A Theory of Macroprudential Policies in the Presence of Nominal Rigidities Emmanuel Farhi, Harvard Iván Werning, MIT Thursday, March 20, 14
Tools for Macro Stabilization? Great Moderation: soft consensus monetary policy Great Recession: broken consensus rising popularity of macroprudential policies Challenge for economists: comprehensive framework encompassing monetary and macroprudential policies Thursday, March 20, 14
This Paper Take up this challenge What key market failures? What policy interventions? Thursday, March 20, 14
General Model Arrow-Debreu with frictions: price rigidities constraints on monetary policy Instruments: monetary policy macroprudential policy: taxes/quantity restrictions in financial markets Study constrained efficient allocations (2nd best) Thursday, March 20, 14
Key Results Aggregate demand externalities from private financial decisions Generically monetary policy not sufficient macroprudential policies required Formula for optimal policies intuitive measurable sufficient statistics Thursday, March 20, 14
Example Deleveraging and liquidity trap (Eggertson-Krugman) borrowers and savers borrowers take on debt credit tightens...borrowers delever zero lower bound recession Result: macroprudential restriction on ex-ante borrowing Thursday, March 20, 14
Growing Literature Farhi-Werning 2012a, Farhi-Werning 2012b Schmitt-Grohe-Uribe 2012 Korinek-Simsek 2013 ... Thursday, March 20, 14
Model Agents i ∈ I { X i j , s } Goods indexed by... ”state” s ∈ S j ∈ J s commodity “States”: states, periods trade across states...financial markets taxes or quantity controls available Thursday, March 20, 14
Preferences and Technology Preferences of agent i U i ( { X i ∑ j , s } ; s ) s ∈ S Production possibility set F ( { Y j , s } ) ≤ 0 Thursday, March 20, 14
Agents’ Budget Sets D i s Q s ≤ Π i ∑ s ∈ S P j , s X i j , s ≤ − T i s + ( 1 + τ i D , s ) D i ∑ s j ∈ J s { X i j , s } ∈ B i s Thursday, March 20, 14
Agents’ Budget Sets D i s Q s ≤ Π i ∑ s ∈ S P j , s X i j , s ≤ − T i s + ( 1 + τ i D , s ) D i ∑ s j ∈ J s macroprudential tax { X i j , s } ∈ B i s borrowing constraint Thursday, March 20, 14
Government Budget Set D g ∑ s Q s ≤ 0 s ∈ S s ) + D g ( T i s − τ i D , s D i ∑ s = 0 i ∈ I Thursday, March 20, 14
Nominal Rigidities Price feasibility set (vector) Γ ( { P j , s } ) ≤ 0 Captures many forms of nominal rigidities and constraints on monetary policy Thursday, March 20, 14
Market Structure... Supply of goods...follow Diamond-Mirrlees (1971): postpone discussion of market structure “as if” government controls prices and production Applications: spell out market structure monopolistic competition with nominal rigidities enough taxes to control prices... ...but not enough to trivialize price rigidities...(2nd best) Thursday, March 20, 14
Equilibrium 1. Agents optimize 2. Government budget constraint satisfied 3. Technologically feasible 4. Markets clear 5. Nominal rigidities Thursday, March 20, 14
Planning Problem Planning problem λ i V i s ( I i s , P s ∑ i ∈ I ∑ s , P s ) max I i s ∈ S X i j , s ( I i F ( { ∑ s , P s ) } ) ≤ 0 i ∈ I Γ ( { P j , s } ) ≤ 0 Thursday, March 20, 14
Planning Problem indirect utility function Planning problem λ i V i s ( I i s , P s ∑ i ∈ I ∑ s , P s ) max I i s ∈ S X i j , s ( I i F ( { ∑ s , P s ) } ) ≤ 0 i ∈ I Γ ( { P j , s } ) ≤ 0 Thursday, March 20, 14
Wedges j ∗ ( s ) Define wedges given reference good τ j , s P j ∗ ( s ) , s F j , s = 1 − τ j , s P j , s F j ∗ ( s ) , s First best... τ j , s = 0 Thursday, March 20, 14
FOCs Incomes λ i V i µ F j ∗ ( s ) , s I , s = P j , s X i I i s X i P j ∗ ( s ) , s j , s I , j , s 1 − ∑ j ∈ J s j , s τ j , s I i X i s social vs. private marginal utility of income Prices µ F j ∗ ( s ) , s ν · Γ k , s = ∑ P j , s τ j , s S i P j ∗ ( s ) , s ∑ k , j , s i ∈ I j ∈ J s Thursday, March 20, 14
Corrective Interventions Proposition (Corrective Financial Taxes). 1 1 + τ i D , s = P j , s X i I i s X i j , s I , j , s 1 − ∑ j ∈ J s j , s τ j , s I i X i s Imperfect stabilization with monetary policy Role for macroprudential policies: corrective taxation (financial taxes) quantity restrictions (financial regulation) Thursday, March 20, 14
Aggregate Demand Externalities Assume “state” where a certain good is depressed Force agents with high propensity to spend on that good to move income to that “state”... ... increases spending...income...spending.... ...stabilization benefits... ...not internalized by private agents Thursday, March 20, 14
Aggregate Demand Externalities Assume “state” where a certain good is depressed Keynesian cross Force agents with high propensity to spend on that good to move income to that “state”... ... increases spending...income...spending.... ...stabilization benefits... ...not internalized by private agents Thursday, March 20, 14
Generic Inefficiency Generic Inefficiency. Generically, equilibria without financial taxes are constrained Pareto inefficient. Parallels the Geanakoplos-Polemarchakis (86) result for pecuniary externalities Bottom line: monetary policy generically not sufficient macroprudential policies necessary complement Thursday, March 20, 14
Applications In paper liquidity trap and deleveraging international liquidity traps and sudden stops fixed exchanges rates Many others: multiplie sectors ... Map into general framework! Thursday, March 20, 14
Applications In paper see also Korinek-Simsek (2013) liquidity trap and deleveraging international liquidity traps and sudden stops fixed exchanges rates see also Farhi-Werning (2012a,b), Schmitt-Grohe-Uribe (2012) Many others: multiplie sectors ... Map into general framework! Thursday, March 20, 14
Liquidity Trap and Deleveraging Two types: borrowers and savers Consume and work in every period Three periods t=1,2...deleveraging and liquidity trap as in Eggertsson and Krugman (2012) t=0... endogenize ex-ante borrowing decisions Thursday, March 20, 14
Ex-Ante Borrowing Restrictions Proposition (Ex-Ante Borrowing Restrictions). Labor wedges (inverse measure of output gap) τ 0 = 0 τ 1 ≥ 0 τ 2 ≤ 0 Impose binding debt restriction on borrowers at t = 0 or equivalent tax on borrowing τ B 0 = τ 1 / ( 1 − τ 1 ) Borrowers... high mpc in period 1 Savers... low mpc in period 1 Restricting period-0 borrowing stimulates in period 1 Not internalized by agents Thursday, March 20, 14
Monetary vs. Macroprudential Policy Policy debate: use monetary policy to lean against credit booms monetary policy targets full employment + no inflation, macroprudential policies targets financial stability Model...during credit boom use monetary and macroprudential policies together no tradeoff macro vs. financial stability τ 0 = 0 Thursday, March 20, 14
Conclusion Joint theory: monetary policy macroprudential policies (financial taxes or regulation) Formula for optimal macroprudential policies: intuitive measurable sufficient statistics Also implications for redistribution Thursday, March 20, 14
Conclusion Many applications: liquidity trap and deleveraging international liquidity trap and sudden stop fixed exchange rates ... Thursday, March 20, 14
Liquidity Trap and Deleveraging Two types: borrowers and savers Three periods t=1,2...deleveraging and liquidity trap as in Eggertsson and Krugman (2012) t=0... endogenize ex-ante borrowing decisions Main result restrict borrowing at t=0 macroprudential regulation Thursday, March 20, 14
Households Type-1 agents (savers), mass φ 1 2 V 1 = β t [ u ( C 1 t ) − v ( N 1 ∑ t )] t = 0 1 P t C 1 t + B 1 t ≤ W t N 1 t + Π 1 B 1 t + t + 1 1 + i t Type-2 agents (borrowers), mass φ 2 2 V 2 = β t u ( C 2 ∑ t ) t = 0 1 P t C 2 t + B 2 t ≤ E 2 B 2 t + t + 1 1 + i t B 2 1 ≤ P 1 ¯ B 2 2 ≤ P 2 ¯ B 1 B 2 Thursday, March 20, 14
Households Type-1 agents (savers), mass φ 1 2 V 1 = β t [ u ( C 1 t ) − v ( N 1 ∑ t )] t = 0 1 P t C 1 t + B 1 t ≤ W t N 1 t + Π 1 B 1 t + t + 1 1 + i t Type-2 agents (borrowers), mass φ 2 2 V 2 = β t u ( C 2 ∑ t ) t = 0 1 P t C 2 t + B 2 t ≤ E 2 B 2 t + environment t + 1 1 + i t policy B 2 1 ≤ P 1 ¯ B 2 2 ≤ P 2 ¯ B 1 B 2 Thursday, March 20, 14
Firms Final good produced competitively ✓ Z 1 e ◆ e − 1 e − 1 Y t = ( j ) dj 0 Y e t Each variety produced monopolistically technology Y t ( j ) = A t N t ( j ) price set once and for all 2 t − 1 1 ∑ ∏ Π t ( j ) max 1 + i s P ( j ) t = 0 s = 0 ◆ − e ✓ P ( j ) − 1 + t L ◆ ✓ P ( j ) Π t ( j ) = W t C t A t P Thursday, March 20, 14
Government Government budget constraint 1 B g B g t + 1 + τ L W t N 1 t = t 1 + i t Type-specific lump sum taxes in period 0 to achieve any distribution of debt... B g 0 + B 1 0 + B 2 0 = 0 Thursday, March 20, 14
Equilibrium Households optimize Firms optimize Government budget constraints hold Markets clear Thursday, March 20, 14
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