Monetary Policy and the Redistribution Channel Adrien Auclert - PowerPoint PPT Presentation

Introduction Sufficient statistic: real interest rate change ◮ Focus on m = r . Cyclical monetary policy, stable inflation ◮ Exposure i , r : “Unhedged (interest)-rate exposure” . Transitory dr : − maturing liabilities i URE i = maturing assets i � �� � � �� � including income including consumption ◮ E r = Cov I ( MPC i , URE i ) measurable in household surveys ◮ Italy [Jappelli, Pistaferri 2014] & US [Johnson, Parker, Souleles 2006] ◮ E r < 0. Redistribution channel ⇒ C ↑ when r ↓ ◮ Adds to the substitution channel , same magnitude if EIS ≃ 0 . 1 to 0 . 3 ◮ Implication for general equilibrium models ◮ Monetary policy shocks have larger output effects ◮ Sufficient statistics provide a novel calibration procedure Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 5 / 35

Introduction Dynamic general equilibrium model ◮ GE model calibrated to U.S. economy matches E r and predicts: Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 6 / 35

Introduction Dynamic general equilibrium model ◮ GE model calibrated to U.S. economy matches E r and predicts: 1. E r more negative when assets and liabilities have shorter maturities ◮ If U.S. only had adjustable rate mortgages, surprise rate change would more than double current effect ◮ Cross-country S-VAR evidence [Calza, Monacelli, Stracca 2013] Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 6 / 35

Introduction Dynamic general equilibrium model ◮ GE model calibrated to U.S. economy matches E r and predicts: 1. E r more negative when assets and liabilities have shorter maturities ◮ If U.S. only had adjustable rate mortgages, surprise rate change would more than double current effect ◮ Cross-country S-VAR evidence [Calza, Monacelli, Stracca 2013] 2. Interest rate increases and cuts have asymmetric effects ◮ r ↑ lowers output more than r ↓ increases it ◮ [Cover 1992, de Long Summers 1988, Tenreyro Thwaites 2013] ◮ Here: asymmetric response of borrowers close to their credit limits Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 6 / 35

Introduction Limits of analysis ◮ Framework that accommodates ◮ Heterogeneity ◮ Nominal and real financial assets of arbitrary duration ◮ Precautionary savings, borrowing constraints ◮ Abstracts away from ◮ Risk premia ◮ Refinancing ◮ Illiquidity and cash holdings ◮ Collateral price effects on borrowing constraints Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 7 / 35

Introduction Related literature ◮ Monetary policy and redistribution [empirics] ◮ Inflation: Doepke and Schneider (2006) ◮ Earnings: Coibion, Gorodnichenko, Kueng, Silvia (2012) ◮ Consumption effects: Di Maggio et al (2014); Keys et al (2014) ◮ Monetary policy shocks and the transmission mechanism [theory] ◮ Christiano, Eichenbaum, Evans (1999, 2005), ... ◮ Role of mortgage structure: Calza, Monacelli, Stracca (2013), Rubio (2011), Garriga, Kydland and Sustek (2013) ◮ Heterogenous effects : Gornemann, Kuester and Nakajima (2014) ◮ MPC heterogeneity [theory and empirics] ◮ Measurement, comovement with balance sheets: Johnson et al (2006), Parker et al (2013), Mian, Rao, Sufi (2013), Baker (2013), ... ◮ Aggregate demand effects: Gal´ ı, L´ opez-Salido, Vall´ es (2007), Eggertsson-Krugman (2012), Farhi-Werning (2013), Korinek-Simsek (2015) ◮ Role of incomplete markets: Guerrieri-Lorenzoni (2015), Oh-Reis (2013), Sheedy (2014), McKay-Reis (2014) Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 8 / 35

Introduction Outline Partial equilibrium: E r as sufficient statistic 1 Single agent, perfect foresight Incomplete markets Aggregation Measuring E r 2 General equilibrium model 3 Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 9 / 35

Partial equilibrium: E r as sufficient statistic Single agent, perfect foresight Outline Partial equilibrium: E r as sufficient statistic 1 Single agent, perfect foresight Incomplete markets Aggregation Measuring E r 2 General equilibrium model 3 Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 9 / 35

Partial equilibrium: E r as sufficient statistic Single agent, perfect foresight Perfect foresight, no uncertainty ◮ Single agent ◮ arbitrary non-satiable preferences and time horizon ◮ earns a stream of real income { y t } and wages { w t } (certain) ◮ faces real term structure { t q t + s } s ≥ 1 ◮ holds long-term real assets: { t − 1 b t + s } s ≥ 0 (TIPS, PLAM) Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 10 / 35

Partial equilibrium: E r as sufficient statistic Single agent, perfect foresight Perfect foresight, no uncertainty ◮ Single agent ◮ arbitrary non-satiable preferences and time horizon ◮ earns a stream of real income { y t } and wages { w t } (certain) ◮ faces real term structure { t q t + s } s ≥ 1 ◮ holds long-term real assets: { t − 1 b t + s } s ≥ 0 (TIPS, PLAM) ◮ Solves: U ( { c t , n t } ) max � s.t. c t = y t + w t n t + ( t − 1 b t ) + ( t q t + s ) ( t − 1 b t + s − t b t + s ) s ≥ 1 Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 10 / 35

Partial equilibrium: E r as sufficient statistic Single agent, perfect foresight Perfect foresight, no uncertainty ◮ Single agent ◮ arbitrary non-satiable preferences and time horizon ◮ earns a stream of real income { y t } and wages { w t } (certain) ◮ faces real term structure { t q t + s } s ≥ 1 ◮ holds long-term real assets: { t − 1 b t + s } s ≥ 0 (TIPS, PLAM) ◮ Date-0 holdings: { − 1 b t + s } s ≥ 0 , term structure q t = ( 0 q t ) ◮ Solves: U ( { c t , n t } ) max � s.t. c t = y t + w t n t + ( t − 1 b t ) + ( t q t + s ) ( t − 1 b t + s − t b t + s ) s ≥ 1 Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 10 / 35

Partial equilibrium: E r as sufficient statistic Single agent, perfect foresight Perfect foresight, no uncertainty ◮ Single agent ◮ arbitrary non-satiable preferences and time horizon ◮ earns a stream of real income { y t } and wages { w t } (certain) ◮ faces real term structure { t q t + s } s ≥ 1 ◮ holds long-term real assets: { t − 1 b t + s } s ≥ 0 (TIPS, PLAM) ◮ Date-0 holdings: { − 1 b t + s } s ≥ 0 , term structure q t = ( 0 q t ) ◮ Solves: U ( { c t , n t } ) max � � � s.t. q t c t = q t ( y t + w t n t ) + q t ( − 1 b t ) t ≥ 0 t ≥ 0 t ≥ 0 � �� � Financial wealth W F Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 10 / 35

Partial equilibrium: E r as sufficient statistic Single agent, perfect foresight Perfect foresight, no uncertainty ◮ Single agent ◮ arbitrary non-satiable preferences and time horizon ◮ earns a stream of real income { y t } and wages { w t } (certain) ◮ faces real term structure { t q t + s } s ≥ 1 ◮ holds long-term real assets: { t − 1 b t + s } s ≥ 0 (TIPS, PLAM) ◮ Date-0 holdings: { − 1 b t + s } s ≥ 0 , term structure q t = ( 0 q t ) ◮ Solves: U ( { c t , n t } ) max � � � s.t. q t c t = q t ( y t + w t n t ) + q t ( − 1 b t ) t ≥ 0 t ≥ 0 t ≥ 0 � �� � Financial wealth W F ◮ → Initial balance sheet composition irrelevant conditional on W F Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 10 / 35

Partial equilibrium: E r as sufficient statistic Single agent, perfect foresight Perfect foresight, no uncertainty ◮ Single agent ◮ arbitrary non-satiable preferences and time horizon ◮ earns a stream of real income { y t } and wages { w t } (certain) ◮ faces real term structure { t q t + s } s ≥ 1 ◮ holds long-term real assets: { t − 1 b t + s } s ≥ 0 (TIPS, PLAM) ◮ Date-0 holdings: { − 1 b t + s } s ≥ 0 , term structure q t = ( 0 q t ) ◮ Solves: U ( { c t , n t } ) max � � � s.t. q t c t = q t ( y t + w t n t ) + q t ( − 1 b t ) t ≥ 0 t ≥ 0 t ≥ 0 � �� � Financial wealth W F ◮ → Initial balance sheet composition irrelevant conditional on W F ◮ Mortgage M : ARM − 1 b 0 = − M ⇔ PLAM − 1 b t = − m if � T t =0 q t m = M Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 10 / 35

Partial equilibrium: E r as sufficient statistic Single agent, perfect foresight Comparative statics exercise max U ( { c t , n t } ) � � � � s.t. q t c t = y t + w t n t + ( − 1 b t ) q t t ≥ 0 t ≥ 0 dx x r q t Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 11 / 35

Partial equilibrium: E r as sufficient statistic Single agent, perfect foresight Comparative statics exercise max U ( { c t , n t } ) � � � � s.t. q t c t = y t + w t n t + ( − 1 b t ) q t t ≥ 0 t ≥ 0 dx x r q t Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 11 / 35

Partial equilibrium: E r as sufficient statistic Single agent, perfect foresight Comparative statics exercise max U ( { c t , n t } ) � � � � s.t. q t c t = y t + w t n t + ( − 1 b t ) q t t ≥ 0 t ≥ 0 dx x r y t Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 11 / 35

Partial equilibrium: E r as sufficient statistic Single agent, perfect foresight Comparative statics exercise max U ( { c t , n t } ) � � y t + w t n t + ( − 1 b t ) + ( − 1 B t ) � � s.t. q t c t = q t P t t ≥ 0 t ≥ 0 dx x r y P t Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 11 / 35

Partial equilibrium: E r as sufficient statistic Single agent, perfect foresight Comparative statics U ( { c t , n t } ) max � � s.t. q t c t = q t ( y t + w t n t + ( − 1 b t )) ≡ W t ≥ 0 t ≥ 0 ◮ t = 0 → unexpected one-time shock to the real term structure ( dq 0 q 0 = dr ) ◮ First-order change in consumption dc 0 ? Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 12 / 35

Partial equilibrium: E r as sufficient statistic Single agent, perfect foresight Comparative statics U ( { c t , n t } ) max � � s.t. q t c t = q t ( y t + w t n t + ( − 1 b t )) ≡ W t ≥ 0 t ≥ 0 ◮ t = 0 → unexpected one-time shock to the real term structure ( dq 0 q 0 = dr ) ◮ First-order change in consumption dc 0 ? dc 0 ≃ ∂ c 0 dc h ∂ W · ( y 0 + w 0 n 0 + ( − 1 b 0 ) − c 0 ) dr + 0 ���� � �� � Substitution effect Wealth effect Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 12 / 35

Partial equilibrium: E r as sufficient statistic Single agent, perfect foresight Comparative statics U ( { c t , n t } ) max � � s.t. q t c t = q t ( y t + w t n t + ( − 1 b t )) ≡ W t ≥ 0 t ≥ 0 ◮ t = 0 → unexpected one-time shock to the real term structure ( dq 0 q 0 = dr ) ◮ First-order change in consumption dc 0 ? dc 0 ≃ ∂ c 0 dc h ∂ W · ( y 0 + w 0 n 0 + ( − 1 b 0 ) − c 0 ) dr + 0 ���� � �� � Substitution effect Wealth effect ◮ Welfare change dU ≃ U c 0 · ( y 0 + w 0 n 0 + ( − 1 b 0 ) − c 0 ) dr Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 12 / 35

Partial equilibrium: E r as sufficient statistic Single agent, perfect foresight Comparative statics U ( { c t , n t } ) max � � s.t. q t c t = q t ( y t + w t n t + ( − 1 b t )) ≡ W t ≥ 0 t ≥ 0 ◮ t = 0 → unexpected one-time shock to the real term structure ( dq 0 q 0 = dr ) ◮ First-order change in consumption dc 0 ? dc 0 ≃ ∂ c 0 dc h ∂ W · ( y 0 + w 0 n 0 + ( − 1 b 0 ) − c 0 ) dr + 0 ���� � �� � Substitution effect Wealth effect ◮ Welfare change dU ≃ U c 0 · ( y 0 + w 0 n 0 + ( − 1 b 0 ) − c 0 ) dr ◮ Composition of balance sheet matters : e.g. “hedged”when − 1 b 0 = c 0 − ( y 0 + w 0 n 0 ) ∀ t Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 12 / 35

Partial equilibrium: E r as sufficient statistic Single agent, perfect foresight Comparative statics U ( { c t , n t } ) max � � s.t. q t c t = q t ( y t + w t n t + ( − 1 b t )) ≡ W t ≥ 0 t ≥ 0 ◮ t = 0 → unexpected one-time shock to the real term structure ( dq 0 q 0 = dr ) ◮ First-order change in consumption dc 0 ? − 1 URE 0 dc 0 ≃ ∂ c 0 � �� � dc h ∂ W · ( y 0 + w 0 n 0 + ( − 1 b 0 ) − c 0 ) dr + 0 ���� Substitution effect ◮ Welfare change dU ≃ U c 0 · ( − 1 URE 0 ) dr ◮ Composition of balance sheet matters : e.g. “hedged”when − 1 b 0 = c 0 − ( y 0 + w 0 n 0 ) ∀ t → − 1 URE 0 = 0 Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 12 / 35

Partial equilibrium: E r as sufficient statistic Single agent, perfect foresight Comparative statics U ( { c t , n t } ) max � � s.t. q t c t = q t ( y t + w t n t + ( − 1 b t )) ≡ W t ≥ 0 t ≥ 0 ◮ t = 0 → unexpected one-time shock to the real term structure ( dq 0 q 0 = dr ) ◮ First-order change in consumption dc 0 ? MPC − 1 URE 0 ���� ∂ c 0 � �� � dc h dc 0 ≃ · ( y 0 + w 0 n 0 + ( − 1 b 0 ) − c 0 ) dr + 0 ∂ y 0 ���� Substitution effect ◮ Welfare change dU ≃ U c 0 · ( − 1 URE 0 ) dr ◮ Composition of balance sheet matters : e.g. “hedged”when − 1 b 0 = c 0 − ( y 0 + w 0 n 0 ) ∀ t → − 1 URE 0 = 0 Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 12 / 35

Partial equilibrium: E r as sufficient statistic Single agent, perfect foresight Unhedged interest rate exposure maturing assets � �� � URE ≡ − 1 URE 0 = ( − 1 b 0 ) − c 0 y 0 + w 0 n 0 + � �� � maturing liabilities ◮ When all financial wealth W F has short maturity: ◮ URE = y + wn + W F − c ◮ Holder of short-term assets tends to gain when r rises ◮ One-time dr change, generic U dc 0 = MPC · URE · dr + dc h 0 Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 13 / 35

Partial equilibrium: E r as sufficient statistic Single agent, perfect foresight Unhedged interest rate exposure maturing assets � �� � URE ≡ − 1 URE 0 = ( − 1 b 0 ) − c 0 y 0 + w 0 n 0 + � �� � maturing liabilities ◮ When all financial wealth W F has short maturity: ◮ URE = y + wn + W F − c ◮ Holder of short-term assets tends to gain when r rises ◮ One-time dr change, separable � β t U ( c t ) dc = MPC · URE · dr − σ c (1 − MPC ) dr ◮ σ ≡ − U c cU cc local EIS Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 13 / 35

Partial equilibrium: E r as sufficient statistic Single agent, perfect foresight Unhedged interest rate exposure maturing assets � �� � URE ≡ − 1 URE 0 = ( − 1 b 0 ) − c 0 y 0 + w 0 n 0 + � �� � maturing liabilities ◮ When all financial wealth W F has short maturity: ◮ URE = y + wn + W F − c ◮ Holder of short-term assets tends to gain when r rises ◮ One-time dr change, separable � β t U ( c t ) + date-0 income dy dc = MPC ( dy + UREdr ) − σ c (1 − MPC ) dr ◮ σ ≡ − U c cU cc local EIS Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 13 / 35

Partial equilibrium: E r as sufficient statistic Single agent, perfect foresight Unhedged interest rate exposure maturing assets � �� � URE ≡ − 1 URE 0 = ( − 1 b 0 ) − c 0 y 0 + w 0 n 0 + � �� � maturing liabilities ◮ When all financial wealth W F has short maturity: ◮ URE = y + wn + W F − c ◮ Holder of short-term assets tends to gain when r rises ◮ One-time dr change, separable � β t U ( c t ) + date-0 income dy ◮ + permanent change in price level dP (with nominal assets) � � dy + UREdr − NNP dP dc = MPC − σ c (1 − MPC ) dr P ◮ σ ≡ − U c cU cc local EIS � � ◮ NNP ≡ � − 1 B t t ≥ 0 q t net nominal position Details P t Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 13 / 35

Partial equilibrium: E r as sufficient statistic Incomplete markets Outline Partial equilibrium: E r as sufficient statistic 1 Single agent, perfect foresight Incomplete markets Aggregation Measuring E r 2 General equilibrium model 3 Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 13 / 35

Partial equilibrium: E r as sufficient statistic Incomplete markets Incomplete markets, idiosyncratic risk ◮ Assume now incomplete markets with idiosyncratic uncertainty on { y t , w t } ◮ Nominal bonds with geometric-decay coupon Λ t , rate δ N ◮ Perfect foresight over nominal bond price Q t and price level P t �� � β t U ( c t , n t ) E max t P t c t = P t y t + P t w t n t + Λ t + Q t ( δ N Λ t − Λ t +1 ) Λ t +1 ≥ − P t λ ◮ Define net nominal position NNP t and unhedged interest rate exposure NNP t ≡ (1 + Q t δ N ) Λ t P t URE t ≡ y t + w t n t + Λ t − c t = Q t (Λ t +1 − δ N Λ t ) P t P t Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 14 / 35

Partial equilibrium: E r as sufficient statistic Incomplete markets Individual consumption response: one-time change ◮ Inelastic labor supply n ◮ At time 0: permanent increase in price level dP , purely transitory change in income dY = dy + ndw and the real interest rate dr = − dQ Q Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 15 / 35

Partial equilibrium: E r as sufficient statistic Incomplete markets Individual consumption response: one-time change ◮ Inelastic labor supply n ◮ At time 0: permanent increase in price level dP , purely transitory change in income dY = dy + ndw and the real interest rate dr = − dQ Q Sufficient statistics for consumption response to transitory shocks To first order, the consumption response at date 0 is given by � � dY + UREdr − NNP dP dc ≃ MPC − σ c (1 − MPC ) dr P where MPC = ∂ c ∂ y is the consumption response to a one-time transitory income shock (MPC=1 if constrained) and σ = − U c cU cc is the local EIS Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 15 / 35

Partial equilibrium: E r as sufficient statistic Incomplete markets Individual consumption response: one-time change ◮ Inelastic labor supply n ◮ At time 0: permanent increase in price level dP , purely transitory change in income dY = dy + ndw and the real interest rate dr = − dQ Q Sufficient statistics for consumption response to transitory shocks To first order, the consumption response at date 0 is given by � � dY + UREdr − NNP dP dc ≃ MPC − σ c (1 − MPC ) dr P where MPC = ∂ c ∂ y is the consumption response to a one-time transitory income shock (MPC=1 if constrained) and σ = − U c cU cc is the local EIS ◮ Logic: consumer is at an interior optimum → behaves identically with respect to all changes in his balance sheet (or borrowing limit adapts) ◮ Extensions: elastic labor supply, trees with dividends, ... Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 15 / 35

Partial equilibrium: E r as sufficient statistic Aggregation Outline Partial equilibrium: E r as sufficient statistic 1 Single agent, perfect foresight Incomplete markets Aggregation Measuring E r 2 General equilibrium model 3 Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 15 / 35

Partial equilibrium: E r as sufficient statistic Aggregation Aggregation: environment ◮ Environment: ◮ Closed economy with no government ◮ i = 1 . . . I heterogenous agents (date-0 income Y i = y i + w i n i ) ◮ All participate in financial markets and face the same prices ◮ Aggregate up (transitory shock, here inelastic labor supply) � � dP dc i ≃ MPC i dY i + URE i dr − NNP i − σ i c i (1 − MPC i ) dr P Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 16 / 35

Partial equilibrium: E r as sufficient statistic Aggregation Aggregation: environment ◮ Environment: ◮ Closed economy with no government ◮ i = 1 . . . I heterogenous agents (date-0 income Y i = y i + w i n i ) ◮ All participate in financial markets and face the same prices ◮ Aggregate up (transitory shock, here inelastic labor supply) � � dP dc i ≃ MPC i dY i + URE i dr − NNP i − σ i c i (1 − MPC i ) dr P ◮ Markets clear at date 0: ◮ Assets � NNP i = 0 i ◮ Goods � � � C ≡ c i = Y i ≡ Y ⇒ URE i = 0 i i i Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 16 / 35

Partial equilibrium: E r as sufficient statistic Aggregation Aggregation with heterogeneity Aggregate consumption response to transitory shock �� � � � Y i MPC i , dY i − Y i dY dP dC ≃ Y MPC i dY + C ov I − C ov I ( MPC i , NNP i ) Y P � �� � i � �� � Fisher channel � �� � Earnings heterogeneity channel Aggregate income channel     �   + C ov I ( MPC i , URE i ) − σ i (1 − MPC i ) c i  dr    � �� � i Interest rate exposure channel � �� � Substitution channel Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 17 / 35

Partial equilibrium: E r as sufficient statistic Aggregation Aggregation with heterogeneity Aggregate consumption response to transitory shock �� � � � Y i MPC i , dY i − Y i dY dP dC ≃ Y MPC i dY + C ov I − C ov I ( MPC i , NNP i ) Y P � �� � i � �� � Fisher channel � �� � Earnings heterogeneity channel Aggregate income channel     �   + C ov I ( MPC i , URE i ) − σ i (1 − MPC i ) c i  dr    � �� � i Interest rate exposure channel � �� � Substitution channel ◮ Logic of Keynesian model: “ dC = dY ”given dr ◮ Two sources of“first-round”effects of r ↓ on consumption ◮ Second-round effects: income and price adjustment ◮ With representative-agent (New-Keynesian model), fixed point is dC = − σ Cdr Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 17 / 35

Partial equilibrium: E r as sufficient statistic Aggregation Aggregation with heterogeneity Aggregate consumption response to transitory shock � � � Y i � � � MPC i , dY i − Y i dY dC dY MPC i , NNP i dP ≃ E I Y Y MPC i Y + Cov I − Cov I E I [ c i ] E I [ c i ] C P � �� � � �� � � �� � M E P dE h   � � � �   MPC i , URE i c i   +  Cov I − σ E I (1 − MPC i )  dr   E I [ c i ] E I [ c i ] � �� � � �� � E r S ◮ σ : weighted average of σ i ◮ M , E P , E r and S are measurable ◮ do not depend on the source of the shock ◮ do not require identification (except for MPC) ◮ dE h more complex Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 18 / 35

Partial equilibrium: E r as sufficient statistic Aggregation Focus on slope term dC C ≃ M dY dP Y + dE h + E P P + ( E r − σ S ) dr � � ◮ Next : go to data, find E r = Cov I MPC i , URE i < 0 E I [ c i ] ◮ compare to σ using σ ∗ = − E r S Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 19 / 35

Partial equilibrium: E r as sufficient statistic Aggregation Focus on slope term dC C ≃ M dY dP Y + dE h + E P P − S ( σ ∗ + σ ) dr � � ◮ Next : go to data, find E r = Cov I MPC i , URE i < 0 E I [ c i ] ◮ compare to σ using σ ∗ = − E r S Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 19 / 35

Partial equilibrium: E r as sufficient statistic Aggregation Focus on slope term dC C ≃ M dY dP Y + dE h + E P P − S ( σ ∗ + σ ) dr � � ◮ Next : go to data, find E r = Cov I MPC i , URE i < 0 E I [ c i ] ◮ compare to σ using σ ∗ = − E r S ◮ But : usually, in household data E I [ URE i ] > 0. Why? ◮ Maturity mismatch in the household sector (counterpart of banks) ◮ Government with flow borrowing requirements (negative URE) ◮ My benchmark: “Ricardian view”(uniform rebate). E r still correct. Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 19 / 35

Partial equilibrium: E r as sufficient statistic Aggregation Focus on slope term dC C ≃ M dY dP Y + dE h + E P P − S ( σ ∗ + σ ) dr � � ◮ Next : go to data, find E r = Cov I MPC i , URE i < 0 E I [ c i ] ◮ compare to σ using σ ∗ = − E r S ◮ But : usually, in household data E I [ URE i ] > 0. Why? ◮ Maturity mismatch in the household sector (counterpart of banks) ◮ Government with flow borrowing requirements (negative URE) ◮ My benchmark: “Ricardian view”(uniform rebate). E r still correct. � � ◮ If none of the gains are rebated: E NR = E I URE i MPC i r E I [ c i ] Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 19 / 35

Partial equilibrium: E r as sufficient statistic Aggregation Focus on slope term dC C ≃ M dY dP Y + dE h + E P � � E NR P + − σ S dr r � � ◮ Next : go to data, find E r = Cov I MPC i , URE i < 0 E I [ c i ] ◮ compare to σ using σ ∗ = − E r S ◮ But : usually, in household data E I [ URE i ] > 0. Why? ◮ Maturity mismatch in the household sector (counterpart of banks) ◮ Government with flow borrowing requirements (negative URE) ◮ My benchmark: “Ricardian view”(uniform rebate). E r still correct. � � ◮ If none of the gains are rebated: E NR = E I URE i MPC i r E I [ c i ] ◮ E NR − σ S > 0? r Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 19 / 35

Partial equilibrium: E r as sufficient statistic Aggregation Focus on slope term dC C ≃ M dY dP Y + dE h + E P � � E NR P + − σ S dr r � � ◮ Next : go to data, find E r = Cov I MPC i , URE i < 0 E I [ c i ] ◮ compare to σ using σ ∗ = − E r S ◮ But : usually, in household data E I [ URE i ] > 0. Why? ◮ Maturity mismatch in the household sector (counterpart of banks) ◮ Government with flow borrowing requirements (negative URE) ◮ My benchmark: “Ricardian view”(uniform rebate). E r still correct. � � ◮ If none of the gains are rebated: E NR = E I URE i MPC i r E I [ c i ] ◮ E NR − σ S > 0? r “Interestingly [...] low rates could even hurt overall spending” Raghuram Rajan, November 2013 Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 19 / 35

Measuring E r Outline Partial equilibrium: E r as sufficient statistic 1 Single agent, perfect foresight Incomplete markets Aggregation Measuring E r 2 General equilibrium model 3 Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 19 / 35

Measuring E r Map to data 1. Construct a URE measure at the household level URE i = Y i − C i + B i − D i ◮ Y i : income from all sources ◮ C i : consumption (incl. durables, mtge paymts, excl. house purchase) ◮ B i : maturing asset stocks (especially deposits) ◮ D i : maturing liability stocks (adjustable rate mortgages, cons. credit) 2. Use a procedure to evaluate MPC i at the household or group level ◮ Italy Survey of Household Income and Wealth 2010 ◮ Survey measure [Jappelli Pistaferri 2014] Question ◮ US Consumer Expenditure Survey 2001-2002 ◮ Estimate from randomized receipts of tax rebates [JPS 2006] Details 3. Estimate E r , S , σ ∗ = − E r S and E NR Summary Statistics r Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 20 / 35

Measuring E r Both surveys and methods show that E r < 0 MPC vs URE: Italian data grouped by URE centile MPC vs URE : CEX tax rebate estimation .7 .8 .6 .6 Estimated MPC in group Average MPC in centile .4 .5 .2 .4 0 .3 −.2 −5.67 .03 .26 .59 1.15 11.44 −1.03 [−0.54] 0.17 [0.13] 3.00 [1.40] Normalized URE: centile mean Normalized URE: group mean [median] � � MPC i , URE i ⇒ E r = Cov I < 0 E I [ c i ] Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 21 / 35

Measuring E r Italian data estimation ◮ Household-level information on MPC and URE : compute directly � � � � � � MPC i , URE i c i URE i E r = � � � S = � � = � E I E NR E I Cov I (1 − MPC i ) MPC i r E I [ c i ] E I [ c i ] E I [ c i ] Time Horizon Annual Parameter Estimate 95% C.I. � Redistribution elasticity E r -0.06 [-0.09; -0.04] � Hicksian scaling factor S 0.55 [0.53; 0.57] � σ ∗ = − � E r Equivalent EIS 0.12 [0.06; 0.17] � S � No-rebate elasticity E NR 0.21 [0.17; 0.23] r All statistics computed using survey weights Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 22 / 35

Measuring E r CEX data estimation from JPS ◮ Run MPC estimation over J = 3 groups of URE and compute: � � � � �� �� URE j MPC j , URE j � E r = � = � � S = � � E NR E J E J MPC j Cov J 1 − MPC j r E I [ c i ] E I [ c i ] Consumption measure Food Parameter Estimate 95% C.I. � Redistribution elasticity E r -0.24 [-0.42; -0.07] � Hicksian scaling factor S 0.82 [0.69; 0.95] � σ ∗ = − � E r Equivalent EIS 0.30 [0.05; 0.54] � S � No-rebate elasticity E NR -0.12 [-0.27; 0.02] r Confidence intervals are bootstrapped by resampling households 100 times with replacement Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 23 / 35

General equilibrium model Outline Partial equilibrium: E r as sufficient statistic 1 Single agent, perfect foresight Incomplete markets Aggregation Measuring E r 2 General equilibrium model 3 Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 23 / 35

General equilibrium model General equilibrium model ◮ Objectives ◮ Propose a rationale for sign and magnitude of E r and σ ∗ in the data ◮ Understand the role of (mortgage) market structure ◮ Evaluate the aggregate effect of persistent shocks ◮ Explore non-linearities in economy’s response ◮ Model is stylized ◮ “ARM”experiment only illustrative ◮ Earnings heterogeneity ( dE h ) not disciplined by data ◮ Unexpected shock Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 24 / 35

General equilibrium model Preferences and production ◮ Measure 1 of households i with GHH preferences: � ∞ � � t u � � � � �� E β i c i n i t − v t t t =0 ◮ CES in net consumption σ , constant elasticity of labor supply ψ ◮ All uncertainty is purely idiosyncratic ◮ Idiosyncratic productivity process Π e ( e ′ | e ) ◮ Independent discount factor process Π β ( β ′ | β ) ◮ Aggregate state s = ( e , β ) is in its stationary distribution ◮ Two-tiered production: ◮ Measure 1 of intermediate good firms, identical linear production � x j t = A t l j e i t n i , j t = A t t di i ◮ Final good Y t : aggregator of x j t , elasticity ǫ Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 25 / 35

General equilibrium model Markets and government ◮ Incomplete markets : risk-free nominal bond + borrowing constraint ◮ Affine tax and transfer schedule on labor income alone : � � P t c i t = (1 − τ ) W t e i t n i t + P t T t + Λ i δ N Λ i t − Λ i t + Q t t +1 Q t Λ i t +1 ≥ − DP t ◮ Perfectly competitive final good ( P t ) and labor markets ( W t ) ◮ Monopolistically competitive intermediate goods ( P j t ) Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 26 / 35

General equilibrium model Markets and government ◮ Incomplete markets : risk-free nominal bond + borrowing constraint ◮ Affine tax and transfer schedule on labor income alone : � � P t c i t = (1 − τ ) W t e i t n i t + P t T t + Λ i δ N Λ i t − Λ i t + Q t t +1 Q t Λ i t +1 ≥ − DP t ◮ Perfectly competitive final good ( P t ) and labor markets ( W t ) ◮ Monopolistically competitive intermediate goods ( P j t ) ◮ Government collects all profits , runs a balanced budget with no debt � � � � P j t x j t − W t l j W t e i t n i P t T t = dj + τ t di t j i � ◮ No external supply of assets: market clearing i Q t Λ i t +1 di = 0 Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 26 / 35

General equilibrium model Steady-state neutrality of maturity structure Maturity neutrality The flexible-price steady state (constant productivity A , constant inflation rate Π = 1, constant gross debt limit D ) is invariant to δ N ◮ Constant term structure of interest rates ◮ → short and long-term assets span the same set of contingencies ◮ Unhedged interest rate exposures t + T t + Λ i t ≡ (1 − τ ) W t URE i e i t n i t − c i t P t P t vary with maturity structure, but are refinanced at constant R ◮ Change δ N → change average duration of assets, leave all else equal ◮ Experiment: Calibrate δ N to U.S. then set δ N = 0: “only ARMs” Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 27 / 35

General equilibrium model Calibration ◮ Calibration: quarterly frequency ◮ Targets: ◮ Annual eqbm. R = 3% and debt/PCE ratio of 113% (U.S. 2013) ◮ Asset/liability duration of 4.5 years (from Doepke-Schneider) ◮ Y = C = 1 and E [ n ] = 1 ◮ Average quarterly MPC = 0 . 25 Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 28 / 35

General equilibrium model Calibration ◮ Calibration: quarterly frequency ◮ Targets: ◮ Annual eqbm. R = 3% and debt/PCE ratio of 113% (U.S. 2013) ◮ Asset/liability duration of 4.5 years (from Doepke-Schneider) ◮ Y = C = 1 and E [ n ] = 1 ◮ Average quarterly MPC = 0 . 25 ◮ Parameters: ◮ Time preference process Π β : patient ( β P ) 4 = 0 . 97/imp. ( β I ) 4 = 0 . 82 ◮ 50% of impatient agents ◮ Average state duration of 50 years ◮ Elasticity of labor supply ψ = 1 ◮ Elasticity of substitution in net consumption σ = 0 . 5 ◮ Asset/liability coupon decay rate δ N = 0 . 95 ◮ Borrowing limit as fraction of average consumption D = 185% ◮ Productivity discretized AR(1), ρ = 0 . 95 and τ ∗ = 0 . 4 Details Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 28 / 35

General equilibrium model Redistribution channel in the model ◮ For transitory monetary policy shock, can show: dC C ≃ M dY dP + T dY P − S ( σ ∗ + σ ) dr Y + dE h + E P Y ���� E Y dY � �� � Y Complementarity channel Steady-state value δ N = 0 . 95 δ N = 0 Details and compare to data U.S. “Only ARMs” − 0 . 09 Redistribution elasticity for r E r 0 . 57 Hicksian scaling factor S σ ∗ = − E r 0 . 15 Equivalent EIS S 0 . 16 Income weighted MPC M − 0 . 09 Earnings heterogeneity factor E Y 1 . 77 Redistribution elasticity for P E P 0 . 46 Consumption-labor compl. term T Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 29 / 35

General equilibrium model Redistribution channel in the model ◮ For transitory monetary policy shock, can show: dC C ≃ M dY dP + T dY P − S ( σ ∗ + σ ) dr Y + dE h + E P Y ���� E Y dY � �� � Y Complementarity channel Steady-state value δ N = 0 . 95 δ N = 0 Details and compare to data U.S. “Only ARMs” − 0 . 09 − 1 . 76 Redistribution elasticity for r E r 0 . 57 Hicksian scaling factor S σ ∗ = − E r 0 . 15 3 Equivalent EIS S 0 . 16 Income weighted MPC M − 0 . 09 Earnings heterogeneity factor E Y 1 . 77 Redistribution elasticity for P E P 0 . 46 Consumption-labor compl. term T Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 29 / 35

General equilibrium model Sticky prices ◮ In a steady-state, suppose prices are fully sticky: P t = P t − 1 ◮ Central bank stabilizes, nominal interest rate = steady-state R ◮ Replicates the flexible-price allocation ◮ Monetary policy shock : unexpectedly lowers the nominal rate R t = ρ R t − 1 + (1 − ρ ) R − ǫ t Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 30 / 35

General equilibrium model Sticky prices ◮ In a steady-state, suppose prices are fully sticky: P t = P t − 1 ◮ Central bank stabilizes, nominal interest rate = steady-state R ◮ Replicates the flexible-price allocation ◮ Monetary policy shock : unexpectedly lowers the nominal rate R t = ρ R t − 1 + (1 − ρ ) R − ǫ t ◮ Fisher channel is shut down ◮ Full nonlinear solution keeping track of wealth distribution ◮ find sequence { w t } ensuring market clearing C t = Y t ◮ Borrowing limits keep real value of payments next period fixed Details Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 30 / 35

General equilibrium model Transitory monetary policy easing Transitory monetary policy shock (persistence=0) 1.4 Real interest rate impulse Output response: US calibration 1.2 Output response: representative agent t=0 predicted values from sufficient statistic 1 Per cent deviation from steady-state 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -1 0 1 2 3 4 5 6 7 8 9 10 Time in quarters Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 31 / 35

General equilibrium model Transitory monetary policy easing Transitory monetary policy shock (persistence=0) 1.4 Real interest rate impulse Output response: US calibration 1.2 Output response: Only ARMs Output response: representative agent t=0 predicted values from sufficient statistic 1 Per cent deviation from steady-state 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -1 0 1 2 3 4 5 6 7 8 9 10 Time in quarters Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 32 / 35

General equilibrium model Prolonged monetary policy easing Persistent monetary policy shock (persistence=0.5) 1.6 Real interest rate impulse Output response: US calibration 1.4 Output response: Only ARMs Output response: representative agent 1.2 Per cent deviation from steady-state 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -1 0 1 2 3 4 5 6 7 8 9 10 Time in quarters Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 33 / 35

General equilibrium model Asymmetric effects Effect on output of a change in r (General Equilibrium) 8 US benchmark calibration First-order approx. ARM-only calibration 6 First-order approx. 4 Percentage change in output 2 0 -2 -4 -6 -8 -500 -400 -300 -200 -100 0 100 200 300 400 500 1-quarter change in real interest rate (basis points, annualized) Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 34 / 35

Conclusion Conclusion ◮ Monetary policy redistributes: ◮ One reason why it affects aggregate consumption ◮ Likely to be the dominant one in ARM countries � � ◮ Sufficient statistics, E m = Cov I MPC i , Exposure i , m , establish orders of magnitude and discipline model calibrations ◮ Implications for policy: ◮ Capital gains can act against MPC-aligned redistribution ◮ The effects of monetary policy may vary (with E r ) over the cycle Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 35 / 35

Additional slides Thank you! Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 36 / 35

Additional slides Additional wealth effects ◮ Introduce nominal assets: Return ◮ price level { P t } (perfectly foreseen) ◮ nominal holdings: { − 1 B t + s } s ≥ 0 (deposits, bonds, mortgage) ◮ Fisher equation for nominal term structure Q t + s = q t + s P t P t + s ◮ Unexpected shock to { q t } as well as ◮ Price level { P 0 , P 1 . . . } ◮ Real income stream { y 0 , y 1 . . . } ◮ Real wage sequence { w 0 , w 1 . . . } ◮ Write first-order change in consumption dc 0 , hours dn 0 , welfare dU using x 0 , p t ≡ ∂ x h MPC ≡ ∂ c 0 MPN ≡ ∂ n 0 p t ǫ h 0 ∂ y 0 , ∂ y 0 , x 0 , x 0 ∈ { c 0 , n 0 } p t ∈ { q t , w t } ∂ p t Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 37 / 35

Additional slides Consumption, hours and welfare response Impulse response to the shock To first order, dU ≃ U c 0 d Ω and   dq t dw t � � ǫ h ǫ h dc 0 ≃ MPCd Ω + c 0 q t +  c 0 , q t c 0 , w t w t t ≥ 0 t ≥ 0   � dq t � dw t ǫ h ǫ h dn 0 ≃ MPNd Ω + n 0 q t +  n 0 , q t n 0 , w t w t t ≥ 0 t ≥ 0 where � � � � − 1 B t dq t ( q t y t ) dy t � � d Ω = q t y t + w t n t + ( − 1 b t ) + − c t q t + P t y t t ≥ 0 t ≥ 0 � �� � � �� � − 1 URE t Real unearned income change � dP t � ( q t w t n t ) dw t − 1 B t � � + − Q t w t P 0 P t t ≥ 0 t ≥ 0 � �� � � �� � Real earned income change Revaluation of net nominal position Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 38 / 35

Additional slides SHIW MPC question ◮ In the 2010 survey [analyzed by Jappelli and Pistaferri 2014] Imagine you unexpectedly receive a reimbursement equal to the amount your household earns in a month. How much of it would you save and how much would you spend? Please give the percentage you would save and the percentage you would spend. ◮ In the 2012 survey Imagine you receive an unexpected inheritance equal to your household’s income for a year. Over the next 12 months, how would you use this windfall? Setting the total equal to 100, divide it into parts for three possible uses: 1. Portion saved for future expenditure or to repay debt ( MPS ) 2. Portion spent within the year on goods and services that last in time (jewellery and valuables, motor vehicles, home renovation, furnishing, dental work, etc.) that otherwise you would not have bought or that you were waiting to buy ( MPD ) 3. Portion spent during the year on goods and services that do not last in time (food, clothing, travel, holidays, etc.) that ordinarily you would not have bought ( MPC ) Back Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 39 / 35

Additional slides Johnson, Parker, Souleles (2006) tax rebates ◮ Sort all households into J quantiles of URE ◮ Run main estimating equation from JPS: J � C i , m , t +1 − C i , m , t = α m + β X i , t + MPC j R i , t +1 QURE i , j + u i , t +1 j =1 ◮ C i , m , t : level of i ’s consumption expenditure in month m and date t ◮ X i , t : age and family composition ◮ R i , t +1 : dollar amount of the rebate receipt ◮ QURE i , j = 1 if household i ∈ interest rate exposure group MPC j ◮ Estimation of MPC j exploits randomized variation in timing of receipt of tax rebate among households in URE group j Back Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 40 / 35

Additional slides Datasets: summary statistics SHIW 2010 CEX 2001 Variable mean n.s.d. mean n.s.d. Income from all sources ( Y i , per year) 36,114 0.90 45,617 1.01 Consumption incl. mortgage payments ( C i , per year) 27,976 0.61 36,253 0.79 Deposits and maturing assets ( B i ) 14,200 1.45 7,147 0.77 ARM mortgage liabilities and consumer credit ( D i ) 6,228 1.03 2,872 0.22 Unhedged interest rate exposure ( URE i , per year) 16,110 1.92 13,639 1.27 Unhedged interest rate exposure ( URE i , per Q) 10,007 7.07 6,616 3.39 Marginal Propensity to Spend (annual) 0.47 0.35 Count 7,951 9,443 “mean” : sample mean computed using sample weights (in B C for SHIW; current USD for CEX) � � Xi “n.s.d” : normalized standard deviation, sd I for X i = Y i , C i , B i , URE i and sd I ( MPC i ) for MPC E I [ Ci ] Back Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 41 / 35

Additional slides Calibration (continued) ◮ Idiosyncratic productivity process: discretized AR (1) � log e t = ρ log e t − 1 + σ e 1 − ρ 2 ǫ t ǫ t ∼ N (0 , 1) e (1 + ψ ) 2 ◮ Lognormal stationary distribution of pre-tax earnings, var. σ 2 ◮ Set σ e (1 + ψ ) = 1 . 04 to empirical counterpart in 2009 PSID ◮ τ ∗ = 0 . 4 matches typical calibration for (post-tax) earnings ◮ Moderate persistence level: ρ = 0 . 95 (quarterly) Back 1 PSID 2009 Pre-tax labor earnings distribution Model pre-tax labor earnings 0.9 Model post-tax&transfer labor earnings Model post-tax&transfer net labor earnings Typical calibration (variance of log earnings=0.6) 0.8 Perfect equality line Cumulative labor earnings proportion 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Cumulative population proportion Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 42 / 35

Additional slides Constrained agents and MPCs in steady state 0.8 0.3 Patient Patient, low income (S=1) Impatient Patient, high income (S=7) Impatient, low income (S=1) 0.7 Impatient, high income (S=7) 0.25 Fraction of agents at the borrowing limit 0.6 0.2 0.5 MPC 0.4 0.15 0.3 0.1 0.2 0.05 0.1 0 0 1 2 3 4 5 6 7 8 9 10 -200 -180 -160 -140 -120 -100 -80 -60 -40 -20 0 Discretized income state (S) Net financial asset position (% of annual per capita PCE) Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 43 / 35

Additional slides Redistribution elasticity E r in the model and in data 0 -0.2 -0.4 -0.6 -0.8 E r -1 -1.2 -1.4 Redistribution elasticity in model Benchmark calibration -1.6 Italy: SHIW data US CEX: Food estimate US CEX: All nondurable -1.8 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Asset/Liability duration in years Back Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 44 / 35

Additional slides Other moments ◮ Construct counterpart to Q Λ: net interest-paying assets (Deposits, IRAs and other assets minus all debts) Mean sd P5 P25 Median P75 P95 P99 PSID 2009 1.17 32.51 -28.42 -6.88 0.00 1.78 35.86 113.90 Q Λ E [ c ] Model 0 17.96 -7.4 -7.27 -6.11 0.32 25.96 54.05 Units: average quarterly consumption Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 45 / 35

Additional slides Transition after shocks ◮ Debt limit maintains next period real coupon payments fixed: D t = Q t d ⇔ λ t +1 ≥ − d ◮ When Π t = 1, B.C. of agents at the borrowing limit: Steady-state value δ N = 0 . 95 δ N = 0   � y i � min 0 . 413 0 . 413  d + Q t � � c i t = y i   t − Q × − D (1 − δ N )  d 0 . 413 7 . 455 � �� � − 0 . 358 − 7 . 400 URE URE ( R − 1) D 0 . 055 0 . 055 Back Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 46 / 35

Additional slides Monetary policy and the redistribution channels Aggregate income ↑ Aggregate MPC Substitution Monetary accomodation Real interest rate ↓ Aggregate demand ↑ Standard New-Keynesian model (fully sticky prices) Individual incomes ↑ Back Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 47 / 35

Additional slides Monetary policy and the redistribution channels Aggregate income ↑ Aggregate MPC Substitution Monetary accomodation Real interest rate ↓ Aggregate demand ↑ Interest-rate exposure Standard New-Keynesian model (fully sticky prices) Individual incomes ↑ Redistribution channels Back Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 47 / 35

Additional slides Monetary policy and the redistribution channels Aggregate income ↑ Aggregate MPC Substitution Monetary accomodation Real interest rate ↓ Aggregate demand ↑ Interest-rate exposure Standard New-Keynesian model (fully sticky prices) Earnings heterogeneity Individual incomes ↑ Redistribution channels Back Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 47 / 35