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Monetary Policy and the Redistribution Channel Adrien Auclert Stanford (visiting Princeton) DNB Annual Conference November 20, 2015 Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 1 / 35 Introduction How does monetary

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SLIDE 1

Monetary Policy and the Redistribution Channel

Adrien Auclert

Stanford (visiting Princeton)

DNB Annual Conference November 20, 2015

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 1 / 35

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SLIDE 2

Introduction

◮ How does monetary policy work? ◮ Why does it affect consumption?

◮ Traditional view: intertemporal substitution Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 2 / 35

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SLIDE 3

Introduction

◮ How does monetary policy work? ◮ Why does it affect consumption?

◮ Traditional view: intertemporal substitution

◮ Redistributive effects between“borrowers”and“savers”

?

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 2 / 35

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SLIDE 4

Introduction

◮ How does monetary policy work? ◮ Why does it affect consumption?

◮ Traditional view: intertemporal substitution

◮ Redistributive effects between“borrowers”and“savers”

?

◮ Traditional view: netting out Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 2 / 35

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SLIDE 5

Introduction

◮ How does monetary policy work? ◮ Why does it affect consumption?

◮ Traditional view: intertemporal substitution

◮ Redistributive effects between“borrowers”and“savers”

?

◮ Traditional view: netting out

◮ This paper: redistribution is part of the transmission mechanism

◮ Those who gain from r ↓ have higher MPCs: redistribution channel Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 2 / 35

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Introduction

Who gains and who loses?

My colleagues and I know that people who rely on investments that pay a fixed interest rate, such as certificates of deposit, are receiving very low returns, a situation that has involved significant hardship for some. Ben Bernanke, October 2012 The Federal Reserve’s policies have benefited the relatively well off; it is trying to raise the prices of assets which are overwhelmingly owned by the rich. Martin Wolf, Financial Times, September 2014

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 3 / 35

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SLIDE 7

Introduction

Who gains and who loses?

My colleagues and I know that people who rely on investments that pay a fixed interest rate, such as certificates of deposit, are receiving very low returns, a situation that has involved significant hardship for some. Ben Bernanke, October 2012 The Federal Reserve’s policies have benefited the relatively well off; it is trying to raise the prices of assets which are overwhelmingly owned by the rich. Martin Wolf, Financial Times, September 2014

◮ Asset durations matter

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 3 / 35

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SLIDE 8

Introduction

Who gains and who loses?

My colleagues and I know that people who rely on investments that pay a fixed interest rate, such as certificates of deposit, are receiving very low returns, a situation that has involved significant hardship for some. Ben Bernanke, October 2012 The Federal Reserve’s policies have benefited the relatively well off; it is trying to raise the prices of assets which are overwhelmingly owned by the rich. Martin Wolf, Financial Times, September 2014

◮ Asset durations matter ◮ But also: consumption and income plans

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 3 / 35

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SLIDE 9

Introduction

Who gains and who loses?

My colleagues and I know that people who rely on investments that pay a fixed interest rate, such as certificates of deposit, are receiving very low returns, a situation that has involved significant hardship for some. Ben Bernanke, October 2012 The Federal Reserve’s policies have benefited the relatively well off; it is trying to raise the prices of assets which are overwhelmingly owned by the rich. Martin Wolf, Financial Times, September 2014

◮ Asset durations matter ◮ But also: consumption and income plans ◮ Moreover: monetary policy affects inflation, earnings, etc.

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 3 / 35

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Introduction

Where we are headed

◮ Monetary policy → macroeconomic aggregates m = r, P, Y

◮ Real interest rates (r), inflation (P), and the level of output (Y )

◮ Household i ∈ I has

◮ balance sheet Exposurei,m to dm ◮ Exposurei,P [Doepke and Schneider 2006] ◮ marginal propensity to consume MPCi

◮ Does i gain when monetary policy changes?

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 4 / 35

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SLIDE 11

Introduction

Where we are headed

◮ Monetary policy → macroeconomic aggregates m = r, P, Y

◮ Real interest rates (r), inflation (P), and the level of output (Y )

◮ Household i ∈ I has

◮ balance sheet Exposurei,m to dm ◮ Exposurei,P [Doepke and Schneider 2006] ◮ marginal propensity to consume MPCi

◮ Does i gain when monetary policy changes?

Wealth effect =

m Exposurei,m · dm

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 4 / 35

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SLIDE 12

Introduction

Where we are headed

◮ Monetary policy → macroeconomic aggregates m = r, P, Y

◮ Real interest rates (r), inflation (P), and the level of output (Y )

◮ Household i ∈ I has

◮ balance sheet Exposurei,m to dm ◮ Exposurei,P [Doepke and Schneider 2006] ◮ marginal propensity to consume MPCi

◮ Does i gain when monetary policy changes?

Wealth effect =

m Exposurei,m · dm ◮ Effect of redistribution through m on aggregate consumption?

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 4 / 35

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SLIDE 13

Introduction

Where we are headed

◮ Monetary policy → macroeconomic aggregates m = r, P, Y

◮ Real interest rates (r), inflation (P), and the level of output (Y )

◮ Household i ∈ I has

◮ balance sheet Exposurei,m to dm ◮ Exposurei,P [Doepke and Schneider 2006] ◮ marginal propensity to consume MPCi

◮ Does i gain when monetary policy changes?

Wealth effect =

m Exposurei,m · dm ◮ Effect of redistribution through m on aggregate consumption?

Redistribution elasticity = Em = CovI

  • MPCi, Exposurei,m
  • Adrien Auclert (Stanford)

Redistribution Channel November 20, 2015 4 / 35

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SLIDE 14

Introduction

Where we are headed

◮ Monetary policy → macroeconomic aggregates m = r, P, Y

◮ Real interest rates (r), inflation (P), and the level of output (Y )

◮ Household i ∈ I has

◮ balance sheet Exposurei,m to dm ◮ Exposurei,P [Doepke and Schneider 2006] ◮ marginal propensity to consume MPCi

◮ Does i gain when monetary policy changes?

Wealth effect =

m Exposurei,m · dm ◮ Effect of redistribution through m on aggregate consumption?

Redistribution elasticity = Em = CovI

  • MPCi, Exposurei,m
  • ◮ Em: sufficient statistic [Harberger 1964, Chetty 2009]

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 4 / 35

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SLIDE 15

Introduction

Sufficient statistic: real interest rate change

◮ Focus on m = r. Cyclical monetary policy, stable inflation ◮ Exposurei,r: “Unhedged (interest)-rate exposure”

.

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 5 / 35

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Introduction

Sufficient statistic: real interest rate change

◮ Focus on m = r. Cyclical monetary policy, stable inflation ◮ Exposurei,r: “Unhedged (interest)-rate exposure”

. Transitory dr:

UREi = maturing assetsi

  • including income

− maturing liabilitiesi

  • including consumption

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 5 / 35

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SLIDE 17

Introduction

Sufficient statistic: real interest rate change

◮ Focus on m = r. Cyclical monetary policy, stable inflation ◮ Exposurei,r: “Unhedged (interest)-rate exposure”

. Transitory dr:

UREi = maturing assetsi

  • including income

− maturing liabilitiesi

  • including consumption

◮ Er = CovI (MPCi, UREi) measurable in household surveys

◮ Italy [Jappelli, Pistaferri 2014] & US [Johnson, Parker, Souleles 2006] Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 5 / 35

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SLIDE 18

Introduction

Sufficient statistic: real interest rate change

◮ Focus on m = r. Cyclical monetary policy, stable inflation ◮ Exposurei,r: “Unhedged (interest)-rate exposure”

. Transitory dr:

UREi = maturing assetsi

  • including income

− maturing liabilitiesi

  • including consumption

◮ Er = CovI (MPCi, UREi) measurable in household surveys

◮ Italy [Jappelli, Pistaferri 2014] & US [Johnson, Parker, Souleles 2006] ◮ Er < 0. Redistribution channel ⇒ C ↑ when r ↓ Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 5 / 35

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SLIDE 19

Introduction

Sufficient statistic: real interest rate change

◮ Focus on m = r. Cyclical monetary policy, stable inflation ◮ Exposurei,r: “Unhedged (interest)-rate exposure”

. Transitory dr:

UREi = maturing assetsi

  • including income

− maturing liabilitiesi

  • including consumption

◮ Er = CovI (MPCi, UREi) measurable in household surveys

◮ Italy [Jappelli, Pistaferri 2014] & US [Johnson, Parker, Souleles 2006] ◮ Er < 0. Redistribution channel ⇒ C ↑ when r ↓ ◮ Adds to the substitution channel, same magnitude if EIS≃ 0.1 to 0.3 Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 5 / 35

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SLIDE 20

Introduction

Sufficient statistic: real interest rate change

◮ Focus on m = r. Cyclical monetary policy, stable inflation ◮ Exposurei,r: “Unhedged (interest)-rate exposure”

. Transitory dr:

UREi = maturing assetsi

  • including income

− maturing liabilitiesi

  • including consumption

◮ Er = CovI (MPCi, UREi) measurable in household surveys

◮ Italy [Jappelli, Pistaferri 2014] & US [Johnson, Parker, Souleles 2006] ◮ Er < 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

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SLIDE 21

Introduction

Dynamic general equilibrium model

◮ GE model calibrated to U.S. economy matches Er and predicts:

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 6 / 35

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SLIDE 22

Introduction

Dynamic general equilibrium model

◮ GE model calibrated to U.S. economy matches Er and predicts:

  • 1. Er 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

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SLIDE 23

Introduction

Dynamic general equilibrium model

◮ GE model calibrated to U.S. economy matches Er and predicts:

  • 1. Er 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

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SLIDE 24

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

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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´

  • pez-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

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Introduction

Outline

1

Partial equilibrium: Er as sufficient statistic Single agent, perfect foresight Incomplete markets Aggregation

2

Measuring Er

3

General equilibrium model

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 9 / 35

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SLIDE 27

Partial equilibrium: Er as sufficient statistic Single agent, perfect foresight

Outline

1

Partial equilibrium: Er as sufficient statistic Single agent, perfect foresight Incomplete markets Aggregation

2

Measuring Er

3

General equilibrium model

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 9 / 35

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SLIDE 28

Partial equilibrium: Er 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 {yt} and wages {wt} (certain) ◮ faces real term structure {tqt+s}s≥1 ◮ holds long-term real assets: {t−1bt+s}s≥0 (TIPS, PLAM) Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 10 / 35

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Partial equilibrium: Er 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 {yt} and wages {wt} (certain) ◮ faces real term structure {tqt+s}s≥1 ◮ holds long-term real assets: {t−1bt+s}s≥0 (TIPS, PLAM)

◮ Solves:

max U ({ct, nt}) s.t. ct = yt + wtnt + (t−1bt) +

  • s≥1

(tqt+s) (t−1bt+s − tbt+s)

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 10 / 35

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SLIDE 30

Partial equilibrium: Er 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 {yt} and wages {wt} (certain) ◮ faces real term structure {tqt+s}s≥1 ◮ holds long-term real assets: {t−1bt+s}s≥0 (TIPS, PLAM)

◮ Date-0 holdings: {−1bt+s}s≥0, term structure qt = (0qt) ◮ Solves:

max U ({ct, nt}) s.t. ct = yt + wtnt + (t−1bt) +

  • s≥1

(tqt+s) (t−1bt+s − tbt+s)

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 10 / 35

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SLIDE 31

Partial equilibrium: Er 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 {yt} and wages {wt} (certain) ◮ faces real term structure {tqt+s}s≥1 ◮ holds long-term real assets: {t−1bt+s}s≥0 (TIPS, PLAM)

◮ Date-0 holdings: {−1bt+s}s≥0, term structure qt = (0qt) ◮ Solves:

max U ({ct, nt}) s.t.

  • t≥0

qtct =

  • t≥0

qt (yt + wtnt) +

  • t≥0

qt (−1bt)

  • Financial wealth W F

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 10 / 35

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SLIDE 32

Partial equilibrium: Er 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 {yt} and wages {wt} (certain) ◮ faces real term structure {tqt+s}s≥1 ◮ holds long-term real assets: {t−1bt+s}s≥0 (TIPS, PLAM)

◮ Date-0 holdings: {−1bt+s}s≥0, term structure qt = (0qt) ◮ Solves:

max U ({ct, nt}) s.t.

  • t≥0

qtct =

  • t≥0

qt (yt + wtnt) +

  • t≥0

qt (−1bt)

  • Financial wealth W F

◮ → Initial balance sheet composition irrelevant conditional on W F

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 10 / 35

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SLIDE 33

Partial equilibrium: Er 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 {yt} and wages {wt} (certain) ◮ faces real term structure {tqt+s}s≥1 ◮ holds long-term real assets: {t−1bt+s}s≥0 (TIPS, PLAM)

◮ Date-0 holdings: {−1bt+s}s≥0, term structure qt = (0qt) ◮ Solves:

max U ({ct, nt}) s.t.

  • t≥0

qtct =

  • t≥0

qt (yt + wtnt) +

  • t≥0

qt (−1bt)

  • Financial wealth W F

◮ → Initial balance sheet composition irrelevant conditional on W F ◮ Mortgage M: ARM −1b0 = −M ⇔ PLAM −1bt = −m if T

t=0 qtm = M

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 10 / 35

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SLIDE 34

Partial equilibrium: Er as sufficient statistic Single agent, perfect foresight

Comparative statics exercise

max U ({ct, nt}) s.t.

  • t≥0

qtct =

  • t≥0

qt

  • yt + wtnt + (−1bt)
  • t

dx x

r q

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 11 / 35

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SLIDE 35

Partial equilibrium: Er as sufficient statistic Single agent, perfect foresight

Comparative statics exercise

max U ({ct, nt}) s.t.

  • t≥0

qtct =

  • t≥0

qt

  • yt + wtnt + (−1bt)
  • t

dx x

r q

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 11 / 35

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SLIDE 36

Partial equilibrium: Er as sufficient statistic Single agent, perfect foresight

Comparative statics exercise

max U ({ct, nt}) s.t.

  • t≥0

qtct =

  • t≥0

qt

  • yt + wtnt + (−1bt)
  • t

dx x

r y

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 11 / 35

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SLIDE 37

Partial equilibrium: Er as sufficient statistic Single agent, perfect foresight

Comparative statics exercise

max U ({ct, nt}) s.t.

  • t≥0

qtct =

  • t≥0

qt

  • yt + wtnt + (−1bt) + (−1Bt)

Pt

  • t

dx x

r y P

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 11 / 35

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SLIDE 38

Partial equilibrium: Er as sufficient statistic Single agent, perfect foresight

Comparative statics

max U ({ct, nt}) s.t.

  • t≥0

qtct =

  • t≥0

qt (yt + wtnt + (−1bt)) ≡ W

◮ t = 0 → unexpected one-time shock to the real term structure ( dq0

q0 = dr)

◮ First-order change in consumption dc0?

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 12 / 35

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SLIDE 39

Partial equilibrium: Er as sufficient statistic Single agent, perfect foresight

Comparative statics

max U ({ct, nt}) s.t.

  • t≥0

qtct =

  • t≥0

qt (yt + wtnt + (−1bt)) ≡ W

◮ t = 0 → unexpected one-time shock to the real term structure ( dq0

q0 = dr)

◮ First-order change in consumption dc0?

dc0 ≃ ∂c0 ∂W · (y0 + w0n0 + (−1b0) − c0) dr

  • Wealth effect

+ dch

  • Substitution effect

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 12 / 35

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SLIDE 40

Partial equilibrium: Er as sufficient statistic Single agent, perfect foresight

Comparative statics

max U ({ct, nt}) s.t.

  • t≥0

qtct =

  • t≥0

qt (yt + wtnt + (−1bt)) ≡ W

◮ t = 0 → unexpected one-time shock to the real term structure ( dq0

q0 = dr)

◮ First-order change in consumption dc0?

dc0 ≃ ∂c0 ∂W · (y0 + w0n0 + (−1b0) − c0) dr

  • Wealth effect

+ dch

  • Substitution effect

◮ Welfare change dU ≃ Uc0 · (y0 + w0n0 + (−1b0) − c0) dr

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 12 / 35

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SLIDE 41

Partial equilibrium: Er as sufficient statistic Single agent, perfect foresight

Comparative statics

max U ({ct, nt}) s.t.

  • t≥0

qtct =

  • t≥0

qt (yt + wtnt + (−1bt)) ≡ W

◮ t = 0 → unexpected one-time shock to the real term structure ( dq0

q0 = dr)

◮ First-order change in consumption dc0?

dc0 ≃ ∂c0 ∂W · (y0 + w0n0 + (−1b0) − c0) dr

  • Wealth effect

+ dch

  • Substitution effect

◮ Welfare change dU ≃ Uc0 · (y0 + w0n0 + (−1b0) − c0) dr ◮ Composition of balance sheet matters: e.g. “hedged”when

−1b0 = c0 − (y0 + w0n0)

∀t

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 12 / 35

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SLIDE 42

Partial equilibrium: Er as sufficient statistic Single agent, perfect foresight

Comparative statics

max U ({ct, nt}) s.t.

  • t≥0

qtct =

  • t≥0

qt (yt + wtnt + (−1bt)) ≡ W

◮ t = 0 → unexpected one-time shock to the real term structure ( dq0

q0 = dr)

◮ First-order change in consumption dc0?

dc0 ≃ ∂c0 ∂W ·

−1URE0

  • (y0 + w0n0 + (−1b0) − c0) dr +

dch

  • Substitution effect

◮ Welfare change dU ≃ Uc0 · (−1URE0) dr ◮ Composition of balance sheet matters: e.g. “hedged”when

−1b0 = c0 − (y0 + w0n0)

∀t →

−1URE0 = 0

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 12 / 35

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SLIDE 43

Partial equilibrium: Er as sufficient statistic Single agent, perfect foresight

Comparative statics

max U ({ct, nt}) s.t.

  • t≥0

qtct =

  • t≥0

qt (yt + wtnt + (−1bt)) ≡ W

◮ t = 0 → unexpected one-time shock to the real term structure ( dq0

q0 = dr)

◮ First-order change in consumption dc0?

dc0 ≃

MPC

  • ∂c0

∂y0 ·

−1URE0

  • (y0 + w0n0 + (−1b0) − c0) dr +

dch

  • Substitution effect

◮ Welfare change dU ≃ Uc0 · (−1URE0) dr ◮ Composition of balance sheet matters: e.g. “hedged”when

−1b0 = c0 − (y0 + w0n0)

∀t →

−1URE0 = 0

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 12 / 35

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SLIDE 44

Partial equilibrium: Er as sufficient statistic Single agent, perfect foresight

Unhedged interest rate exposure

URE ≡ −1URE0 =

maturing assets

  • y0 + w0n0 +

(−1b0) − c0

  • 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

dc0 = MPC · URE · dr + dch

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 13 / 35

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SLIDE 45

Partial equilibrium: Er as sufficient statistic Single agent, perfect foresight

Unhedged interest rate exposure

URE ≡ −1URE0 =

maturing assets

  • y0 + w0n0 +

(−1b0) − c0

  • 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 βtU (ct)

dc = MPC · URE · dr−σc (1 − MPC) dr

◮ σ ≡ − Uc

cUcc local EIS

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 13 / 35

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SLIDE 46

Partial equilibrium: Er as sufficient statistic Single agent, perfect foresight

Unhedged interest rate exposure

URE ≡ −1URE0 =

maturing assets

  • y0 + w0n0 +

(−1b0) − c0

  • 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 βtU (ct) + date-0 income dy

dc = MPC (dy + UREdr) − σc (1 − MPC) dr

◮ σ ≡ − Uc

cUcc local EIS

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 13 / 35

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SLIDE 47

Partial equilibrium: Er as sufficient statistic Single agent, perfect foresight

Unhedged interest rate exposure

URE ≡ −1URE0 =

maturing assets

  • y0 + w0n0 +

(−1b0) − c0

  • 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 βtU (ct) + date-0 income dy ◮ + permanent change in price level dP (with nominal assets)

dc = MPC

  • dy + UREdr − NNP dP

P

  • − σc (1 − MPC) dr

◮ σ ≡ − Uc

cUcc local EIS

◮ NNP ≡

t≥0 qt

  • −1Bt

Pt

  • net nominal position

Details Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 13 / 35

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SLIDE 48

Partial equilibrium: Er as sufficient statistic Incomplete markets

Outline

1

Partial equilibrium: Er as sufficient statistic Single agent, perfect foresight Incomplete markets Aggregation

2

Measuring Er

3

General equilibrium model

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 13 / 35

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SLIDE 49

Partial equilibrium: Er as sufficient statistic Incomplete markets

Incomplete markets, idiosyncratic risk

◮ Assume now incomplete markets with idiosyncratic uncertainty on {yt, wt} ◮ Nominal bonds with geometric-decay coupon Λt, rate δN ◮ Perfect foresight over nominal bond price Qt and price level Pt

max E

  • t

βtU (ct, nt)

  • Ptct = Ptyt + Ptwtnt + Λt + Qt (δNΛt − Λt+1)

Λt+1 ≥ −Ptλ

◮ Define net nominal position NNPt and unhedged interest rate exposure

NNPt ≡ (1 + QtδN) Λt Pt UREt ≡ yt + wtnt + Λt Pt − ct = Qt Pt (Λt+1 − δNΛt)

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 14 / 35

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SLIDE 50

Partial equilibrium: Er 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

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SLIDE 51

Partial equilibrium: Er 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 dc ≃ MPC

  • dY + UREdr − NNP dP

P

  • − σc (1 − MPC) dr

where MPC = ∂c

∂y is the consumption response to a one-time transitory income

shock (MPC=1 if constrained) and σ = − Uc

cUcc is the local EIS

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 15 / 35

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SLIDE 52

Partial equilibrium: Er 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 dc ≃ MPC

  • dY + UREdr − NNP dP

P

  • − σc (1 − MPC) dr

where MPC = ∂c

∂y is the consumption response to a one-time transitory income

shock (MPC=1 if constrained) and σ = − Uc

cUcc 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

slide-53
SLIDE 53

Partial equilibrium: Er as sufficient statistic Aggregation

Outline

1

Partial equilibrium: Er as sufficient statistic Single agent, perfect foresight Incomplete markets Aggregation

2

Measuring Er

3

General equilibrium model

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 15 / 35

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SLIDE 54

Partial equilibrium: Er as sufficient statistic Aggregation

Aggregation: environment

◮ Environment:

◮ Closed economy with no government ◮ i = 1 . . . I heterogenous agents (date-0 income Yi = yi + wini) ◮ All participate in financial markets and face the same prices

◮ Aggregate up (transitory shock, here inelastic labor supply)

dci ≃ MPCi

  • dYi + UREidr − NNPi

dP P

  • − σici (1 − MPCi) dr

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 16 / 35

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SLIDE 55

Partial equilibrium: Er as sufficient statistic Aggregation

Aggregation: environment

◮ Environment:

◮ Closed economy with no government ◮ i = 1 . . . I heterogenous agents (date-0 income Yi = yi + wini) ◮ All participate in financial markets and face the same prices

◮ Aggregate up (transitory shock, here inelastic labor supply)

dci ≃ MPCi

  • dYi + UREidr − NNPi

dP P

  • − σici (1 − MPCi) dr

◮ Markets clear at date 0:

◮ Assets

  • i

NNPi = 0

◮ Goods

C ≡

  • i

ci =

  • i

Yi ≡ Y ⇒

  • i

UREi = 0

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 16 / 35

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SLIDE 56

Partial equilibrium: Er as sufficient statistic Aggregation

Aggregation with heterogeneity

Aggregate consumption response to transitory shock

dC ≃

  • i

Yi Y MPCi

  • dY
  • Aggregate income channel

+ CovI

  • MPCi, dYi − Yi dY

Y

  • Earnings heterogeneity channel

− CovI (MPCi, NNPi)

  • Fisher channel

dP P +      CovI (MPCi, UREi)

  • Interest rate exposure channel

−

  • i

σi (1 − MPCi) ci

  • Substitution channel

     dr

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 17 / 35

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SLIDE 57

Partial equilibrium: Er as sufficient statistic Aggregation

Aggregation with heterogeneity

Aggregate consumption response to transitory shock

dC ≃

  • i

Yi Y MPCi

  • dY
  • Aggregate income channel

+ CovI

  • MPCi, dYi − Yi dY

Y

  • Earnings heterogeneity channel

− CovI (MPCi, NNPi)

  • Fisher channel

dP P +      CovI (MPCi, UREi)

  • Interest rate exposure channel

−

  • i

σi (1 − MPCi) ci

  • Substitution channel

     dr

◮ 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 = −σCdr

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 17 / 35

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SLIDE 58

Partial equilibrium: Er as sufficient statistic Aggregation

Aggregation with heterogeneity

Aggregate consumption response to transitory shock

dC C ≃ EI Yi Y MPCi

  • M

dY Y + CovI

  • MPCi, dYi − Yi dY

Y

EI [ci]

  • dEh

−CovI

  • MPCi, NNPi

EI [ci]

  • EP

dP P +     CovI

  • MPCi, UREi

EI [ci]

  • Er

−σ EI

  • (1 − MPCi)

ci EI [ci]

  • S

     dr

◮ σ: weighted average of σi ◮ M, EP, Er 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

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SLIDE 59

Partial equilibrium: Er as sufficient statistic Aggregation

Focus on slope term

dC C ≃ MdY Y + dE h + EP dP P + (Er − σS) dr

◮ Next: go to data, find Er = CovI

  • MPCi, UREi

EI [ci]

  • < 0

◮ compare to σ using σ∗ = − Er

S

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 19 / 35

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SLIDE 60

Partial equilibrium: Er as sufficient statistic Aggregation

Focus on slope term

dC C ≃ MdY Y + dE h + EP dP P − S (σ∗ + σ) dr

◮ Next: go to data, find Er = CovI

  • MPCi, UREi

EI [ci]

  • < 0

◮ compare to σ using σ∗ = − Er

S

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 19 / 35

slide-61
SLIDE 61

Partial equilibrium: Er as sufficient statistic Aggregation

Focus on slope term

dC C ≃ MdY Y + dE h + EP dP P − S (σ∗ + σ) dr

◮ Next: go to data, find Er = CovI

  • MPCi, UREi

EI [ci]

  • < 0

◮ compare to σ using σ∗ = − Er

S

◮ But: usually, in household data EI [UREi] > 0. Why?

◮ Maturity mismatch in the household sector (counterpart of banks) ◮ Government with flow borrowing requirements (negative URE) ◮ My benchmark: “Ricardian view”(uniform rebate). Er still correct. Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 19 / 35

slide-62
SLIDE 62

Partial equilibrium: Er as sufficient statistic Aggregation

Focus on slope term

dC C ≃ MdY Y + dE h + EP dP P − S (σ∗ + σ) dr

◮ Next: go to data, find Er = CovI

  • MPCi, UREi

EI [ci]

  • < 0

◮ compare to σ using σ∗ = − Er

S

◮ But: usually, in household data EI [UREi] > 0. Why?

◮ Maturity mismatch in the household sector (counterpart of banks) ◮ Government with flow borrowing requirements (negative URE) ◮ My benchmark: “Ricardian view”(uniform rebate). Er still correct.

◮ If none of the gains are rebated: ENR

r

= EI

  • MPCi

UREi EI [ci]

  • Adrien Auclert (Stanford)

Redistribution Channel November 20, 2015 19 / 35

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SLIDE 63

Partial equilibrium: Er as sufficient statistic Aggregation

Focus on slope term

dC C ≃ MdY Y + dE h + EP dP P +

  • ENR

r

− σS

  • dr

◮ Next: go to data, find Er = CovI

  • MPCi, UREi

EI [ci]

  • < 0

◮ compare to σ using σ∗ = − Er

S

◮ But: usually, in household data EI [UREi] > 0. Why?

◮ Maturity mismatch in the household sector (counterpart of banks) ◮ Government with flow borrowing requirements (negative URE) ◮ My benchmark: “Ricardian view”(uniform rebate). Er still correct.

◮ If none of the gains are rebated: ENR

r

= EI

  • MPCi

UREi EI [ci]

  • ◮ ENR

r

− σS > 0?

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 19 / 35

slide-64
SLIDE 64

Partial equilibrium: Er as sufficient statistic Aggregation

Focus on slope term

dC C ≃ MdY Y + dE h + EP dP P +

  • ENR

r

− σS

  • dr

◮ Next: go to data, find Er = CovI

  • MPCi, UREi

EI [ci]

  • < 0

◮ compare to σ using σ∗ = − Er

S

◮ But: usually, in household data EI [UREi] > 0. Why?

◮ Maturity mismatch in the household sector (counterpart of banks) ◮ Government with flow borrowing requirements (negative URE) ◮ My benchmark: “Ricardian view”(uniform rebate). Er still correct.

◮ If none of the gains are rebated: ENR

r

= EI

  • MPCi

UREi EI [ci]

  • ◮ ENR

r

− σS > 0? “Interestingly [...] low rates could even hurt overall spending” Raghuram Rajan, November 2013

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 19 / 35

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SLIDE 65

Measuring Er

Outline

1

Partial equilibrium: Er as sufficient statistic Single agent, perfect foresight Incomplete markets Aggregation

2

Measuring Er

3

General equilibrium model

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 19 / 35

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SLIDE 66

Measuring Er

Map to data

  • 1. Construct a URE measure at the household level

UREi = Yi − Ci + Bi − Di

◮ Yi: income from all sources ◮ Ci: consumption (incl. durables, mtge paymts, excl. house purchase) ◮ Bi: maturing asset stocks (especially deposits) ◮ Di: maturing liability stocks (adjustable rate mortgages, cons. credit)

  • 2. Use a procedure to evaluate MPCi 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 Er, S, σ∗ = − Er

S and ENR r

Summary Statistics Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 20 / 35

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SLIDE 67

Measuring Er

Both surveys and methods show that Er < 0

.3 .4 .5 .6 .7 Average MPC in centile −5.67 .03 .26 .59 1.15 11.44 Normalized URE: centile mean

MPC vs URE: Italian data grouped by URE centile

−.2 .2 .4 .6 .8 Estimated MPC in group −1.03 [−0.54] 0.17 [0.13] 3.00 [1.40] Normalized URE: group mean [median]

MPC vs URE : CEX tax rebate estimation

⇒ Er = CovI

  • MPCi, UREi

EI [ci]

  • < 0

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 21 / 35

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SLIDE 68

Measuring Er

Italian data estimation

◮ Household-level information on MPC and URE: compute directly

  • Er =

CovI

  • MPCi, UREi

EI [ci]

  • S =

EI

  • (1 − MPCi)

ci EI [ci]

  • ENR

r

= EI

  • MPCi

UREi EI [ci]

  • Time Horizon

Annual Parameter Estimate 95% C.I. Redistribution elasticity

  • Er
  • 0.06

[-0.09; -0.04] Hicksian scaling factor

  • S

0.55 [0.53; 0.57] Equivalent EIS

  • σ∗ = −
  • Er
  • S

0.12 [0.06; 0.17] No-rebate elasticity

  • ENR

r

0.21 [0.17; 0.23]

All statistics computed using survey weights Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 22 / 35

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SLIDE 69

Measuring Er

CEX data estimation from JPS

◮ Run MPC estimation over J = 3 groups of URE and compute:

  • ENR

r

= EJ

  • MPCj

UREj EI [ci]

  • Er =

CovJ

  • MPCj, UREj

EI [ci]

  • S =

EJ

  • 1 − MPCj
  • Consumption measure

Food Parameter Estimate 95% C.I. Redistribution elasticity

  • Er
  • 0.24

[-0.42; -0.07] Hicksian scaling factor

  • S

0.82 [0.69; 0.95] Equivalent EIS

  • σ∗ = −
  • Er
  • S

0.30 [0.05; 0.54] No-rebate elasticity

  • ENR

r

  • 0.12

[-0.27; 0.02]

Confidence intervals are bootstrapped by resampling households 100 times with replacement Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 23 / 35

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SLIDE 70

General equilibrium model

Outline

1

Partial equilibrium: Er as sufficient statistic Single agent, perfect foresight Incomplete markets Aggregation

2

Measuring Er

3

General equilibrium model

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 23 / 35

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SLIDE 71

General equilibrium model

General equilibrium model

◮ Objectives

◮ Propose a rationale for sign and magnitude of Er 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

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SLIDE 72

General equilibrium model

Preferences and production

◮ Measure 1 of households i with GHH preferences:

E ∞

  • t=0
  • βi

t

t u

  • ci

t − v

  • ni

t

  • ◮ CES in net consumption σ, constant elasticity of labor supply ψ

◮ All uncertainty is purely idiosyncratic

◮ Idiosyncratic productivity process Πe (e′|e) ◮ Independent discount factor process Πβ (β′|β) ◮ Aggregate state s = (e, β) is in its stationary distribution

◮ Two-tiered production:

◮ Measure 1 of intermediate good firms, identical linear production

xj

t = Atlj t = At

  • i

ei

tni,j t di

◮ Final good Yt: aggregator of xj

t, elasticity ǫ

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 25 / 35

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SLIDE 73

General equilibrium model

Markets and government

◮ Incomplete markets: risk-free nominal bond + borrowing constraint ◮ Affine tax and transfer schedule on labor income alone:

Ptci

t = (1 − τ) Wtei tni t + PtTt + Λi t + Qt

  • δNΛi

t − Λi t+1

  • QtΛi

t+1 ≥ −DPt

◮ Perfectly competitive final good (Pt) and labor markets (Wt) ◮ Monopolistically competitive intermediate goods (Pj

t)

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 26 / 35

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SLIDE 74

General equilibrium model

Markets and government

◮ Incomplete markets: risk-free nominal bond + borrowing constraint ◮ Affine tax and transfer schedule on labor income alone:

Ptci

t = (1 − τ) Wtei tni t + PtTt + Λi t + Qt

  • δNΛi

t − Λi t+1

  • QtΛi

t+1 ≥ −DPt

◮ Perfectly competitive final good (Pt) and labor markets (Wt) ◮ Monopolistically competitive intermediate goods (Pj

t)

◮ Government collects all profits, runs a balanced budget with no debt

PtTt =

  • j
  • Pj

txj t − Wtlj t

  • dj + τ
  • i

Wtei

tni tdi

◮ No external supply of assets: market clearing

  • i QtΛi

t+1di = 0

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 26 / 35

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SLIDE 75

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 δN

◮ Constant term structure of interest rates

◮ → short and long-term assets span the same set of contingencies

◮ Unhedged interest rate exposures

URE i

t ≡ (1 − τ) Wt

Pt ei

tni t + Tt + Λi t

Pt − ci

t

vary with maturity structure, but are refinanced at constant R

◮ Change δN → change average duration of assets, leave all else equal ◮ Experiment: Calibrate δN to U.S. then set δN = 0: “only ARMs”

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 27 / 35

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SLIDE 76

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

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SLIDE 77

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 Πβ: patient (βP)4 = 0.97/imp. (βI)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 δN = 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

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SLIDE 78

General equilibrium model

Redistribution channel in the model

◮ For transitory monetary policy shock, can show:

dC C ≃ MdY Y + dE h

  • EY dY

Y

+EP dP P − S (σ∗ + σ) dr +T dY Y

Complementarity channel

Steady-state value

Details and compare to data

δN = 0.95 δN = 0

U.S. “Only ARMs”

Redistribution elasticity for r Er

−0.09

Hicksian scaling factor S

0.57

Equivalent EIS σ∗ = − Er

S

0.15

Income weighted MPC M

0.16

Earnings heterogeneity factor EY

−0.09

Redistribution elasticity for P EP

1.77

Consumption-labor compl. term T

0.46

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 29 / 35

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SLIDE 79

General equilibrium model

Redistribution channel in the model

◮ For transitory monetary policy shock, can show:

dC C ≃ MdY Y + dE h

  • EY dY

Y

+EP dP P − S (σ∗ + σ) dr +T dY Y

Complementarity channel

Steady-state value

Details and compare to data

δN = 0.95 δN = 0

U.S. “Only ARMs”

Redistribution elasticity for r Er

−0.09 −1.76

Hicksian scaling factor S

0.57

Equivalent EIS σ∗ = − Er

S

0.15 3

Income weighted MPC M

0.16

Earnings heterogeneity factor EY

−0.09

Redistribution elasticity for P EP

1.77

Consumption-labor compl. term T

0.46

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 29 / 35

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SLIDE 80

General equilibrium model

Sticky prices

◮ In a steady-state, suppose prices are fully sticky: Pt = Pt−1 ◮ Central bank stabilizes, nominal interest rate = steady-state R

◮ Replicates the flexible-price allocation

◮ Monetary policy shock: unexpectedly lowers the nominal rate

Rt = ρRt−1 + (1 − ρ) R − ǫt

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 30 / 35

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SLIDE 81

General equilibrium model

Sticky prices

◮ In a steady-state, suppose prices are fully sticky: Pt = Pt−1 ◮ Central bank stabilizes, nominal interest rate = steady-state R

◮ Replicates the flexible-price allocation

◮ Monetary policy shock: unexpectedly lowers the nominal rate

Rt = ρRt−1 + (1 − ρ) R − ǫt

◮ Fisher channel is shut down ◮ Full nonlinear solution keeping track of wealth distribution

◮ find sequence {wt} ensuring market clearing Ct = Yt

◮ Borrowing limits keep real value of payments next period fixed

Details Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 30 / 35

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SLIDE 82

General equilibrium model

Transitory monetary policy easing

Time in quarters

  • 1

1 2 3 4 5 6 7 8 9 10 Per cent deviation from steady-state

  • 0.4
  • 0.2

0.2 0.4 0.6 0.8 1 1.2 1.4 Transitory monetary policy shock (persistence=0) Real interest rate impulse Output response: US calibration Output response: representative agent t=0 predicted values from sufficient statistic Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 31 / 35

slide-83
SLIDE 83

General equilibrium model

Transitory monetary policy easing

Time in quarters

  • 1

1 2 3 4 5 6 7 8 9 10 Per cent deviation from steady-state

  • 0.4
  • 0.2

0.2 0.4 0.6 0.8 1 1.2 1.4 Transitory monetary policy shock (persistence=0) Real interest rate impulse Output response: US calibration Output response: Only ARMs Output response: representative agent t=0 predicted values from sufficient statistic Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 32 / 35

slide-84
SLIDE 84

General equilibrium model

Prolonged monetary policy easing

Time in quarters

  • 1

1 2 3 4 5 6 7 8 9 10 Per cent deviation from steady-state

  • 0.4
  • 0.2

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Persistent monetary policy shock (persistence=0.5) Real interest rate impulse Output response: US calibration Output response: Only ARMs Output response: representative agent Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 33 / 35

slide-85
SLIDE 85

General equilibrium model

Asymmetric effects

1-quarter change in real interest rate (basis points, annualized)

  • 500
  • 400
  • 300
  • 200
  • 100

100 200 300 400 500 Percentage change in output

  • 8
  • 6
  • 4
  • 2

2 4 6 8 Effect on output of a change in r (General Equilibrium) US benchmark calibration First-order approx. ARM-only calibration First-order approx. Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 34 / 35

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SLIDE 86

Conclusion

Conclusion

◮ Monetary policy redistributes:

◮ One reason why it affects aggregate consumption ◮ Likely to be the dominant one in ARM countries ◮ Sufficient statistics, Em = CovI

  • MPCi, Exposurei,m
  • , establish orders
  • f magnitude and discipline model calibrations

◮ Implications for policy:

◮ Capital gains can act against MPC-aligned redistribution ◮ The effects of monetary policy may vary (with Er) over the cycle Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 35 / 35

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SLIDE 87

Additional slides

Thank you!

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 36 / 35

slide-88
SLIDE 88

Additional slides

Additional wealth effects

◮ Introduce nominal assets:

Return ◮ price level {Pt} (perfectly foreseen) ◮ nominal holdings: {−1Bt+s}s≥0 (deposits, bonds, mortgage) ◮ Fisher equation for nominal term structure Qt+s = qt+s Pt

Pt+s

◮ Unexpected shock to {qt} as well as

◮ Price level {P0, P1 . . .} ◮ Real income stream {y0, y1 . . .} ◮ Real wage sequence {w0, w1 . . .}

◮ Write first-order change in consumption dc0, hours dn0, welfare dU using

MPC ≡ ∂c0 ∂y0 , MPN ≡ ∂n0 ∂y0 , ǫh

x0,pt ≡ ∂xh

∂pt pt x0 , x0 ∈ {c0, n0} pt ∈ {qt, wt}

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 37 / 35

slide-89
SLIDE 89

Additional slides

Consumption, hours and welfare response

Impulse response to the shock

To first order, dU ≃ Uc0dΩ and dc0 ≃ MPCdΩ + c0  

t≥0

ǫh

c0,qt

dqt qt +

  • t≥0

ǫh

c0,wt

dwt wt   dn0 ≃ MPNdΩ + n0  

t≥0

ǫh

n0,qt

dqt qt +

  • t≥0

ǫh

n0,wt

dwt wt   where dΩ =

  • t≥0

qt

  • yt + wtnt + (−1bt) +
  • −1Bt

Pt

  • − ct
  • −1UREt

dqt qt +

  • t≥0

(qtyt) dyt yt

  • Real unearned income change

+

  • t≥0

(qtwtnt) dwt wt

  • Real earned income change

−

  • t≥0

Qt

  • −1Bt

P0 dPt Pt

  • Revaluation of net nominal position

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 38 / 35

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SLIDE 90

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

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Additional slides

Johnson, Parker, Souleles (2006) tax rebates

◮ Sort all households into J quantiles of URE ◮ Run main estimating equation from JPS:

Ci,m,t+1 − Ci,m,t = αm + βXi,t +

J

  • j=1

MPCjRi,t+1QUREi,j + ui,t+1

◮ Ci,m,t: level of i’s consumption expenditure in month m and date t ◮ Xi,t: age and family composition ◮ Ri,t+1: dollar amount of the rebate receipt ◮ QUREi,j = 1 if household i ∈ interest rate exposure group MPCj

◮ Estimation of MPCj 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

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Additional slides

Datasets: summary statistics

SHIW 2010 CEX 2001 Variable mean n.s.d. mean n.s.d. Income from all sources (Yi, per year) 36,114 0.90 45,617 1.01 Consumption incl. mortgage payments (Ci, per year) 27,976 0.61 36,253 0.79 Deposits and maturing assets (Bi) 14,200 1.45 7,147 0.77 ARM mortgage liabilities and consumer credit (Di) 6,228 1.03 2,872 0.22 Unhedged interest rate exposure (UREi, per year) 16,110 1.92 13,639 1.27 Unhedged interest rate exposure (UREi, 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) “n.s.d” : normalized standard deviation, sdI

  • Xi

EI [Ci ]

  • for Xi = Yi , Ci , Bi , UREi and sdI (MPCi ) for MPC

Back Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 41 / 35

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SLIDE 93

Additional slides

Calibration (continued)

◮ Idiosyncratic productivity process: discretized AR(1)

log et = ρ log et−1 + σe

  • 1 − ρ2ǫt

ǫt ∼ N (0, 1)

◮ Lognormal stationary distribution of pre-tax earnings, var. σ2

e (1 + ψ)2

◮ Set σe (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

Cumulative population proportion 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Cumulative labor earnings proportion 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 PSID 2009 Pre-tax labor earnings distribution Model pre-tax labor earnings Model post-tax&transfer labor earnings Model post-tax&transfer net labor earnings Typical calibration (variance of log earnings=0.6) Perfect equality line

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 42 / 35

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Constrained agents and MPCs in steady state

Discretized income state (S) 1 2 3 4 5 6 7 8 9 10 Fraction of agents at the borrowing limit 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Patient Impatient Net financial asset position (% of annual per capita PCE)

  • 200
  • 180
  • 160
  • 140
  • 120
  • 100
  • 80
  • 60
  • 40
  • 20

MPC 0.05 0.1 0.15 0.2 0.25 0.3 Patient, low income (S=1) Patient, high income (S=7) Impatient, low income (S=1) Impatient, high income (S=7)

Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 43 / 35

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Redistribution elasticity Er in the model and in data

Asset/Liability duration in years 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Er

  • 1.8
  • 1.6
  • 1.4
  • 1.2
  • 1
  • 0.8
  • 0.6
  • 0.4
  • 0.2

Redistribution elasticity in model Benchmark calibration Italy: SHIW data US CEX: Food estimate US CEX: All nondurable Back Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 44 / 35

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Other moments

◮ Construct counterpart to QΛ: net interest-paying assets (Deposits,

IRAs and other assets minus all debts)

Mean sd P5 P25 Median P75 P95 P99

QΛ E[c]

PSID 2009 1.17 32.51

  • 28.42
  • 6.88

0.00 1.78 35.86 113.90 Model 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

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Transition after shocks

◮ Debt limit maintains next period real coupon payments fixed:

Dt = Qtd ⇔ λt+1 ≥ −d

◮ When Πt = 1, B.C. of agents at the borrowing limit:

ci

t = y i t−

  d + Qt Q ×

  • −D (1 − δN)
  • URE

   Steady-state value δN = 0.95 δN = 0

min

  • yi

0.413 0.413 d 0.413 7.455 URE −0.358 −7.400 (R − 1) D 0.055 0.055

Back Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 46 / 35

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Monetary policy and the redistribution channels

Monetary accomodation Real interest rate ↓ Aggregate demand ↑ Aggregate income ↑ Individual incomes ↑ Substitution Aggregate MPC

Standard New-Keynesian model (fully sticky prices) Back Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 47 / 35

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SLIDE 99

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Monetary policy and the redistribution channels

Monetary accomodation Real interest rate ↓ Aggregate demand ↑ Aggregate income ↑ Individual incomes ↑ Substitution Interest-rate exposure Aggregate MPC

Standard New-Keynesian model (fully sticky prices) Redistribution channels Back Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 47 / 35

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SLIDE 100

Additional slides

Monetary policy and the redistribution channels

Monetary accomodation Real interest rate ↓ Aggregate demand ↑ Aggregate income ↑ Individual incomes ↑ Substitution Interest-rate exposure Aggregate MPC Earnings heterogeneity

Standard New-Keynesian model (fully sticky prices) Redistribution channels Back Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 47 / 35

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SLIDE 101

Additional slides

Monetary policy and the redistribution channels

Monetary accomodation Real interest rate ↓ Aggregate demand ↑ Aggregate income ↑ Hours worked ↑ Individual incomes ↑ Substitution Interest-rate exposure Aggregate MPC Complementarity Earnings heterogeneity

Standard New-Keynesian model (fully sticky prices) Consumption/labor complementarities Redistribution channels Back Adrien Auclert (Stanford) Redistribution Channel November 20, 2015 47 / 35