Dealing with the Trilemma: Optimal Capital Controls with Fixed Exchange Rates

Transcription

1 Dealing wih he Trilemma: Opimal Capial Conrols wih Fixed Exchange Raes by Emmanuel Farhi and Ivan Werning June 15 Ricardo Reis Columbia Universiy

2 Porugal s challenge risk premium

3 Porugal s challenge sudden sop Figure 2: Toal and privae capial inflows, seleced souhern euro-area counries, (% 27 GDP) 12 1 Greece Ireland Jan-2 Sep-2 May-3 Jan-4 Sep-4 May-5 Jan-6 Sep-6 May-7 Jan-8 Sep-8 May-9 Jan-1 Sep-1 May-11 Jan-2 Sep-2 May-3 Jan-4 Sep-4 May-5 Jan-6 Sep-6 May-7 Jan-8 Sep-8 May-9 Jan-1 Sep-1 May-11 Jan-2 Sep-2 May-3 Jan-4 Sep-4 May-5 Jan-6 Sep-6 May-7 Jan-8 Sep-8 May-9 Jan-1 Sep-1 May-11 Jan-2 Sep-2 May-3 Jan-4 Sep-4 May-5 Jan-6 Sep-6 May-7 Jan-8 Sep-8 May-9 Jan-1 Sep-1 May Porugal Spain

4 Porugal s challenge public assisance Figure 5: Decomposiion of cumulaive capial inflows (% of 27 GDP)

5 Porugal s challenge adjusmen

6 Risk premium and Mundell s rilemma Arbirage condiion for domesic invesor: 1+i = (1 + τ ) E +1 E (1 + i )(1 + Ψ ) Wih flexible exchange rae, a risk-premium shock or sudden sop comes wih a devaluaion of he currency. Wih fixed exchange rae, domesic ineres raes mus rise one-o-one. Wih fixed exchange raes surrender conrol over moneary policy. This paper: cyclical Tobin ax on capial flows. Firs quesions: Hasn his been done? Is i feasible?

7 A simpler framework 1. Two periods,, Log uiliy in consumpion σ =1. 3. Small open economy, foreign variables are exogenous. 4. Insead of Calvo, can do neoclassical or simple sicky-informaion by saying ha a dae, only λ share of agens know abou he shock, by period 1, all know i. 5. Cole-Obsfeld: Shares of expendiure consan, Cobb-Douglas aggregaors, rade is balanced.

8 Six equaions for =, 1: Q = [ The model s equaions α +(1 α)s η 1 Q = S 1 α Y = (1 α) ( Q S ] 1 η 1 ) η C + αλ S γ C N = Y /A N = S C A [ (1 α) C C Q + αλ ] 1. Price index / consumpion aggregaor linking real exchange rae o ToT 2. Goods marke clearing 3. Producion funcion

9 The model s equaions The Backus-Smih condiion: C 1 C 1 Q 1 = C C Q (1 + τ)(1+ψ) The budge consrain, ( aking NFA as exogenous: Y NFA = C ) ( 1 Y1 β C ) 1 1 S S 1 Flexible prices: NFA = α Q C ( C C Q Λ ) + αβ Q 1 C1 ( C1 C 1 Q 1 Λ 1 ) P H, P Rigid prices: = Q S = M C N φ A S = E P /P H, =1 Q =1

10 Policymaker s problem C 1 max τ { ln(c ) N 1+φ 1+φ + β C ( ln(c 1 ) N 1+φ 1 1+φ C1 Q = 1 C Q (1 + τ)(1+ψ) ( ) ( ) C C1 NFA = α C Q Λ + αβ C1 Q Λ 1 1 Q 1/(1 α) C [ N = (1 α) C ] A C Q + αλ Q α/(1 α) = M C N φ A or Q =1. )}

11 Zero opimal capial conrols If shocks o A 1 /A,C 1 /C,NFA, Λ 1 /Λ. C 1 max τ { ln(c ) N 1+φ 1+φ + β C ( ln(c 1 ) N 1+φ 1 1+φ C1 Q = 1 C Q (1 + τ)(1+ψ) ( ) ( ) C C1 NFA = α C Q Λ + αβ C1 Q Λ 1 1 Q 1/(1 α) C [ N = (1 α) C ] A C Q + αλ Q α/(1 α) = M C N φ A or Q =1. )}

12 Firs lesson Capial conrols are an ineremporal ool. If he shocks or disorions affec boh periods equally, capial conrols will no help and should no be used. No longer rue wih sicky prices, because shocks cause relaive-price disorions.

13 Capial conrols and price rigidiy C 1 max τ { ln(c ) N 1+φ 1+φ + β C ( ln(c 1 ) N 1+φ 1 1+φ C1 Q = 1 C Q (1 + τ)(1+ψ) ( ) ( ) C C1 NFA = α C Q Λ + αβ C1 Q Λ 1 1 Q 1/(1 α) C [ N = (1 α) C ] A C Q + αλ Q α/(1 α) = M C N φ A or Q =1. If shocks o A,C, hen: zero if flexible prices (Cosino e al, 211) no zero wih rigid prices. Inuiion: Adjusing afer-ax real ineres rae. )}

14 Second lesson Capial conrols are an ineremporal ool ha affecs he real ineres raes and help can if prices are rigid and shocks are emporary. Even in limi of closed economy, capial conrols sill affec real ineres rae.

15 C 1 Capial conrols and expendiure-swiching max τ { ln(c ) N 1+φ 1+φ + β C ( ln(c 1 ) N 1+φ 1 1+φ C1 Q = 1 C Q (1 + τ)(1+ψ) ( ) ( ) C C1 NFA = α C Q Λ + αβ C1 Q Λ 1 1 Q 1/(1 α) C [ N = (1 α) C ] A C Q + αλ Q α/(1 α) = M C N φ A or Q =1. If shock o Λ, non-zero capial conrols, bu second bes. )}

16 Third lesson Capial conrols also shif demand agains domesic goods. Their use mus balance ineremporal effec agains expendiure swiching. In a free rade area hey can ypically only reach a second bes. Bu if allow for ariffs, can separae hese wo margins.

17 Risk premium shocks Wih flexible prices shocks can be offse by capial conrols leaning agains he wind: C 1 C 1 Q 1 = C C Q (1 + τ)(1+ψ) If capial conrols are no used, and prices are flexible, a sudden sop leads o: Oupu falling. Curren accoun surplus in shor run.

18 Negaive risk premium shock ŷ τ = i i ψ nx ˆ and nx ŝ and s Figure 7: Mean-revering risk premium shock, α =.4. green - no conrols, blue - opimal conrols

19 Missing from sudden-sops Mauriy mismach and liquidiy Asse fire sales Foreign-denominaed deb Impored inpus bough on credi Financial acceleraor Moneary policy could, in principle serilize shifs in flows, preven risk premia from changing

20 Skepicism abou capial conrols 1. Empirical evidence ha conrols on capial inflows have almos no effec on oal inflows (Osry e al, 211). 2. Edwards (1999): conrols on ouflows rarely work, breed corrupion. 3. Magu, Reinhar, Rogoff (211): exhausive sudy of capial conrols again wih discouraging resuls. 4. Role of rade credi and FDI. 5. The mauriy of flows. 6. I prefer anoher inerpreaion of τ, he cyclical Tobin ax: domesic financial repression.