Banks and Liquidity Crises in Emerging Market Economies

Transcription

1 Banks and Liquidity Crises in Emerging Market Economies Tarishi Matsuoka Tokyo Metropolitan University May, 2015 Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

2 Introduction Introduction After financial liberalizations in the 1980s, crises have become more frequent and more costly events. Emerging markets experienced a banking or currency crisis or both. Examples: Chile in 1982, Mexico in 1994, Argentina in 1995, Brazil in 1996, East Asia in 1997, Russia in 1998 and Argentina in Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

3 Introduction Facts 1 Capital inflow increases the probability and size of a banking crisis. Kaminsky & Reinhart (1999), Reinhart & Reinhart (2009), Reinhart & Rogoff (2008) 2 Financial institutions take on significant amounts of short-term debt relative to liquid reserves. Sachs et al. (1996), Radelet & Sachs (1998), Chang & Velasco (1998) 3 A banking crisis is closely linked to an asset-price boom and burst. Kaminsky & Reinhart (1999), Reinhart & Rogoff (2008) Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

4 Introduction Sudden Stops Current Account Balance (% of GDP) Current Account Balance of Asean 5 (% of GDP) 50 Thailand Korea 40 Indonesia Malaysia 30 Philippines Years Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

5 Introduction Too Much Short-Term Foreign Debt Short-Term Debt To International Reserves Ratio: Indonesia Korea Malaysia Philippines Thailand Asean-5 June June source: Chang and Velasco (1998) Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

6 Introduction Collapse of Asset Prices Stock market capitalization to GDP (%) Stock market capitalization to GDP (%) Thailand Korea Indonesia Malaysia Philippines Years Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

7 Introduction The aim of this paper Develop a theory with financial markets and financial institutions Show how these interactions cause economy-wide banking crises. capital inflow increases the asset price volatility and the size of a crisis Ask: Can public policies stabilize the financial system? liquidity regulation public deposit insurance Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

8 Introduction Main Results The model generates two types of equilibria: a no-default equilibrium banks have enough liquidity to pay all depositors during bank runs all banks remain solvent. a mixed-equilibrium. ex ante identical banks choose different strategies some banks default with positive probability the asset price is more volatile. defaulting banks increase as capital inflow increases Liquidity regulation may stabilize the financial system, but public deposit insurance may not. Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

9 Introduction Related Literature Multiple equilibria: Calvo (1988), Obstfeld (1996), Cole & Kehoe (1996, 2000), Chang & Velasco (2000a, b, 2001) Fundamental bank runs: Allen & Gale (2000a,b) Financial frictions: Caballero and Krishnamurthy (2001), Aoki, Benigno & Kiyotaki (2009), Mendoza & Quadrini (2010), & Mendoza (2010) Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

10 The Model The Model Three periods, t = 0, 1, 2. A [0, 1] continuum of ex ante identical agents. Each agent has an endowment only in t = 0. Diamond-Dybvig preferences: early consumer (consume at t = 1) late consumer (consume at t = 2) with prob. λ θ with prob. 1 λ θ Aggregate uncertainty: λ L with prob. π, λ θ = λ H with prob. 1 π, where 0 < λ L < λ H and 0 < π < 1. Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

11 The Model Two types of assets: a short asset (y) = less productive but liquid a long asset (x) = productive but illiquid Competitive (interbank) asset market at t = 1. P θ = the price of the long asset period t = 0 t = 1 t = 2 endowment short asset P 0 long asset -1 0 R > 1 Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

12 The Model International capital market: international creditors are risk neutral. the net interest rate is zero. Assumptions: International creditors can not access to the domestic asset market. Only banks can access to the international capital market. Borrowing limit f Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

13 The Model Banking Banks offer (c 1, c 2L, c 2H ) and collect funds at t = 0. non-contingent (incomplete) deposit contract c 1 is fixed at t = 0. Banks can access to the asset market at t = 1 buy or sell the long asset agents are excluded Banks can access to the international capital market at t = 0, 1, 2 lend as much as possible borrow at most the amount f > 0 Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

14 The Model The timing of events In period 0: agents deposit all their endowments banks borrow funds in the international market banks divide deposits between short and long assets. In period 1: state and depositors types have been realized the asset market opens. some depositors receive payments (c 1 ) from the banks. banks repay short-term foreign debt (b 01 ) and borrow short term (b 1θ ). In period 2: remaining depositors withdraw their deposits from the banks they consume c 2. banks repay short-term (b 1θ ) and long-term foreign debt (b 02 ). Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

15 The Model Constrained Efficient Allocation The planner s problem max E θ [λ θ u(c 1 ) + (1 λ θ )u(c 2θ )], subject to x + y 1 + b 01 + b 02, λ θ c 1 + b 01 y + b 1θ, (1 λ θ )c 2θ + b 1θ + b 02 Rx + (y + b 1θ b 01 λ θ c 1 ), b 01 + b 02 f, b 1θ + b 02 f, c 1 c 2θ. Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

16 The Model Constrained Efficient Allocation Since R > 1, the international borrowing constraints are binding b 01 + b 02 = f, b 1H + b 02 = f. At the optimum, λ H c 1 = y + b 1H b 01 = y. Then, (1 λ H )c 2H = Rx f. Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

17 The Model Constrained Efficient Allocation FOC: πλ L + (1 π)λ H λ H u π ( y λ H ) ( ) ( ) R(1 + f) f (R 1 + λ L R 1 + λl u λ H )y λ H 1 λ L ( ) R(1 + f y) f R(1 π)u = 0. (1) 1 λ H Optimal levels of consumption: c 1 = y λ H, c 2H = R(1 + f λ y ) f R(1 + f) f (R 1 + L, c λ 2L = H )y. 1 λ H 1 λ L Optimal foreign debt structure (b 01, {b 1θ } θ=l,h, b 02 ) is indeterminate. Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

18 The Model Decentralized Banking Economy Two types of equilibria: a no-default equilibrium all banks are symmetric and take a safe portfolio. all banks remain solvent. a mixed-equilibrium. ex ante identical banks choose different strategies some banks default with positive probability Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

19 Equilibrium The no default equilibrium (1) Consider first an equilibrium in which all banks offer a run-preventing contract The problem of banks: max E θ [λ θ u(c 1 ) + (1 λ θ )u(c 2θ )], s.t. x + y 1 + b 01 + b 02, λ θ c 1 + b 01 y + b 1θ, θ, ( (1 λ θ )c 2θ + b 1θ + b 02 R x + y + b ) 1θ b 01 λ θ c 1, θ, P θ b 01 + b 02 f, b 1θ + b 02 f, c 1 c 2θ, θ, θ. Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

20 Equilibrium The no default equilibrium (2) FOCs: [πλ L + (1 π)λ H ]u R (c 1 ) = πλ L u R (c 2L ) + (1 π)λ H u (c 2H ), (2) P L P ( H π 1 1 ) ( ) 1 u (c 2L ) (1 π) 1 u (c 2H ), (3) P L P H with equality if y < 1 + f The asset market at period 1 clears if λ L c 1 < λ H c 1 = y. (4) Since λ L c 1 < y, excess liquidity at period 1 in state L: P L = R. (5) Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

21 Equilibrium The no default equilibrium (3) Combining (2) (4) yields ( ) y [πλ L + (1 π)λ H ]u λ H ( ) R(1 + f) f (R 1 + λ L = π [λ H (R 1) + λ L ] u λ H )y 1 λ L which determines y uniquely. Eq. (1) is equivalent to (6). + λ H R(1 π)u ( R(1 + f y) f 1 λ H ), (6) Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

22 Equilibrium The no default equilibrium (4) Proposition 2 The no-default equilibrium is unique and achieves the constrained efficient allocation. Equilibrium asset prices: P L = R > 1, (7) (1 π)ru (c 2H P H = π(r 1)u (c 2L ) + (1 π)ru (c < 1. 2H ) (8) Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

23 Equilibrium The mixed equilibrium In equilibrium, not all banks default simultaneously. Suppose that all banks default at t = 1. all depositors try to withdraw their funds in state θ = H all banks sell the long assets at t = 1. the price must be P H = 0. Given P H = 0, a bank would hold enough liquidity at t = 0 and make a large capital gain by purchasing the long assets at t = 1. Thus, an equilibrium where banks can default must be mixed. Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

24 Equilibrium Two types of banks Two types of banks arise endogenously! Safe banks [ρ]: hold a lot of the short asset at t = 0 offer deposit contracts promising low payments at t = 1 to remain solvent. Risky banks [1 ρ]: invest so much in the long asset offer deposit contracts promising high payments at t = 1 that may cause defaults. Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

25 Equilibrium Safe banks (1) The optimization problem of the safe banks is similar to the one in the no default equilibrium. The problem of the safe banks: subject to max E θ [λ θ u(c s 1) + (1 λ θ )u(c s 2θ)] x s + y s 1 + b s 01 + b s 02, λ θ c s 1 + b s 01 y s + b s 1θ, θ ( ) (1 λ θ )c s 2θ + b s 1θ + b s 02 R x s + ys + b s 1θ b s 01 λ θ c s 1, θ P θ b s 01 + b s 02 f, b s 1θ + b s 02 f, c s 1 c s 2θ θ θ. Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

26 Equilibrium Binding borrowing constraints: Then, Safe banks (2) b s 01 + b s 02 = f, (9) b s 1θ + bs 02 = f, θ (10) x s + y s = 1 + f, (11) ( (1 λ θ )c s 2θ + f = R x s + ys λ θ c s ) 1, (12) P θ FOCs: [πλ L + (1 π)λ H ]u (c s R 1) = πλ L u (c s R P 2L) + (1 π)λ H u (c s L P 2H), (13) ( H π 1 1 ) ( ) 1 u (c s P 2L) (1 π) 1 u (c s L P 2H), (14) H with equality if x s > 0. Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

27 Equilibrium Risky banks (1) Risky banks default in state θ = H. The problem of the risky banks: ( ) max π[λ Lu(c r 1) + (1 λ L)u(c r c r 1 2L)] + (1 π)u c r 1 + (1 + r 1)b r (y r + P Hx r ), 01 subject to x r + y r 1 + b r 01 + b r 02, λ L c r 1 + (1 + r 1 )b r 01 y r + b r 1L + P L x r, ( (1 λ L )c r 2L + b r 1L + (1 + r 2 )b r 02 R x r (1 + r ) 1)b r 01 + λ L c r 1 y r b r 1L, P L b r 01 + b r 02 f, b r 1L + b r 02 f, c r 1 c r 2L. Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

28 Equilibrium Risky banks (2) FOCs: u (c r 1) + 1 π πλ L u ( c r 1 (y r + P Hx r ) ) (y r + P Hx r )(1 + r 1)b r 01 (c r 1 + (1 + r1)br 01 )2 = R P L u (c r 2L), c r 1 + (1 + r1)br 01 (15) ( πr 1 1 ) ( ) c u (c r 2L) = (1 π)u r 1 (y r + P H x r ) c r 1 (1 P H ) P L c r 1 + (1 + r 1)b r 01 c r 1 + (1 + r 1)b r + µ 8, 01 (16) ) ( ) π (r 2 RPL c r 1 u (c r 2L) = (1 π)u r 1 (y r + P H x r ) (y r + P H x r )(1 + r 1 )c r 1 c r 1 + (1 + r 1)b r 01 (c r 1 + (1 + r 1)b r 01 )2 µ 5 µ 6 + µ 7, (17) where µ 5, µ 6, µ 7, µ 8 are the multipliers on the non-negativity constraints for b r 1L, br 01, br 02, and yr. Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

29 Equilibrium The mixed equilibrium The depositors must be indifferent between depositing their funds in a safe or risky bank W s = W r (18) The market clearing conditions ρ(y s + b s 1L λ L c s 1 b s 01) = (1 ρ)((1 + r 1 )b r 01 + λ L c r 1 y r b r 1L), (19) ρ(y s + b s 1H λ H c s 1 b s 01) = (1 ρ)p H x r. (20) No-arbitrage conditions are: 1 = π(1 + r 1 ) + (1 π) (1 + r 1)(y r + P H x r ) c r 1 + (1 + r 1)b r, 01 (21) 1 = π(1 + r 2 ). (22) Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

30 Equilibrium Term structure of interest rates r 1 < r 2. The mixed equilibrium is characterized by the vector (c s 1, {cs 2θ }, {bs 0t }, {bs 1θ }, ys, c r 1, cr 2L, {br 0t }, {br 1θ }, yr, {P θ }, {r t }, ρ) satisfying (7) (20). Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

31 Equilibrium Existence of Equilibria I analyze the parameter space in which two types of equilibria exist. Are the strategies of the risky banks optimal? the no default equilibrium exists if no bank finds it optimal to default given P L and P H. the mixed equilibrium exists if some banks a risky portfolio. Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

32 Equilibrium A Deviating Bank (1) Consider a problem of a bank that tries to choose a risky portfolio in the no-default equilibrium. The deviating bank offers a risky contract to depositors given P L and P R defined by (7) and (8). ( ) max π[λ Lu(c d 1) + (1 λ L)u(c d c d 1 2L)] + (1 π)u c d 1 + (1 + r (y d + P Hx d ) 1)b d 01 subject to x d + y d = 1 + b d 01 + b d 02, λ L c d 1 + (1 + r 1 )b d 01 y d + b d 1L + P L x d, ( (1 λ L)c d 2L + b d 1L + (1 + r 2)b d 02 R x d (1 + r ) 1)b d 01 + λ L c d 1 y d b d 1L, P L b d 01 + b d 02 f, b d 1L + b d 02 f, c d 1 c d 2L. Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

33 Equilibrium A Deviating Bank (2) Let W d denote the corresponding maximized expected utility that the deviating bank can offer. Proposition 3 If W N > W d, then there exists a no-default equilibrium. Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

34 Basic Examples Basic Examples (1) Utility function: u(c) = log(c). Parameters: λ L = 0.8, λ H = 0.81, and R = 1.5. Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

35 Basic Examples Basic Examples (2) Ex. π f Types of eqm. Price volatility (P L /P H ) ρ E[u] 1A No default /0.6628= B No default /0.6628= C No default /0.6628= A Mixed /0.5189= B Mixed /0.4905= C Mixed /0.4646= Table: Numerical examples Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

36 Basic Examples Basic Examples (3) Ex. π f (y, x) (c 1, c 2L, c 2H ) (b 01, b 1L, b 1H, b 02 ) 1A (0.8888, ) (1.0973, , ) indeterminate 1B (0.9427, ) (1.1638, , ) indeterminate 1C (0.9966, ) (1.2304, , ) indeterminate Table: Allocations in the no-default equilibrium Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

37 Basic Examples Basic Examples (4) Ex. π f (y s, x s ) (y r, x r ) 2A (0.9085, ) (0.0000, ) 2B (0.9652, ) (0.0000, ) 2C (1.0212, ) (0.0000, ) (c s 1, cs 2L, cs 2H ) (c r 1, cr 2L, yr + P H x r ) (1.0979, , ) (1.3251, , ) (1.1643, , ) (1.4026, , ) (1.2306, , ) (1.4848, , ) (b s 01, bs 1L, bs 1H, bs 02 ) (b r 01, br 1L, br 1H, br 02 ) indeterminate (0.0000, , , indeterminate (0.0000, , , indeterminate (0.0000, , , Table: Allocations in the mixed equilibrium Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

38 Basic Examples Basic Examples (5) The ratio of short term debt to international liquidity reserves η ρ( λc s 1 + bs 01 ) + (1 ρ)( λc r 1 + (1 + r 1)b r 01 ) ρy s + (1 ρ)y r, where λ πλ L + (1 π)λ H. Setting b s 01 = 0.2f and bs 02 = (1 0.2)f In Example 2, η is increasing in f. η = when f = 0.3 η = when f = 0.5 η = when f = 0.7 Consistent with empirical evidence! Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

39 Basic Examples Extension (1): Risk Aversion CRRA utility function: where σ 1. u(c) = c1 σ 1 σ, Ex. σ π f Types of eqm. Price volatility (P L/P H) ρ E[u] 2A Mixed /0.5189= B Mixed /0.4905= C Mixed /0.4646= A Mixed /0.3952= B Mixed /0.4012= C Mixed /0.4049= A No default /0.4237= B No default /0.4237= C No default /0.4237= Table: Numerical examples for CRRA utility function. Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

40 Basic Examples Extension (2): Short-Term Debt Suppose that no long-term borrowing is allowed at period 0. b 02 = 0 or r 2 =. Transaction costs, information costs Ex. π f Types of eqm. Price volatility (P L/P H) ρ E[u] 5A Mixed /0.4579= B Mixed /0.4271= C Mixed /0.4063= Table: Numerical examples for foreign short-term debt Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

41 Basic Examples Sudden Stop capital net outflow at period 0: f < 0. capital net outflow at period 1 in state H: ρb s 01 + (1 ρ)(1 φ)(y r + P H x r ) (ρb s 1H + (1 ρ)b r }{{}}{{ 1H) } capital outflow capital inflow =(1 ρ)(1 φ)(y r + P H x r ) > 0. where φ = c r 1/(c r 1 + (1 + r 1 )f). Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

42 Basic Examples Discussion Q. Is the mixed equilibrium is constrained efficient? Ex. π f mixed eqm., E[u] constrained efficient, E[u] 2A B C A. No. The mixed equilibrium attains higher welfare than the planner. Why? Default relaxes the constraint of non-contingent contracts. No justification for policy interventions! Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

43 Basic Examples Policy Implications Realistic features that are not modeled here can justify the policy. a crisis may have significant negative impacts on the real sector. e.g., increasing unemployment, decreasing output, etc. Q. Can the government eliminate a crisis at the expense of welfare? Two policies: Liquidity regulation Public deposit insurance Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

44 Basic Examples Liquidity Regulation Liquidity regulation: y ξ(1 + f), 0 ξ 1 Ex. π f ξ Types of eqm. Price volatility (P L/P H) ρ E[u] 2A Mixed /0.5189= B Mixed /0.4905= C Mixed /0.4646= A Mixed /0.4802= B Mixed /0.4371= C Mixed /0.4007= A No default /0.4243= B No default /0.4243= C No default /0.4243= Table: The effects of liquidity regulations: y ξ(1 + f) Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

45 Basic Examples Public Deposit Insurance (1) In state H at period 1, the government imposes a lump-sum tax on the safe banks, τ. transfer ϕ to the depositors of the risky banks. (1 ρ)ϕ = ρτ. Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

46 Basic Examples Public Deposit Insurance (2) Ex. π f DI (ϕ, τ) Eqm. Price volatility (P L /P H ) ρ E[u 2A (0.0000, ) Mixed /0.5189= B (0.0000, ) Mixed /0.4905= C (0.0000, ) Mixed /0.4646= A (0.1000, ) Mixed /0.5794= B (0.1000, ) Mixed /0.5251= C (0.1000, ) Mixed /0.4854= A (0.2000, ) Mixed /0.5493= B (0.2000, ) Mixed /0.5050= C (0.2000, ) Mixed /0.4701= Table: The effects of government deposit insurance Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47

47 Conclusion Conclusion This paper have developed a small-open-economy version of a banking model with financial market. The model generates two types of equilibria: the no-default equilibrium the mixed equilibrium The model matches many features of East Asia crisis in Liquidity regulation may stabilize the financial system, but public deposit insurance may not. Tarishi Matsuoka (TMU) Banking Crises in Emerging Market Economies May, / 47