Managing Credit Booms and Busts A Pigouvian Taxation Approach Olivier Jeanne Anton Korinek JHU and UMD Conference on the Future of Monetary Policy Rome, October 1st, 2010 Jeanne and Korinek (2010) Managing Credit Booms and Busts The Future of Monetary Policy 1 / 35
Key Question Key Question How should policymakers respond to booms and busts in credit markets and asset markets? Jeanne and Korinek (2010) Managing Credit Booms and Busts The Future of Monetary Policy 2 / 35
Key Assumptions Key Assumptions Financial markets are imperfect: borrowing is subject to constraints constraints depend on asset prices potential for feedback spirals between collapsing asset prices tightening borrowing constraints declining spending → financial accelerator, debt deflation, ... Jeanne and Korinek (2010) Managing Credit Booms and Busts The Future of Monetary Policy 3 / 35
Feedback Spirals Economic shock Falling Spending Tightening Constraint Adverse Movement in Relative Prices Jeanne and Korinek (2010) Managing Credit Booms and Busts The Future of Monetary Policy 4 / 35
Feedback Spirals Economic shock Falling Spending Tightening Constraint Adverse Movement in Relative Prices Jeanne and Korinek (2010) Managing Credit Booms and Busts The Future of Monetary Policy 4 / 35
Key Findings Key Results endogenous borrowing constraints amplify volatility 1 decentralized equilibrium is socially suboptimal: 2 excessive debt excessive exposure to binding constraints excessive volatility (systemic risk) strong case for macroprudential regulation 3 Jeanne and Korinek (2010) Managing Credit Booms and Busts The Future of Monetary Policy 5 / 35
Relationship to Literature Financial accelerator effects: Fisher (1933), Kiyotaki-Moore (1997), Bernanke-Gertler-Gilchrist (1999), etc. Deleveraging externalities: Gromb and Vayanos (2002), Lorenzoni (2008), Korinek (2009) Optimal policy in DSGE models with financial accelerator: Bianchi (2010), Benigno et al. (2010), Bianchi-Mendoza (2010) Empirical importance of amplification: Adrian and Brunnermeier (2009), Adrian and Shin (2009ab), etc. Jeanne and Korinek (2010) Managing Credit Booms and Busts The Future of Monetary Policy 6 / 35
Model Structure DSGE Setup in infinite discrete time Two sets of agents: Insiders who exclusively own an asset (tree), representing e.g. 1 entrepreneurs: more productive at operating an asset households: put higher utility on owning their home locals in small open economy: value local assets more speculators: more risk-tolerant towards an asset agents with informational advantage Outsiders: large in comparison, provide credit at rate R 2 Debt is the only financial contract Jeanne and Korinek (2010) Managing Credit Booms and Busts The Future of Monetary Policy 7 / 35
Insiders Optimization problem of representative insider: Hold a t = 1 unit of tree Obtain endowment income ( 1 − α ) y t and income from tree α y t every period Trade trees, but solely among insiders Hold financial wealth w t with outsiders Maximize utility � ∞ � where u ( c s ) = c 1 − γ � β s − t u ( c s ) U t = E t s 1 − γ s = t c t + a t + 1 p t + w t + 1 s.t. = ( 1 − α ) y t + a t ( p t + α y t ) + w t R and subject to a moral hazard problem that limits borrowing to w t + 1 ≥ − φ p t − ψ R Jeanne and Korinek (2010) Managing Credit Booms and Busts The Future of Monetary Policy 8 / 35
Equilibrium State of economy: summarized by ( w , y ) Dynamics captured by 3 equilibrium functions: c ( w , y ) , p ( w , y ) and λ ( w , y ) Equilibrium conditions: � c ( w ′ , y ′ ) − γ �� − 1 /γ � � � c ( w , y ) = min w + e + y + φ p ( w , y ) , β RE p ( w , y ) = β E [ u ′ ( c ( w ′ , y ′ ))( y ′ + p ( w ′ , y ′ )) + φλ ( w ′ , y ′ ) p ( w ′ , y ′ )] u ′ ( c ( w , y )) λ ( w , y ) = c ( w , y ) − γ − β RE c ( w ′ , y ′ ) − γ � � Transition equation for wealth: w ′ / R = w + y − c ( w , y ) Jeanne and Korinek (2010) Managing Credit Booms and Busts The Future of Monetary Policy 9 / 35
Solution Method Define grids y g , d g for output shock and net worth Solution through reverse time iteration: in step k , start with functions c k ( w , y ) , p k ( w , y ) and λ k ( w , y ) for any ( w ′ , y ) derive unconstrained t − 1 solution for any ( w ′ > 0 , y ) derive constrained t − 1 solution for any y , determine threshold ¯ w ( y ) for binding constraints concatenate constrained/unconstrained functions interpolate c k + 1 ( w , y ) , p k + 1 ( w , y ) and λ k + 1 ( w , y ) → endogenous gridpoints bifurcation method Jeanne and Korinek (2010) Managing Credit Booms and Busts The Future of Monetary Policy 10 / 35
Unconstrained Equilibrium Unconstrained equilibrium (for sufficiently high net worth and output) Given policy functions c k ( w , y ) , p k ( w , y ) , λ k ( w , y ) for next period, c ′− γ �� − 1 /γ � � consumption c unc ( w ′ , y ) = β RE net worth w unc ( w ′ , y ) = c unc − y + w ′ R � � u ′ ( c unc ) · ( α y ′ + p ′ ) u ′ ( c ′ ) asset price p unc ( w ′ , y ) = β E shadow price λ unc = 0 w = − φ p unc − ψ threshold level of net worth is w ≥ ¯ Jeanne and Korinek (2010) Managing Credit Booms and Busts The Future of Monetary Policy 11 / 35
Constrained Equilibrium Constrained equilibrium (for low net worth, low output shock) Given policy functions c k ( w , y ) , p k ( w , y ) , λ k ( w , y ) for next period, � � asset price p con ( w ′ , y ) = − 1 w ′ R + ψ from binding constraint φ consistent with a level of consumption of � − 1 � β E { u ′ ( c ′ ) · ( α y ′ + p con )+ φλ ′ p ′ | y } c con ( w ′ , y ) = γ p con net worth w con ( w ′ , y ) = c con − y − φ p con − ψ shadow price λ con ( w ′ , y ) = u ′ ( c con ) − β RE [ u ′ ( c ′ )] ⇒ combine constrained/unconstrained policy functions ⇒ interpolate next iteration c k + 1 ( w , y ) , p k + 1 ( w , y ) , λ k + 1 ( w , y ) Jeanne and Korinek (2010) Managing Credit Booms and Busts The Future of Monetary Policy 12 / 35
Amplification c RHS = w + y + φ p(c) LHS = c c Figure: Equilibrium equation: c ≤ w + y + φ p ( c ) + ψ Jeanne and Korinek (2010) Managing Credit Booms and Busts The Future of Monetary Policy 13 / 35
Policy Functions 6 p 5 4 3 2 c 1 0 λ −1 w’ −2 m −1.5 −1 −0.5 0 Figure: Equilibrium policy functions Jeanne and Korinek (2010) Managing Credit Booms and Busts The Future of Monetary Policy 14 / 35
Constrained Social Planner Introduce a constrained social planner who is subject to the same borrowing limits as insiders coordinates (regulates) borrowing choices in the economy internalizes effect of choices on asset prices optimizes every period (no commitment) Jeanne and Korinek (2010) Managing Credit Booms and Busts The Future of Monetary Policy 15 / 35
Constrained Social Planner Social planner’s optimality condition: � ∂ p t + 1 � u ′ ( c t ) = λ t + β RE t u ′ ( c t + 1 ) + φλ t + 1 ∂ w t + 1 ∂ p t + 1 Interpretation of externality term φλ t + 1 ∂ w t + 1 : ∂ p t + 1 ∂ w t + 1 captures asset price increase resulting from higher wealth φ reflects resulting relaxation in borrowing constraint λ t + 1 E t [ u ′ ( c t + 1 )] represents utility cost of constraint externality active if borrowing constraint is binding in the future Jeanne and Korinek (2010) Managing Credit Booms and Busts The Future of Monetary Policy 16 / 35
Equilibrium with Social Planner Social planner solution: planner takes on less debt in periods before constraint is binding (systemic precautionary savings) less debt, less severe future constraints less volatility and financial fragility → social planner reduces debt and uncertainty Jeanne and Korinek (2010) Managing Credit Booms and Busts The Future of Monetary Policy 17 / 35
Implementation of Constrained Social Optimum Implementation through Pigouvian taxation: Introduce tax τ t = τ ( w t , y t ) on borrowing − w t + 1 / R Rebate lump sum T t = − τ t · w t + 1 / R � ∞ � � β s − t u ( c s ) max U t = E t s = t c t + ( 1 − τ t ) w t + 1 s.t. = y t + w t + T t R w t + 1 ≥ − φ p t − ψ R To implement constrained optimum, tax must satisfy � � ∂ p t + 1 φβ RE t λ t + 1 ∂ w t + 1 τ ( w t , y t ) = u ′ ( c t ) Jeanne and Korinek (2010) Managing Credit Booms and Busts The Future of Monetary Policy 18 / 35
Implementation of Constrained Social Optimum Alternative mechanisms to implement Pigouvian tax: Direct taxation of debt (note: opposite of interest deductability on debt!) Prudential regulation: uses existing frameworks Limits on leverage / margin requirements Risk management systems Jeanne and Korinek (2010) Managing Credit Booms and Busts The Future of Monetary Policy 19 / 35
Recommend
More recommend
