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Introduction Model Asset Prices Discussion Conclusions A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson University of California, Irvine Impulse and Propagation Mechanisms Workshop NBER Summer Institute July 11, 2016

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Page 1: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

A Macroeconomic Model of Equities and Real,Nominal, and Defaultable Debt

Eric T. SwansonUniversity of California, Irvine

Impulse and Propagation Mechanisms WorkshopNBER Summer Institute

July 11, 2016

Page 2: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Motivation

Goal: Show that a simple macroeconomic model (with Epstein-Zinpreferences) is consistent with a wide variety of asset pricing facts

equity premium puzzlelong-term bond premium puzzle (nominal and real)credit spread puzzle

Reduces separate puzzles in finance to a single, unifying puzzle:Why does risk aversion in the model need to be so high?

uncertainty: Weitzman (2007), Barillas-Hansen-Sargent(2010), et al.rare disasters: Rietz (1988), Barro (2006), et al.long-run risks: Bansal-Yaron (2004) et al.heterogeneous agents: Mankiw-Zeldes (1991), Guvenen(2009), Schmidt (2015), et al.financial intermediaries: Adrian-Etula-Muir (2013)

Page 3: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Motivation

Goal: Show that a simple macroeconomic model (with Epstein-Zinpreferences) is consistent with a wide variety of asset pricing facts

equity premium puzzlelong-term bond premium puzzle (nominal and real)credit spread puzzle

Reduces separate puzzles in finance to a single, unifying puzzle:Why does risk aversion in the model need to be so high?

uncertainty: Weitzman (2007), Barillas-Hansen-Sargent(2010), et al.rare disasters: Rietz (1988), Barro (2006), et al.long-run risks: Bansal-Yaron (2004) et al.heterogeneous agents: Mankiw-Zeldes (1991), Guvenen(2009), Schmidt (2015), et al.financial intermediaries: Adrian-Etula-Muir (2013)

Page 4: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Motivation

Goal: Show that a simple macroeconomic model (with Epstein-Zinpreferences) is consistent with a wide variety of asset pricing facts

equity premium puzzlelong-term bond premium puzzle (nominal and real)credit spread puzzle

Reduces separate puzzles in finance to a single, unifying puzzle:Why does risk aversion in the model need to be so high?

uncertainty: Weitzman (2007), Barillas-Hansen-Sargent(2010), et al.rare disasters: Rietz (1988), Barro (2006), et al.long-run risks: Bansal-Yaron (2004) et al.

heterogeneous agents: Mankiw-Zeldes (1991), Guvenen(2009), Schmidt (2015), et al.financial intermediaries: Adrian-Etula-Muir (2013)

Page 5: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Motivation

Goal: Show that a simple macroeconomic model (with Epstein-Zinpreferences) is consistent with a wide variety of asset pricing facts

equity premium puzzlelong-term bond premium puzzle (nominal and real)credit spread puzzle

Reduces separate puzzles in finance to a single, unifying puzzle:Why does risk aversion in the model need to be so high?

uncertainty: Weitzman (2007), Barillas-Hansen-Sargent(2010), et al.rare disasters: Rietz (1988), Barro (2006), et al.long-run risks: Bansal-Yaron (2004) et al.heterogeneous agents: Mankiw-Zeldes (1991), Guvenen(2009), Schmidt (2015), et al.financial intermediaries: Adrian-Etula-Muir (2013)

Page 6: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Motivation

Implications for Finance:unifying explanation for asset pricing puzzlesstructural model of asset prices (provides intuition, robustnessto breaks and policy interventions)

Implications for Macro:show how to match risk premia in DSGE frameworkstart to endogenize asset price–macroeconomy feedback

Secondary theme: Keep the model as simple as possible

Two key ingredients:Epstein-Zin preferencesnominal rigidities

Page 7: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Motivation

Implications for Finance:unifying explanation for asset pricing puzzlesstructural model of asset prices (provides intuition, robustnessto breaks and policy interventions)

Implications for Macro:show how to match risk premia in DSGE frameworkstart to endogenize asset price–macroeconomy feedback

Secondary theme: Keep the model as simple as possible

Two key ingredients:Epstein-Zin preferencesnominal rigidities

Page 8: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Motivation

Implications for Finance:unifying explanation for asset pricing puzzlesstructural model of asset prices (provides intuition, robustnessto breaks and policy interventions)

Implications for Macro:show how to match risk premia in DSGE frameworkstart to endogenize asset price–macroeconomy feedback

Secondary theme: Keep the model as simple as possible

Two key ingredients:Epstein-Zin preferencesnominal rigidities

Page 9: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Motivation

Implications for Finance:unifying explanation for asset pricing puzzlesstructural model of asset prices (provides intuition, robustnessto breaks and policy interventions)

Implications for Macro:show how to match risk premia in DSGE frameworkstart to endogenize asset price–macroeconomy feedback

Secondary theme: Keep the model as simple as possible

Two key ingredients:Epstein-Zin preferencesnominal rigidities

Page 10: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Households

Period utility function:

u(ct , lt ) ≡ log ct − ηl1+χt

1 + χ

additive separability between c and lSDF comparable to finance literaturelog preferences for balanced growth, simplicity

Flow budget constraint:

at+1 = eit at + wt lt + dt − ct

Calibration: (IES = 1), χ = 3, l = 1 (η = .54)

Page 11: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Generalized Recursive Preferences

Household chooses state-contingent {(ct , lt )} to maximize

V (at ; θt ) = max(ct ,lt )

u(ct , lt )− βα−1 log [Et exp(−αV (at+1; θt+1))]

Calibration: β = .992, RRA (Rc) = 60 (α = 59.15)

Page 12: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Firms

Firms are very standard:continuum of monopolistic firms (gross markup λ)Calvo price setting (probability 1− ξ)Cobb-Douglas production functions, yt (f ) = Atk1−θ lt (f )θ

fixed firm-specific capital stocks k

Random walk technology: log At = log At−1 + εt

simplicitycomparability to finance literaturehelps match equity premium

Calibration: λ = 1.1, ξ = 0.8, θ = 0.6, σA = .007, (ρA = 1), k4Y = 2.5

Page 13: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Fiscal and Monetary Policy

No government purchases or investment:

Yt = Ct

Taylor-type monetary policy rule:

it = r + πt + φπ(πt − π) + φy (yt − y t )

“Output gap” (yt − y t ) defined relative to moving average:

y t ≡ ρyy t−1 + (1− ρy )yt

Rule has no inertia:simplicityRudebusch (2002, 2006)

Calibration: φπ = 0.5, φy = 0.75, π = .008, ρy = 0.9

Page 14: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Solution Method

Write equations of the model in recursive form

Divide nonstationary variables (Yt , Ct , wt , etc.) by At

Solve using perturbation methods around nonstoch. steady state

first-order: no risk premiasecond-order: risk premia are constantthird-order: time-varying risk premiahigher-order: more accurate over larger region

Model has 2 state variables (yt , ∆t ), one shock (εt )

Page 15: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Solution Method

Write equations of the model in recursive form

Divide nonstationary variables (Yt , Ct , wt , etc.) by At

Solve using perturbation methods around nonstoch. steady statefirst-order: no risk premiasecond-order: risk premia are constantthird-order: time-varying risk premiahigher-order: more accurate over larger region

Model has 2 state variables (yt , ∆t ), one shock (εt )

Page 16: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Impulse Responses

0 10 20 30 40 500.0

0.2

0.4

0.6

0.8

1.0percent

TechnologyAt

Page 17: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Impulse Responses

0 10 20 30 40 500.0

0.2

0.4

0.6

0.8

1.0percent

ConsumptionCt

Page 18: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Impulse Responses

10 20 30 40 50

-1.0

-0.8

-0.6

-0.4

-0.2

0.0ann. pct.

Inflationπt

Page 19: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Impulse Responses

10 20 30 40 50

-0.5

-0.4

-0.3

-0.2

-0.1

0.0ann. pct.

Short-term nominal interest rate it

Page 20: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Impulse Responses

0 10 20 30 40 500.0

0.1

0.2

0.3

0.4

0.5ann. pct.

Short-term real interest rate rt

Page 21: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Nonlinear vs. Linear Impulse Responses

0 10 20 30 40 500.0

0.2

0.4

0.6

0.8

1.0percent

Price DispersionΔt

Introduction Model Asset Prices Discussion Conclusions

Nonlinear vs. Linear Impulse Responses

1st-order solution

5th-order solution

0 10 20 30 40 500.0

0.2

0.4

0.6

0.8

1.0

percentConsumptionCt

Page 22: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Firms’ Optimal Price and Price Dispersion

0AB

0

log Δt

pt*

Ptlog

Page 23: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Nonlinear vs. Linear Impulse Responses

0 10 20 30 40 500.0

0.2

0.4

0.6

0.8

1.0percent

Price DispersionΔt

Introduction Model Asset Prices Discussion Conclusions

Nonlinear vs. Linear Impulse Responses

1st-order solution

5th-order solution

0 10 20 30 40 500.0

0.2

0.4

0.6

0.8

1.0

percentConsumptionCt

Page 24: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Nonlinear vs. Linear Impulse Responses

1st-order solution

5th-order solution

0 10 20 30 40 500.0

0.2

0.4

0.6

0.8

1.0

percentConsumptionCt

Page 25: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Nonlinear vs. Linear Impulse Responses

10 20 30 40 50

-0.4

-0.2

0.0

0.2

0.4

percentLabor Lt

Introduction Model Asset Prices Discussion Conclusions

Nonlinear vs. Linear Impulse Responses

1st-order solution

5th-order solution

0 10 20 30 40 500.0

0.2

0.4

0.6

0.8

1.0

percentConsumptionCt

Page 26: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Equity: Levered Consumption Claim

Equity pricepe

t = Etmt+1(Cνt+1 + pe

t+1)

where ν is degree of leverage

Realized gross return:

Ret+1 ≡

Cνt+1 + pe

t+1

pet

Equity premiumψe

t ≡ EtRet+1 − ert

Calibration: ν = 3

Page 27: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Equity: Levered Consumption Claim

Equity pricepe

t = Etmt+1(Cνt+1 + pe

t+1)

where ν is degree of leverage

Realized gross return:

Ret+1 ≡

Cνt+1 + pe

t+1

pet

Equity premiumψe

t ≡ EtRet+1 − ert

Calibration: ν = 3

Page 28: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Equity: Levered Consumption Claim

Equity pricepe

t = Etmt+1(Cνt+1 + pe

t+1)

where ν is degree of leverage

Realized gross return:

Ret+1 ≡

Cνt+1 + pe

t+1

pet

Equity premiumψe

t ≡ EtRet+1 − ert

Calibration: ν = 3

Page 29: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Equity: Levered Consumption Claim

Equity pricepe

t = Etmt+1(Cνt+1 + pe

t+1)

where ν is degree of leverage

Realized gross return:

Ret+1 ≡

Cνt+1 + pe

t+1

pet

Equity premiumψe

t ≡ EtRet+1 − ert

Calibration: ν = 3

Page 30: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Table 2: Equity Premium

In the data: 3–6.5 percent per year (e.g., Campbell, 1999,Fama-French, 2002)

Risk aversion Rc Shock persistence ρA Equity premium ψe

10 1 0.6230 1 1.9660 1 4.1990 1 6.70

60 .995 1.8660 .99 1.0860 .98 0.5360 .95 0.17

Page 31: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Table 2: Equity Premium

In the data: 3–6.5 percent per year (e.g., Campbell, 1999,Fama-French, 2002)

Risk aversion Rc Shock persistence ρA Equity premium ψe

10 1 0.6230 1 1.9660 1 4.1990 1 6.70

60 .995 1.8660 .99 1.0860 .98 0.5360 .95 0.17

Page 32: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Table 2: Equity Premium

In the data: 3–6.5 percent per year (e.g., Campbell, 1999,Fama-French, 2002)

Risk aversion Rc Shock persistence ρA Equity premium ψe

10 1 0.6230 1 1.9660 1 4.1990 1 6.70

60 .995 1.8660 .99 1.0860 .98 0.5360 .95 0.17

Page 33: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Table 2: Equity Premium

In the data: 3–6.5 percent per year (e.g., Campbell, 1999,Fama-French, 2002)

Risk aversion Rc Shock persistence ρA Equity premium ψe

10 1 0.6230 1 1.9660 1 4.1990 1 6.70

60 .995 1.8660 .99 1.0860 .98 0.5360 .95 0.17

Page 34: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Equity Premium

10 20 30 40 50

-80

-60

-40

-20

0ann. bp

Equity premiumψte

Page 35: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Real Government Debt

Real n-period zero-coupon bond price:

p(n)t = Et mt+1p(n−1)

t+1 ,

p(0)t = 1, p(1)

t = e−rt

Real yield:

r (n)t = −1

nlog p(n)

t

Real term premium:ψ

(n)t = r (n)

t − r (n)t

wherer (n)t = −1

nlog p(n)

t

p(n)t = e−rt Et p

(n−1)t+1

Page 36: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Real Government Debt

Real n-period zero-coupon bond price:

p(n)t = Et mt+1p(n−1)

t+1 ,

p(0)t = 1, p(1)

t = e−rt

Real yield:

r (n)t = −1

nlog p(n)

t

Real term premium:ψ

(n)t = r (n)

t − r (n)t

wherer (n)t = −1

nlog p(n)

t

p(n)t = e−rt Et p

(n−1)t+1

Page 37: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Real Government Debt

Real n-period zero-coupon bond price:

p(n)t = Et mt+1p(n−1)

t+1 ,

p(0)t = 1, p(1)

t = e−rt

Real yield:

r (n)t = −1

nlog p(n)

t

Real term premium:ψ

(n)t = r (n)

t − r (n)t

wherer (n)t = −1

nlog p(n)

t

p(n)t = e−rt Et p

(n−1)t+1

Page 38: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Real Government Debt

Real n-period zero-coupon bond price:

p(n)t = Et mt+1p(n−1)

t+1 ,

p(0)t = 1, p(1)

t = e−rt

Real yield:

r (n)t = −1

nlog p(n)

t

Real term premium:ψ

(n)t = r (n)

t − r (n)t

wherer (n)t = −1

nlog p(n)

t

p(n)t = e−rt Et p

(n−1)t+1

Page 39: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Real Government Debt

Real n-period zero-coupon bond price:

p(n)t = Et mt+1p(n−1)

t+1 ,

p(0)t = 1, p(1)

t = e−rt

Real yield:

r (n)t = −1

nlog p(n)

t

Real term premium:ψ

(n)t = r (n)

t − r (n)t

wherer (n)t = −1

nlog p(n)

t

p(n)t = e−rt Et p

(n−1)t+1

Page 40: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Nominal Government Debt

Nominal n-period zero-coupon bond price:

p$(n)t = Et mt+1e−πt+1p$(n−1)

t+1 ,

p$(0)t = 1, p$(1)

t = e−it

Nominal yield:

i(n)t = −1

nlog p$(n)

t

Nominal term premium:

ψ$(n)t = i(n)

t − i(n)t

wherei(n)t = −1

nlog p$(n)

t

p$(n)t = e−it Et p

$(n−1)t+1

Page 41: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Nominal Government Debt

Nominal n-period zero-coupon bond price:

p$(n)t = Et mt+1e−πt+1p$(n−1)

t+1 ,

p$(0)t = 1, p$(1)

t = e−it

Nominal yield:

i(n)t = −1

nlog p$(n)

t

Nominal term premium:

ψ$(n)t = i(n)

t − i(n)t

wherei(n)t = −1

nlog p$(n)

t

p$(n)t = e−it Et p

$(n−1)t+1

Page 42: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Real Yield Curve

Table 3: Real Zero-Coupon Bond Yields

2-yr. 3-yr. 5-yr. 7-yr. 10-yr. (10y)−(3y)

US TIPS, 1999–2015a 1.29 1.55 1.82US TIPS, 2004–2015a 0.14 0.28 0.60 0.89 1.22 0.94US TIPS, 2004–2007a 1.39 1.52 1.74 1.91 2.09 0.57UK indexed gilts, 1983–1995b 6.12 5.29 4.34 4.12 −1.17UK indexed gilts, 1985–2015c 1.91 2.05 2.16 2.25 0.34UK indexed gilts, 1990–2007c 2.79 2.78 2.79 2.80 0.01

macroeconomic model 1.94 1.93 1.93 1.93 1.93 0.00

aGürkaynak, Sack, and Wright (2010) online datasetbEvans (1999)cBank of England web site

Page 43: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Real Yield Curve

Table 3: Real Zero-Coupon Bond Yields

2-yr. 3-yr. 5-yr. 7-yr. 10-yr. (10y)−(3y)

US TIPS, 1999–2015a 1.29 1.55 1.82US TIPS, 2004–2015a 0.14 0.28 0.60 0.89 1.22 0.94US TIPS, 2004–2007a 1.39 1.52 1.74 1.91 2.09 0.57UK indexed gilts, 1983–1995b 6.12 5.29 4.34 4.12 −1.17UK indexed gilts, 1985–2015c 1.91 2.05 2.16 2.25 0.34UK indexed gilts, 1990–2007c 2.79 2.78 2.79 2.80 0.01

macroeconomic model 1.94 1.93 1.93 1.93 1.93 0.00

aGürkaynak, Sack, and Wright (2010) online datasetbEvans (1999)cBank of England web site

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Introduction Model Asset Prices Discussion Conclusions

Nominal Yield Curve

Table 4: Nominal Zero-Coupon Bond Yields

1-yr. 2-yr. 3-yr. 5-yr. 7-yr. 10-yr. (10y)−(1y)

US Treasuries, 1961–2015a 5.27 5.50 5.68 5.97 6.18US Treasuries, 1971–2015a 5.42 5.66 5.86 6.18 6.43 6.71 1.29US Treasuries, 1990–2007a 4.56 4.84 5.06 5.41 5.68 5.98 1.42UK gilts, 1970–2015b 6.92 7.10 7.26 7.51 7.70 7.89 0.96UK gilts, 1990–2007b 6.20 6.29 6.38 6.47 6.50 6.48 0.28

macroeconomic model 5.35 5.59 5.80 6.09 6.27 6.44 1.09

aGürkaynak, Sack, and Wright (2007) online datasetbBank of England web site

Supply shocks make nominal long-term bonds risky: inflation risk

Page 45: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Nominal Yield Curve

Table 4: Nominal Zero-Coupon Bond Yields

1-yr. 2-yr. 3-yr. 5-yr. 7-yr. 10-yr. (10y)−(1y)

US Treasuries, 1961–2015a 5.27 5.50 5.68 5.97 6.18US Treasuries, 1971–2015a 5.42 5.66 5.86 6.18 6.43 6.71 1.29US Treasuries, 1990–2007a 4.56 4.84 5.06 5.41 5.68 5.98 1.42UK gilts, 1970–2015b 6.92 7.10 7.26 7.51 7.70 7.89 0.96UK gilts, 1990–2007b 6.20 6.29 6.38 6.47 6.50 6.48 0.28

macroeconomic model 5.35 5.59 5.80 6.09 6.27 6.44 1.09

aGürkaynak, Sack, and Wright (2007) online datasetbBank of England web site

Supply shocks make nominal long-term bonds risky: inflation risk

Page 46: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Nominal Yield Curve

Table 4: Nominal Zero-Coupon Bond Yields

1-yr. 2-yr. 3-yr. 5-yr. 7-yr. 10-yr. (10y)−(1y)

US Treasuries, 1961–2015a 5.27 5.50 5.68 5.97 6.18US Treasuries, 1971–2015a 5.42 5.66 5.86 6.18 6.43 6.71 1.29US Treasuries, 1990–2007a 4.56 4.84 5.06 5.41 5.68 5.98 1.42UK gilts, 1970–2015b 6.92 7.10 7.26 7.51 7.70 7.89 0.96UK gilts, 1990–2007b 6.20 6.29 6.38 6.47 6.50 6.48 0.28

macroeconomic model 5.35 5.59 5.80 6.09 6.27 6.44 1.09

aGürkaynak, Sack, and Wright (2007) online datasetbBank of England web site

Supply shocks make nominal long-term bonds risky: inflation risk

Page 47: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Nominal Term Premium

10 20 30 40 50

-10

-8

-6

-4

-2

0ann. bp

Nominal term premiumψt$(40)

Page 48: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Defaultable Debt

Default-free depreciating nominal consol:

pct = Et mt+1e−πt+1(1 + δpc

t+1)

Yield to maturity:

ict = log( 1

pct

+ δ)

Nominal consol with default:

pdt = Et mt+1e−πt+1

[(1− 1d

t+1)(1 + δpdt+1) + 1d

t+1 ωt+1 pdt

]Yield to maturity:

idt = log( 1

pdt

+ δ)

The credit spread is idt − ict

Page 49: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Defaultable Debt

Default-free depreciating nominal consol:

pct = Et mt+1e−πt+1(1 + δpc

t+1)

Yield to maturity:

ict = log( 1

pct

+ δ)

Nominal consol with default:

pdt = Et mt+1e−πt+1

[(1− 1d

t+1)(1 + δpdt+1) + 1d

t+1 ωt+1 pdt

]Yield to maturity:

idt = log( 1

pdt

+ δ)

The credit spread is idt − ict

Page 50: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Defaultable Debt

Default-free depreciating nominal consol:

pct = Et mt+1e−πt+1(1 + δpc

t+1)

Yield to maturity:

ict = log( 1

pct

+ δ)

Nominal consol with default:

pdt = Et mt+1e−πt+1

[(1− 1d

t+1)(1 + δpdt+1) + 1d

t+1 ωt+1 pdt

]

Yield to maturity:

idt = log( 1

pdt

+ δ)

The credit spread is idt − ict

Page 51: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Defaultable Debt

Default-free depreciating nominal consol:

pct = Et mt+1e−πt+1(1 + δpc

t+1)

Yield to maturity:

ict = log( 1

pct

+ δ)

Nominal consol with default:

pdt = Et mt+1e−πt+1

[(1− 1d

t+1)(1 + δpdt+1) + 1d

t+1 ωt+1 pdt

]Yield to maturity:

idt = log( 1

pdt

+ δ)

The credit spread is idt − ict

Page 52: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Defaultable Debt

Default-free depreciating nominal consol:

pct = Et mt+1e−πt+1(1 + δpc

t+1)

Yield to maturity:

ict = log( 1

pct

+ δ)

Nominal consol with default:

pdt = Et mt+1e−πt+1

[(1− 1d

t+1)(1 + δpdt+1) + 1d

t+1 ωt+1 pdt

]Yield to maturity:

idt = log( 1

pdt

+ δ)

The credit spread is idt − ict

Page 53: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Table 5: Credit Spread

average ann. cyclicality of average cyclicality of creditdefault prob. default prob. recovery rate recovery rate spread (bp)

.006 0 .42 0 34.0

If default isn’t cyclical, then it’s not risky

Page 54: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Table 5: Credit Spread

average ann. cyclicality of average cyclicality of creditdefault prob. default prob. recovery rate recovery rate spread (bp)

.006 0 .42 0 34.0

If default isn’t cyclical, then it’s not risky

Page 55: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Default Rate is Countercyclical

Macroeconomic Conditions and the Puzzles

A. Default rates and credit spreads

O Moody's Recovery Rates - • - Altman Recovery Rates (

Long-Term Mean

1985 2005

B. Recovery rates

1990 1995 2000

Figure 1. Default rates, credit spreads, and recovery rates over the business cy cle. Panel A plots the Moody's annual corporate default rates during 1920 to 2008 and the monthly Baa-Aaa credit spreads during 1920/01 to 2009/02. Panel B plots the average recovery rates during 1982 to 2008. The "Long-Term Mean" recovery rate is 41.4%, based on Moody's data. Shaded areas

are NBER-dated recessions. For annual data, any calendar year with at least 5 months being in a

recession as defined by NBER is treated as a recession year.

default component of the average 10-year Baa-Treasury spread in this model rises from 57 to 105 bps, whereas the average optimal market leverage of a Baa-rated firm drops from 50% to 37%, both consistent with the U.S. data.

Figure 1 provides some empirical evidence on the business cycle movements in default rates, credit spreads, and recovery rates. The dashed line in Panel A plots the annual default rates over 1920 to 2008. There are several spikes in the default rates, each coinciding with an NBER recession. The solid line plots the monthly Baa-Aaa credit spreads from January 1920 to February 2009. The

spreads shoot up in most recessions, most visibly during the Great Depression, the savings and loan crisis in the early 1980s, and the recent financial crisis in 2008. However, they do not always move in lock-step with default rates

(the correlation at an annual frequency is 0.65), which suggests that other

factors, such as recovery rates and risk premia, also affect the movements

in spreads. Next, business cycle variation in the recovery rates is evident in

This content downloaded from 67.98.229.10 on Fri, 11 Apr 2014 19:22:23 PMAll use subject to JSTOR Terms and Conditions

source: Chen (2010)

Page 56: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Recovery Rate is Procyclical

Macroeconomic Conditions and the Puzzles

A. Default rates and credit spreads

O Moody's Recovery Rates - • - Altman Recovery Rates (

Long-Term Mean

1985 2005

B. Recovery rates

1990 1995 2000

Figure 1. Default rates, credit spreads, and recovery rates over the business cy cle. Panel A plots the Moody's annual corporate default rates during 1920 to 2008 and the monthly Baa-Aaa credit spreads during 1920/01 to 2009/02. Panel B plots the average recovery rates during 1982 to 2008. The "Long-Term Mean" recovery rate is 41.4%, based on Moody's data. Shaded areas

are NBER-dated recessions. For annual data, any calendar year with at least 5 months being in a

recession as defined by NBER is treated as a recession year.

default component of the average 10-year Baa-Treasury spread in this model rises from 57 to 105 bps, whereas the average optimal market leverage of a Baa-rated firm drops from 50% to 37%, both consistent with the U.S. data.

Figure 1 provides some empirical evidence on the business cycle movements in default rates, credit spreads, and recovery rates. The dashed line in Panel A plots the annual default rates over 1920 to 2008. There are several spikes in the default rates, each coinciding with an NBER recession. The solid line plots the monthly Baa-Aaa credit spreads from January 1920 to February 2009. The

spreads shoot up in most recessions, most visibly during the Great Depression, the savings and loan crisis in the early 1980s, and the recent financial crisis in 2008. However, they do not always move in lock-step with default rates

(the correlation at an annual frequency is 0.65), which suggests that other

factors, such as recovery rates and risk premia, also affect the movements

in spreads. Next, business cycle variation in the recovery rates is evident in

This content downloaded from 67.98.229.10 on Fri, 11 Apr 2014 19:22:23 PMAll use subject to JSTOR Terms and Conditions

source: Chen (2010)

Page 57: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Table 5: Credit Spread

average ann. cyclicality of average cyclicality of creditdefault prob. default prob. recovery rate recovery rate spread (bp)

.006 0 .42 0 34.0

.006 −0.3 .42 0 130.9

.006 −0.3 .42 2.5 143.1

.006 −0.15 .42 2.5 78.9

.006 −0.6 .42 2.5 367.4

.006 −0.3 .42 1.25 137.0

.006 −0.3 .42 5 155.2

Page 58: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Table 5: Credit Spread

average ann. cyclicality of average cyclicality of creditdefault prob. default prob. recovery rate recovery rate spread (bp)

.006 0 .42 0 34.0

.006 −0.3 .42 0 130.9

.006 −0.3 .42 2.5 143.1

.006 −0.15 .42 2.5 78.9

.006 −0.6 .42 2.5 367.4

.006 −0.3 .42 1.25 137.0

.006 −0.3 .42 5 155.2

Page 59: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Table 5: Credit Spread

average ann. cyclicality of average cyclicality of creditdefault prob. default prob. recovery rate recovery rate spread (bp)

.006 0 .42 0 34.0

.006 −0.3 .42 0 130.9

.006 −0.3 .42 2.5 143.1

.006 −0.15 .42 2.5 78.9

.006 −0.6 .42 2.5 367.4

.006 −0.3 .42 1.25 137.0

.006 −0.3 .42 5 155.2

Page 60: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Discussion

1 IES ≤ 1 vs. IES > 1

2 Volatility shocks

3 Endogenous conditional heteroskedasticity

4 Monetary and fiscal policy shocks

5 Financial accelerator

Page 61: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Intertemporal Elasticity of Substitution

Long-run risks literature typically assumes IES > 1, for tworeasons:

ensures equity prices rise (by more than consumption) inresponse to an increase in technologyensures equity prices fall in response to an increase involatility

However, IES > 1 is not necessary for these criteria to be satisfied,particularly when equity is a levered consumption claim.

Model here satisfies both criteria with IES = 1 (or even < 1).

Page 62: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Intertemporal Elasticity of Substitution

Long-run risks literature typically assumes IES > 1, for tworeasons:

ensures equity prices rise (by more than consumption) inresponse to an increase in technologyensures equity prices fall in response to an increase involatility

However, IES > 1 is not necessary for these criteria to be satisfied,particularly when equity is a levered consumption claim.

Model here satisfies both criteria with IES = 1 (or even < 1).

Page 63: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Intertemporal Elasticity of Substitution

Long-run risks literature typically assumes IES > 1, for tworeasons:

ensures equity prices rise (by more than consumption) inresponse to an increase in technologyensures equity prices fall in response to an increase involatility

However, IES > 1 is not necessary for these criteria to be satisfied,particularly when equity is a levered consumption claim.

Model here satisfies both criteria with IES = 1 (or even < 1).

Page 64: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Intertemporal Elasticity of Substitution

Long-run risks literature typically assumes IES > 1, for tworeasons:

ensures equity prices rise (by more than consumption) inresponse to an increase in technologyensures equity prices fall in response to an increase involatility

However, IES > 1 is not necessary for these criteria to be satisfied,particularly when equity is a levered consumption claim.

Model here satisfies both criteria with IES = 1 (or even < 1).

Page 65: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Impulse Responses to Technology Shock

10 20 30 40 50

-80

-60

-40

-20

0ann. bp

Equity premiumψte

Page 66: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Impulse Responses to Technology Shock

0 10 20 30 40 500.0

0.5

1.0

1.5

2.0

2.5

percentEquity price pt

e

Page 67: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Intertemporal Elasticity of Substitution

Long-run risks literature typically assumes IES > 1, for tworeasons:

ensures equity prices rise (by more than consumption) inresponse to an increase in technologyensures equity prices fall in response to an increase involatility

However, IES > 1 is not necessary for these criteria to be satisfied,particularly when equity is a levered consumption claim.

Model here satisfies both criteria with IES = 1 (or even < 1).

Extend model above to include volatility shocks:

logσA,t = (1− ρσ) log σA + ρσ logσA,t−1 + εσt

Calibration: ρσ = .98, Var(εσt ) = (0.1)2

Page 68: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Intertemporal Elasticity of Substitution

Long-run risks literature typically assumes IES > 1, for tworeasons:

ensures equity prices rise (by more than consumption) inresponse to an increase in technologyensures equity prices fall in response to an increase involatility

However, IES > 1 is not necessary for these criteria to be satisfied,particularly when equity is a levered consumption claim.

Model here satisfies both criteria with IES = 1 (or even < 1).

Extend model above to include volatility shocks:

logσA,t = (1− ρσ) log σA + ρσ logσA,t−1 + εσt

Calibration: ρσ = .98, Var(εσt ) = (0.1)2

Page 69: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Intertemporal Elasticity of Substitution

Long-run risks literature typically assumes IES > 1, for tworeasons:

ensures equity prices rise (by more than consumption) inresponse to an increase in technologyensures equity prices fall in response to an increase involatility

However, IES > 1 is not necessary for these criteria to be satisfied,particularly when equity is a levered consumption claim.

Model here satisfies both criteria with IES = 1 (or even < 1).

Extend model above to include volatility shocks:

logσA,t = (1− ρσ) log σA + ρσ logσA,t−1 + εσt

Calibration: ρσ = .98, Var(εσt ) = (0.1)2

Page 70: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Impulse Responses to Volatility Shock

10 20 30 40 500.0070

0.0072

0.0074

0.0076

0.0078

0.0080VolatilityσA ,t

Page 71: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Impulse Responses to Volatility Shock

10 20 30 40 50

-0.5

-0.4

-0.3

-0.2

-0.1

0.0percent

ConsumptionCt

Page 72: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Impulse Responses to Volatility Shock

10 20 30 40 50

-0.5

-0.4

-0.3

-0.2

-0.1

0.0ann. pct.

Inflationπt

Page 73: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Impulse Responses to Volatility Shock

0 10 20 30 40 500

20

40

60

80

100ann. bp

Equity premiumψte

Page 74: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Impulse Responses to Volatility Shock

10 20 30 40 50

-5

-4

-3

-2

-1

0percent

Equity price pte

Page 75: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Impulse Responses to Volatility Shock

0 10 20 30 40 500

5

10

15

20

25ann. bp

Nominal term premiumψt$ (40)

Page 76: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Endogenous Conditional Heteroskedasticity

Note that

ψet ≡ EtRe

t+1 − ert

=Et (Cν

t+1 + pet+1)

pet

− ert

=Et (Cν

t+1 + pet+1)

Etmt+1(Cνt+1 + pe

t+1)− 1

Etmt+1

=Etmt+1 Et (Cν

t+1 + pet+1)− Etmt+1(Cν

t+1 + pet+1)

Etmt+1 pet

=−Covt

(mt+1,Re

t+1)

Etmt+1

= −Covt

( mt+1

Etmt+1, re

t+1

)

Page 77: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Endogenous Conditional Heteroskedasticity

Note that

ψet ≡ EtRe

t+1 − ert

=Et (Cν

t+1 + pet+1)

pet

− ert

=Et (Cν

t+1 + pet+1)

Etmt+1(Cνt+1 + pe

t+1)− 1

Etmt+1

=Etmt+1 Et (Cν

t+1 + pet+1)− Etmt+1(Cν

t+1 + pet+1)

Etmt+1 pet

=−Covt

(mt+1,Re

t+1)

Etmt+1

= −Covt

( mt+1

Etmt+1, re

t+1

)

Page 78: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Endogenous Conditional Heteroskedasticity

Note that

ψet ≡ EtRe

t+1 − ert

=Et (Cν

t+1 + pet+1)

pet

− ert

=Et (Cν

t+1 + pet+1)

Etmt+1(Cνt+1 + pe

t+1)− 1

Etmt+1

=Etmt+1 Et (Cν

t+1 + pet+1)− Etmt+1(Cν

t+1 + pet+1)

Etmt+1 pet

=−Covt

(mt+1,Re

t+1)

Etmt+1

= −Covt

( mt+1

Etmt+1, re

t+1

)

Page 79: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Endogenous Conditional Heteroskedasticity

ψet = −Covt

( mt+1

Etmt+1, re

t+1

)

Risk premium can only vary over time if SDF or asset return isconditionally heteroskedastic

Traditional finance approach: assume shocks are heteroskedastic

Here, conditional heteroskedasticity is endogenous

Nonlinear solution contains terms of form

xtεt+1

so covariance Covt depends on state xt

Page 80: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Endogenous Conditional Heteroskedasticity

ψet = −Covt

( mt+1

Etmt+1, re

t+1

)Risk premium can only vary over time if SDF or asset return is

conditionally heteroskedastic

Traditional finance approach: assume shocks are heteroskedastic

Here, conditional heteroskedasticity is endogenous

Nonlinear solution contains terms of form

xtεt+1

so covariance Covt depends on state xt

Page 81: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Endogenous Conditional Heteroskedasticity

ψet = −Covt

( mt+1

Etmt+1, re

t+1

)Risk premium can only vary over time if SDF or asset return is

conditionally heteroskedastic

Traditional finance approach: assume shocks are heteroskedastic

Here, conditional heteroskedasticity is endogenous

Nonlinear solution contains terms of form

xtεt+1

so covariance Covt depends on state xt

Page 82: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Endogenous Conditional Heteroskedasticity

ψet = −Covt

( mt+1

Etmt+1, re

t+1

)Risk premium can only vary over time if SDF or asset return is

conditionally heteroskedastic

Traditional finance approach: assume shocks are heteroskedastic

Here, conditional heteroskedasticity is endogenous

Nonlinear solution contains terms of form

xtεt+1

so covariance Covt depends on state xt

Page 83: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Endogenous Conditional Heteroskedasticity

ψet = −Covt

( mt+1

Etmt+1, re

t+1

)Risk premium can only vary over time if SDF or asset return is

conditionally heteroskedastic

Traditional finance approach: assume shocks are heteroskedastic

Here, conditional heteroskedasticity is endogenous

Nonlinear solution contains terms of form

xtεt+1

so covariance Covt depends on state xt

Page 84: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Impulse Responses for Conditional Variance

10 20 30 40 50

-50

-40

-30

-20

-10

0percent

Conditional Variance Vart [(Ct+1/Ct)-1]

Page 85: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Impulse Responses for Conditional Variance

10 20 30 40 50

-50

-40

-30

-20

-10

0percent

Conditional Variance Vart [exp(-αVt+1)/Etexp(-αVt+1)]

Page 86: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Impulse Responses to Pos. and Neg. Tech. Shocks

no previous shock in period 0

previous shock of .007 in period 0

10 20 30 40 50

-0.4

-0.2

0.2

0.4

percentPrice DispersionΔt

no previous shock in period 0

previous shock of .007 in period 0

10 20 30 40 50

-0.4

-0.2

0.2

0.4

percentPrice DispersionΔt

0 10 20 30 40 500.0

0.2

0.4

0.6

0.8

1.0percent

ConsumptionCt

10 20 30 40 50

-1.0

-0.8

-0.6

-0.4

-0.2

0.0percent

ConsumptionCt

Page 87: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Price Dispersion

0AB

0

log Δt

pt*

Ptlog

Page 88: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Monetary and Fiscal Policy Shocks

Rudebusch and Swanson (2012) consider similar model withtechnology shockgovernment purchases shockmonetary policy shock

All three shocks help the model fit macroeconomic variables

But technology shock is most important (by far) for fitting assetprices:

technology shock is more persistenttechnology shock makes nominal assets risky

Page 89: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Monetary and Fiscal Policy Shocks

Rudebusch and Swanson (2012) consider similar model withtechnology shockgovernment purchases shockmonetary policy shock

All three shocks help the model fit macroeconomic variables

But technology shock is most important (by far) for fitting assetprices:

technology shock is more persistenttechnology shock makes nominal assets risky

Page 90: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Monetary and Fiscal Policy Shocks

Rudebusch and Swanson (2012) consider similar model withtechnology shockgovernment purchases shockmonetary policy shock

All three shocks help the model fit macroeconomic variables

But technology shock is most important (by far) for fitting assetprices:

technology shock is more persistenttechnology shock makes nominal assets risky

Page 91: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

No Financial Accelerator

With model-implied stochastic discount factor mt+1, we can priceany asset

Economy affects mt+1 ⇒ economy affects asset prices

However, asset prices have no effect on economy

Clearly at odds with financial crisis

To generate feedback, want financial intermediaries whose networth depends on assets

...but not in this paper

Page 92: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

No Financial Accelerator

With model-implied stochastic discount factor mt+1, we can priceany asset

Economy affects mt+1 ⇒ economy affects asset prices

However, asset prices have no effect on economy

Clearly at odds with financial crisis

To generate feedback, want financial intermediaries whose networth depends on assets

...but not in this paper

Page 93: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

No Financial Accelerator

With model-implied stochastic discount factor mt+1, we can priceany asset

Economy affects mt+1 ⇒ economy affects asset prices

However, asset prices have no effect on economy

Clearly at odds with financial crisis

To generate feedback, want financial intermediaries whose networth depends on assets

...but not in this paper

Page 94: A Macroeconomic Model of Equities and Real, Nominal, and ...swanson2/pres/nbersi2016ezap.pdf · A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson

Introduction Model Asset Prices Discussion Conclusions

Conclusions

1 The standard textbook New Keynesian model (with Epstein-Zinpreferences) is consistent with a wide variety of asset pricingfacts/puzzles

2 Unifies asset pricing puzzles into a single puzzle—Why does riskaversion in macro models need to be so high?(Literature provides good answers to this question)

3 Provides a structural framework for intuition about risk premia

4 Suggests a way to model feedback from risk premia tomacroeconomy