Master EPP - Sciences Po & Ecole polytechnique Eco 572 : International Economics - Solutions for the Final Test December 3, 2014

International Macro : A Comparison Between Two Exchange-Rate Crisis Models 1 mt − pt = φy − βit

φ > 0, β > 0

∗

(1)

pt = p − st

(2)

i1 = i∗ + s1 − se2

(3)

i2 = i∗

(4)

1. Speculative Attack Model s1 = s¯ + m ¯ − me2 −

1 (m1 − m) ¯ β

(5)

s2 = s¯ + m ¯ − m2 mt = θrt + (1 − θ)dt

(6) 1>θ>0

(7)

µ>0

(8)

d2 = d1 + µ,

1.1. m ¯ denotes demand for money in equilibrium under the fixed exchange rate system (both prices and interest rates are flexible so equilibrium is reached immediately). It is the money supply target that the Central Bank will aim to reach through sterilization operations (sales of forex reserves). Using (1) and p1 = p∗ − s¯ yields : m1 − m ¯ = p1 − βi1 − (p∗ − s¯ − βi∗ ) = β(i∗ − i1 ) ⇔ i1 = i∗ −

m1 − m ¯ β

Similarly using (1) and (2) yields : m2 − m ¯ = p2 − βi∗ − (p∗ − s¯ − βi∗ ) = p2 − p∗ + s¯ = s¯ − s2 ⇔ s2 = s¯ + m ¯ − m2 implying se2 = s¯ + m ¯ − me2 Finally using (3) and the equation for i1 yields s1 = i1 − i∗ + se2 = −

m1 − m ¯ + s¯ + m ¯ − me2 β

A positive money supply shock at t = 1 reduces the theoretical floating value of the ER, as money market equilibrium requires a price increase and an interest rate decrease. A positive future money supply shock expected at t = 1 reduces further the theoretical floating value of the ER. There is a difference in intensity depending on the elasticity of money demand w.r.t. interest rates (β) : in the short run interest rates will absorb some of the shock. A positive money supply shock at t = 2 reduces the theoretical floating value of the ER in a similar way. 1.2. There is a speculative attack if agents expect that the theoretical value of the exchange rate when reserves are zero is lower than the parity defended by the CB. 1. Adapted from Olivier Jeanne (1996), ”Les mod` eles de crise de change : un essai de synth` ese”, Economie et pr´ evision, no 123-124, pages 147-162.

1

First, compute that theoretical value. When reserves are zero (5) implies that s1 = −

(1 − θ)d1 − m ¯ + s¯ + m ¯ − (1 − θ)(d1 + µe ) β

¯ 1 −m +m ¯ − (1 − θ)(d1 + µe ) < 0 It follows that the floating value is lower than the parity if − (1−θ)d β Second, this condition is met when the expected value of credit growth (µe ) is high enough (implicitly, se2 is low enough). When that happens all FX traders immediately understand that the CB cannot withstand a speculative attack. They will want to be the first to sell so that they can be the lucky ones that will get some of the reserves at s¯. Since all traders will do this the fixed ER system will collapse. The speculative attack occurs at t = 1 because all FX traders will want to be the first served. The reason a floating exchange rate reacts so quickly to expectations on future money supply is UIP (this partly explains the volatility of nominal exchange rates as discussed in lecture 8).

1.3. One should monitor all fundamental economic variables affecting µe to assess the risk of speculative attacks. This includes all variables affecting money supply growth : expectations on interest rates, money supply growth, but also fiscal deficit growth, CA deficits, foreign interest rates, possibility of credit bubbles... 2. Escape Clause Model 2

L2 = [U2 (s2 )] + C1s2 −s1 =∆ , c > 0 U2 = ρU1 − λ(π2 − π2e ) with 0 < ρ < 1, 0 < λ < 1 2.1. If the exchange rate remains equal to s¯ at t = 2, then (2) implies that inflation will be zero. Therefore if agents expect no devaluation they will infer from the model that inflation will be zero. If there is a (surprise) devaluation (2) implies that inflation (and surprise inflation) will be equal to ∆. One can compare the loss functions if the CB devalues and if it doesn’t : 2

Lnodev = (ρU1 )

2

Ldev = (ρU1 − λ∆) + C It follows that there is no devaluation if and only if 2

2

Lnodev < Ldev ⇔ (ρU1 ) < (ρU1 − λ∆) + C ⇔ Ψ > −λ∆ If Ψ > −λ∆ the CB will prefer to defend the peg and no devaluation will occur, as expected. 2.2. If agents expect a devaluation, they will infer from (2) and expect π e = ∆. If the CB does not devalue, there will be no inflation, and negative surprise inflation −∆. If the CB devalues inflation will indeed be equal to ∆ and there will be no surprise inflation. Compare the loss functions if the CB devalues and if it doesn’t : 2

Lnodev = (ρU1 + λ∆) 2

Ldev = (ρU1 ) + C It follows that there is a devaluation if and only if 2

2

Ldev < Lnodev ⇔ (ρU1 ) + C < (ρU1 − λ∆) ⇔ Ψ < λ∆ If Ψ < λ∆ the CB will prefer to devalue and a devaluation will occur, as expected. 2

2.3. If Ψ < −λ∆, there is an ER crisis no matter the expectations. If Ψ > λ∆, there is no ER crisis no matter the expectations. If Ψ takes intermediate values, then there will be an ER crisis if agents expect it, and no ER crisis if they don’t (multiple equilibria). In other words for intermediate values of Ψ there are self-fulfilling ER crises : it is enough for agents to believe that the crisis will occur for the crisis to occur. 2.4. Relative to question 1.3, one would like to monitor variables behind Ψ : past unemployment rates, unemployment persistence, political costs of devaluations. One could extend the U2 equation to include supply shocks and those variables should also be monitored. In the case of the French devaluation of 1993, high unemployment may have led markets to believe that the BdF would not want to defend its peg in case of a bad supply shock, despite otherwise good monetary and fiscal policy fundamentals.

International Trade : Factor Proportions, Productivity Differences and Comparative Advantage Y1 = F1 (L1 , S1 ) = AL1 1

1

Y2 = F2 (L2 , S2 ) = (L2 ) 2 S 2 1−α U (Q1 , Q2 ) = Qα 1 Q2

1. Profits can be written as functions of factor demands : Π1 = (p1 A − wL )L1 1

1

Π2 = (p2 (L2 ) 2 S 2 − wL L2 − wS S2 First order conditions for profit maximization : p1 A = wL 1 1 −1 p2 (L2 ) 2 S 2 = wL 2 1 1 1 p2 (L2 ) 2 S − 2 = wS 2

The last two equations imply wL L2 = wS S2 . Together with the S market clearing condition this implies L2 wS = S wL Input substitutability implies that input demand is a decreasing function of that input’s relative price. Unit cost in sector 1 is simply equal to wL c1 (wL , wS ) = A 2 +wS S2 Unit cost in sector 2 can be found by evaluating wLY2L(L at optimal values of the factor demands. wL L2 = 2,S2 ) wS S2 implies that this expression can be considerably simplified :

c2 (wL , wS ) =

2wS S2 wS 12 (w ) S2 L

3

1

1

= 2(wL ) 2 (wS ) 2

One can plot in {wL , wS } space the curves p1 = c1 (wL , wS ) (vertical line) and p2 = c2 (wL , wS ) (downwardsloping hyperbola). 2. Because of perfect competition there are no profits and national income equals total factor income. Maximazing utility subject to the budget constraint implies : λp1 = αQ1α−1 Q1−α 2 −α λp2 = (1 − α)αQα 1 Q2

leading to the familar demand functions Q1 = α

I p1

Q2 = (1 − α)

I p2

Goods market clearing in autarky implies Y1 = Q1 and Y2 = Q2 so that (1 − α) YI1 p2 1 − α AL1 = = p1 α (L2 ) 12 S 21 α YI2 3. In autarky equilibrium both the MRT and MRS are equal to the price ratio. 1 1 (1 − α) YI2 2(wL ) 2 (wS ) 2 p2 = = wL p1 α YI1 A 1

⇔

p2 2A(L2 ) 2 = 1 p1 S2

We must solve for L2 : (1 − α) YI2 α YI1 ⇔

(1 − α)L1 1

1

1

=

2A(L2 ) 2 1

S2 1

=

2(L2 ) 2

α (L2 ) 2 S 2 1−α L1 ⇔ L2 = 2α

1

S2

Together with the L market clearing condition this implies 1+α L 2α 1−α L2 = L 1+α L1 =

and finally 1

2 2A( 1−α p2 1+α L) = 1 p1 S2 1

2 so that κ = 2( 1−α 1+α ) .

4

4. In autarky the relative price of good 2 will be higher in Home than Foreign. The world price will be in between those prices and Foreign will export good 2, Home will export good 1. Home has a comparative advantage in good 1 in the sense that  H  F p1 p1 < p2 p2 since 

p2 p1

H

 =2

p2 p1

F

HOS theory predicts that countries export the product that is intensive in their abundant factor. In Home L is abundant (relative to Foreign) so that good 1 is cheaper in autarky and will be exported. Scarcity in S increases wS L = LS2 = 1−α the relative price of S, as can be seen from w 1+α S , which makes good 2 relatively more expensive in L Home in autarky. The Stolper-Samuelson theorem predicts that in Home the real reward to S will decrease while the real reward wS wS will decrease. The exact opposite will happen in Foreign, w will to L will increase, so that the relative price w L L increase. In Home, trade liberalization will reallocate output towards sector 1 which will lead to an increase in the relative demand for L, with constant relative supply. 5. This time 

p2 p1

H =

2 3



p2 p1

F

so that Home has comparative advantage in good 2 and will export it under free trade. Factor prices will not be equalized (we are not in the HOS conditions any more) as can be seen from the figure in {wL , wS } space. Common factor prices are only possible when goods prices are common and technologies (unit cost functions) are common. Here goods prices are common, but technologies are not. 6. If α > α∗ then κ < κ∗ and 

p2 p1

H