Reserve Accumulation, Macroeconomic Stabilization and Sovereign Risk

Reserve Accumulation, Macroeconomic Stabilization and Sovereign Risk Javier Bianchi 1 César Sosa-Padilla 2 2018 SED Annual Meeting 1 Minneapolis Fed & NBER 2 University of Notre Dame

Motivation EMEs with fixed exchange rates hold more foreign reserves... 30 25 20 15 10 5 0 1990 1995 2000 2005 2010 2015 data details 1/35

Motivation (ctd)... and have accumulated reserves faster. 20 18 16 14 12 10 8 6 4 2 0 2000 2002 2004 2006 2008 2010 2012 2014 2016 data details 2/35

Motivation (ctd) Adoption of fixed or quasi-fixed exchange rate is prevalent 3/35

Motivation (ctd) Adoption of fixed or quasi-fixed exchange rate is prevalent Share of countries w/ less flexible exchange rates 60% 80% (Ilzetzki et. al. 2017) 3/35

Motivation (ctd) Adoption of fixed or quasi-fixed exchange rate is prevalent Share of countries w/ less flexible exchange rates 60% 80% (Ilzetzki et. al. 2017) Has gone up w/ adoption of Euro among Adv. Economies 3/35

Motivation (ctd) Conventional view: central banks w/ fixed exchange rate hold more reserves to prevent speculative attacks on currencies (Krugman) With higher reserves, less need to resort to inflation tax to make up for inconsistent fiscal/monetary policy. In practice, however, central banks can also borrow to avoid resorting to inflation tax In this paper, we explore an alternative channel linking precautionary motives and macroeconomic stabilization 4/35

What we do Sovereign default model with long-term debt and foreign reserve accumulation, and downward wage rigidity. Rollover risk induces large fluctuations in borrowing costs When borrowing costs are high, aggregate demand contracts causing involuntary unemployment Holdings of reserves (liquid assets) allow to mitigate fall in demand and increase in unemployment In good times, government issues debt and buy reserves for macroeconomic stabilization 5/35

Main Elements of the Model Small open economy (SOE) with T NT goods: Stochastic endowment for tradables y T Non-tradables produced with labor: y N = F (h) Wages are downward rigid in domestic currency With fixed exchange rate, π = 0 and L.O.P., wages are rigid in tradable goods w w Government issues non-contingent long-duration bonds (b) and saves in one-period risk free assets (a), all in units of T Default entails one-period exclusion and utility loss φ(y) Risk averse foreign lenders risk-premium shocks 6/35

Households Households preferences over consumption E 0 β t {u(c t )} t=0 c = C(c T, c N ) = [ω(c T ) µ + (1 ω)(c N ) µ ] 1/µ Budget constraint in units of tradables ct T + pt N ct N = yt T + φ N t + w t ht s τ Endowment of hours h, but ht s < h when w w binds. Optimality p N t = 1 ω ω ( c T t c N t ) 1+µ 7/35

Firms Maximize profits given by φ N t = max pt N F (h t ) w t h t h t w t : price of non-tradables and wages in units of tradables Firms optimality condition is p N t F (h t ) = w t 8/35

Asset/Debt Structure Long-term bond: Bond pays δ [ 1, (1 δ), (1 δ) 2, (1 δ) 3,... ] Law of motion for bonds b t+1 = b t (1 δ) + i t price is q 9/35

Asset/Debt Structure Long-term bond: Bond pays δ [ 1, (1 δ), (1 δ) 2, (1 δ) 3,... ] Law of motion for bonds b t+1 = b t (1 δ) + i t price is q Risk-free asset pays one unit of consumption price is q a Government s budget constraint if repay: g + q a a t+1 + b t δ = τ t + a t + q t (b t+1 (1 δ)b t ) }{{} i t debt issuance Government s budget constraint in default: g + q a a t+1 = τ t + a t 9/35

Foreign Investors Pricing kernel is a function of innovation to domestic output ε and a global factor ν = {0, 1} (assumed to be independent) m t,t+1 = e r ν(κε t+1+0.5κ 2 σ 2 ε), with κ 0, Implies constant risk free rate: E s sm(s, s ) = e r = q a Bond price given by: { q = E s s m(s, s )(1 d ) [ δ + (1 δ) q ]} ) d = ˆd(a, b, s ), q = q(a, b, s ) 10/35

Recursive Problem V ( ) b, a, y T = max {(1 ( ) ( )} d)v r b, a, y T + dv d a, y T d {0,1} 11/35

Recursive Problem V ( ) b, a, y T = max {(1 ( ) ( )} d)v r b, a, y T + dv d a, y T d {0,1} Value of repayment: V r ( b, a, y T ) = { max u ( c T, F (h) ) + βe y b,a,h,c T T y [V (b, a, y T )]} T subject to c T + g + q a a = a + y T + q ( b, a, y T ) (b (1 δ)b) δb [λ] w 1 ω ( ) c T 1+µ F (h) ω F (h) [ξ] h h [η] 11/35

Recursive Problem (ctd) Value of default: V d ( a, y T ) { = max u ( c T, F (h) ) ( ψ d y T ) + βe y c T,h,a T y [V (0, a, y T )]} T subject to c T + g + q a a = y T + a, [λ] w 1 ω ( ) c T 1+µ F (h) [ξ] ω F (h) h h [η] 12/35

Optimality Conditions Labor Market Assume F (h) = h α with α (0, 1). Also assume (just for simplicity): µ = 0. Optimality in labor market implies: ( ) 1 ω α h d (w) = ω w ct 13/35

Optimality Conditions Labor Market Assume F (h) = h α with α (0, 1). Also assume (just for simplicity): µ = 0. Optimality in labor market implies: Equilibrium employment: h(w) = ( ) 1 ω α h d (w) = ω w ct ( 1 ω ) α ω w ct for w = w h for w > w 13/35

Labor Market Equilibrium 14/35

Optimality Conditions FOC wrt c T : c T : u T + ξ ( 1 ω ω ) α w = λ ξ multiplier on the w w constraint 15/35

Optimality Conditions FOC wrt c T : c T : u T + ξ ( 1 ω ω ) α w = λ ξ multiplier on the w w constraint Tradable consumption has 2 benefits: 1. direct utility 2. reduction of unemployment 15/35

Optimality Conditions FOC wrt c T : c T : u T + ξ = λ ξ multiplier on the w w constraint Tradable consumption has 2 benefits: 1. direct utility 2. reduction of unemployment 15/35

Optimality Conditions FOC wrt c T : c T : u T + ξ = λ ξ multiplier on the w w constraint Tradable consumption has 2 benefits: 1. direct utility 2. reduction of unemployment For labor, we have: h : u N αh α 1 = η + ξ, η multiplier on the h h constraint 15/35

Optimal Portfolio: gains from borrowing to buy reserves Let ã denote reserves that can be purchased when issuing an additional unit of debt for an initial state s: ã = q(ã, b, s) + q(ã,b,s) b. q a q(ã,b,s) a The future marginal benefit of doing this is: E s s { Mg. utility benefts }} { }{{} ã (u (c ) + ξ ) Reserves { Mg. utility costs }} { [δ + (1 δ)q ](1 d )(u (c ) + ξ )) }{{} Debt repayments Reserves pay-off in all states high marginal value when unemployment is high macroeconomic stabilization 16/35

Higher reserves can reduce future unemployment 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 5 10 15 17/35

Higher reserves can reduce future unemployment 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 5 10 15 Now: consider a policy that issues debt to increase reserves, keeping NFA constant. 17/35

Higher reserves can reduce future unemployment 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 5 10 15 Note: NFA is constant across portfolios higher reserves can reduce future unemployment 18/35

Higher reserves can reduce future unemployment 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 5 10 15 Note: NFA is constant across portfolios higher reserves can reduce future unemployment 19/35

Quantitative Analysis Today: Calibrate flexible wage economy (Bianchi, Hatchondo and Martinez) and show effects of wage rigidity. 1 model period = 1 year. Use Mexican data (archetypical EME). 20/35

Quantitative Analysis Functional forms Utility function: u(c) = c1 γ 1 1 γ, with γ 1 Utility cost of defaulting: ψ d (y T ) = α 0 + α 1 log(y T ) Tradable income process: log(y T t ) = (1 ρ)µ y + ρlog(y T t 1) + ɛ t with ρ < 1 and ɛ t N(0, σ 2 ɛ ) 21/35

Quantitative Analysis (ctd) Parameter Description Value r Risk-free rate 0.04 β Domestic discount factor 0.92 π LH Prob. of transiting to high risk-premium 0.15 π HL Prob. of transiting to low risk-premium 0.8 σ ɛ Std. dev of innovation to log(y T ) 0.034 ρ Autocorrelation of log(y T ) 0.66 µ y Mean of log(y T ) 1 2 σ2 ɛ g Government consumption 0.12 δ Coupon decaying rate 0.2845 ω Share of tradables 0.3 1 + µ Inverse of the intratemporal elast. of subs. γ Parameters set by simulation α 0 Default cost parameter 2.45 α 0 Default cost parameter 19 κ H Pricing kernel parameter 23 γ Coefficient of relative risk aversion 3.3 w Lower bound on wages 1.25 22/35

Results 1. Simulations moments. 2. Default sets and spreads. 3. Welfare exercises. 23/35

Results: data and simulation moments Targeted Data Model Flex. w Rigid w σ(c)/σ(y) 1.0 1.0 1.0 Mean debt (b/y T ) 43.0 44.6 17.1 Mean r s 2.4 2.5 2.4 r s w/ risk-prem. shock 2.0 2.0 1.6 Non-Targeted σ(r s ) 0.9 2.0 1.9 ρ(r s, y) -0.5-0.8-0.8 ρ(c, y) 0.8 0.9 0.9 Mean Reserves (a/y T ) 8.5 7.3 14.4 Mean Reserves/Debt (a/b) 0.20 0.17 0.85 Unemployment 3.9 0.0 2.8 24/35

Results: default regions 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Default incentives increase in debt and decrease in reserves. 25/35

Results: default regions 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Default incentives increase in debt and decrease in reserves. Wage rigidity increases default incentives 26/35

Results: default regions and NFA 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Default incentives increase in debt and decrease in reserves. Wage rigidity increases default incentives Gross positions matter for default. 27/35

Results: spreads, reserves and wage rigidity 10 9 8 7 6 5 4 3 2 1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 Wage rigidity increases spreads. 28/35

Results: spreads, reserves and wage rigidity 10 9 8 7 6 5 4 3 2 1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 Wage rigidity increases spreads. Reserves decrease spreads, and more when wages are rigid. 29/35

Results: welfare We ll compute welfare gains of moving from a baseline economy to an alternative economy: [ ((1 ) γ)(1 β)valternative + 1 1/(1 γ) Welfare gain = 100 1] (1 γ)(1 β)v baseline + 1 We re interested in studying: Gains of eliminating wage rigidity Gains of being having access to reserves To do the latter: define a No-Reserves economy (which can have or not wage rigidity). 30/35

Results: welfare gains of eliminating wage rigidity Baseline Alternative Welf. Gain Benchmark Benchmark 2.48 w/ wage rigidity w/ flexible wage No-Reserves No-Reserves 4.80 w/ wage rigidity w/ flexible wage Eliminating wage rigidity is welfare enhancing. Even more when reserve accumulation is not possible. plots 31/35

Results: welfare gains of access to reserve accumulation Baseline Alternative Welf. Gain No-Reserves Benchmark 0.15 w/ flexible wage w/ flexible wage No-Reserves Benchmark 2.41 w/ wage rigidity w/ wage rigidity Being able to accumulate reserves is welfare enhancing. Even more when facing wage rigidities. plots 32/35

Conclusions Studied use of foreign reserves for macro stabilization goals in a SOE with: 1. nominal rigidities 2. fixed exchange rates, and 3. sovereign default risk When borrowing costs are high, aggregate demand contracts causing involuntary unemployment Holdings of reserves (liquid assets) allow to mitigate fall in demand and increase in unemployment In good times, government issues debt and buy reserves for macroeconomic stabilization 33/35

Conclusions (ctd) We found that: Mechanism is quantitatively relevant: Avg. reserves are twice as large. Avg. reserves/debt ratio is 4 times as large. Wage rigidity increase default incentives and spreads. Reserves decrease default incentives and spreads. Reserves help reduce future unemployment risk. There are sizeable welfare gains of: accumulating reserves and eliminating wage rigidities. 34/35

Conclusions (ctd) Other implications: Maastrict clauses establish limits for gross debt positions in Eurozone Analysis suggests that minimum holdings of assets should be established. A stock of foreign reserves might mitigate temptations to exit 35/35

THANKS! 35/35

Countries in our dataset (back) We use the IMF Classif. of Exch. Rate Arrangements (as of 2016) We follow Kondo and Hur (2016) and focus on 23 EMEs: Argentina India Poland Brazil Indonesia Romania Chile Malaysia Russia China Mexico South Africa Colombia Morocco South Korea Czech Republic Pakistan Thailand Egypt Peru Turkey Hungary Philippines Table 1: EME classification: follow Financial Times and the London Stock Exchange (FTSE), Morgan Stanley Capital International (MSCI), the Economist, Standard & Poor s (S&P), and Dow Jones Indexes.

Welfare gains of eliminating wage rigidity (back) 6.5 6 5 4 6 5.5 5 3 4.5 2 4 1 3.5 0.8 0.9 1 1.1 1.2 1.3 0.8 0.9 1 1.1 1.2 1.3 Figure 1: Benchmark Figure 2: No-Reserves

Welfare gains of access to reserve accumulation (back) 3 6 2 5 4 1 3 0 2-1 1 0-2 -1 0.8 0.9 1 1.1 1.2 1.3 0.8 0.9 1 1.1 1.2 1.3 Figure 3: Flexible wages Figure 4: Rigid wages

Results: welfare gains of eliminating wage rigidity Initial debt = Avg. in simulations (14%). Initial reserves= zero. Baseline Alternative Welf. Gain Benchmark Benchmark 3.31 w/ wage rigidity w/ flexible wage No-Reserves No-Reserves 4.81 w/ wage rigidity w/ flexible wage Eliminating wage rigidity is welfare enhancing. Even more when reserve accumulation is not possible.

Results: welfare gains of access to reserve accumulation Initial debt = Avg. in simulations (14%). Initial reserves= zero. Baseline Alternative Welf. Gain No-Reserves Benchmark -0.32 w/ flexible wage w/ flexible wage No-Reserves Benchmark 1.12 w/ wage rigidity w/ wage rigidity Being able to accumulate reserves can be welfare enhancing, especially with wage rigidities.

Welfare gains of eliminating wage rigidity (back) Initial debt = Avg. in simulations (14%). Initial reserves= zero. 6.5 6 6 5 5.5 4 5 3 4.5 2 4 1 3.5 0.8 0.9 1 1.1 1.2 1.3 0.8 0.9 1 1.1 1.2 1.3 Figure 5: Benchmark Figure 6: No-Reserves

Welfare gains of access to reserve accumulation (back) Initial debt = Avg. in simulations (14%). Initial reserves= zero. 3 2 1 5 4 3 0 2-1 1-2 0-1 -3 0.8 0.9 1 1.1 1.2 1.3 0.8 0.9 1 1.1 1.2 1.3 Figure 7: Flexible wages Figure 8: Rigid wages