Financial Crises, Dollarization and Lending of Last Resort in Open Economies

Financial Crises, Dollarization and Lending of Last Resort in Open Economies Luigi Bocola Stanford, Minneapolis Fed, and NBER Guido Lorenzoni Northwestern and NBER Restud Tour Reunion Conference May 2018

Motivation Liability dollarization common in emerging economies Large literature on foreign-currency debt as source of financial instability Currency depreciations increase debt burden Why foreign-currency borrowing? Less studied in the literature We propose a theory of liability dollarization and study how it interacts with policy interventions 1 / 20

Our story in a nutshell We build on two main empirical observations Liability and asset dollarization Excess returns on local currency vs dollar (UIP violation) In our theory, both facts driven by insurance motives of domestic savers Study Lending of Last Resort in this environment Successful ex-post interventions might reduce risk-taking ex-ante Fragility may persist because of lack of fiscal capacity 2 / 20

Overview of the talk 1 The Model 2 Equilibria in absence of government interventions Continuation equilibria: t = 1, 2 Dollarization: t = 0 3 Lending of last resort Ex-post interventions and notion of credibility Ex-ante analysis and role for foreign currency reserves

Environment Small open economy, three periods t = 0, 1, 2. Domestic agents: households and bankers Two goods: tradable (T) and non-tradable (N) Production function of tradables y T t = (K t) α (L t) 1 α Endowment e N of non-tradables Banks have access to technology for producing capital 1 unit of T one unit of capital Households have access to less efficient technology for producing capital φ units of T one unit of capital, φ > 1 3 / 20

Households and Bankers Households have preferences [ 2 ( (c E β t ) T ω ( ) U t c N 1 ω ) ] t and budget constraint t=0 c T t + p t c N t + q T t a T t+1 + q N t p t a N t+1 w t + p t e N h + a T t + p t a N t + Π t Bankers consume only at t = 2. Their budget constraint at t = 0, 1 is k t+1 = [ r t k t + p t e N b b T t p t b N ] T t +qt b T t+1 + q N t p t b N t+1 }{{} n t They face a collateral constraint b T t+1 + p t+1 b N t+1 θk t+1 4 / 20

Firms, foreign investors and equilibrium Firms rent L t and K t (from banks and households) to produce a T good Foreign investors are risk neutral, and can purchase only T bonds A competitive equilibrium is prices {p t, r t, w t, q T t, q N t }, households choices {c T t, c N t, a T t+1, an t+1 }, bankers choices {k t+1, b T t+1, bn t+1 }, firms choices {K t, L t, k t } such that All choices are individually optimal Markets clear c N t = e N a N t = b N t K t = k t + k t 5 / 20

The market for N goods In equilibrium p t is constant No uncertainty, consumption of T smoothed across periods So, demand for N goods constant, so its supply Equilibrium condition in N good market [ a T (1 ω) 1 + pa N 1 + w 1 + βw 2 + (1 + β)pe N ] h (1 + β) }{{} Demand of non-tradables = p(e N h + e N b ) }{{} Supply of non-tradables Since future wages are w 2 = (1 α)k α 2 we have an increasing relation p = P(K 2 ) 6 / 20

The market for capital Three cases in the capital market If n(p) big enough, capital is at the first best βr 2 = 1 K 2 = (αβ) 1/(1 α) K If n 1(p) small enough, inferior technology is operative βr 2 = φ K 2 = ( ) 1/(1 α) αβ K φ For intermediate range, capital increasing in n(p) βr 2 > 1 K 2 = n1(p) 1 βθ So we have another mapping K 2 = K(p) K(.) increasing in p if balance sheet is mismatched (e N b bn 1 ) 7 / 20

Continuation equilibria (a) Unique continuation equilibrium (b) Multiple continuation equilibria Feedback between p and K 2 can lead to multiple equilibria (at most 2 stable). Low p equilibrium Pareto dominated (low consumption, low net worth) 8 / 20

Mismatch and multiplicity Necessary condition for multiplicity is that e N b bn 1 is large enough Holding total debt constant, a higher b N 1 reduces the potential of crisis 9 / 20

Dollarization Will banks choose positions that insulate the economy from crises? Answer: Not necessarely Banks have a hedging motive: want to issue N debt because N debt depreciates in a crisis Households have a hedging motive too: want to save in T because these assets provide insurance in a crisis Households hedging motive may dominate Theory of dollarization: banks borrow in dollars because it is relatively cheap. It is cheap because dollars appreciate in a crisis 10 / 20

Portfolio choices at date 0 For banks, marginal value of wealth is λ b,t = (r 2 θ)/(1 βθ) [ ] q T 0 λ b,0 = βe[λ b,1 ] q N p1 0 λ b,0 = βe λ b,1 p 0 For households, we have that q T 0 λ h,0 = βe[λ h,1 ] [ ] q N p1 0 λ h,0 = βe λ h,1 p 0 with λ t = (c T t ) ω(1 γ) 1 Two assets/two states (equivalence with complete markets) state by state (c T 1 ) ω(1 γ) 1 = Φβ r 2 θ 1 βθ 11 / 20

Safe equilibria If households risk aversion is small enough, the every equilibrium is safe Suppose that households risk aversion satisfies (φ βθ)[1 + ω(γ 1)] < β(1 α) Then, the financial positions chosen at date 0 guarantee that there is a unique continuation equilibrium. In safe equilibrium, there is no risk of a crisis This implies that (1 + i T 0 ) = (1 + i N 0 )E [ p1 p 0 ] Issuing N bonds is not expensive for banks no mismatch, no risk 12 / 20

Fragile equilibria If γ larger, safe equilibria can coexists with fragile equilibria Take a vector {a T 1, an 1, bt 1, an 1, K 1} such that the economy features multiple continuation equilibria. Then, there exists a coefficient of relative risk aversion γ and date 0 initial positions that generate an equilibrium in which {a T 1, an 1, bt 1, an 1, K 1} are optimal and crises occur with positive probability. In fragile equilibrium, there is risk of a crisis This implies that (1 + i T 0 ) < (1 + i N 0 )E [ p1 p 0 ] Issuing N bonds is expensive for banks mismatch and risk Numerical example 13 / 20

Introducing a Lender of Last Resort Introduce a benevolent government at t = 1 Lends T b to banks in exchange for repayment R β 1 T b No superior enforcement ability b T 2 + R θk 2 Finances operations with labor taxes τ t ξ and by borrowing A T 2 Government maximizes social welfare W 2 β t 1 U(c T t, e N ) + Φβc T b t=1 Φ chosen so that no redistributive motives at competitive equilibria 14 / 20

Timing Need a notion of credibility for LOLR. Split t = 1 in two sub-periods i Agents form expectation about future government policy and Trade on N market and determine p 1 Set maximum they are willing to lend to government A = ξw e 2 + R e ii Government sets optimal policy and remaining markets clear An equilibrium has Government maximize, taking as given p 1 and A Private sector expectations consistent with government optimality 15 / 20

Optimal policy Let M = ξ(1 α)k α 1 βa 16 / 20

Optimal policy Let M = ξ(1 α)k α 1 βa If M < M, the government sets T b = 0. Else, it sets T b = M 16 / 20

Fixed point Let M B be the value of M in the bad equilibrium with no intervention M B = ξ(1 α)k α 1 + βξ(1 α)k α 2 The government uniquely implements the first best if and only if M B > M. Why can t the government eliminate bad equilibrium? When n 1 and M are low, government does not intervene When private sector expects no intervention, n 1 and M low Key observation: what matters is fiscal capacity in bad equilibrium 17 / 20

The role of reserves Suppose government enters t = 1 with positions A T 1 and AN 1 The value of these positions is A T 1 + p 1 A N 1 When private sector holds pessimistic expectations, p 1 is low If government takes positions A N 1 < 0 < AT 1 that satify A T 1 + p B 1 A N 1 > M M N it can uniquely implement good equilibrium at t = 1 Interpretation: borrowing in domestic currency to accumulate foreign currency reserves makes LOLR commitment credible 18 / 20

Ex-ante effects of reserves Suppose A T 1 and AN 1. Two effects at date 0 1 For given interest rates, interventions that lower r 2 in bad equilibrium induces banks to issue more dollar debt More risk taking from banks 2 As households save more in N, interest rates on N bonds decrease, which induces bank to borrow in T debt Less risk taking from banks If by accumulating reserves at t = 0 the government eliminates equilibrium multiplicity, the intervention does not lead to more risk taking 19 / 20

Conclusion A new theory of dollarization Insurance motive of savers makes local currency borrowing expensive Studied LOLR Introduced notion of credibility for LOLR Reserves can enhance credibility They promote financial stability ex-ante and ex-post, even if never used Current work: hedging and financial amplification 20 / 20

Additional Material

Safe equilibrium Safe Fragile a N 1, bn 1 0.40 0.00 a T 1 0.01 0.17 b T 1 0.16 0.46 St. dev. of log w 2 0.00 0.07 St. dev. of log p 1 0.00 0.025 Covar. of log w 2 and log p 1 0.00 0.002 E[(1 + i N 0 )(p 1/p 0 )] 1.01 1.06 (1 + i T 0 ) 1.01 1.01 Households save in N bonds Banks issue N debt. Unique equilibrium from t = 1 Households non-financial income stable, no incentives to save in T bonds

Fragile equilibrium Safe Fragile a N 1, bn 1 0.40 0.00 a T 1 0.01 0.17 b T 1 0.16 0.46 St. dev. of log w 2 0.00 0.07 St. dev. of log p 1 0.00 0.025 Covar. of log w 2 and log p 1 0.00 0.002 E[(1 + i N 0 )(p 1/p 0 )] 1.01 1.06 (1 + i T 0 ) 1.01 1.01 Households save in T bonds Banks issue T debt. Multiple equilibria at t = 1 because of mismatch Households non-financial income risky: T assets provide insurance Return