Exchange Rate Policies at the Zero Lower Bound

Exchange Rate Policies at the Zero Lower Bound Manuel Amador, Javier Bianchi, Luigi Bocola, Fabrizio Perri MPLS Fed and UMN MPLS Fed MPLS Fed and Northwestern MPLS Fed Bank of France, November 2017 The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System

Interest Parity Condition ) st+1 (1 + i t ) = ( 1 + i t s t i t nominal interest rate, s t today s exchange rate i t foreign interest rate, s t+1 tomorrow s exchange rate 1/35

Interest Parity Condition ) st+1 (1 + i t ) = ( 1 + i t s t i t nominal interest rate, s t today s exchange rate i t foreign interest rate, s t+1 tomorrow s exchange rate Central bank goal: depreciate exchange rate today (higher s t ) i 1/35

A Theory Simple monetary model of exchange rate policy Limited international arbitrage Central bank intervention in FX markets Main Result: At ZLB, central bank can achieve exchange rate objectives by accumulating foreign reserves But it is costly. Costs can be measured by IP deviations and foreign reserves 2/35

Why do we care? Nominal interest rates, 3M (%) CHF/EUR exchange rate 6 4 USD 1.6 2 1.4 0-2 CHF 2005 2010 2015 1.2 1.0 2005 2010 2015 125 100 75 Foreign reserves / GDP (%) 300 200 Covered interest parity deviation (bp) 50 25 100 0 2005 2010 2015 0 2005 2010 2015 3/35

Environment Two periods, one good, deterministic, open monetary economy See paper for infinite horizon Uncertainty case dealt in ABBP 2017 Three agents: 1. Households: Standard consumption/saving problem, hold money 2. Foreign investors: Buy domestic/foreign assets, and have limited wealth w 3. Central Bank Issues money (M), buys domestic/foreign assets (A, F ) Implements exchange rate policy (s 1, s 2). 4/35

Prices Exchange rate: s t = # of domestic currency per foreign currency Price of good abroad constant (in units of foreign currency) and normalized at 1 Law of one price holds: P t = s t Nominal interest rate on domestic currency assets: 1 + i Real interest rate on domestic assets: 1 + r (1 + i) s1 s 2 Nominal (and real) interest rate on foreign currency assets, 1 + i Perfectly elastic supply of foreign assets 5/35

Households max u(c 1) + h c 1,c 2,f,a,m ( m s 1 y 1 + T 1 = c 1 + m + a + f y 2 + T 2 = c 2 f 0 s 1 ) + βu(c 2 ) (1 + i)a + m s 2 (1 + i )f MIU with satiation level y t : households endowment, c t : consumption m: money holdings, a: domestic bond holdings, f: foreign assets T t : transfers from central bank (CB) 6/35

Foreign Investors Invest at home in either assets or money, a, m or internationally in foreign assets f Linear utility over second period consumption Have limited initial wealth w and cannot borrow limits to international arbitrage s.t. max f,a,m c w = f + a + m s 1 c = (1 + i )f + (1 + i) a + m s 2 s 2 f 0, a 0, m 0 7/35

Central Bank Pursues an exogenously given exchange rate policy, (s 1, s 2 ) Manages balance sheet to achieve this objective Issues money, M 0 redeemed at s 2. Buys foreign reserves F 0 and domestic assets A. Makes transfers to HH, (T 1, T 2 ) M s 1 = F + A s 1 + T 1 (1 + i )F + (1 + i) A s 2 = M s 2 + T 2 8/35

Monetary Equilibrium given (s 1, s 2 ) A monetary equilibrium given the exchange rate policy (s 1, s 2 ) is: (i) a domestic nominal interest rate; (ii) consumption and asset positions for HH & foreign investors; (iii) money supply, asset purchases, and transfers; HH and foreigners maximize, CB budget constraints holds, Market clearing for domestic assets: a + a + A = 0 m + m = M 9/35

Eqm. Conditions Euler equation for domestic assets: And for foreign bonds: Interest Parity condition u (c 1 ) = β(1 + i) s 1 s 2 u (c 2 ) u (c 1 ) β(1 + i )u (c 2 ) (1 + i) (1 + i ) s 2 s 1 (IP) 10/35

Eqm. Conditions Euler equation for domestic assets: And for foreign bonds: Interest Parity condition u (c 1 ) = β(1 + i) s 1 s 2 u (c 2 ) u (c 1 ) β(1 + i )u (c 2 ) (1 + i) (1 + i ) s 2 s 1 (IP) If IP holds with strict inequality, all private agents invest only in domestic assets (f = 0, f = 0) 10/35

CB interventions in non-monetary economy 11/35

Interventions in non-monetary economy Forget about exchange rates and money Let r and r the real returns on domestic and foreign bonds HH s BC + Government + Market clearing c 1 + c 2 1 + r = y 1 + y 2 1 + r [ ] r r 1 + r }{{} (F + f) Interest Rate diff. 0 HH optimality ( r r 1+r )f = 0 12/35

Interventions in non-monetary economy Forget about exchange rates and money Let r and r the real returns on domestic and foreign bonds HH s BC + Government + Market clearing + HH opt. c 1 + c 2 1 + r = y 1 + y 2 1 + r [ ] r r 1 + r }{{} (F ) Interest Rate diff. 0 HH optimality ( r r 1+r )f = 0 12/35

The Effects of CB Interventions c 2 (y 1,y 2 ) A < w 1+r? c 1 13/35

The Effects of CB Interventions c 2 CB intervention: F (ỹ 1, ỹ 2 ) A w 1+r? c 1 13/35

The Effects of CB Interventions c 2 u 0 (c 1) u 0 = (1 + r) (c 2) c 1 = y 1 F + w c 2 = y 2 +(1+r? )F (1 + r) w (ỹ 1, ỹ 2 ) A B w 1+r? 1+r c 1 13/35

The Effects of CB Interventions c 2 r r? F 1+r (ỹ 1, ỹ 2 ) A B w 1+r? 1+r c 1 13/35

Taking Stock If w large enough, intervention is neutral HH s undo the effect by borrowing If w not large enough, interventions allow CB to sustain r > i HH s attempt to undo the effect by borrowing, but foreign wealth constraint is hit competition drives up r Consumption is distorted and CB incurs losses Welfare is decreasing in F. Best non-monetary eqm is F = 0 14/35

Monetary Economy Exchange Rate Objective (s 1, s 2 ) Two cases depending on whether nominal rate consistent with IP is consistent with ZLB: 15/35

Monetary Economy Exchange Rate Objective (s 1, s 2 ) Two cases depending on whether nominal rate consistent with IP is consistent with ZLB: (1) Away from ZLB: If (1 + i ) s 2 s 1 > 1 CB can implement (s 1, s 2 ) by setting F = 0 and nominal rate 1 + i = (1 + i ) s 2 s 1 > 1 This achieves the best non-monetary eqm 15/35

Monetary Economy (2) At ZLB: If (1 + i ) s 2 s 1 < 1 16/35

Monetary Economy (2) At ZLB: If (1 + i ) s 2 s 1 < 1 < 1 + i 1 + i > (1 + i ) s 2 s 1 16/35

Monetary Economy (2) At ZLB: If (1 + i ) s 2 s 1 < 1 < 1 + i 1 + i > (1 + i ) s 2 s 1 Exchange rate policy and ZLB open gap in IP 16/35

Monetary Economy (2) At ZLB: If (1 + i ) s 2 s 1 < 1 < 1 + i 1 + i > (1 + i ) s 2 s 1 Exchange rate policy and ZLB open gap in IP Domestic assets attractive Foreign investors go all in 16/35

Monetary Economy (2) At ZLB: If (1 + i ) s 2 s 1 < 1 < 1 + i 1 + i > (1 + i ) s 2 s 1 Exchange rate policy and ZLB open gap in IP Domestic assets attractive Foreign investors go all in One implementation: CB issues more liabilities and buys foreign assets to support exchange rate policy 16/35

Monetary Economy: At the ZLB c 2 F A B w 1+r? 1+r = s1 s2 c 1 17/35

Costs of FX Interventions Recap: Central Bank can sustain a depreciated exchange rate at the ZLB by accumulating foreign assets, but there are costs associated. 18/35

Costs of FX Interventions Recap: Central Bank can sustain a depreciated exchange rate at the ZLB by accumulating foreign assets, but there are costs associated. Questions: What are the determinants of these losses? Is financial openness good or bad? 18/35

What determines the costs from intervention? Factors that increase the potential for capital inflows raise the necessity and costs of FX interventions at the ZLB, despite being desirable away from ZLB: More foreign wealth, w Lower international rates, i Irrational expectations of appreciation of domestic currency Role for capital controls 19/35

More w at the ZLB c 2 w 0 > w A w 1+r = s 1 1+r? s 2 c 1 20/35

More w at the ZLB c 2 w 0 > w A w w 0 1+r = s 1 1+r? s 2 c 1 20/35

More w at the ZLB c 2 additional losses: r r? F 1+r w 0 > w B A w 0 1+r? 1+r = s 1 s 2 c 1 20/35

More w at the ZLB Larger inflows, but larger outflows! c 2 additional losses: r r? F 1+r w 0 > w B A w 0 1+r? 1+r = s 1 s 2 c 1 20/35

Alternative policy instruments Capital controls Quantity: lower w improves welfare Optimal w implies F = 0 Prices: taxes on foreign purchases of domestic assets Optimal tax implies IP holds with equality Note: At the ZLB need to tax foreign holdings of money Negative nominal interest rates Allow the CB to restore interest parity and eliminate losses Contrasts with usual reason to allow for negative rates 21/35

Why would CB follow such policies? So far, exchange rate policy (s 1, s 2 ) exogenous Endogeneize (s 1, s 2 ) in model with nominal rigidities A shock to β makes devaluation optimal If recession is severe enough, CB is at ZLB and intervene by buying foreign assets 22/35

A simple sticky-wage model Two sectors, producing T-NT goods Output in sector j produced with Cobb-Douglas, y j t = (lj t )α Nominal wages are fixed in domestic currency, and constant over time p w Firms in both sectors maximize profits Firms FOC: Π j t = max p j l j t y t pw l j t s t t l N t = ( ) αp N t s 1 1 α t p w l T t = ( ) 1 αst 1 α p w 23/35

The problem of the Central Bank The Central Bank chooses (i, s 1, s 2, F ) to maximize HH s welfare taking as given optimality of HH s, firms, and foreign investors Let p w,fb t be the real wage that achieves the first best level of production, v (n t ) = u T (c T )f (l T t ) v (n t ) = u N (c N )f (l N t ) Absent ZLB, CB chooses (s 1, s 2 ) to achieve first best Depreciate when output inefficiently low Appreciate when output inefficiently high 24/35

Central Bank s Solution If (1 + i ) sfb 2 s fb 1 1, then ZLB does not bind Setting i consistent with IP, s fb 1, s fb 2 achieves first-best If (1 + i ) sfb 2 s fb 1 < 1, then CB trade-offs losses of production efficiency with losses from FX interventions Solution: intervene only when losses of production efficiencies are sufficiently large 25/35

Numerical example: discount factor shock 0.91 0.660 0.90 0.90 0.655 0.89 0.89 0.650 0.88 0.88 1.00 1.05 1.10 1.15 0.645 1.00 1.05 1.10 1.15 0.87 1.00 1.05 1.10 1.15 2.0 1.5 1.0 0.5 0.08 0.06 0.04 0.02 5 4 3 2 1 0 1.00 1.05 1.10 1.15 0 1.00 1.05 1.10 1.15 0 1.00 1.05 1.10 1.15 An increase in β lowers c today relative to tomorrow First best requires CB depreciating today relative to tomorrow i until ZLB. After that, F > if large recession 26/35

Empirical Analysis

Understanding FX Interventions Model has two main implications 1. FX interventions and IP deviations go hand in hand 2. Interventions are necessary at ZLB Are these predictions consistent with basic facts about foreign reserves, IP deviations and nominal interest rates? Cross-section of advanced economies (2000-2016) Look at a different ZLB period: Switzerland in the late 1970s 27/35

Foreign Reserves and CIP deviations Annualized CIP gap (basis points) 50 40 30 20 10 0-10 SWE GBR SWE JPN CAN CHE CAN GBR AUS NZL AUS NZL Reserves and CIP deviations DNK JPN pre 2007 post 2010 10 20 30 40 50 60 70 Reserves/GDP (%) CHE Positive relation between reserves and CIP gaps 28/35

CIP deviations and Nominal Interest Rates Annualized CIP gap (basis points) 50 40 30 20 10 0-10 CHE JPN JPN GBR Interest rates and CIP deviations DNK pre 2007 post 2010 SWE SWE CHE CAN CAN GBR AUS AUS NZL NZL 0 2 4 6 Nominal interest rate (%) Deviations from CIP for countries with rates close to zero 29/35

A Different ZLB Period 5 Nominal Interest Rate, 3M (%) 2.6 CHF per USD 4 2.4 3 2 2.2 2.0 1.8 1 1.6 0 24 22 20 18 16 14 12 10 8 II III IV I II III IV I II 1977 1978 1979 Foreign Reserves / GDP (%) II III IV I II III IV I II 1977 1978 1979 1.4 160 140 120 100 80 60 40 II III IV I II III IV I II 1977 1978 1979 CIP Deviations (Bp) II III IV I II III IV I II 1977 1978 1979 Shaded areas represent months in which the Swiss interest rate was below 0.5%. A similar pattern observed for Switzerland in the 1970s 30/35

Quantifying the costs of FX Interventions Losses: [ 1 1 + i 1 + i s 2 s 1 ] } {{ } IP deviation F }{{} foreign reserves 31/35

Quantifying the costs of FX Interventions CIP deviations and Reserves Annualized CIP gap (basis points) 300 200 100 0 CIP deviation reserves/gdp 2005 2010 2015 100 50 0 Reserves/GDP (%) 32/35

Quantifying the costs of FX Interventions Losses 1.0 0.8 % of monthly GDP 0.6 0.4 0.2 3 month MA 0 2005 2010 2015 Losses can be sizable (1% of monthly GDP) 33/35

Agenda: Which assets should CB buy? ABBP 2017: Exchange Rate Policy + Uncertainty Two goals: minimize losses and intertemporal distortions New principles for optimal reserve management Relatively closed economies: Invest in foreign assets that pay when the currency appreciates. Lower marginal utility when money pays a higher return Idea: Make money less attractive to hold, reducing intertemporal distortions Relatively open economies: Make sure that foreign investors demand domestic currency Reduce losses 34/35

Conclusions Simple monetary model of exchange rate policy Limited international arbitrage Central bank intervention in FX markets At ZLB, accumulation of foreign assets is necessary and costly Framework can rationalize recent evidence on reserves, CIP, and interest rates Agenda: A theory of timing of peg abandonment (Reverse Speculative Attacks, ABBP, 2016) Optimal Reserve Management 35/35