The Risk Channel of Unconventional Monetary Policy Dejanir Silva - - PowerPoint PPT Presentation

The Risk Channel of Unconventional Monetary Policy

Dejanir Silva

UIUC dejanir@illinois.edu

November, 2017

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Dramatic change in central bank portfolio

• 500.00

1,000.00 1,500.00 2,000.00 2,500.00 3,000.00 3,500.00 4,000.00 4,500.00 5,000.00 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

USD Billions

Composition FED Balance Sheet:

Other Assets Agency and MBS Holdings Treasury Holdings

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Stimulus and potential side effect

Goal: stimulate economy Federal Reserve on objective of asset purchases ”... help to make broader financial conditions more accommodative through the purchase of longer-term securities.”

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Stimulus and potential side effect

Goal: stimulate economy Federal Reserve on objective of asset purchases ”... help to make broader financial conditions more accommodative through the purchase of longer-term securities.” Potential side effect: risk-taking BIS, commenting on central bank policy: ”Extraordinarily low interest rates and compressed risk premia once again pushed investors into riskier assets in their search for yield [...]”

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Stimulus and potential side effect

Goal: stimulate economy Federal Reserve on objective of asset purchases ”... help to make broader financial conditions more accommodative through the purchase of longer-term securities.” Potential side effect: risk-taking BIS, commenting on central bank policy: ”Extraordinarily low interest rates and compressed risk premia once again pushed investors into riskier assets in their search for yield [...]” Policy evaluation:

• Integrated view: effects on the real economy and on financial risk-taking

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What are the effects of unconventional monetary policy on financial markets and the real economy?

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What are the effects of unconventional monetary policy on financial markets and the real economy?

1) Heterogeneous Risk-Aversion 2) Limited Asset Market Participation

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What are the effects of unconventional monetary policy on financial markets and the real economy?

1) Heterogeneous Risk-Aversion

• Active traders: Savers more risk-averse than Bankers

2) Limited Asset Market Participation

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What are the effects of unconventional monetary policy on financial markets and the real economy?

1) Heterogeneous Risk-Aversion

• Active traders: Savers more risk-averse than Bankers

Drop in share of wealth of bankers Aggregate risk aversion Price of risky asset and investment

2) Limited Asset Market Participation

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What are the effects of unconventional monetary policy on financial markets and the real economy?

1) Heterogeneous Risk-Aversion

• Active traders: Savers more risk-averse than Bankers

Drop in share of wealth of bankers Aggregate risk aversion Price of risky asset and investment

2) Limited Asset Market Participation

• Passive traders who hold market portfolio

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What are the effects of unconventional monetary policy on financial markets and the real economy?

1) Heterogeneous Risk-Aversion

• Active traders: Savers more risk-averse than Bankers

Drop in share of wealth of bankers Aggregate risk aversion Price of risky asset and investment

2) Limited Asset Market Participation

• Passive traders who hold market portfolio

Asset purchases by the CB Net supply of risk to active traders Price of risky asset during crises

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Main findings

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Main findings

1 Output growth rate: Crises vs normal times

• Asset purchases ⇒ rise in output growth during crises
• Expectation of less severe crises ⇒ less output growth in normal times

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Main findings

1 Output growth rate: Crises vs normal times

• Asset purchases ⇒ rise in output growth during crises
• Expectation of less severe crises ⇒ less output growth in normal times

2 Risk concentration and probability of crises

• Asset purchases ⇒ fall in risk concentration and endogenous volatility
• Stationary distribution: Probability of future crises falls

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Main findings

1 Output growth rate: Crises vs normal times

• Asset purchases ⇒ rise in output growth during crises
• Expectation of less severe crises ⇒ less output growth in normal times

2 Risk concentration and probability of crises

• Asset purchases ⇒ fall in risk concentration and endogenous volatility
• Stationary distribution: Probability of future crises falls

3 Unwinding of asset purchases (exit strategies)

• Late exit ⇒ higher price of risky assets in the unwinding period
• Expectation of late exit ⇒ lower price of risky assets in crises

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Main findings

1 Output growth rate: Crises vs normal times

• Asset purchases ⇒ rise in output growth during crises
• Expectation of less severe crises ⇒ less output growth in normal times

2 Risk concentration and probability of crises

• Asset purchases ⇒ fall in risk concentration and endogenous volatility
• Stationary distribution: Probability of future crises falls

3 Unwinding of asset purchases (exit strategies)

• Late exit ⇒ higher price of risky assets in the unwinding period
• Expectation of late exit ⇒ lower price of risky assets in crises

4 Long-term bonds and term premium

• Trade-off between risk and term premium

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Related literature

• Large literature on unconventional monetary policy
• Theory: Del Negro et al. (2011), Curdia and Woodford (2011), Gertler and Karadi (2013),

Araujo et al. (2015), Bhatarai et al. (2014), Caballero and Farhi (2014)

• Empirics: Gagnon et al. (2011), Krishnamurthy and Vissing-Jorgensen (2011), Joyce et al.

(2012), D’Amico and King (2013), Greenwood and Vayanos (2014)

• Balance sheet channel:
• Holmstrom and Tirole (1997), Bernanke et al. (1999), Adrian et al. (2010), He and

Krishnamurthy (2013), Brunnermeier and Sannikov (2014), Di Tella (2015)

• Portfolio balance effects:
• Gurley and Shaw (1960), Tobin and Brainard (1963), Brunner and Meltzer (1973)
• Limited asset market participation:
• Grossman and Weiss (1983), Rotemberg (1984), Alvarez et al. (2002), Mankiw and Zeldes

(1991), Allen and Gale (1994), Basak and Cuoco (1998), Brav et al. (2002), Guvenen (2009), Vayanos and Villa (2009)

• Heterogeneous-investors asset pricing:
• Dumas (1989), Wang (1996), Chan and Kogan (2002), Garleanu and Pedersen (2011),

Longstaff and Wang (2012), Barro and Mollerus (2014), Drechsler et al. (2014), Garleanu and Panageas (2015)

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Outline

1

Environment

2

Balance sheet recession and the risk channel

3

Risk concentration and financial stability

4

Exit strategies

5

Long-term bonds

6

Effectiveness of asset purchases

7

Conclusion

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Outline

1

Environment

2

Balance sheet recession and the risk channel

3

Risk concentration and financial stability

4

Exit strategies

5

Long-term bonds

6

Effectiveness of asset purchases

7

Conclusion

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Overview of the environment:

• Continuous-time. Two goods: consumption and capital

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Overview of the environment:

• Continuous-time. Two goods: consumption and capital
• Firms produce final goods using capital
• Investment adjustment costs

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Overview of the environment:

• Continuous-time. Two goods: consumption and capital
• Firms produce final goods using capital
• Investment adjustment costs
• Active traders (bankers and savers) trade risky and riskless assets
• Heterogeneity: savers are more risk averse than bankers

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Overview of the environment:

• Continuous-time. Two goods: consumption and capital
• Firms produce final goods using capital
• Investment adjustment costs
• Active traders (bankers and savers) trade risky and riskless assets
• Heterogeneity: savers are more risk averse than bankers
• Passive traders hold market portfolio (no rebalancing)
• Consume dividends plus transfers from the central bank

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Overview of the environment:

• Continuous-time. Two goods: consumption and capital
• Firms produce final goods using capital
• Investment adjustment costs
• Active traders (bankers and savers) trade risky and riskless assets
• Heterogeneity: savers are more risk averse than bankers
• Passive traders hold market portfolio (no rebalancing)
• Consume dividends plus transfers from the central bank
• Central bank issues riskless liabilities and buy risky assets
• Rebates the proceeds to passive traders

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Firms

• Linear technology:

Yt = AKt

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Firms

• Linear technology:

Yt = AKt

• Law of motion of capital:

dKt Kt = gtdt + σdZt

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Firms

• Linear technology:

Yt = AKt

• Law of motion of capital:

dKt Kt = gtdt + σdZt

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Firms

• Linear technology:

Yt = AKt

• Law of motion of capital:

dKt Kt = gtdt + σdZt

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Firms

• Linear technology:

Yt = AKt

• Law of motion of capital:

dKt Kt = gtdt + σdZt

• Problem of the firm

St

• qtKt

= max

g

Et   ∞

t

πs πt (A − ι(gs)) Ks

• dividends

ds   (1)

where ι′(·), ι′′(·) > 0.

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Firms

• Linear technology:

Yt = AKt

• Law of motion of capital:

dKt Kt = gtdt + σdZt

• Problem of the firm

St

• qtKt

= max

g

Et   ∞

t

πs πt (A − ι(gs)) Ks

• dividends

ds   (1)

where ι′(·), ι′′(·) > 0.

8 / 36

Firms

• Linear technology:

Yt = AKt

• Law of motion of capital:

dKt Kt = gtdt + σdZt

• Problem of the firm

St

• qtKt

= max

g

Et   ∞

t

πs πt (A − ι(gs)) Ks

• dividends

ds   (1)

where ι′(·), ι′′(·) > 0.

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Firms

• Linear technology:

Yt = AKt

• Law of motion of capital:

dKt Kt = gtdt + σdZt

• Problem of the firm

St

• qtKt

= max

g

Et   ∞

t

πs πt (A − ι(gs)) Ks

• dividends

ds   (1)

where ι′(·), ι′′(·) > 0.

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Firms

• Linear technology:

Yt = AKt

• Law of motion of capital:

dKt Kt = gtdt + σdZt

• Problem of the firm

St

• qtKt

= max

g

Et   ∞

t

πs πt (A − ι(gs)) Ks

• dividends

ds   (1)

where ι′(·), ι′′(·) > 0.

• The SPD πt satisfies (determined in equilibrium):

dπt πt = − rt

• int. rate

dt − ηt

• mkt. price of risk

dZt

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Firms

• Linear technology:

Yt = AKt

• Law of motion of capital:

dKt Kt = gtdt + σdZt

• Problem of the firm

St

• qtKt

= max

g

Et   ∞

t

πs πt (A − ι(gs)) Ks

• dividends

ds   (1)

where ι′(·), ι′′(·) > 0.

• The SPD πt satisfies (determined in equilibrium):

dπt πt = − rt

• int. rate

dt − ηt

• mkt. price of risk

dZt

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Active traders

• Decision problem of active traders (bankers j = b, savers j = s):

Vj = max

(cj,αj) Uj(cj)

(2) subject to nj,t ≥ 0 and dnj,t nj,t =

• rt + αj,t(µR,t − rt) − cj,t

nj,t

• dt + αj,tσR,tdZt

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Active traders

• Decision problem of active traders (bankers j = b, savers j = s):

Vj = max

(cj,αj) Uj(cj)

(2) subject to nj,t ≥ 0 and dnj,t nj,t =

• rt + αj,t(µR,t − rt) − cj,t

nj,t

• dt + αj,tσR,tdZt

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Active traders

• Decision problem of active traders (bankers j = b, savers j = s):

Vj = max

(cj,αj) Uj(cj)

(3) subject to nj,t ≥ 0 and dnj,t nj,t =

• rt + αj,t(µR,t − rt) − cj,t

nj,t

• dt + αj,tσR,t

≡σj,t

dZt

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Active traders

• Decision problem of active traders (bankers j = b, savers j = s):

Vj = max

(cj,σj) Uj(cj)

(4) subject to nj,t ≥ 0 and dnj,t nj,t =

• rt + αj,t(µR,t − rt) − cj,t

nj,t

• dt + σj,tdZt

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Active traders

• Decision problem of active traders (bankers j = b, savers j = s):

Vj = max

(cj,σj) Uj(cj)

(5) subject to nj,t ≥ 0 and dnj,t nj,t =     rt + αj,tσR,t

≡σj,t

µR,t − rt σR,t

• ηt

− cj,t nj,t      dt + σj,tdZt

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Active traders

• Decision problem of active traders (bankers j = b, savers j = s):

Vj = max

(cj,σj) Uj(cj)

(6) subject to nj,t ≥ 0 and dnj,t nj,t =

• rt + σj,tηt − cj,t

nj,t

• dt + σj,tdZt

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Active traders

• Decision problem of active traders (bankers j = b, savers j = s):

Vj = max

(cj,σj) Uj(cj)

(6) subject to nj,t ≥ 0 and dnj,t nj,t =

• rt + σj,tηt − cj,t

nj,t

• dt + σj,tdZt
• Preferences: continuous-time EZ
• EIS ψ > 1 and risk aversion γj
• Savers are more risk averse than bankers: γs > 1 > γb

Empirical studies on heterogeneous risk aversion 9 / 36

Active traders

• Decision problem of active traders (bankers j = b, savers j = s):

Vj = max

(cj,σj) Uj(cj)

(6) subject to nj,t ≥ 0 and dnj,t nj,t =

• rt + σj,tηt − cj,t

nj,t

• dt + σj,tdZt
• Preferences: continuous-time EZ
• EIS ψ > 1 and risk aversion γj
• Savers are more risk averse than bankers: γs > 1 > γb

Empirical studies on heterogeneous risk aversion

• Mortality risk ⇒ stationary distribution

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Risk Concentration and Balance sheets

Proposition (Risk Concentration)

Suppose γs > γb, γs − γb small, then σb,t − σs,t > 0.

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Risk Concentration and Balance sheets

Proposition (Risk Concentration)

Suppose γs > γb, γs − γb small, then σb,t − σs,t > 0.

Riskless liability

Risky Claims

Riskless asset

Net Worth

Bankers Savers

Net Worth Risky Claims

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Passive Traders and the Central Bank

• Passive traders invest on market portfolio ⇒ np,t = αSt

cp,t = αDt

• dividends

+ Tt

• transfers

(7)

Evidence on passive behavior/limited participation 11 / 36

Passive Traders and the Central Bank

• Passive traders invest on market portfolio ⇒ np,t = αSt

cp,t = αDt

• dividends

+ Tt

• transfers

(7)

Evidence on passive behavior/limited participation

• Central bank is subject to No-Ponzi condition and

dncb,t ncb,t =

• rt + σcb,tηt − Tt

ncb,t

• dt + σcb,tdZt

(8)

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Passive Traders and the Central Bank

• Passive traders invest on market portfolio ⇒ np,t = αSt

cp,t = αDt

• dividends

+ Tt

• transfers

(7)

Evidence on passive behavior/limited participation

• Central bank is subject to No-Ponzi condition and

dncb,t ncb,t =

• rt + σcb,tηt − Tt

ncb,t

• dt + σcb,tdZt

(8)

11 / 36

Passive Traders and the Central Bank

• Passive traders invest on market portfolio ⇒ np,t = αSt

cp,t = αDt

• dividends

+ Tt

• transfers

(7)

Evidence on passive behavior/limited participation

• Central bank is subject to No-Ponzi condition and

dncb,t ncb,t =

• rt + σcb,tηt − Tt

ncb,t

• dt + σcb,tdZt

(8)

11 / 36

Passive Traders and the Central Bank

• Passive traders invest on market portfolio ⇒ np,t = αSt

cp,t = αDt

• dividends

+ Tt

• transfers

(7)

Evidence on passive behavior/limited participation

• Central bank is subject to No-Ponzi condition and

dncb,t ncb,t =

• rt + σcb,tηt − Tt

ncb,t

• dt + σcb,tdZt

(8)

11 / 36

Passive Traders and the Central Bank

• Passive traders invest on market portfolio ⇒ np,t = αSt

cp,t = αDt

• dividends

+ Tt

• transfers

(7)

Evidence on passive behavior/limited participation

• Central bank is subject to No-Ponzi condition and

dncb,t ncb,t =

• rt + σcb,tηt − Tt

ncb,t

• dt + σcb,tdZt

(8) (σcb,t, Tt) determined by policy rules σcb,t = σcb(xt, wt); Tt = T(xt, wt)

where (xt, wt) is the vector of state variables.

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Aggregate State Variables and Market Clearing

Define (xt, wt) as follows xt = nb,t nb,t + ns,t wt = ncb,t nb,t + ns,t + ncb,t

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Aggregate State Variables and Market Clearing

Define (xt, wt) as follows xt = nb,t nb,t + ns,t wt = ncb,t nb,t + ns,t + ncb,t

12 / 36

Aggregate State Variables and Market Clearing

Define (xt, wt) as follows xt = nb,t nb,t + ns,t wt = ncb,t nb,t + ns,t + ncb,t

12 / 36

Aggregate State Variables and Market Clearing

Define (xt, wt) as follows xt = nb,t nb,t + ns,t wt = ncb,t nb,t + ns,t + ncb,t Market clearing condition for risk: xtσb,t + (1 − xt)σs,t = ωr

t(σ + σq,t)

• net supply of risk

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Aggregate State Variables and Market Clearing

Define (xt, wt) as follows xt = nb,t nb,t + ns,t wt = ncb,t nb,t + ns,t + ncb,t Market clearing condition for risk: xtσb,t + (1 − xt)σs,t = ωr

t(σ + σq,t)

• net supply of risk

12 / 36

Aggregate State Variables and Market Clearing

Define (xt, wt) as follows xt = nb,t nb,t + ns,t wt = ncb,t nb,t + ns,t + ncb,t Market clearing condition for risk: xtσb,t + (1 − xt)σs,t = ωr

t(σ + σq,t)

• net supply of risk

ωr

t ≡

share of risk held by active traders share of wealth held by active traders

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Aggregate State Variables and Market Clearing

Define (xt, wt) as follows xt = nb,t nb,t + ns,t wt = ncb,t nb,t + ns,t + ncb,t Market clearing condition for risk: xtσb,t + (1 − xt)σs,t = ωr

t(σ + σq,t)

• net supply of risk

ωr

t ≡

share of risk held by active traders share of wealth held by active traders Market clearing condition for consumption: xt ˆ cb,t + (1 − xt)ˆ cs,t = ωd

t

A − ι(gt) qt

12 / 36

Aggregate State Variables and Market Clearing

Define (xt, wt) as follows xt = nb,t nb,t + ns,t wt = ncb,t nb,t + ns,t + ncb,t Market clearing condition for risk: xtσb,t + (1 − xt)σs,t = ωr

t(σ + σq,t)

• net supply of risk

ωr

t ≡

share of risk held by active traders share of wealth held by active traders Market clearing condition for consumption: xt ˆ cb,t + (1 − xt)ˆ cs,t = ωd

t

A − ι(gt) qt

12 / 36

Aggregate State Variables and Market Clearing

Define (xt, wt) as follows xt = nb,t nb,t + ns,t wt = ncb,t nb,t + ns,t + ncb,t Market clearing condition for risk: xtσb,t + (1 − xt)σs,t = ωr

t(σ + σq,t)

• net supply of risk

ωr

t ≡

share of risk held by active traders share of wealth held by active traders Market clearing condition for consumption: xt ˆ cb,t + (1 − xt)ˆ cs,t = ωd

t

A − ι(gt) qt ωd

t ≡ share of dividends consumed by active traders

share of wealth held by active traders

Definition equilibrium Definition (ωr

t , ωd t )

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Unconventional Monetary Policy: Policy Rule

0.2 0.4 0.6 0.8 1

x

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 1-ωr

Banker’s share of wealth: xt

• Strong balance sheet ⇒ ωr = 1
• Weak balance sheet ⇒ ωr < 1

Unconventional ”Greenspan’s put”

• CB intervene in bad times

Transfers/low values of w 13 / 36

Outline

1

Environment

2

Balance sheet recession and the risk channel

3

Risk concentration and financial stability

4

Exit strategies

5

Long-term bonds

6

Effectiveness of asset purchases

7

Conclusion

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Two benchmarks

1) Homogeneous risk-aversion (γb = γs):

• No risk concentration

σb,t = σs,t

• Balanced growth path
• No balance sheet recession

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Two benchmarks

1) Homogeneous risk-aversion (γb = γs):

• No risk concentration

σb,t = σs,t

• Balanced growth path
• No balance sheet recession

2) Full participation benchmark:

No passive traders. Fix initial (σcb, T) and consider (σ∗

cb, T ∗).

• Savers exactly offset policy change: σ∗

s,tn∗ s,t − σs,tns,t = −

• σ∗

cb,tn∗ cb,t − σcb,tncb,t

• Neutrality result: no changes in consumption, prices, and investment
• Modigliani-Miller / Ricardian Equivalance type of result (see Wallace (1981)).

14 / 36

Net worth multipliers and demand for risk

Net worth multipliers: Vb(nb,t; xt, wt) = (ζtnb,t)1−γb 1 − γb Vs(ns,t; xt, wt) = (ξtns,t)1−γs 1 − γs

• Net worth multiplier ζt(xt, wt) (determined in equilibrium)

dζt ζt = µζ,tdt + σζ,tdZt

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Net worth multipliers and demand for risk

Net worth multipliers: Vb(nb,t; xt, wt) = (ζtnb,t)1−γb 1 − γb Vs(ns,t; xt, wt) = (ξtns,t)1−γs 1 − γs

• Net worth multiplier ζt(xt, wt) (determined in equilibrium)

dζt ζt = µζ,tdt + σζ,tdZt

15 / 36

Net worth multipliers and demand for risk

Net worth multipliers: Vb(nb,t; xt, wt) = (ζtnb,t)1−γb 1 − γb Vs(ns,t; xt, wt) = (ξtns,t)1−γs 1 − γs

• Net worth multiplier ζt(xt, wt) (determined in equilibrium)

dζt ζt = µζ,tdt + σζ,tdZt Demand for risk: σb,t = ηt γb

• myopic

+ 1 − γb γb σζ,t

• hedging

;

15 / 36

Net worth multipliers and demand for risk

Net worth multipliers: Vb(nb,t; xt, wt) = (ζtnb,t)1−γb 1 − γb Vs(ns,t; xt, wt) = (ξtns,t)1−γs 1 − γs

• Net worth multiplier ζt(xt, wt) (determined in equilibrium)

dζt ζt = µζ,tdt + σζ,tdZt Demand for risk: σb,t = ηt γb

• myopic

+ 1 − γb γb σζ,t

• hedging

;

• Myopic demand: current returns

15 / 36

Net worth multipliers and demand for risk

Net worth multipliers: Vb(nb,t; xt, wt) = (ζtnb,t)1−γb 1 − γb Vs(ns,t; xt, wt) = (ξtns,t)1−γs 1 − γs

• Net worth multiplier ζt(xt, wt) (determined in equilibrium)

dζt ζt = µζ,tdt + σζ,tdZt Demand for risk: σb,t = ηt γb

• myopic

+ 1 − γb γb σζ,t

• hedging

;

• Myopic demand: current returns
• Hedging demand: cyclicality of returns

15 / 36

Market price of risk

ηt = γt

• agg. risk aversion

     ωr

t(σ + σq,t)

• net supply of risk

−

• xt

1 − γb γb σζ,t + (1 − xt)1 − γs γs σξ,t

• avg. hedging demand

     where γt ≡ xt γb + 1 − xt γs −1

16 / 36

Market price of risk

ηt = γt

• agg. risk aversion

     ωr

t(σ + σq,t)

• net supply of risk

−

• xt

1 − γb γb σζ,t + (1 − xt)1 − γs γs σξ,t

• avg. hedging demand

     where γt ≡ xt γb + 1 − xt γs −1

16 / 36

Market price of risk

ηt = γt

• agg. risk aversion

     ωr

t(σ + σq,t)

• net supply of risk

−

• xt

1 − γb γb σζ,t + (1 − xt)1 − γs γs σξ,t

• avg. hedging demand

     where γt ≡ xt γb + 1 − xt γs −1

Risky Claims

Deposits

Risky Claims Net Worth

Bankers Savers

Net Worth Risky Claims

Riskless liability Riskless asset

16 / 36

Market price of risk

ηt = γt

• agg. risk aversion

     ωr

t(σ + σq,t)

• net supply of risk

−

• xt

1 − γb γb σζ,t + (1 − xt)1 − γs γs σξ,t

• avg. hedging demand

     where γt ≡ xt γb + 1 − xt γs −1

Risky Claims

Riskless liability

Risky Claims Net Worth

Bankers Savers

Net Worth

Riskless asset

16 / 36

Market price of risk

ηt = γt

• agg. risk aversion

     ωr

t(σ + σq,t)

• net supply of risk

−

• xt

1 − γb γb σζ,t + (1 − xt)1 − γs γs σξ,t

• avg. hedging demand

     where γt ≡ xt γb + 1 − xt γs −1

Risky Claims Net Worth

Bankers Savers

Net Worth

Riskless liability Riskless asset

Risky Claims 16 / 36

Market price of risk

ηt = γt

• agg. risk aversion

     ωr

t(σ + σq,t)

• net supply of risk

−

• xt

1 − γb γb σζ,t + (1 − xt)1 − γs γs σξ,t

• avg. hedging demand

     where γt ≡ xt γb + 1 − xt γs −1

Risky Claims Net Worth

Bankers Savers

Net Worth

Riskless liability Riskless asset

Risky Claims 16 / 36

Market price of risk

ηt = γt

• agg. risk aversion

     ωr

t(σ + σq,t)

• net supply of risk

−

• xt

1 − γb γb σζ,t + (1 − xt)1 − γs γs σξ,t

• avg. hedging demand

     where γt ≡ xt γb + 1 − xt γs −1

Risky Claims Net Worth

Bankers Savers

Net Worth

Riskless liability Riskless asset

Risky Claims 16 / 36

Balance sheet recession

qt = A − ι(gt) rt + (σ + σq,t)ηt − µS,t ι′(gt) = qt

17 / 36

Balance sheet recession

qt = A − ι(gt) rt + (σ + σq,t)ηt − µS,t ι′(gt) = qt

17 / 36

Balance sheet recession

qt = A − ι(gt) rt + (σ + σq,t)ηt − µS,t ι′(gt) = qt

17 / 36

Balance sheet recession

qt = A − ι(gt) rt + (σ + σq,t)ηt − µS,t ι′(gt) = qt

0.2 0.4 0.6 0.8 1 x 0.7 0.75 0.8 0.85 0.9 0.95 log(q) Price of capital 0.2 0.4 0.6 0.8 1 x 0.2 0.4 0.6 0.8 1 η Market price of risk

Numerical solution 17 / 36

Balance sheet recession

qt = A − ι(gt) rt + (σ + σq,t)ηt − µS,t ι′(gt) = qt

0.2 0.4 0.6 0.8 1 x 0.7 0.75 0.8 0.85 0.9 0.95 log(q) Price of capital 0.2 0.4 0.6 0.8 1 x 0.2 0.4 0.6 0.8 1 η Market price of risk Laissez-faire Central bank

Numerical solution 17 / 36

Effect on Interest Rates

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x

0.5 1 1.5 2 2.5 3

r Interest rate

Weak balance sheet of bankers:

• High aggregate risk aversion
• Precautionary savings

18 / 36

Effect on Interest Rates

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x

0.5 1 1.5 2 2.5 3

r Interest rate

Weak balance sheet of bankers:

• High aggregate risk aversion
• Precautionary savings

Effect of asset purchases:

• Precautionary savings
• Intertemporal substitution

18 / 36

Taking stock: crises vs normal times

Balance sheet recession

• Weak balance sheet of bankers ⇒ high risk premium
• High risk premium ⇒ low price of risky asset
• EIS > 1 important for this result

19 / 36

Taking stock: crises vs normal times

Balance sheet recession

• Weak balance sheet of bankers ⇒ high risk premium
• High risk premium ⇒ low price of risky asset
• EIS > 1 important for this result

Unconventional monetary policy

• Asset purchases ⇒ drop in market price of risk / rise in interest rates
• Crises ⇒ risk premium dominates
• Normal times ⇒ interest rate dominates

19 / 36

Outline

1

Environment

2

Balance sheet recession and the risk channel

3

Risk concentration and financial stability

4

Exit strategies

5

Long-term bonds

6

Effectiveness of asset purchases

7

Conclusion

19 / 36

Risk Concentration and Financial Stability

So far:

• Effect on crises and normal times
• What about probability of crises?
• Concerns about reach-for-yield

20 / 36

Risk Concentration and Financial Stability

So far:

• Effect on crises and normal times
• What about probability of crises?
• Concerns about reach-for-yield

Endogenous risk

• Concentration of risk on bankers is endogenous
• Risk concentration ⇒ endogenous volatility
• Endogenous volatility ⇒ stationary distribution

20 / 36

Myopic and Hedging Demands

σb,t = ηt γb

• myopic

+ 1 − γb γb σζ,t

• hedging

;

21 / 36

Myopic and Hedging Demands

σb,t = ηt γb

• myopic

+ 1 − γb γb σζ,t

• hedging

;

21 / 36

Myopic and Hedging Demands

σb,t = ηt γb

• myopic

+ 1 − γb γb σζ,t

• hedging

;

21 / 36

Myopic and Hedging Demands

σb,t = ηt γb

• myopic

+ 1 − γb γb σζ,t

• hedging

;

21 / 36

Myopic and Hedging Demands

σb,t = ηt γb

• myopic

+ 1 − γb γb σζ,t

• hedging

;

• Sensitivity to ηt: decreasing in γb.

0.2 0.4 0.6 0.8 1

x

5 10 15

σb / (σ+σq) Leverage

0.2 0.4 0.6 0.8 1

x

5 10 15

Myopic component Myopic component

0.2 0.4 0.6 0.8 1

x

• 3.5
• 3
• 2.5
• 2
• 1.5
• 1
• 0.5

Hedging component Hedging component

21 / 36

Myopic and Hedging Demands

σb,t = ηt γb

• myopic

+ 1 − γb γb σζ,t

• hedging

;

• Sensitivity to ηt: decreasing in γb.
• γb < 1, σζ,t < 0 ⇒ negative hedging dem.

0.2 0.4 0.6 0.8 1

x

5 10 15

σb / (σ+σq) Leverage

0.2 0.4 0.6 0.8 1

x

5 10 15

Myopic component Myopic component

0.2 0.4 0.6 0.8 1

x

• 3.5
• 3
• 2.5
• 2
• 1.5
• 1
• 0.5

Hedging component Hedging component

21 / 36

UMP and Risk Concentration

σb,t = ηt γb + 1 − γb γb σζ,t; σs,t = ηt γs + 1 − γs γs σξ,t;

0.2 0.4 0.6 0.8 1

x

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

σb - σs Risk concentration

0.2 0.4 0.6 0.8 1

x

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Myopic component Myopic component

0.2 0.4 0.6 0.8 1

x

• 0.25
• 0.2
• 0.15
• 0.1
• 0.05

Hedgind component Hedging component

22 / 36

Hedging and return-sensitivity effects

Two opposing forces:

UMP reduces counter-cyclicality

• f returns

Bankers increase hedging demand Risk more concentrated on bankers (hedging)

23 / 36

Hedging and return-sensitivity effects

Two opposing forces:

UMP reduces counter-cyclicality

• f returns

Bankers increase hedging demand Risk more concentrated on bankers (hedging) Risk less concentrated on bankers (return-sensitivity) Bankers reduce myopic demand UMP reduces current returns

23 / 36

Hedging and return-sensitivity effects

Two opposing forces:

UMP reduces counter-cyclicality

• f returns

Bankers increase hedging demand Risk more concentrated on bankers (hedging) Risk less concentrated on bankers (return-sensitivity) Bankers reduce myopic demand UMP reduces current returns

Why does risk concentration fall? (intuition)

• Hedging effect relies on drop of endogenous volatility
• If hedging effect dominates ⇒ increase in risk concentration
• Endogenous volatility would increase: contradiction

23 / 36

Endogenous volatility

σq,t = qx,t qt σx,t + qw,t qt σw,t σx,t = xt(1 − xt) (σb,t − σs,t)

• risk concentration

24 / 36

Endogenous volatility

σq,t = qx,t qt σx,t + qw,t qt σw,t σx,t = xt(1 − xt) (σb,t − σs,t)

• risk concentration

24 / 36

Endogenous volatility

σq,t = qx,t qt σx,t + qw,t qt σw,t σx,t = xt(1 − xt) (σb,t − σs,t)

• risk concentration

24 / 36

Endogenous volatility

σq,t = qx,t qt σx,t + qw,t qt σw,t σx,t = xt(1 − xt) (σb,t − σs,t)

• risk concentration

0.2 0.4 0.6 0.8 1

x

0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02

σq Endogenous Volatility

0.2 0.4 0.6 0.8 1

x

0.2 0.4 0.6 0.8 1 1.2 1.4

σb-σs Risk Concentration

24 / 36

Endogenous volatility

σq,t = qx,t qt σx,t + qw,t qt σw,t σx,t = xt(1 − xt) (σb,t − σs,t)

• risk concentration

0.2 0.4 0.6 0.8 1

x

0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02

σq Endogenous Volatility

0.2 0.4 0.6 0.8 1

x

0.2 0.4 0.6 0.8 1 1.2 1.4

σb-σs Risk Concentration Laissez-faire Central bank

24 / 36

Stationary Distribution and Tail risk

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

g (%) PDF

Stationary distribution for gt:

• Negative skewness

25 / 36

Stationary Distribution and Tail risk

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

g (%) PDF

Stationary distribution for gt:

• Negative skewness
• Positive shocks = negative shocks

25 / 36

Stationary Distribution and Tail risk

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

g (%) PDF

Stationary distribution for gt:

• Negative skewness
• Positive shocks = negative shocks
• Suppose g above average
• Positive shock has small effect
• Small difference in propensity to

hold risk

25 / 36

Stationary Distribution and Tail risk

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

g (%) PDF

Stationary distribution for gt:

• Negative skewness
• Positive shocks = negative shocks
• Suppose g above average
• Positive shock has small effect
• Small difference in propensity to

hold risk

• Suppose g below average
• Negative shock has large effect
• Large difference in propensity to

hold risk

25 / 36

UMP and Financial Stability

0.5 1 1.5 2 2.5 3

number of std. deviations below the mean

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

probability

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

g (%) PDF

Laissez-faire Central bank

26 / 36

Taking stock: financial stability effects

Laissez-faire

• Risk concentration ⇒ endogenous volatility
• Stationary distribution ⇒ negative skewness

27 / 36

Taking stock: financial stability effects

Laissez-faire

• Risk concentration ⇒ endogenous volatility
• Stationary distribution ⇒ negative skewness

Unconventional monetary policy

• Two effects on risk-taking
• Hedging effect (reach-for-yield)
• Return-sensitivity effect
• Risk concentration falls ⇒ endogenous volatility falls
• Stability vs growth trade-off
• Tail risk falls
• Average output growth rate falls

27 / 36

Outline

1

Environment

2

Balance sheet recession and the risk channel

3

Risk concentration and financial stability

4

Exit strategies

5

Long-term bonds

6

Effectiveness of asset purchases

7

Conclusion

27 / 36

Exit strategies

Unwinding asset purchases

• Effect of selling assets in the market
• Expectation (communication) of central bank policy matters

28 / 36

Exit strategies

Unwinding asset purchases

• Effect of selling assets in the market
• Expectation (communication) of central bank policy matters

Early vs late exit

• Early exit: aggressive policy of selling assets
• Late exit: sale of assets smoothed over longer period
• Important: state-contingent exit

28 / 36

Exit strategies: policy rules

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x

0.05 0.1 0.15 0.2 0.25 0.3 0.35

1-ωr Policy rules

Early Late

Start unwinding at point:

• Early exit strategy: x = 0.2.
• Late exit strategy: x = 0.4.

29 / 36

Exit strategies

0.2 0.4 0.6 0.8 1

x

• 1
• 0.5

0.5 1 1.5

∆ η (%) Market price of risk Early minus Late

30 / 36

Exit strategies

0.2 0.4 0.6 0.8 1

x

• 5

5 10 15 20 25 30 35

∆ log(q) (bp) Price of capital

0.2 0.4 0.6 0.8 1

x

• 1
• 0.5

0.5 1 1.5

∆ η (%) Market price of risk Early minus Late

30 / 36

Expectation effects of exit strategies

Expectation of early exit:

• Central bank promises “fire sale” after good shock
• Returns are more procyclical under early exit
• Procyclicality of returns ⇒ rise in hedging demand for risk
• Market price of risk falls

31 / 36

Expectation effects of exit strategies

Expectation of early exit:

• Central bank promises “fire sale” after good shock
• Returns are more procyclical under early exit
• Procyclicality of returns ⇒ rise in hedging demand for risk
• Market price of risk falls

Effect on normal times

• Early exit ⇒ increase in market price of risk outside crises
• Weaker intertemporal substitution effect
• Higher asset prices in normal times

31 / 36

Outline

1

Environment

2

Balance sheet recession and the risk channel

3

Risk concentration and financial stability

4

Exit strategies

5

Long-term bonds

6

Effectiveness of asset purchases

7

Conclusion

31 / 36

Long-term bonds and term premium

Risky assets vs long-term bonds

• Purchases of risky assets ⇒ price of long-term bonds
• Effects on term structure of interest rates

32 / 36

Long-term bonds and term premium

Risky assets vs long-term bonds

• Purchases of risky assets ⇒ price of long-term bonds
• Effects on term structure of interest rates

Long-term bond

• Decaying coupon: e−δbt (δb controls duration)
• Term premium ⇒ average of term premium on zero coupon bonds
• Parsimonious way of capturing effect on term structure

32 / 36

Long-term bonds and term premium

yt = Et ∞

t

δbe−δb(s−t)rsds

• avg. expected interest rate

+ ∞

t

(s − t)δ2

be−δb(s−t)τt,sds

• avg. term premium

0.2 0.4 0.6 0.8 1

x

• 50

50 100 150 200 250

yield (basis points) Yield of long-term bond

0.2 0.4 0.6 0.8 1

x

• 50

50 100 150 200 250

average interest rate (basis points) Average Expected Interest Rate

0.2 0.4 0.6 0.8 1

x

• 70
• 60
• 50
• 40
• 30
• 20
• 10

10

term premium (basis points) Average Term premium 33 / 36

Outline

1

Environment

2

Balance sheet recession and the risk channel

3

Risk concentration and financial stability

4

Exit strategies

5

Long-term bonds

6

Effectiveness of asset purchases

7

Conclusion

33 / 36

Effectiveness of Unconventional Monetary Policy

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x

0.1 0.2 0.3 0.4 0.5 0.6

η Price of risk

ωr = 1.0 ωr = 0.9 ωr = 0.8 ωr = 0.7 ωr = 0.6

Flat policy rule:

• ωr = ωr
• No state dependency coming from

policy.

34 / 36

Effectiveness of Unconventional Monetary Policy

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x

0.1 0.2 0.3 0.4 0.5 0.6

η Price of risk

ωr = 1.0 ωr = 0.9 ωr = 0.8 ωr = 0.7 ωr = 0.6

Flat policy rule:

• ωr = ωr
• No state dependency coming from

policy. State-dependency:

• Policy more effective when banks

undercapitalized.

• Demand for risk less elastic in

those states.

34 / 36

Effectiveness of Asset Purchases

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x

0.08 0.1 0.12 0.14 0.16 0.18 0.2

|∆ η| / η Price of risk (semi-elasticity)

ωr: 1.0 to 0.9 ωr: 0.9 to 0.8 ωr: 0.8 to 0.7 ωr: 0.7 to 0.6

Non-linear effects

• Mg. effect increases with scale
• Endogenous vol ⇒ amplification
• Estimates may understate effect of

large interventions.

35 / 36

Effectiveness of Asset Purchases

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x

0.08 0.1 0.12 0.14 0.16 0.18 0.2

|∆ η| / η Price of risk (semi-elasticity)

ωr: 1.0 to 0.9 ωr: 0.9 to 0.8 ωr: 0.8 to 0.7 ωr: 0.7 to 0.6

Non-linear effects

• Mg. effect increases with scale
• Endogenous vol ⇒ amplification
• Estimates may understate effect of

large interventions. Intuition

• High volatility ⇒ hedging
• Hedging dampens effect on risk

concentration

• Smaller reduction in volatility

35 / 36

Outline

1

Environment

2

Balance sheet recession and the risk channel

3

Risk concentration and financial stability

4

Exit strategies

5

Long-term bonds

6

Effectiveness of asset purchases

7

Conclusion

35 / 36

Conclusion

This paper:

• Effects of UMP on asset prices, growth, and financial stability

Effects of asset purchases:

• Less severe crises ⇒ less growth in normal times
• Endogenous volatility and probability of crises fall
• Expectation of late exit ⇒ adverse effect on prices
• Trade-off between risk and term premium

Next steps:

• Optimal policy
• Quantifying different channels
• International aspects of central bank balance sheet

36 / 36

Thanks.

36 / 36

Equilibrium

An equilibrium is a set of stochastic process for prices (r, η, π, S), quantities (g, cb, cs, cp, σb, σs) and government policy (σcb, T) such that i) g solves problem (1) given π. ii) (cj, σj) solves (6), given (r, η). iii) cp satisfies (7) given (Y , T). iv) (σcb, {Tj}) satisfies (8) given (r, η). v) Markets clear: cb,t + cs,t + cp,t = Yt − ι(gt)Kt nb,t + ns,t + np,t + ncb,t = St nb,tσb,t + ns,tσs,t + np,tσp,t + ncb,tσcb,t = σS,tSt

Aggregate State Variables and Market Clearing 36 / 36

Definition of ωr(x, w) and ωd(x, w)

• ωr(x, w) is defined as

ωr(x, w) ≡ 1 − wσcb(x,w)

σ+σq(x,w)

1 − w

• ωd(x, w) is defined as

ωd(x, w) ≡ 1 − wq(x,w) ˆ

T(x,w) A−ι(g(x,w))

1 − w

Aggregate State Variables and Market Clearing 36 / 36

Homogeneous preferences benchmark

Homogeneous risk tolerances: Suppose σcb,t = Tj,t = ncb,t = 0. If γb = γs ≡ γ and nb,0 = ns,0, then

1 Market price of risk and risk exposures:

ηt = γσ; σb,t = σs,t = σ

2 Growth rate and the price of capital:

αA − ι(gt) pt = ρ − (1 − ψ−1)

• gt − γσ2

2

• ;

ι′(gt) = pt

3 Interest rate and consumption-wealth ratios:

rt = ρ+ψ−1gt−(1+ψ−1)γσ2 2 ; ˆ cb,t = ˆ cs,t = ρ−(1−ψ−1)

• gt − γσ2

2

• Two dimensions of heterogeneity

36 / 36

Two dimensions of heterogeneity (ctd)

Full participation benchmark: Suppose Tw = 0, α = 1, and fix an initial policy rule (σcb, Tb, Ts). Consider (σ∗

cb, T ∗ b , T ∗ s ) such that Tj,0 = T ∗ j,0 (using initial prices).

1 Prices, consumption, and investment do not change:

(r∗, η∗, S∗, c∗

b, c∗ s , g∗) = (r, η, S, cb, cs, g)

2 Investors exactly offset the portfolio of the central bank:

σ∗

j,tn∗ j,t = σj,tnj,t −

• σ∗

Tj,t − σTj,t

• (9)

where dTj,t = µTj,tdt + σTj,tdZt and σTb,t + σTs,t = σcb,tncb,t; σ∗

Tb,t + σ∗ Ts,t = σ∗ cb,tn∗ cb,t

Two dimensions of heterogeneity 36 / 36

Numerical solution

1 Compute q(x, w) using the condition:

xρψζ(x, w)1−ψ + (1 − x)ρψξ(x, w)1−ψ = ωd(x, w)αA − ι(g(q(x, w))) q(x, w)

2 Compute (σx, σw). Applying Ito’s lemma, compute (σq,t, σζ,t, σξ,t)

σq,t = qx,t qt σx,t + qw,t qt σw,t;

3 Compute ηt and, given ηt, compute (µx,t, µw,t). 4 Applying Ito’s lemma, compute (µq,t, µζ,t, µξ,t)

µq,t = qx,t qt µx,t + qw,t qt µw,t + 1 2 qxx,t qt σ2

x,t + 2qxw,t

qt σx,tσw,t + qww,t qt σ2

w,t

• 5 Compute rt. Plug (rt, ηt, σj,t, σζ,t) into HJB equation to obtain the

system of PDEs.

Balance Sheet Recession 36 / 36

Policy Rule: Transfers

0.2 0.4 0.6 0.8 1 w 0.99 0.995 1 1.005 1.01 1.015 ωd

Transfer depend on wt only

• Lower transfers when wt is low
• Higher transfers when wt is high

Policy rule

For wt = 0, then 1 − ωr

t = 0 (no risk exposure for central bank)

• For wt ≤ w (w small), interpolate policy rule

36 / 36

Evidence: Passive Traders/LAMP

Passive trading behavior

• Ameriks and Zeldes (2004) find 44% of households made no change in

asset location over a period of 10 years

• Brunnermeier and Nagel (2008) use PSID to show that households

rebalance very slowly their portfolio

• Calvet, Campbell, and Sodini (2009) find weak response of portfolio

shares to returns in Swedish data

• Kaplan, Violante, and Weidener (2014) document a large fraction of

”Wealthy Hand-to-Mouth” using data from several countries

Passive Traders and the Central Bank 36 / 36

Evidence: Preference Heterogeneity

Studies that find evidence of heterogeneous risk aversion

• Barsky, Juster, Kimball, and Shapiro (1997) uses Health and Retirement

Study (HRS)

• Kimball, Sahm, and Shapiro (2008) uses PSID
• Chiaporri and Paiella (2011) uses data for Italy
• Chiaporri, Samphantharak, Schulhofer-Wohl, and Townsend (2012) uses

Thai data

Active traders 36 / 36