The Optimal Currency Area in a Liquidity Trap

Transcription

1 The Optimal Currency Area in a Liquidity Trap David Cook and Michael B. Devereux Very preliminary draft June 21, 2012

2 Determinants of the optimal currency area I Long debate about the conditions necessary for successful single currency area I Traditional factors I A) Labor mobility (+) I B) Country Specific shocks (-) I C) Fiscal integration (+) I Discussion of eurozone suggests that factors B) and C) were achilles heel I Most commentary on European crisis: I Overwhelming a rmation of traditional OCA theory? I Huge asymmetry in shocks to Southern versus Northern Europe I Inability to adjust relative prices: need for internal devaluation

3 But what is the counterfactual? I OCA theory presumes activist monetary policy I Global Financial Crisis severely hindered use of monetary policy in many jurisdictions I Many countries at or close to zero lower bound I Large debt shocks pushing natural real interests negative I Comparison should be between SCA and flexible exchange rate system at ZLB I Makes flexible exchange rates look even better? I Krugman: Europe in LT - needs exchange rate adjustment I Svensson foolproof plan for Japan requires exchange rate flexibility

4 This paper I OCA in a liquidity trap I Plain vanilla NK 2 country model I Assemble model so that OCA theory holds exactly with activist monetary policy I Country specific demand shocks I Always better to have flexible exchange rates I A. Exchange rate adjusts to stabilize country specific shocks I B. Monetary policy can be used actively to o set shocks I But now assume that we have large (country-specific) shocks I Pushing region into ZLB I Then it turns out the SCA dominates flexible exchange rates I Macro shocks more stabilized in absence of ER adjustment I Ex ante, when large shocks dominate, EU higher under a SCA

5 Understanding this result I Combination of zero lower bound and integrated international capital markets I With activist monetary policy, country experiencing shock has fall in its relative real interest rate I Depreciation of exchange rate - helps to absorb shock I But when large shocks and no interest rate adjustment I Relative real interest rates rise in country of shock I Exchange rate appreciates - exacerbates the response to the shock I Absence of monetary instrument (plus open capital markets) removes ability to direct the exchange rate I By contrast, in SCA, no nominal exchange rate at all I Shock causes a real exchange rate depreciation I RER response same in and out of LT I SCA acts as kind of precommitment - removing possibility for perverse ER response

6 Caveats I Not an argument for SCA I But key defects in eurozone related to sovereign risk, moral hazard and regulatory negligence I Can make case that relative price (RER) adjustment not at centre of eurozone defects (Berka Devereux Engel 2012) I Here, just saying that in case of large shocks, e relative price adjustment not guaranteed. cient

7 Related literature I Standard model of SCA (Benigno 2004) I Compare with standard model of flexible ER (Clarida et al. 2002) I Assume large shocks and temporary ZLB (Eggertson 2010) I Related to recent literature on ZLB (Fujiwara et al. 2011, Erceg et al. 2011)

8 Model Description Standard Two Country New Keynesian Model: I Complete Assets Markets I Calvo Price Adjustment I Home bias in preferences I Time Preference Shocks I Simplicity allows full closed form objects I But logic is very general

9 Model Home Preferences X 1 U t = E 0 (U(C t, t ) V (N t )) t=0 t is a preference shock, and U 12 > 0 (proxy for deleveraging shock) Composite consumption defined as C t = C v/2 v/2 Ht C1 Ft, v 1 Simplifying assumptions for analytical solution Standard Euler equations, labor supply, price setting

10 Natural Real Interest Rates World average and relative, x W t = x t+x t 2 and x R t = x t x t 2. Shock continues (ends) with probability µ, (1 µ) Take example of home country shock Home natural rate +( + )(v 1) " er t = r + (1 µ) c t y ( + ) 2 Foreign natural rate is: er t = r + ( + )(v 1) " (1 µ) c t y ( + ) 2 For v = 1, natural real interest rates are identical

11 Connected through capital mobility Degree of openness determines strength of connection! r*!!! 0 V F ε H (1) 1) v 1 2 r!

12 Cook-Devereux 2012 Multiple Currencies: Optimal monetary policy Then in what follows assume that v< v, sor = r =0! r*! 0!!! F! *!

13 World Averages and Relatives: Averages: W t = k(( + )by W t " W t )+ E t W t+1 E t (by W t+1 by W t )=E t (" W t+1 " W t )+E t r W t E t W t+1 Relatives: R t = k(( + D )by R t DE t (by R t+1 by R t )= (v 1) D "R t )+ E t R t+1 (v 1) D E t(" R t+1 " R t )+E t r R t R t+1

14 Monetary policy with positive interest rates With multiple currencies, each country follows interest rate rule r t = + t Therefore: r W t = + W t, r R t = R t. Under a single currency: r SCA t = + W t, r R,SCA t =0

15 Some convenient properties I Behaviour of world economy is identical under a SCA and multiple currencies I True both with positive interest rates and when when constrained by ZLB I Under multiple currencies, nominal interest rate defined by s t s t 1 = R t + t t 1

16 Solution of Relative Economy I Under multiple currencies, analogous solution. I But with SCA, r R,SCA t indeterminate R,SCA t = k(( + D )by R,SCA t DE t (by R,SCA t+1 by R,SCA t )= = 0, so relative equations are (v 1) D "R t )+ E t R,SCA t+1 (v 1) D E t(" R t+1 " R t )+E t I Need backward condition given by: R t = ( t t 1 ) 0 R,SCA t+1

17 Note: property of a SCA I Produces responses of relative variables akin to response of level variables under ZLB I Nakamura and Steinsonn state level GS multipliers in the US I So SCA leads to less stable relative variables (OCA theory) I But, as we see, this is not true when, under multiple currencies, relative interest rates constrained by ZLB

18 Savings shocks: multiple currencies, activist monetary policy Assume that " W < 0, and " R < 0 I Shock to world saving and relative saving I Solutions for world averages: by W = [(1 µ)(1 µ)+k( µ)] " W W = (1 µ) k " W where (1 µ)(1 µ)+( µ)k( + ) > 0

19 Multiple currencies, activist policy Solutions for world relatives by R = [(1 µ)(1 µ)+k( µ)] D (v 1)" R D R = (1 µ) k (v 1)" R D where D D (1 µ)(1 µ)+( µ)k( + D ) > 0 D

20 Multiple currencies, activist policy I Solution for terms of trade b = k ( µ) D 2(v 1)" R I For " R < 0, the terms of trade depreciates I Also nominal exchange rate depreciates I Both world averages and world relatives are determined by parameters of monetary rule D (1)

21 Multiple currencies, activist policy I Deviations from e cient levels ey W = + " W ey R = D + D (v 1)" R I < 1, and D < 1. e = (v 1) D + D D 2" R I Relative to e cient response: I y W and y R fall too much I rises too little I Note that a ects deviations

22 Single Currency Area, activist policy I Response of world averages exactly the same I World relatives solved by b t 1 b t = k ( D + ) [b t + 2 I Has simple solution given by (v 1) ( D + ) 2"R ]+ E t (b t b t+1 ) b t = b t 1 + 2" R 0 < <1, = k (v 1) 2 D D1 < 0 I Response does not depend on

23 Single Currency Area, activist policy I Deviations from e cient levels e t = b t 1 +(v 1)2" R + D (1 + (1 µ)) D D1 ey R t = Db t 1 2 +(v 1)" R + D (1 + (1 µ)) D D1 I Deviations are again negative I Greater in absolute terms than under multiple currencies and flexible exchange rates

24 Comparison under activist policies 5 x Figure 1: Demand Shocks under a Taylor Rule R sca R flex boxoff y R sca y R flex sca flex s W y W

25 Solutions in a liquidity trap I Assume shocks push down both rates to zero bound I Solution for world averages - obtained by link to future exit from liquidity trap by W = [(1 µ)(1 µ) kµ] 1 " 2 where 1 > 0. W = (1 µ) k I Response exceeds that under activist policy 1 " 2

26 World relatives in a LT: multiple currencies I Multiple currencies by R = [(1 µ)(1 µ) kµ] D1 (v 1)" 2D where D1 > 0 R = (1 µ) k D1 (v 1)" 2D I Again, exceeds that under activist policy

27 Response of terms of trade I Multiple currencies b = k (µ) I The terms of trade appreciates D (v 1)" 2D I Likewise, nominal exchange rate appreciates bs t bs t 1 = R t +(b t b t 1 ) I Even though home inflation falls, nominal exchange rate falls by more, so get a terms of trade appreciation

28 Basic intuition I Although interest rates cannot move, capital markets still integrated I So up to 1st order, interest rate parity holds E t t+1 = E t t+1 + E t (b t+1 b t ) I Fall in relative home PPI inflation leads to a rise in home relative real interest rates I requiring an anticipated terms of trade deterioration. I Implies an immediate appreciation.

29 I In terms of deviations ey W = + 1 " W ey R = D + D1 (v 1)" R e = 1 < 1, and D1 < 1. (v 1) D + I Exceeds gaps under activism D D1 2" R

30 Now comparison with SCA I Solutions for world averages exactly as in multiple currencies case I Solutions for world relatives exactly as in policy activist case I Now can show that gaps more negative under flexible exchange rates than in SCA

31 Comparison of MC and SCA under LT Figure 4: Demand Shocks under a Liquidity Trap R sca R flex 0.2 y R sca y R flex W y W 0.1 sca flex

32 Result I Flexible exchange rates impart greater instability I Response of exchange rate compounds original shock I But since interest rates zero, countries have no lever to a ect exchange rate (with open capital markets) I Hence, SCA acts as an e movement cient limitation on perverse ER

33 Welfare evaluation Table 1 Welfare Loss Policy Taylor Rule Zero Bound Limit Multiple Currency Single Currency Area

34 Extensions I Limiting capital mobility I Without capital mobility, interest rates move in di erent directions I Foreign interest rate may adjust I E cient response my a) dominate outcome with capital mobility, b) dominate SCA I Fiscal adjustments I Can introduce capital taxes subsidies to induce e cient response I Note that need these even with multiple currencies I Quite di erent than taxes for internal devaluation I Empirical evidence I Some suggestion that low interest rate currencies appreciated: US, Japan

35 Caveats I Not an argument for SCA unconditionally I Message is that exchange rate adjustment not always e cient I SCA can prevent ine cient adjustment I Other aspects of SCA may be more damaging (moral hazard, decentralized regulation)