Ine¢cient Borrowing in Production Economies Gianluca Benigno, Huigang Chen, Chris Otrok, Alessandro Rebucci and Eric Young Ente Einaudi, Rome, 2010 Benigno, Chen, Otrok, Rebucci, Young () Ente Einaudi, Rome, 2010 1 / 27
Motivation Crisis associated with …nancial market imperfections cause signi…cant economic dislocation ("Sudden Stop",Calvo (1998) and recent 2007-2009 crisis). An important question is whether the likelihood and the severity of these crises are a¤ected by excessive borrowing in normal times (i.e. overborrowing). Benigno, Chen, Otrok, Rebucci, Young () Ente Einaudi, Rome, 2010 2 / 27
Motivation Policy debate has emphasized the role of macro-prudential policies (ex-ante policies) Policy debate: Korinek (2009), Bianchi (2009), Jeanne and Korinek (2010), Bianchi 1 and Mendoza (2010): various speci…cation (endowment, production, relative price, asset price) ) overborrowing and stress the role of ex-ante policies (i.e. tax on debt) Benigno et al. (2009,2010), Caballero (2010), Nikolov (2009) ) stress 2 the role of ex-post policies. Logic of policy prescriptions: If there is overborrowing, policy should focus on ex ante prevention. 1 If there is no overborrowing, policy should focus on ex post 2 intervention. Benigno, Chen, Otrok, Rebucci, Young () Ente Einaudi, Rome, 2010 3 / 27
Contribution Examine ine¢cient borrowing in multi–sector production economies. Main results: Production economies might display underborrowing. 1 Welfare gains from possible policy actions in crisis times are higher than 2 in normal times (~more scope for ex-post rather than ex-ante policies). ) no clear cut rationale to prefer prevention over intervention policies Benigno, Chen, Otrok, Rebucci, Young () Ente Einaudi, Rome, 2010 4 / 27
Outline Model and its properties Mechanisms behind ine¢cient borrowing Quantitative analysis Welfare analysis and Conclusions Benigno, Chen, Otrok, Rebucci, Young () Ente Einaudi, Rome, 2010 5 / 27
How do we model sudden stop? Following Mendoza (2002, 2010): Two Sector (Traded and Nontraded) Small Open Economy with 1 Flexible prices Occasionally binding borrowing constraint 2 Crisis is endogenous and nested in regular cycles 3 The model can describe both bad and good times (match many of 4 the quantitative features of emerging market business cycles, inside and outside sudden stop periods) Benigno, Chen, Otrok, Rebucci, Young () Ente Einaudi, Rome, 2010 6 / 27
Scope for policy intervention: General idea (Arnott, Greenwald and Stiglitz, 1994): with …nancial frictions agents take actions that makes sense from an individual point of view but do not take into account the impact of their actions in the aggregate. Scope for policy arises because of the presence of this externality (pecuniary externality or systemic externality) In general the presence of the externality creates scope for policy action even during normal times. In the context of our model scope for policy emerges in the two-sector economy: agents do not internalize the e¤ects of their choices on relative prices. Benigno, Chen, Otrok, Rebucci, Young () Ente Einaudi, Rome, 2010 7 / 27
Model: Preferences Households maximize: 8 ! 1 � ρ 9 < = H δ ∞ 1 U j � E 0 j , t : β t ∑ C j , t � ; , 1 � ρ δ t = 0 Consumption basket C is a composite of tradable and non-tradables goods: � κ � � � κ � 1 � � κ � 1 κ κ + ( 1 � ω ) κ � 1 1 1 C T C N C t � ω . κ κ t t Aggregate price index increasing in relative price of non-tradables � � 1 � κ � � 1 1 � κ P N P t = ω + ( 1 � ω ) ; t Benigno, Chen, Otrok, Rebucci, Young () Ente Einaudi, Rome, 2010 8 / 27
Model: Budget and Credit Constraint Access to international capital markets is not only incomplete: C T t + P N t C N t = π t + W t H t � B t + 1 + ( 1 + i ) B t , But also imperfect: B t + 1 > � 1 � φ [ π t + W t H t ] φ The constraint limits B to a fraction of current income. Constraint binds only occasionally. Benigno, Chen, Otrok, Rebucci, Young () Ente Einaudi, Rome, 2010 9 / 27
Model: Household FOCs Marginal utility of current consumption is higher when constraint is binding (time pro…le of relative price a¤ects time pro…le of consumption) � � B t + 1 : µ t = λ t + β ( 1 + i ) E t µ t + 1 Labor supply higher if constraint is binding: ! � ρ � � H δ = µ t W t + 1 � φ j , t H δ � 1 H t : C j , t � W t λ t , j , t δ φ Non-tradable consumption choice: ! � ρ � � � 1 H δ κ C 1 j , t 1 C N κ = µ t P N C j , t � ( 1 � ω ) C N : κ t , t δ Marginal utility of tradable consumption determines multiplier ! � ρ � � � 1 H δ κ C 1 1 j , t C T κ = µ t . C T : C j , t � ω κ t δ Benigno, Chen, Otrok, Rebucci, Young () Ente Einaudi, Rome, 2010 10 / 27
Model: Firms Traded and Nontraded goods are produced with variable labor input: t H 1 � α N t H 1 � α T Y N = A N , Y T = A T t t t t The …rm (owned by the consumer) chooses labor to maximize pro…ts: � � 1 � α T � � 1 � α N π t = A T H T + P N t A N H N � W t H t . t t t t Labor demand schedules: � 1 � α N � � � � α N P N t A N H N W t = , t t : � 1 � α T � � � � α T A T H T W t = . t t Benigno, Chen, Otrok, Rebucci, Young () Ente Einaudi, Rome, 2010 11 / 27
Model: Interaction between Credit Friction and Consumption Choices in CE Role of credit constraint in the non-binding region If the constraint might bind in the next period we have � � �� µ t = β ( 1 + i ) E t λ t + 1 + β ( 1 + i ) E t µ t + 2 Intratemporal equilibrium condition κ � � � 1 1 C N ( 1 � ω ) κ t = P N κ � � � 1 t 1 C T ω κ t Precautionary saving motive determines a decline in relative price. Benigno, Chen, Otrok, Rebucci, Young () Ente Einaudi, Rome, 2010 12 / 27
Model: Interaction between Credit friction and Labor Market/Production Choices Equilibrium in CE Role of production economy in the non-binding region. Household choose intratemporal allocation of consumption � � 1 � α N � � 1 � 1 κ A N H N ( 1 � ω ) κ t t P N t = κ � � � 1 1 C T ω κ t Household choose labor supply � � 1 � ω � � � 1 � κ � � � 1 κ � 1 H δ � 1 P N MPL T = 1 + t t t ω Firm technology determines intrasectoral labor allocation: t = MPL T P N t MPL NT t System of equation determines H T t , H N and P N for given borrowing (i.e. C T t ). t t If # C T )# P N )" H ; intrasectoral allocation will " H T and # H N so that # C N and ) amplify further decline in C T . Benigno, Chen, Otrok, Rebucci, Young () Ente Einaudi, Rome, 2010 13 / 27
Model: Interaction between Credit friction and Labor Market Equilibrium in CE To what extent this mechanism is robust? wealth e¤ects determined by the fact that in multisector economy with 1 GHH relative price will a¤ect household labor supply choice.This e¤ect will arise also in one sector economy without GHH preferences this mechanism is independent from the way the collateral constraint is 2 speci…ed (i.e. in terms of relative price of non-tradables or asset prices) this mechanism operates also when there is a working capital 3 constraint. Benigno, Chen, Otrok, Rebucci, Young () Ente Einaudi, Rome, 2010 14 / 27
Model: Constraints of the Social Planner Problem Resource constraint on tradables C T t = Y T t � B t + 1 + ( 1 + i ) B t . Resource:constraint on nontradable goods � � 1 � α N C N = Y N = A N H N t t Credit constraint from a country perspective: h t Y N i B t + 1 � � 1 � φ Y T + P N , φ Pricing rule as in the CE (Kehoe and Levine, 1993): � � 1 � α N � � 1 � 1 κ A N H N ( 1 � ω ) κ t t P N t = κ � � � 1 1 C T ω κ t Benigno, Chen, Otrok, Rebucci, Young () Ente Einaudi, Rome, 2010 15 / 27
Model: First Order Conditions The …rst order conditions for the planner problem are given by � � 1 � α N � � ∂ P N 1 � φ C T : U C ( C t ) C C T = µ SP t A N H N 1 , t � λ t , (1) t t φ ∂ C T t C N : U C ( C t ) C C N = µ SP 2 , t , (2) h i B t + 1 : µ SP 1 , t = λ SP µ SP + β ( 1 + i ) E t (3) t 1 , t + 1 and " # � � � 1 � α T � λ SP 1 + 1 � φ t H � α T H T H δ � 1 µ SP 1 , t A T t t : U C ( C t ) = (4) t t φ µ SP 1 , t � � � 1 � α N � � � � α N H N H δ � 1 µ SP H N t : U C ( C t ) = 2 , t A t t t 2 3 ! 1 � � � � ( 1 � α N ) � � 1 κ κ � 1 � λ SP C T ( 1 � ω ) κ 4 1 + 1 � φ t t A N H N 5 (5) t t µ SP φ ω κ 2 , t Benigno, Chen, Otrok, Rebucci, Young () Ente Einaudi, Rome, 2010 16 / 27
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