a shift in the AA, a fixed exchange rate regime would completely stabilize Y by bringing back the AA to its initial position.

Question 2

Consider the AA-DD-XX model, with a purely floating exchange rate.

(a) Show the short run effects of an increase in the foreign price level on the level of income, the exchange

rate and the balance of payments.

Suggestion: start from a long run equilibrium point with zero current account of the balance of payments (the three lines AA, DD and XX crossing in the same point), even if the question does not say that this is the case. An increase in P* increases the competitiveness of domestic products, thus increasing net exports and aggregate demand. The effect is a rightward shift of DD and of XX as well. The two lines shift by the same vertical amount: after they have shifted, along both lines the same Y values (including the full employment long term equilibrium Y from which the system has been displaced by the change of P*) correspond to values of E appreciated by the same % of the increase in P*. In other words: along both lines any level of Y will correspond to the same real exchange rate as

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before the change in P*, as aggregate demand and net exports depend on the real exchange rate. No reason, in the short run, to shift the AA. The new short term equilibrium is at the crossing of the non-shifted AA with the shifted DD: therefore Y is higher and, as the DD is steeper than the XX – for reasons well explained in the textbook , it is immediately evident from the graph that this new short term equilibrium is above the shifted XX, resulting in an improvement of the current account balance of payments. One could add a comment like: the nominal exchange rate appreciates but – in the short run, when domestic prices cannot change by definition! – not as much as P* increases: therefore the real exchange rate improves, increasing net exports.

(b) Show the effect on the same variables of a transitory decrease of the domestic demand for money (for

every level of income and of the interest rate) .

A decrease in the domestic demand for money, ceteris paribus, exactly like an equivalent increase in the supply of money, shifts the AA to the right (one can prove this with the double graph picturing the money and forex markets together, i.e. the graph from which the AA line is constructed), causing a increase in Y, a depreciation and a trade surplus (a new short run equilibrium where AA and DD cross above the unchanged XX).

(c) How would your answers to (a) and (b) change in case the exchange rate is kept fixed by the central

bank?

To keep a fixed exchange rate the monetary authorities must intervene in the forex market causing a change of the money supply and a corresponding shift of the AA line sufficient to keep E constant. In the case of (a) a rightward shift of the AA is needed further increasing Y and the surplus (as the appreciation is avoided). In the case of (b) the story is simpler, as the AA will go back to its initial position and all the values of the variables will be as before the decrease of Md which the central banks has matched by an equal decrease of Ms to avoid the depreciation.

Question 3

Suppose an economy in long term equilibrium with a given exchange rate (Eo), an interest rate and a real

money demand and supply, suitably described in a double graph featuring both the forex and the domestic

money markets.

(a) Show what happens to the short-term equilibrium in case the future expected exchange rate

suddenly appreciates, with no reaction by monetary authorities.

Simply recall the equation of the open interest parity (OIP) pictured in the upper part of the graph and observe that a decrease in Ee shifts down the OIP line. With no reaction of monetary policy (i.e. no change in the domestic interest rate) the shift causes an appreciation of the market determined value of E equal to the appreciation of the expected exchange rate.

(b) Suppose there is imperfect asset substitutability between domestic and foreign currency

denominated assets. Suppose also that the central bank wants to try and push the exchange rate

back towards the original Eo level without changing the money supply. What type of “sterilised

intervention” should the central bank operate?

To counteract the appreciation of E the central bank must purchase foreign currency putting upward pressure on its price in terms of domestic currency. But this move implies an unwanted

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expansion of the domestic money supply which can be avoided by “sterilizing the intervention”, i.e. selling domestic bonds (previously in the portfolio of the central bank) to reabsorb the money used to purchase foreign assets. Given imperfect substitutability, the resulting change in the mix of domestic and foreign assets in the market will not be without consequences, even if the money supply is unchanged: the risk premium on domestic bonds will increase (as the amount of them included in the portfolio of the central bank has decreased: a smaller A in the textbook formula of the risk premium), which will shift up the open interest parity line and contain or eliminate the appreciation of E.

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Question 1

Are the following three statements TRUE or FALSE? Motivate your answer in a brief way, but

showing that you are applying the right theory and/or using the correct and relevant information. It

can happen that the statement is neither totally true nor totally false: if you really think this is the

case, clearly explain why.

(a) The overshooting of the exchange rate, when a permanent monetary policy change takes place, is

equal, in percentage points, to the immediate change of the interest rate.

True. The overshooting is needed to match the permanent change in the nominal money supply Ms (suppose an increase) with a change in Md, before prices adjust and neutralise the nominal change in money. The needed increase of Md must take place via a reduction of the domestic interest rate R which (as the OIP holds) equals the foreign one (R*) plus the expected depreciation of the domestic currency. But with R* constant, to decrease R an expected appreciation (decrease) of the exchange rate is needed, which contradicts what the market expects when Ms increases. The only solution to this contradiction is an excessive depreciation immediately following the monetary expansion, that generates an expected appreciation to bring back E towards a less depreciated level, rationally expected in the long run, when the price level has completed its job of re-equilibrating the system. The expression “overshooting” designates this excess of the initial depreciation (or appreciation, in case of a monetary restriction). The extent of the overshooting (and of the corresponding expected appreciation) must be coherent with the reason that justifies the phenomenon, namely the needed decrease of the interest rate. Therefore the statement is true. A much shorter (perhaps too short) answer would simply stress that the open interest parity always holds, so that the interest rate differential must equal the expected change in the exchange rate and the latter is by definition the difference between the long term equilibrium exchange rate and the short term level that includes the overshooting.

(b) With a fixed nominal exchange rate, a fiscal restriction causes, in the long run, an appreciation of

the real exchange rate.

False. A long run effect of fiscal policy exists only if the policy is permanent. But (this is a tricky aspect of the question that should not confuse the well prepared student) the long run effect of a permanent fiscal policy is immediately reached also in the short run, at least in the model with rational expectations and other crucial hypotheses that is exposed in the textbook. In that model, permanent fiscal restrictions cause immediate depreciations of the nominal exchange rate (the AA line shifting upwards together with the DD) with no impact on the price level (nor on the level of long term equilibrium real income, while the composition of aggregate demand changes as net exports increase to compensate for the lower net public demand). Therefore the real exchange rate depreciates (both in the short and in the long run).

(c) An exchange rate pass-through equal to zero means that a nominal exchange rate depreciation

does not change the price of imports in foreign currency.

False. The pass-through is the percentage change of import prices denominated in domestic currency divided by the percentage change of the nominal exchange rate. With zero pass-through foreign exporters decide to sell their products to domestic importers at an unchanged domestic price, in spite of the fact that this price will be translated into a lower price in foreign currency (in

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proportion to its appreciation). The reason for this behaviour is probably that they prefer to give up profits (and perhaps suffer temporary losses) than risking to lose clients and market share in the depreciating country. On the contrary, when the pass-through is one the price in foreign currency does not change and the price in domestic currency increases by the same percentage as the exchange rate.

Question 2

Suppose the long-term equilibrium level of the real exchange rate of a country increases

(depreciates).

(a) What can be the cause of such a change?

The textbook offers only one simple “theory” to explain the equilibrium level of the real exchange rate: the theory is expressed with a graph where the real equilibrium exchange rate (on the vertical axis) equates an upward sloping demand for domestic goods (as a proportion of global demand for goods: the latter tends to shift towards domestic goods as they become cheaper because of a higher, depreciated real exchange rate) to a vertical supply (assuming for simplicity that the proportion of goods produced by the domestic country does not depend on prices and exchange rates but only on the country’s productive capacity). On the basis of this model, an increase (depreciation) of the real exchange rate can be caused by a decrease in the relative demand for domestic goods (a leftward shift in the demand line: to sell the unchanged supply a cheaper international price is needed) and/or by an increase in the relative supply of goods produced by the country (a rightward shift in the supply line due, for instance to an increased relative productivity of the domestic country: to sell the result of the increased productivity, for a given global demand, a larger market share must be conquered with a real depreciation).

(b) If the change was expected, what was the consequence of this expectation on the level of the

country’s long term expected real interest rate?

According to the international real interest parity, international real interest rate differentials reflect expected changes in the real exchange rates: the domestic real interest rate is higher than the foreign when the domestic real exchange rate is expected to depreciate. The answer is therefore that the consequence of the expectation (provided that, obviously, the foreign real interest rate is assumed to remain constant) is a higher expected real interest rate of the country.

(c) The fact that the real exchange rate has changed contains a message on the validity of the

Purchasing Power Parity (PPP). How would you state this message?

PPP implies by definition a constant real exchange rate, equal to 1, as the domestic price level, when PPP holds, equals the foreign price level expressed in domestic currency, i.e., multiplied by the exchange rate. Considering shifts in relative global demand and supply of domestic goods means that the PPP hypothesis is excluded.

(d) Suppose that the new level of the long term equilibrium real exchange has been reached and will

never change again. Does this mean that PPP will hold from now on also in the short run? For

answering in general terms use the following example: suppose that a temporary money supply

expansion is performed by the central bank and explain whether or not the PPP will hold in the

short term.

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PPP is essentially a long-term hypothesis: in the short term it does not make much sense as prices are sticky while nominal exchange rates can jump up and down. A temporary money supply expansion will temporarily depreciate the country’s exchange rate leaving the price level unchanged (also abroad, obviously). Therefore also the real exchange rate will temporarily depreciate, decreasing the domestic price level with respect to the foreign price level, both expressed in the same currency: this means that in the short run PPP will not hold even when it holds in the long run.

Question 3

The government of a country in full employment-long-term equilibrium announces an expansionary

fiscal policy, a tax cut, for example, to be financed in deficit by selling government bonds. Describe

the impact of the decision on the short and long equilibrium values of the nominal and real

exchange rate, the nominal and real interest rate, the level of economic activity, the price level, in

two different cases:

(a) When the fiscal expansion is expected by the markets to be temporary

Temporary fiscal expansions shift the DD line to the right until they are inverted. The AA does not shift if they are financed without printing money. The short-term nominal exchange rate temporarily appreciates as much as the real exchange rate (as prices do not change in the short term, because they are sticky, nor in the long term, because the inversion of fiscal policy will eliminate excess demand). In the short term the level of economic activity increases but its expansion will not survive in the long term, when the fiscal expansion disappears. As for interest rates, the temporary increase in Y pushes up Md and the equilibrium interest rate (nominal and real, as prices stay put) but in the long-term equilibrium interest rates are the same as before the temporary fiscal shock.

(b) When the expansion is expected to be permanent and markets believe that the deficit will in fact

be financed by selling public securities on the open market and not by printing money

In this case, as extensively explained in the textbook, rational expectations anticipate the exchange rate appreciation and Ee decreases shifting down also the AA line to cross the shifted DD above the unchanged Y. The only consequence of the permanent fiscal policy has been the appreciation of the nominal and real exchange rate (implying a changed composition of aggregate demand with less net exports and, for instance, more private consumption if the tax cut produces this effect). The price level doesn’t change, as aggregate demand never abandons its long-term equilibrium level. There is no reason for a change in the interest rate.

Consider now your answer to (b) and, in particular, the impact of the fiscal expansion on the price

level. This impact is different if markets expect that the tax cut will end up being financed, at least in

part, with the help of the central bank, increasing the money supply. Can you explain why the

hypothesis on the behaviour of the money supply is so important?

If a permanent increase in money finances part of the tax cut, the long-term price level changes. In case this money creation is expected, the AA line, in the short run, does not shift down as much as required to cross the DD above an unchanged Y: the short-term level of economic activity can increase, thus causing the change in prices in the long run. If the expected increase in the money supply does not take place immediately, the higher level of Y could cause an increase in Md and in

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the interest rate. The whole story becomes more complicated and the transition from the short to the long run depends on the precise behaviour of (still rational?) expectations that one should specify. The hypothesis on the behaviour of the money supply is very important because an unchanged Ms anchors the price level and the rational expectations attached to it (the “rationality” of expectations is another important hypothesis of the model used to study permanent fiscal expansions in the textbook). The intuitive reason that justifies the lack of inflationary consequences of fiscal expansions in full employment is precisely the expectation that the money required to allow prices to increase will not be created. With no monetary creation the only effect of permanent fiscal expansions (as of any increase in another component of aggregate demand) is a crowding out of net exports favoured by an appreciation of the nominal and real exchange rate.

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Question 1

a) Suppose the current account of the balance of payments of a country has a surplus of 100.

Suppose also that the deficit of the public sector is 10 and that aggregate investment is 50. How

much is private saving?

From the fundamental identity equating the current account surplus to the excess of saving over investment plus the public sector surplus, CA=(S-I)+(T-G), one can obtain S=100+50+10=160.

b) What is the difference between direct and portfolio investment in the terminology of the

balance of payments?

Direct investment implies the “control” of the asset abroad that has been acquired by investing: if I buy an apartment that I fully own, a green field where to build a factory, if I become the controlling shareholder of a company, etc. A portfolio investment, on the contrary, is the acquisition of a credit, a security, a minority share-holding, with the sole intention to earn an interest by holding the asset, or a dividend, or to resell the asset at a higher price realising a speculative profit.

c) List at least two reasons to justify the idea that a surplus in the current account of the balance of

payments of a country must not last too long; in other words: a sound, sustainable long term

current account must exclude not only excessively lasting deficits but also surpluses.

Too large a current account surplus for too long poses problems (Ch. 19 of KOM textbook, section on “External balance”). For a given amount of saving, domestic investment becomes insufficient, sacrificing domestic employment as well as the benefits of technological spill-over to other domestic enterprises, decreasing the proceeds of taxes on the returns on capital (as domestic capital is easier to tax than capital owned abroad). The accumulation of credits on foreign debtors becomes excessive generating risks of not being repaid which leads to a loss of national wealth. The country in surplus can be criticized by the rest of the world (for being “mercantilist” and the cause of the deficit of other countries) and become a target for discriminatory import barriers imposed by trading partners with correspondingly growing external deficits.

Question 2

Starting from a long term equilibrium position, with full employment, show

a) that a permanent fiscal restriction, when it is not associated with a change in the money supply, is

not deflationary and causes an improvement of the current account of the balance of payments;

Use the DD-AA-XX model and suppose that the XX corresponding to a balance of payment in equilibrium crosses the other two lines in the same point. A permanent fiscal restriction shifts the DD to the left and (via the expectation of depreciation in the long-run) shifts also (immediately, in the short run) the AA to the right. If there is no change in the money supply prices cannot change, therefore the AA shift will be as large as needed to cross the shifted DD vertically above the starting equilibrium Y. If the fiscal restriction does not hit net exports, the XX doesn’t shift: therefore, given that the new point where DD and AA cross (in the short and in the long run as well) is higher in the graph than before the restriction, it falls above-and-to-the-left of the XX, i.e. in the surplus region. [Note that the reason why prices do not change is that the real demand for

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money Md(R,Y), in the long run, does not change because nothing happens to change the long term equilibrium value of Y and, in the long-run, when the expected change of E is zero, R keeps being equal to R*: therefore also Ms/P must remain constant and, with no change in Ms, this means no change in P.]

b) the short and long-term effect on the exchange rate, on the level of economic activity and on the

price level, of a permanent decrease in exports.

Graphically, a permanent decrease in exports (as in other autonomous components of aggregate demand), can be pictured exactly in the same way as the fiscal restriction in a), provided that the money supply does not change (why should it change? the question does not hypothesize any change of Ms). Therefore, as above, neither Y nor P change in the short and in the long run. [Note that the question does not consider the XX nor the impact of the decrease in exports on the balance of payments; but it easy to conclude that, differently from a), the XX shifts upward and to the left, crossing the other two lines in their new equilibrium point: the resulting depreciation of the exchange rate (nominal and real) is what is needed (ceteris paribus, with no other policy reactions) to neutralise the decrease in exports.

If you deem it useful, add a short comment of your answers to a) and b) stressing what they have in

common.

They both consider changes in one component of real aggregate demand with no associated change in the money supply. Therefore in both cases P stays constant and the only real effect is a modification of the nominal and real exchange rate and of the composition of an unchanged total Y.

Question 3

Are the following three statements TRUE or FALSE? Motivate your answer in a brief way, but showing

that you are applying the right theory and/or using the correct and relevant information. It can happen

that the statement is neither totally true nor totally false: if you really think this is the case, clearly

explain why.

a) It is never possible for a central bank to intervene in the foreign exchange market and influence

the exchange rate without changing the money supply.

False. When domestic and foreign currency denominated bonds are imperfect substitutes, “sterilized interventions” can influence the exchange rate without changing the money supply. If the central bank, for instance, buys foreign bonds (thus potentially increasing its money supply) and, contemporaneously, sells domestic bonds (thus decreasing the money supply, i.e. “sterilizing” the consequences of the previous intervention on the money supply), the market portfolio will contain a larger proportion of bonds denominated in domestic currency, which aren’t considered, by hypothesis, perfectly substitutable with bonds denominated in foreign currency : this will depress the price of the domestic currency, i.e. will tend to depreciate the exchange rate. The result can be obtained using the double graph picturing the forex and the domestic money markets: the sterilized intervention, by decreasing the amount of domestic bonds in the portfolio of the central bank, pushes up the so called “risk premium” ρ(B-A), which is positively correlated with the total amount of domestic public bonds (B) minus those that are kept out of the market and held by the central bank (A). Increasing ρ pushes up the interest parity line on the forex market allowing a depreciation even if the money supply (and therefore the domestic interest rate) does not change.

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b) Fixed exchange rates tend to create “asymmetries” in the international monetary system, while

“symmetry” is an advantage of floating rates.

True. To organise a fixed exchange rate regime an “international currency” (that can also be labelled “reserve currency”) is needed so that each currency’s price is fixed in terms of it. If this “international” currency is also a national currency, the system is asymmetric as monetary policy of the country issuing the reserve currency will have an influence on other countries’ money supplies (that will change when central banks intervene to keep their exchange rate fixed). Important examples of this asymmetry are the dollar dominance during the Bretton Woods system, that died precisely because excessively expansionary US monetary policy was disliked by countries such as Germany, France and Japan, and the German dominance during the EMS years, which contributed to the disinflation of Europe as countries participating in the EMS where “obliged” to follow the anti-inflation policy of Germany to keep their exchange rates pegged to the Deutsche Mark. In theory, the gold standard was a counterexample as the reserve currency was gold and no country had the privilege of issuing it. But in practice (forgetting about the special situation of countries with gold mines) the gold standard functioned in a rather imperfect way as British pounds were kept by countries as reserves without converting them into gold. The system was therefore somewhat asymmetric with the UK enjoying a special degree of freedom in deciding monetary policy for itself and influencing other countries’ money supplies.

c) When PPP holds the difference between domestic and foreign nominal interest rates equals

the difference between domestic and foreign inflation.

True. Market speculation results in the open interest parity, equating the international nominal interest differential to the expected change in the exchange rate. But the latter, if PPP holds, equals the difference between domestic and foreign inflation. Note that one implication of the statement is also that with PPP domestic and foreign real interest rates are equal.

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Question 1

(a) Write the expression of the Purchasing Power Parity (PPP), carefully specifying the meaning of the

variables that enter PPP.

“Absolute” PPP can be written P=EP*, where P and P* are the domestic and foreign price levels and E in the nominal exchange rate of the domestic currency (units of the domestic currency to buy one unit of foreign currency). “Relative” PPP is derived by log-differentiation and can read: Δ%E = π – π*, where the percentage change in E (rate of depreciation) is equal to the difference between the rates of inflation, indicating with π and π* the percentage changes in P and P*.

(b) Assume that price levels are perfectly flexible and put the PPP together with an equation

expressing the equilibrium between the demand and the supply of money. Suppose that Y, real

income, increases. Show how the exchange rate will be affected. Intuitively comment your result.

Has the level of interest rates been affected?

Money market equilibrium equates in the two countries, the real supplies of money (Ms/P and Ms*/P*) with the real demands for money, which depend positively on the country’s Y and negatively on its nominal interest rate. Deriving expressions for the price levels P and P* from these equations and substituting them in the absolute PPP, an expression for E is obtained (a “monetary theory of the exchange rate”) where the domestic level of income has a positive impact on the domestic demand for money in the denominator. Therefore, by increasing the denominator, an increase in Y causes an appreciation of E. Intuitively, the result can be understood as the consequence of increasing Y without increasing M when prices are flexible: there is more demand for the domestic currency (to finance the larger amount of transactions associated with a higher Y) and an unchanged supply of it, which triggers an increase in its price, both in terms of foreign currencies (E decreases) and in terms of domestic goods (P decreases). With perfectly flexible prices there is no difference between short and long term and therefore no expectation of further changes in E: the domestic interest rate keeps being anchored to the unchanged foreign R*. [Note that the question is easy to answer if the right model is picked. PPP + money market equilibrium is the “monetary approach” model of Chapter 16 in the KOM textbook. The chapter is devoted to the long run but it also applies to the short run if, as specified in the question, prices are perfectly flexible, as they are usually supposed to be in the long run. The mistake to be avoided is to start reasoning with the double graph where the forex short term market is graphed together with the money market. This graph is useful to explain changes in the short run with rigid prices; only after that one can allow prices to change and generate a new long term equilibrium. The graph, to be sure, can also indicate the right answer to the question, but only with the following geometrical reasoning, that students aren’t trained to apply by the textbook:

E E0

oip0

E1 oip1

R

M0

M1

M/P ]

Initial equilibrium in E0 and M0. Increasing Y shifts the demand for money line to the right. With no increase in the supply of money, a flexible P decreases shifting down the real money supply line. As PPP is expected, also the expected value of E decreases triggering a shift in the open interest parity line from oip0 to oip1 . The new equilibrium is therefore in E1 and M1. It would be a mistake to look for the new exchange rate starting on the initial oip line in correspondence to the higher interest rate at the crossing point of the new demand for money with the old real supply line. After such a mistake the new long run equilibrium is difficult to reconstruct.

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(c) Assume now that price levels are sticky (rigid in the short run, where PPP does not hold, and fully

flexible in the long run) and show the impact of a permanent increase in Y, on both the exchange

rate and the interest rate, first in the short and then in the long run. (Suggestion: use the double

graph where both the forex and the money markets are represented).

[The model to be used here is the overshooting model of Chapter 15 of the KOM textbook, with the geometry of Figure 15-12, suitably modified to analyze the case of a permanent increase in the demand for money instead of the consequences of a permanent increase in the supply. But the answer is identical to the one to be given in the case of a decrease in the supply (in the money market an excess demand for money to be readjusted results both from increasing the demand and from decreasing the supply).] In the double graph like the one on the left of Figure 15-12, referring to the short run, a rightward shift of the money demand line is considered instead of a downward shift in the money supply line. This causes an increase in the interest rate and an appreciation of the exchange rate, but not along the initial open interest parity line (OIP), because an appreciation is expected also in the long run and the expectation causes an immediate downward shift of the OIP. Therefore in the new short term equilibrium the exchange rate is much stronger and the interest rate higher. The evolution of the system in the long run is analogous, mutatis mutandis, to what is described in the right hand side of Figure 15-12. The excess demand for money, temporarily corrected by the increase in the interest rate, gradually causes a decrease in the price level, thus pushing down the real money supply line and decreasing the interest rate, while in the forex market the exchange rate gradually corrects its initial excess appreciation (“overshooting”). The system ends with an exchange rate stronger than before the increase in Y but weaker than in the short run: the new long term equilibrium exchange rate corresponds to the point, along the lowered OIP, vertically above the initial interest rate. The latter (call it R0) re-equilibrates also the money market as the lower price level has driven the real money supply down to cross the demand for money (the rightward shift of which constitutes the original shock to the system in this exercise) precisely at R0. Intuitively, the overshooting (excessive appreciation) of the exchange rate in the short run has caused an expected depreciation and the latter, in the OIP equation, has allowed the interest rate to rise temporarily, killing the excess demand for money; overtime, prices perform their job, they decrease and they allow the interest rate to decrease and the exchange rate to correct the excessive appreciation.

Question 2

(a) “When there is freedom of capital movements, the domestic real interest rate is always equal to

the foreign real interest rate”. True or false? Why?

False. The freedom of capital movements allows international differences between real interest rates as long as there are expected changes in real exchange rates that contribute to equalize the real yield of investments in different countries. The real interest rate parity (RIP) can be written as follows: r = r*+ Δ%qe , where r and r* are, respectively, the domestic and foreign real interest rates and the second term to the right of the equal sign is the expected depreciation of the real exchange rate of the domestic country. If I invest in the latter I will earn a higher real rate but suffer a real depreciation of the currency in which my investment is denominated: on balance I will earn, in real terms, as much as I would earn investing abroad, which I am allowed to do by the hypothesized freedom of capital movements. RIP can be obtained by differentiating logarithmically the definition of q=EP*/P, thus obtaining Δ%q = Δ%E + π*- π, substituting the expected depreciation with the nominal interest rate differential (i.e. using the open interest parity) and then recognizing that differences between nominal interest rates and inflation rates are real interest rates.

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(b) Suppose that the share of domestic goods and services in the global demand for goods and

services is expected to remain constant, for any given level of the exchange rate. While, due to an

increase in productivity, domestic output is expected to become a larger share of the world’s

output. What are the implications of these hypotheses for the relation between the domestic and

the foreign real interest rate?

The question is based on the textbook’s very simple graphical theory of the equilibrium level of the real exchange rate. The latter equates relative the global demand and supply of a country’s production. Demand increases with a higher real exchange rate (i.e. with a real depreciation, with a stronger relative price competitiveness of the country’s products) while supply can also be though as given by the productivity of the country’s resources and independent on the country’s real exchange rate. With the latter on the vertical axis, the question asks what happens when the vertical supply line is expected to shift to the right with no shift in the demand schedule. The answer is obviously that the expected equilibrium level of the real exchange rate increases (depreciates). From the RIP discussed under a) this implies that the domestic real interest rate is higher than the foreign r*.

Question 3

On the basis of two hypotheses: the purchasing power parity (PPP) and the international “open”

interest parity,

(a) show that the difference between the nominal interest rate in the two countries equals their

inflation differential. What do you conclude about the real interest rates in the two countries?

Relative PPP can be written, with the usual symbols, Δ%E = π – π* ; substituting the open interest to express the depreciation the result is obtained. As in both countries the real interest rate is defined as the difference between the nominal interest rate and the rate of inflation, the conclusion is that the two real interest rates are equal. This is an important implication of PPP.

(b) Substitute the price levels in the PPP with their expression obtained from the equilibrium

relation between the real demand for money and its real supply. Show that, according to the

resulting formula, when the nominal interest rate of a country is increased, its currency

depreciates. This is a counter-intuitive result as we usually think that a higher yield on a

currency strengthens its value. Reconcile the result with intuition: help yourself with the

answer to part a) of the question.

The question is about the “monetary approach” to exchange rate determination explained in Chapter 16 of the textbook. The substitution allows to express the exchange rate as the ratio of the domestic and the foreign nominal money supplies times the ratio of the foreign to the domestic real demand for money. Both demands for money depend negatively on the respective nominal interest rates. Therefore when the domestic nominal interest rate is increased the denominator of the formula decreases, i.e. the exchange rate increases, the domestic currency depreciates. The opposite happens when the foreign nominal interest rate increases. The result can be reconciled with intuition considering that with PPP (which holds by hypothesis in the question) the domestic and the foreign real interest rates are equal; therefore, when one considers a ceteris paribus increase of a country’s nominal interest rate,

21

the increase can only be the result of higher inflation (as the other component of the real interest rate remains equal to the foreign real rate, i.e. constant). With higher inflation the resulting depreciation of the country’s currency is coherent with intuition. A higher nominal return on a currency increases the demand for it, thus triggering its appreciation, only to the extent that it is due to an increase in the real part of the interest rate. A nominal interest rate that is high because of inflation does not increase the attractiveness of a currency: it is a sign of its weakness, as shown by the monetary approach.

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Question 1

Are the following three statements TRUE or FALSE? Motivate your answer in a brief way, but showing

that you are applying the right theory and/or using the correct and relevant information. It can happen

that the statement is neither totally true nor totally false: if you really think this is the case, clearly

explain why.

(a) Excessive government deficits, like in many countries of the euro area, always become deficits of

the balance of payments, thus causing a dangerous accumulation of foreign indebtedness.

False. From the fundamental identity CA = (S-I) – (G-T) one can see that a high (G-T) results in a deterioration of the current account only to the extent that private saving net of investment does not compensate the public deficit with a higher financial balance of the private sector, following an increase in S and/or a decrease in I. According to a hyper-rational (“Ricardo-Barro”) approach, for instance, a higher deficit increases private saving as citizens set aside the money that will be later taxed away to reimburse the excessive public debt: according to such a theory public deficits will not result in balance of payment deficits. The theory may be wrong but, in any case, given the presence of (S-I) in the identity, the statement is false because of the “always”.

(b) In the short run, a permanent increase in the money supply has stronger effects on the exchange

rate and output than an equal temporary increase.

True. When the money supply increases the AA line shifts to the right, increasing output and depreciating the exchange rate. The shift of the AA is larger when the money supply change is believed to be permanent, because a permanent change will also trigger an expected depreciation (which does not happen with a monetary expansion that is expected to disappear in the long run), i.e. a higher value of Ee, which acts as an additional factor (besides the increase in the money supply) in pushing the AA line to the right (as it pushes the open interest parity to the right). Therefore a permanent change in Ms will cause, in the short run, a larger change in Y and E.

(c) When the exchange rate is free to float, temporary fiscal expansion increases output more than

when the exchange rate is fixed.

False. With free floating a temporary fiscal expansion shifts the DD to the right while the AA does not move. The result is an appreciation of the exchange rate. To avoid the latter, a fixed exchange rule requires an expansion of the money supply (a rightward shift also of the AA). With both lines shifting a larger increase in output takes place. Intuitively, fixing the exchange rate requires a monetary expansion to follow the fiscal expansion, thus causing, in the short run, a larger increase in aggregate demand.

Question 2

With the exchange rate on the vertical axis and output on the horizontal axis, draw the AA,DD, and

XX lines describing a situation where there is full employment and equilibrium in the current

balance of payments. Then explain:

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(a) Why the DD and XX lines differ in steepness?

Start from the equilibrium point where the lines cross and consider an increase in the level of economic activity (measured on the horizontal axis) moving along the DD line towards the right. As an increase in Y is only partially absorbed by an increase in domestic consumption (in other words: as the marginal propensity to consume is smaller than 1: the crucial hypothesis in this reasoning and a fundamental hypothesis in the Keynesian macroeconomic equilibrium theory) aggregate demand does not increase as much as the supply, except if net foreign demand (CA: the current account of the balance of payments) does not increase. But along the DD aggregate demand is always equal to aggregate supply, by definition. Which means that moving to the right along the DD drives the exchange rate higher enough to improve CA (from equilibrium to a surplus). The surplus area lies to the left-above the XX. Which proves that the DD is steeper than the XX. In other words: with a higher aggregate supply (and a positive marginal propensity to save out of additional income), in order for aggregate demand to increase by the same amount (has it happens along the DD), the exchange rate must depreciate sufficiently to develop a current account surplus, i.e. more than what is needed to keep the CA in equilibrium (which is the depreciation implied by the positive slope of the XX, needed to compensate for the fact that a higher income increases imports and a depreciation must neutralise this effect also by stimulating exports). As CA is in equilibrium along the XX, and the depreciation along the DD must be larger, the DD must be steeper than the XX.

(b) The reason of the sign of the slope of the AA line

The AA line pictures the combinations of E and Y that keep the money market (or, better, assets markets) in equilibrium. Starting from a point on the AA and considering a higher Y, the demand for money is higher. For a given supply of money the larger demand triggers a higher interest rate that, along the open interest parity line, is associated with a stronger (lower) exchange rate. Therefore the AA associates higher Ys with lower Es: it slopes down.

(c) What happens to the XX line if the foreign price level increases?

An increase in the foreign price level increases the competitiveness of domestic productions: ceteris paribus, exports increase and imports decrease. For any level of the nominal exchange rate, a higher Y is required to increase imports and keep the same current account (or, one could say: for any level of Y a stronger exchange rate is required to neutralize the increase in net exports). Therefore an increase in the foreign price level shifts the XX down and to the right.

Question 3

Graph the short run equilibrium of the market of the euro (in terms of dollars) together with the

equilibrium of the European money market. Show the effect on the exchange rate of the euro of reducing

the US interest rate,

(a) When European monetary policy does not change: suppose first that the US monetary policy leaves

the expected future exchange rate unchanged, and then that the US decision influences

expectations;

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When European monetary policy does not change, nothing changes in the lower part of the double graph, where the domestic money market is represented crossing the demand and supply of money. As the foreign interest rate decreases, the open interest parity line, in the upper part of the graph (where the foreign exchange market is represented), shifts down and to the left. Vertically, above the unchanged domestic interest rate, the equilibrium exchange rate decreases (appreciates: in accord with intuition, as investing in domestic assets is now more convenient). When also the expected future exchange rate depreciates (because, for instance, agents expect the expansionary move of US monetary policy to be permanent), the shift of the open interest parity line is larger (because in the expression R = R*+(Ee-E)/E both R* and Ee decrease) and therefore E appreciates more.

(b) when European interest rates are changed to the same extent as the US; show also the extent of

the required change of the European supply of money.

If the changes in domestic and foreign interest rates are the same, the open interest parity holds with no change in the exchange rate. This happens when the European money supply is increased to the extent needed to shift down the Ms line so that it crosses the Md line at the level of R above which (on the open interest parity shifted by the lower foreign interest rate) the exchange rate is the same as before the US monetary policy move. Graphically:

E

oip0

E0 oip1

R1 R0 R

Ms

ΔM

M/P

ΔM is the required change in the European supply of Money, as it brings the equilibrium interest rate down to R1 from R0 . This change in the domestic interest rate is the same as the change in R* as one can see from the fact that E does not change from the initial value E0 when the lower R* shifts the open interest parity line from oip0 to oip1.

25


Question 1

Are the following three statements TRUE or FALSE? Motivate your answer in a brief way, but

showing that you are applying the right theory and/or using the correct and relevant information. It

can happen that the statement is neither totally true nor totally false: if you really think this is the

case, clearly explain why.

(a) The likelihood of observing an exchange rate overshooting following a given permanent change in

domestic money supply, depends on the degree of flexibility of goods prices, with high degree of

price flexibility making the overshooting phenomenon more likely

False. The first part of the sentence is right: the overshooting is required to trigger an expected change in the exchange rate that allows the interest rate to accommodate the money supply change in the short period, while in the longer period the price level will do the job gradually shrinking the change in the real money supply. Therefore price flexibility is crucial to determine the size and length of the overshooting. But the second part of the sentence is wrong: high flexibility decreases the need for overshooting, makes it less likely, as prices will soon and quickly neutralize the initial change in the real money supply, thus rendering superfluous a change in the interest rate (and the expected change in the exchange rate that, following the overshooting, causes the change in the interest rate) to change money demand in the short run.

(b) If relative PPP is expected to hold, then domestic and foreign expected real interest rates will be

equal

True. PPP implies that the real exchange rate is constant, by definition. The real interest rate parity states that international differences between real interest rates are equal to expected changes in real exchange rates. If the latter are constant, real interest rates are equal.

(c) With a fixed exchange rate, fiscal policy can never improve the position of an economy that

suffers of both internal and the external disequilibrium.

False. An improvement is sometimes possible as can be shown with the graph of the “Four Zones of Economic Discomfort”. When there is both underemployment and excessive current account surplus, for instance, an expanding fiscal policy can improve both external and internal equilibrium. The same happens when a restrictive fiscal policy is used with both overemployment and excessive current account deficit. The problem becomes a “dilemma” when the two disequilibria are badly combined: underemployments and excessive current account deficit or overemployment and excessive current account surplus. In these cases fiscal policy can improve one of the two equilibria but at the cost of worsening the other disequilibrium. In the dilemma situation the cost of keeping the exchange rate fixed is felt in a special way.

Question 2

A country, with a freely floating exchange rate, has a current account deficit that the authorities want to

correct in the short period. They consider three alternatives: monetary policy, temporary fiscal policy and

26

permanent fiscal policy. For each alternative policy specify the sign of the policy change that is needed:

expansion or contraction? Show the short-run impact, on the output and on the exchange rate, of each

policy that corrects the current account deficit. Conclude with a reasoning that compares the three options.

To answer the question an AA-DD-XX graph can be used, with the AA and DD crossing in a point (the initial equilibrium of the system) below the XX (the CA=0 line), i.e. in the current account deficit area. To correct the deficit in the short run that crossing point has to be placed on the XX. Monetary policy alone can do this with an expansionary move, shifting the AA up and to the right until the point where the unchanged DD crosses the XX. This will cause a depreciation and an increase in Y, perhaps unsustainable in the long run if the starting Y is a full employment level of income. Fiscal policy alone, instead, can correct the current account deficit with a restrictive move, temporary shifting the DD up and to the left until the point where the unchanged AA crosses the XX. Which causes a depreciation and a decrease of Y and employment. While the expansionary impact of monetary policy is reinforced by depreciation, the restrictive effect of fiscal policy is only moderated by depreciation, leaving a negative effect of Y. This can be avoided with a credibly permanent fiscal restriction which immediately shifts both the DD and the AA up to cross the XX above the initial level of Y, which is perfect if, as it is convenient to assume, it is a full employment level. Permanent fiscal restriction seems the best choice when the current account disequilibrium is believed to be a permanent problem, as it permanently shifts the composition of demand towards net exports and away of where aggregate demand was pushed by the public budget. On the contrary, if the current account disequilibrium is expected to disappear in the long run, in order to fix it in the short run, temporary monetary policy can do the job at a cost of a temporary overemployment while temporary fiscal restriction causes temporary unemployment.

Question 3

Consider the issue of flexible vs free floating exchange rates: which regime better helps a country to keep

output and employment stable when its economy is hit by an unfavorable disturbance? Answer in three

steps: first show how the two regimes behave when there is a transitory fall in exports; then look at the

case when the fall in exports is expected to be permanent; finally compare the two regimes when, for some

reason (like an increase in investors’ risk aversion) there is a sudden increase in the demand for money for

any level of income.

A transitory fall in exports, with a floating exchange rate, causes a depreciation and some decrease in Y: but the depreciation, stimulating net exports, limits the temporary depression of economic activity. If the exchange rate is kept fixed, on the contrary, the temporary depression is larger. The difference is even neater when the fall in exports is permanent. In this case a floating exchange rate regime allows the AA to shift up (incorporating the expected future depreciated exchange rate value) crossing the DD (shifted because of the fall in exports) above the initial value of Y which therefore stays totally stable. The conclusion is that floating rates guarantee a more stable output when disturbances come from the DD side, i.e., when they are caused by changes in the autonomous components of aggregate demand: intuitively this is the case because exchange rate changes cushion (acting in the opposite sense on net exports) at least in part the impact of the disturbance on Y. An opposite conclusion can be drawn when the disturbances come from the asset market side, like a shift in the AA due to a change in the demand for money. A sudden increase in the demand for money for any level of income shifts the AA to the left, acting in a restrictive way on Y, which would require more money to be financed. If the exchange rate is free to float it appreciates, cutting net exports as much as it is required to contain Y. If the authorities instead keep a fixed exchange rate, they immediately accommodate the increase in the demand for money providing a larger supply of it, thus totally stabilizing output (shifting the AA to the right towards its initial position). With disturbances originated on the money market, fixed exchange rates assure a more stable Y.

27


Question 1




(a) Under imperfect asset substitutability, a country that is fixing the exchange rate of its currency can

– at least temporarily – use monetary policy to pursue domestic objectives.

True. Consider the double graph containing both the forex and the money market equilibrium. On the forex market, equilibrium combinations of the exchange rate and the domestic interest rate are along the open interest parity line and the latter can shift also when the exchange risk premium changes, which happens when a change takes place in the amount of bonds outstanding denominated in the domestic currency, net of those held in the portfolio of the central bank: the higher that amount, the higher the risk premium, the higher-and-more-to-the-right the position of the open interest parity in the upper graph. Suppose the authorities want to expand monetary policy, thus lowering the interest rate, to pursue an expansion in domestic private spending. The lower interest rate would trigger a depreciation of the exchange rate which they do not want to happen. But if the monetary policy expansion has been performed by purchasing domestic government bonds, a smaller ratio of domestic to foreign bonds remains in the market, decreasing the value of the risk premium on the domestic currency and lowering the open interest parity line. The equilibrium exchange rate, corresponding to the lowered interest rate, depreciates less. If this is insufficient to reestablish the initial exchange rate, to be kept fixed, the central bank can push down further the risk premium with sterilized intervention, i.e. by purchasing more domestic bonds and selling an equivalent amount of foreign bonds, thus leaving the money supply and the interest rate at their initially modified, respectively, higher and lower levels, while pushing the open interest parity line down enough to cross the vertical above the equilibrium interest rate at the desired fixed exchange level. Intuitively: with imperfect asset substitutability the central bank can change the mix of domestic and foreign bonds in the market thus manipulating the risk premium which becomes an additional instrument in its hands: with the right combination of money supply and risk premium, the exchange rate and the interest rate become two targets that can be pursued independently.

(b) The Balassa‐Samuelson theory, by explaining inflation caused by the catching‐up process of less

developed countries, provides an explanation of why PPP (Purchasing Power Parity) holds, at least

in the long‐run.

Balassa-Samuelson explains why, during the catching-up process, the prices of non-traded goods increase faster than those of traded goods. PPP holds only for the latter as non-traded have no reason to have their prices equalized with the corresponding goods abroad and they are traded only domestically, with no contact with the currency market. In this sense the statement is false: on the contrary, the Balassa-Samuelson story is one of the reasons to deny PPP between price indices that include also non-traded goods and services. When the catching-up process is finished, the ratio between the price index of non-traded and the price index of traded goods and services is equalized with the same ratio in developed countries. But new shocks are possible and non-traded goods have no reason to fulfill the PPP condition.

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(c) A degree of short‐run pass‐through, from the exchange rate to import prices, smaller than 1,

reinforces the J‐curve effect, making a worsening of the current account the most likely short‐run

outcome of a currency depreciation.

False. With a smaller increase in import prices, the immediate impact of a depreciation on the import bill (when imported volumes are still unchanged) is smaller and therefore a worsening of the current account is less likely and, if it happens, it is a smaller worsening.

Question 2

(a) A balance of payments deficit, with a fixed exchange rate, tends to decrease the official reserves of

a country’s central bank and the money supply of the economy. True or false? Explain your answer

carefully, perhaps also with a numerical example.

True. With a balance of payments deficit outgoing payments in foreign currency are larger than payments received from abroad in foreign currency. Therefore the latter is in short supply and tends to appreciate. To keep a fixed exchange rate (thus preventing the depreciation of the domestic currency) the domestic central bank must intervene in the forex market to sell foreign currency while buying domestic currency. These interventions decrease the official reserves and the outstanding amount of domestic currency (the “money supply”) as well. If the balance of payment deficit is valued 50 units of foreign currency, the effort to keep a fixed exchange rate (at the level of, say, 2 units of domestic currency per unit of foreign currency) will decrease the official reserves by 50 units of foreign currency and the money supply by 100 units of domestic currency. (b) In the sentence above “balance of payments deficit” means a current account deficit. True or false? Why?

False. What matters is the overall balance of payments, net of official transactions. The value of the domestic currency can be pushed down both by current account transactions, like the excess of imports over exports of goods and services, and by financial account operations such as the excess of portfolio or direct investment abroad over investments from abroad. When the exchange rate is left freely floating, the balance of the current account plus the balance of the financial account is zero. But when the central bank intervenes with official transactions, the sum of the current account balance and of the balance of the financial account is the change in official reserves. (c) Answer again part a) of this question considering the case where the country’s central bank

“sterilizes” its intervention on the foreign exchange market. How can this sterilisation take place?

Can in last for ever?

To sterilize the impact of the foreign exchange intervention on the money supply, the central bank must reinsert in the market the money absorbed by selling reserves of foreign currency. This can be done, for instance, with open market purchases of domestic assets such as government bonds. But this cannot last forever if the balance of payments keeps being in deficit: sooner or later the amount of foreign currency reserves will be exhausted and it will become impossible for the central bank to borrow more reserves on international markets or from international organizations such as the IMF. At that point the fixed exchange rate will have to be abandoned together with forex interventions of the central bank. [On the contrary, if interventions are not sterilized, the restrictive monetary policy impact that they cause could help restricting aggregate domestic demand, imports and therefore the balance of payments deficit. After some time the latter could disappear a no more interventions with sales of forex reserves would be needed.]

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Question 3

A country called “China” is pegging its exchange rate to a fixed level. Markets have been expecting the

pegging to continue successfully in the future. Suddenly, markets expectations change: the expected

future exchange rate of the Chinese currency becomes stronger as markets start thinking that the large

Chinese current account surplus will convince Chinese authorities to abandon the pegged level and

appreciate the currency.

(a) Use the double graph including the currency and the money markets to show how a speculative

attack could follow. Suppose Chinese authorities do not change their mind and keep pegging their

currency to the same fixed level. What are the consequences for the Chinese money supply and

Chinese foreign reserves?

The sudden change in expectations causes an inward (down and to the left) shift of the open interest parity line in the upper part of the graph. With the same Chinese interest rate the shift would trigger an appreciation, the expected appreciation. To keep pegging the old exchange rate Chinese authorities must decrease the interest rate that must now correspond to the starting exchange rate on the new open parity line. To decrease the interest rate an expansion of the money supply is required as can be shown in the lower part of the graph. The expansion of the money supply is an automatic result of the interventions of the Chinese central bank on the forex market: purchasing an equivalent amount of foreign reserves (which therefore increase by that amount) additional domestic currency is poured into the money market. (b) By avoiding to appreciate the currency Chinese authorities may be underestimating the problems causes by excessive and too prolonged current account surpluses. Which problems?

The general answer is like for Example 5, Question 1c), from Chapter 19 of KOM. [In the specific case of China external surplus does not sacrifice domestic investment which is very large, with saving even larger and therefore CA=S-I strongly positive. The main problem for China is where to invest the surplus abroad, without risking to loose part of its value when other currencies depreciate, when debtor countries have difficulties in paying back their debts or when the economies of countries that receive Chinese investments (even direct investments by the sovereign fund where part of Chinese reserves are accumulated) are badly managed with poor results in the activities that receive investments from China. Chinese authorities, for example, have criticized US authorities citing the risk of repeated banking and financial crises that could endanger Chinese credits with US banks.]

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Question 1




(a) Instead of expressing the exchange rate of the Turkish lira directly in terms of Chilean pesos, one

can pass through a “vehicle currency” and get the same result.

One can pass through a “vehicle currency” like the US dollar: relying on the “cross exchange rate” rule stating that the number of pesos required to buy one lira must be equal to the number of dollars required to buy one lira times the number of pesos required to buy on dollar. The reason for doing this cross-rate calculation can be the fact that the market for direct exchanges of liras in pesos is thin and illiquid, with infrequent deals, showing unreliable and unstable exchange rates, while both currencies have a rich set of transaction with the dollar, expressing meaningful exchange rate values. The statement is therefore true, except that the “same result” is obtained only when arbitrages keep profiting from possible differences between bilateral and cross exchange rates: for instance, if pesos are cheaper in terms of liras when bought through dollars, arbitrageurs should rapidly eliminate the difference with indirect purchases of pesos which they should then use to repurchase liras directly, thus making them cheaper on the direct bilateral market.

(b) To buy a currency with another I can use a forward contract, which is often called also “a future” because they are exactly the same thing. False, in the sense that they are not exactly the same thing. Both (forex) forwards and futures express prices (exchange rates) for future delivery (of currencies). But while forwards are bilateral “over the counter” contracts that can be tailored to the specific needs (in terms of quantity of currency purchased as well as of maturity and day of the future delivery), futures come in standard amounts on organised markets with standard maturities and dates of execution. To compensate the disadvantage of their standardisation, futures provide a transparent market where a purchase or a sale can be rapidly undone, relying on continuously quoted rates. On the contrary, to undo a forward, a new bilateral over-the-counter agreement must be reached, usually with the same counterpart.

(c) During a given period the only transactions of a country with abroad are the following: import of

raw materials (value: 50 units of foreign currency); interest received on a foreign bond bought in a

previous period (value: 5); reimbursement of a loan that had been granted by a domestic bank to a

foreigner in a previous period (value: 50); purchase of an apartment in the country’s capital by a

foreigner (value: 5). All the transactions are executed by acquiring or selling foreign currency from

or to the domestic central bank, which holds official reserves. Both the current and the official

transactions accounts of the balance of payment of that country in that period are in equilibrium.

To account for the listed transactions one must: write a debit of 50 in the current account (CA) to express imports while subtracting the same amount from official reserves in the official transaction account (OT); write a credit of 5 in the CA to express the positive contribution of the income on the bond received (in a sense it is the price of the services of capital that have been exported in the past and are now used by foreigners), while adding 5 to official reserves; credit

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the financial account (FA) for re-importing 50 of capital, while adding the same amount to official reserves; credit the FA for the direct investment of 5 (the apartment) received from abroad which have also to be added to the official reserves account. The results are: CA=5-50=-45; FA=50+5=+55; OT=-50+5+50+5=+10= CA+FA=-45+55. The statement is therefore false: the current account has a deficit while the financial account has a larger surplus, allowing to account for a net accumulation of reserves in official transactions. Note that this official accumulation is an outflow of capital (the country is investing in foreign currency holdings) that compensates the excess of “above the line” capital inflows over the CA deficit. In a T account: Credits Debits Imports of goods 50 Incomes from capital 5 CA balance 5-50 = - 45 Portfolio investments - 50 Direct investments 5 FA balance (net of OT) 5-(-50)=+55 Change in reserves -50+5+50+5=+10 OT balance 0-10= -10 FA balance gross of OT +55-10=+45 Totals 10 10 Note that the totals balance as, by construction, CA+FA=0, where FA is gross of OT, which can also be written CA+(FA-OT)=OT

Question 2

Controlling the nominal exchange rate and domestic spending, economic policy can try to reach both

“internal” and “external” equilibrium. But when the exchange rate is fixed, the authorities can find

themselves in a “zone of economic discomfort” and in the dilemma whether or not to move towards one of

the two equilibria while they contemporaneously move further away from the other one. Explain, comment

and illustrate which way out are available from the dilemma.

With the nominal exchange rate on the vertical axis and domestic spending on the horizontal axis, internal equilibrium is obtained along a downward sloping line where the restrictive impact (on net external demand) of appreciating the exchange rate is compensated by the expansion of domestic public spending. Above (and to the right of) the internal equilibrium line there is excess aggregate demand, inflation and overemployment, below the same line there is unemployment. External equilibrium, on the contrary, is obtained along an upward sloping line, where depreciation stimulates net exports compensating the increase in imports following an expansion of domestic spending, which also includes purchases of imported goods. Above the line there is CA surplus and vice-versa. If the exchange rate is fixed, the authorities can only move along a horizontal line and both equilibria can be reached only if the fixed exchange rate is at the level where the two equilibrium lines cross. Suppose this is not the case. Increasing domestic spending from low to high levels, the authorities can push the system from a point on the left of both equilibrium lines (where there is unemployment and CA surplus) to points to the right of

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both lines (where there is overemployment and CA deficit), passing through intermediate points that are on the left on one line and on the right of the other. In these intermediate zones the dilemma arises: moving towards one equilibrium causes the system to move further away from the other. The way out can be a change of the fixed exchange rate or a shift in the equilibrium lines. The latter can be the result of structural changes in propensities to spend and import or in the ability to export, for a given exchange rate, but they can also be caused by tariffs or subsidies on imports and exports, spoiling free trade to reach both equilibria without changing the exchange rate.

Question 3

(a) Given constant levels of the domestic and of the foreign interest rates, the only determinant of the ups

and downs of the nominal exchange rate of a country’s currency are fluctuations in expectations, i.e.

changes in the future expected value of that same exchange rate. True or false? Why?

True. It is an implication of the open interest parity equation (and of the corresponding geometrical line on the E,R plane).

(b) Describe the effect of a change (ceteris paribus) in the expected exchange rate, in the short run, on the

level of economic activity and on the market exchange rate, using an AA-DD graph and starting from a

long term equilibrium position.

Suppose an expected depreciation, shifting to the right the open interest parity line and, therefore, the AA. Note that the vertical shifts of both the interest parity line and of the AA are identical to the increase in the future expected exchange rate. The DD has no reason to move. In the short run the exchange rate in fact depreciates (not as much as its expected future value) and the level of economic activity increases.

(c) An increase (depreciation) of the future expected level of the exchange rate can help in driving the

monetary policy of a country out of the so called “liquidity trap”. Explain and suggest how authorities

could induce such a change in expectations.

Consider the representation of the liquidity trap in the AA-DD graph, with the DD crossing the AA in the flat segment (with the AA downward sloping part starting only for higher levels of income). An expected depreciation shifts the whole AA line up (as the intercept of the AA with the E axis is Ee/(1-R*) ). If the expected depreciation is sufficiently large, the upward shift will cause the unchanged DD to cross the shifted AA in its downward sloping part, out of the trap, where a monetary expansion can still expand Y. A change in expectations on the exchange rate could be induced by authorities by trying to create expectations of inflation (higher than abroad, thus somehow relying on relative PPP) explicitly targeting a faster increase in the price index than the one which is actually taking place, and, in any case, preannouncing (the expression “forward guidance” is often use today to indicate such an instrument of monetary policy that relies on influencing expectations) a sufficiently prolonged period of inflationary expansion of the money supply, even if the liquidity trap prevents the transformation of such an expansion in a lower level of interest rates.

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