Bubbles and Credit Constraints


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1 Bubbles and Credit Constraints Jianjun Miao 1 Pengfei Wang 2 1 Boston University 2 HKUST November 2011 Miao and Wang (BU) Bubbles and Credit Constraints November / 30
2 Motivation: US data Miao and Wang (BU) Bubbles and Credit Constraints November / 30
3 S&P Price Index Net percentage of banks tightening standards S&P Price Index St. Louis Financial Stress Index Motivation: US data Miao and Wang (BU) Bubbles and Credit Constraints November / 30
4 Motivation: International evidence Rapid increases in stock prices are linked to heavy capital in ows rapid credit growth rapid investment growth Collapse in stock prices were accompanied by capital out ow decreased investment tightened credit recession Collyns and Senhadji (2002), Gan (2007a,b), Goyal and Yamada (2004), Chaney, Sraer, and Thesmar (2009) Miao and Wang (BU) Bubbles and Credit Constraints November / 30
5 Motivation Bubbles and crashes are linked to booms and busts in credit market Is there any connection between rational bubbles/crashes and credit constraints? Provide a theory of creditdriven stock price bubble Miao and Wang (BU) Bubbles and Credit Constraints November / 30
6 Major Historical Examples Tulipmania ( ) The Mississippi Bubble ( ) The South Sea Bubble (1720) The Bull Market of the Roaring Twenties ( ) The Japanese "Bubble Economy" ( ) dotcom bubble (1990s) China stock and property bubble (2007) US housing market bubbles Miao and Wang (BU) Bubbles and Credit Constraints November / 30
7 Types of Bubbles Creditdriven stock price bubbles Bubbles are accompanied with credit booms Bubbles are on productive assets Bubbles occur in a sector or an industry (Miao and Wang (2011a,b)) Recurrent bubbles with rm entry (Miao and Wang (2011c)) Bubbles in prices of land, gold, paintings, money, etc. Rational vs Irrational bubbles (DeLong et al (1990), Scheinkman and Xiong (2003), Xiong and Yu (2011)) Miao and Wang (BU) Bubbles and Credit Constraints November / 30
8 Basic Intuition Asset pricing equation P t = D t + P t r Exogenous payo s D t and discount rate r Solving forward P t = D t+s s=0 (1 + r) s {z } fundamental + B t {z} bubble Transversality condition rules out bubbles, B t = B t r Miao and Wang (BU) Bubbles and Credit Constraints November / 30
9 Key Issues Rational bubbles are fragile (Santos and Woodford (1997)) A necessary condition is g r or PV of consumption is in nity (Dynamically ine cient OLG) Existing theories typically study bubbles on assets with zero payo or exogenously given payo s What about bubbles on reproducible or productive assets? Dividends are endogenous! Do bubbles crowd out or crowd in capital? Welfare and policy implications of bubbles? Miao and Wang (BU) Bubbles and Credit Constraints November / 30
10 Our Story Firms face stochastic investment opportunities, and borrow to nance investment subject to endogenous credit constraints Pledge rm assets (capital) as collateral (borrow against rm value) Collateral value may contain bubbles Positive feedback loop Optimistic beliefs about asset values (bubbles) =) raise collateral value =) raise lending against these assets =) raise investment =) raise rm value or asset value =) justify initial beliefs Bubbles are selfful lling Another equilibrium without bubble Stochastic bubbles, burst of bubbles =) recession (No shocks to fundamentals) Bubbles on both intrinsically useless assets and productive assets can coexist Miao and Wang (BU) Bubbles and Credit Constraints November / 30
11 A Basic Model Discrete time t = 0, dt, 2dt,... Continuous time dt! 0 No aggregate uncertainty Risk neutral (can be relaxed) households supply labor inelastically (one unit). e rt C t dt, t2f0,dt,2dt,...g Can introduce endogenous labor supply A continuum of rms indexed by j 2 [0, 1], with technology: Y j t = (K j t ) α (N j t ) 1 α, α 2 (0, 1). Can introduce capacity utilization Solve static labor choice: max F Nt j K j t, N j t w t N j t = R t K j t, Miao and Wang (BU) Bubbles and Credit Constraints November / 30
12 Heterogeneity Investment opportunities arrive independently across rms and over time ( K j t+dt = (1 δdt) Kt j + It j with probability πdt (1 δdt) Kt j, with probability 1 πdt Can use idiosyncratic investment speci c shocks with continuous distribution K j t+dt = (1 δdt) K t j + ε j tit j dt Can use idiosyncratic productivity shocks Y j t = (A j tk j t ) α (N j t ) 1 α Miao and Wang (BU) Bubbles and Credit Constraints November / 30
13 Credit Constraints Intraperiod loans (can be relaxed) L j t, I j t R t K j t + L j t Assume no equity nancing (can be relaxed) Let V t X j denote the market value of assets X j Credit constraint: L j t e rdt V t+dt (ξkt j ). Pledge assets ξkt j as collateral (e ectively rm value) ξ represents nancial frictions Kiyotaki and Moore (1997) collateral constraint L j t ξq t K j t. Miao and Wang (BU) Bubbles and Credit Constraints November / 30
14 Optimal Contract with Limited Commitment Albuquerque and Hopenhayn (2004), Alvarez and Jermann (2000), Jerman and Quadrini (2010) Borrow L j t and repay L j t only when investment opportunity arrives If rm defaults, lender seizes assets ξk j t Assets are not speci c to the owner Lender reorganizes the rm and obtains goingconcern value e rdt V t+dt (ξk j t ) The rm has all the bargainning power and the lender gets the threat value e rdt V t+dt (ξk j t ) Incentive constraint: e rdt V t+dt ((1 δdt) Kt j + It j ) {z L j t } Not default e rdt V t+dt ((1 δdt) Kt j + It j ) {z e rdt V t+dt (ξkt j ) } Default Miao and Wang (BU) Bubbles and Credit Constraints November / 30
15 Firm s Problem (Optimal Contract) Bellman equation V t (Kt j ) = max It j,l j t subject to R t K j t dt πi j t dt + e rdt V t+dt ((1 + e rdt V t+dt ((1 δdt) K j t )(1 πdt), I j t R t K j t + L j t L j t e rdt V t+dt (ξk j t ) δdt) K j t + I j t )πdt Not a contraction mapping! Miao and Wang (BU) Bubbles and Credit Constraints November / 30
16 Competitive Equilibrium Aggregation K t = R 1 0 K t j dj, I t = R 1 0 I t j dj, N t = R 1 0 Nj t dj, and Y t = R 1 0 Y t j dj Households and rms optimize and markets clear N t = 1, C t + πi t = Y t, K t+dt = (1 δdt) K t + I t πdt. Miao and Wang (BU) Bubbles and Credit Constraints November / 30
17 Usual Solution Firm value takes the form (Hayashi (1982)): Verify: v t Kt j = max It j V t (K j t ) = v t K j t R t K j t dt +e rdt v {z t+dt } (1 δdt) K Q t I j πit j dt + e rdt j v {z t+dt πit dt } Q t j t, t R t Kt j + e rdt j v {z t+dt ξkt } Q t Need Q t > 1 for the investment and collateral constraint to bind Miao and Wang (BU) Bubbles and Credit Constraints November / 30
18 Bubble Solution Firm value takes the form: V t (K j t ) = Positive feedback loop: v t Kt j + b t = max It j v t K j t {z} fundamental R t K j t dt + e rdt v t+dt {z } + b t {z}, bubble b t > 0 πit j dt + e rdt j v {z t+dt πit dt } Q t j t + e rdt b {z t+dt } Q t (1 δdt) K It j R t Kt j + e rdt j v {z t+dt ξkt + e rdt b } {z t+dt } Q t B t B t, Need Q t > 1 for the investment and collateral constraint to bind Miao and Wang (BU) Bubbles and Credit Constraints November / 30
19 Continuous Time Equilibrium System Suppose Q t > 1. Then (B t, Q t, K t ) satisfy: Ḃ t = rb t B t π(q t 1), Q t = (r + δ) Q t R t π(r t + ξq t )(Q t 1), K t = δk t + π(r t K t + ξq t K t + B t ), K 0 given, and the transversality condition: lim e rt Q T K T = 0, T! lim e rt B T = 0, T! Bubbleless equilibrium: B t = 0 Bubbly equilibrium: B t 6= 0 Miao and Wang (BU) Bubbles and Credit Constraints November / 30
20 Why bubbles? Santos and Woodford condition? r > 0, zero economic growth Bubble dynamics Bubble is productive! Ḃ t B t {z} capital gains + π(q t 1) = r {z } dividend yields TV cannot rule out bubble Bubbleless SS is dynamically e cient because K < K GR = (δ/α) α 1 1 =) Tirole (1985) condition does not apply Miao and Wang (BU) Bubbles and Credit Constraints November / 30
21 Bubbly Equilibrium: Steady State There exists (B, Q b, K b ) satisfying B K b = δ π r + δ + ξ 1 + r r + π π > 0, if and only if α (K b ) α 1 = Q b = r π + 1 > 1, 0 < ξ < (1 ξ)r + δ 1 + r δ (1 π) r + π r π + 1, r. (1) In addition, (i) Q b < Q, (ii) K GR > K E > K b > K, and (iii) the bubbleasset ratio B/K b decreases with ξ. Miao and Wang (BU) Bubbles and Credit Constraints November / 30
22 Bubbly Equilibrium Dynamics Suppose condition (1) holds. Then both the bubbly steady state (B, Q b, K b ) and the bubbleless steady state (0, Q, K ) are local saddle points for the nonlinear system for (B t, Q t, K t ). Di erent from indeterminancy (Benhabib or Farmer) Miao and Wang (BU) Bubbles and Credit Constraints November / 30
23 Robustness Intertemporal Borrowing and Saving Idiosyncratic InvestmentSpeci c Shocks: bubbles can arise even if capital can be fully pledgeable, e.g, ξ = 1 Idiosyncratic Productivity Shocks: bubble can generate endogenous TFP through capital reallocation Miao and Wang (BU) Bubbles and Credit Constraints November / 30
24 Stochastic Bubbles Blanchard and Watson (1982), Weil (1987) Suppose a bubble exists initially, B 0 > 0. Between t and t + dt, there is probability θdt that the bubble bursts, B t+dt = 0. Once it bursts, it will never be valued again in the future so that B τ = 0 for all τ t + dt. With probability 1 θdt, the bubble persists so that B t+dt > 0. Take the continuous time limits as dt! 0. Miao and Wang (BU) Bubbles and Credit Constraints November / 30
25 Consumption Stock Price Marginal Q Output Capital Investment Stochastic Bubble Equilibrium Dynamics Time Time Time Miao and Wang (BU) Bubbles and Credit Constraints November / 30
26 Capacity utilization Production function Y j t = (u j tk j t ) α N j t 1 α, (2) where u j t represents the capacity utilization rate. Deprecation rate where ϕ is an increasing and convex function. At equilibrium where u 0 (Q t ) < 0 δ j t = ϕ(u j t), (3) u j t = u(q t ), (4) Miao and Wang (BU) Bubbles and Credit Constraints November / 30
27 Consumption Stock Price Marginal Q Output Capital Investment Capacity utilization Miao and Wang (BU) Bubbles and Credit Constraints November / 30
28 Public Assets and Credit Policy Monetary policy: Lean vs clean debate What types of bubbles? (Mishkin) What causes bubbles? Ine ciency comes from credit constraints Bubbles help relax these constraints, while the collapse of bubbles tightens them Government can supply liquidity to the rms by issuing public bonds. These bonds are backed by lumpsum taxes. M t P t = T t dt + M t+dt P t, Bubble on unbacked public bonds can exist with household short sales constraint. Miao and Wang (BU) Bubbles and Credit Constraints November / 30
29 Optimal Credit Policy Suppose assumption (1) holds. Let the government issues a constant value D = P t M t of government debt given by D t = D K E δ 1 π r ξ > 0, π which is backed by lumpsum taxes T t = T rd for all t. Then this credit policy will eliminate the bubble on rm assets and make the economy achieve the e cient allocation. Unbacked public assets (intrinsically useless assets) can have a bubble value when households face short sales constraint. This bubble may coexist with stock price bubbles and boost the economy when stock market bubbles burst. The equilibrium real allocation is identical to that with stock price bubbles only. Miao and Wang (BU) Bubbles and Credit Constraints November / 30
30 Conclusion We have provided an in nitehorizon model of a production economy with bubbles on productive assets Bubbles help relax collateral constraints and generate dividend yields Collapse of bubbles have adverse impact on the economy When public assets backed by lumpsum taxes are used as collateral, there exists a credit policy that can eleminate bubbles and make the economy achieve e ciency Miao and Wang (BU) Bubbles and Credit Constraints November / 30
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