Uncertainty Shocks, Asset Supply and Pricing over the Business Cycle

Uncertainty Shocks, Asset Supply and Pricing over the Business Cycle Francesco Bianchi

Cosmin Ilut

Martin Schneider

Duke

Duke

Stanford

ESSIM, Izmir, 2013

Bianchi, Ilut, Schneider

Uncertainty Shocks, Asset Supply and Pricing

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Motivation

When stock price is high... I

future excess returns over bonds low

I

net payout to shareholders high

I

net corporate debt increases

At business cycle frequencies I

in recessions: stock price low, net payout low, net debt falls

At lower frequencies I I

1970s: stock price low, payout low, debt flat more quantity volatility in 1970s



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Nonfinancial business sector



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excess return over next 7 years, % p.a.

Excess return predictability:

high prices, low future excess return 2

Predictability regression R = a + b*log(P/D)+ε; , R = 0.42 15 10 5 0 −5 2.5

3 3.5 4 log price payout ratio, % p.a. expected and realized 7 year return

4.5

15 10 5 0

7 year return a+b*log(P/D)

−5 1960 Bianchi, Ilut, Schneider

1970

1980

1990


2000

2010 ESSIM, 2013

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This paper Stylized facts: when uncertainty about financial conditions is low... I

investors demand lower premia

I

firms facing credit market frictions choose more debt & payout

I

low frequency effect from volatility regimes

DSGE model w/ endog. supply of equity & bonds I

nonfinancial firms issue equity & debt

I

firms smooth dividends & face MC of borrowing increasing in debt

I

uncertainty = risk + ambiguity (Knightian uncertainty) uncertainty shocks: regime switching volatility and confidence shocks

I

Estimation I I

data from NIPA and Flow of Funds Bayesian approach using 1st order approximation



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Literature

1

Multiple priors utility: Gilboa & Schmeidler (1989), Epstein & Wang (1994), Epstein & Schneider (2003).

2

Business cycles, asset pricing & uncertainty shocks I

I

3

risk shocks: Gourio (2010), Basu & Bundick (2011), Caldara, Fernandez-Villaverde, Rubio-Ramirez & Yao (2012), Christiano, Motto & Rostagno (2012), Malkhozov & Shamloo (2012) robustness: Cagetti, Hansen, Sargent and Williams (2002), Bidder and Smith (2012), Pahar-Javan & Liu (2012)

Business cycles & firm asset supply: Covas & den Haan (2011), Gourio (2011), Jermann & Quadrini (2011), Adrian & Boyarchenko (2012), Croce, Kung, Nguyen & Schmid (2012)



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Outline of the talk

Preferences I

time-varying confidence

Model overview I I

firm financing asset pricing

Quantitative evaluation I I I

solution estimation and data some results



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Preferences: ambiguity aversion S = state space I I

one element s ∈ S realized every period histories s t ∈ S t

Consumption streams C = (Ct (s t )) Recursive multiple-priors utility Ut C ; s t = u Ct s t + β min E p Ut +1 C ; s t +1 p ∈Pt (s t )

Primitives: I I

felicity u, discount factor β the one-step-ahead belief sets Pt (s t )

Larger set Pt (s t ) → less confidence about st +1



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Ambiguity about mean innovations

DSGE model: s t = history of innovations to exogenous shocks Representation of one-step-ahead belief set Pt for shock xi : xt +1,i = ρi xt,i + σt,i ε t +1,i + µt,i µt,i ∈ [−at,i , at,i ] Stochastic process at,i regulates size of Pt (s t ) I I I

larger at,i = larger set = less confidence about shock xt +1,i min operator selects worst case mean, e.g. −at,i if ambiguity at,i increases, agent acts “as if” bad news about xt +1,i



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Evolution of confidence xt +1,i = ρi xt,i + σt,i ε t +1,i + µt,i µt,i ∈ [−at,i , at,i ] Two sources for evolution of ambiguity at,i = ηt,i σt,i I follows if set Pt is relative entropy ball around p µ =0 1. Intangible information affecting confidence ηt,i = (1 − ρη,i )η i + ρη,i ηt −1,i + ε t,ηi 2. Regime switching volatility σt,i I

volatility lowers confidence; first order effects of changes in volatility

True data generating process I I

∗ with moments converging to i.i.N 0, σ2 deterministic sequence µt,i µ neither agents nor econometrician can identify true sequence



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Model overview RBC-style model with representative agent and firm Household maximizes recursive multiple priors utility I

works for wages, holds bonds, stocks, pays taxes, receives endowment

Firms maximize shareholder value (using HH’s SDF) I I I

margins for firm: investment, labor, net payout, capital structure adjustment costs for net payout to shareholder borrow at MC increasing in debt level

Competitive markets: consumption good, equity, one period bonds Shocks I I

TFP growth, gov’t spending Financial conditions: MC of borrowing, fixed cost

Ambiguity about all shocks I I

independent confidence shocks also affected by common regime switching volatility



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Firm financing decision Firm objective: max PV of net payout max E0∗

∞

∑ M0t Dt

t =1

Dt = Net Income + ∆Bt – borrowing cost – dividend adj. cost Key inputs: I I I

expectations are under the HH’s worst-case conditional porobabilities incentive to smooth dividends financing costs

Property: firms issue more debt if expected dividend growth is larger BC + intertemporal FOC → comovement between Dt and Bt I I

− for ’profit shocks’ (ex. more income today −→ more Dt , less Bt ) + for ’uncertainty shocks’ (ex. high Et∗ Dt +1 −→ more Bt and Dt )



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Price volatility & excess return predictability Loglinearized Euler equation pˆ t = (b ct − Et∗ b ct +1 ) + βEt∗ pˆ t +1 + (1 − β) Et∗ dˆ t +1 Excess return xte+1 = log(pt +1 + dt +1 ) − log pt − log(it ) ≈ β (pˆ t +1 − Et∗ pˆ t +1 ) + (1 − β) dˆ t +1 − Et∗ dˆ t +1 What does econometrician measure? I I I

observes data generated by true DGP; measures Et xte+1 conditional premia reflect Et − Et∗ lower confidence = higher premia

Unconditionally: positive average equity premium because: 1 2

stock return is higher under E than under E ∗ interest rate is lower: size depends on effect on ∆C



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Solution Solution in two steps (Ilut and Schneider, 2012) 1 2

find recursive equilibrium characterize variables under the econometrician’s law of motion Characterizing equilibrium: a guess-and-verify approach

1 2

guess the worst case belief, say p 0 find recursive equilibrium under expected utility & belief p 0 I

I

compute loglinear approximation around “worst-case” steady state (sets risk to zero, but retains worst case mean) DSGE solution can be expressed as a MS-VAR:

St = C (ξ t ) + TSt −1 + Rσ (ξ t −1 ) ε t 3 4

time-variation in constant: from effect of volatility regime ξ t compute value function under worst case belief verify that the guess p 0 indeed achieves the minimum Bianchi, Ilut, Schneider


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Estimation DSGE solution: St = C (ξ t ) + TSt −1 + Rσ (ξ t −1 ) ε t Linearity → estimation using a slight modification of the Kalman filter Identification of ambiguity vs. volatility shocks: I

stochastic volatility shows up as (likely) changes to the second moments

Data: US 1959Q2-2011Q3 I I

I

Macro aggregates: growth rates of Y , C and I Asset prices: value of nonfin corporate equity / gdp, real interest rate, interest rate term spread Asset supply: nonfinancial corporate net payout and net debt / gdp



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Smoothed probability of the High Volatility regime Probability High Volatility Regime 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1960

1965

1970


1975

1980

1985

1990

1995


2000

2005

2010

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Equity price/GDP: effects of volatility regimes P/GDP ratio

Regime sequence 2.5

1.65 1.6 2 1.55 1.5

1.5

1.45 1.4

1

1.35 1.3 1960

1970

1980


1990

2000

2010

0.5 1960

1970


1980

1990

2000

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Contribution

Equity price/GDP: ambiguity over borrowing fixed cost

Shock Data

1.5 1 0.5 1960

1965

1970

1975

1980

1985

1990

1995

2000

2005

2010

1965

1970

1975

1980

1985

1990

1995

2000

2005

2010

Path

2 1 0 −1 1960



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Spectral Decomposition: Low volatility regime ∆C

Div/GDP

1

1

0.5

0.5

0 0

0.5

1

0 0

SP/GDP

0.5

1 µ*

bf/GDP

1

ψf

1

0.5

0.5

0 0

0.5


1

0 0

0.5


1

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Spectral Decomposition: High volatility regime ∆C

Div/GDP

1

1

0.5

0.5

0 0

0.5

1

0 0

SP/GDP

0.5

1 µ*

f

b /GDP

1

ψf

1

0.5

0.5

0 0

0.5


1

0 0

0.5


1

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Conclusion DSGE model to study business cycles and asset prices I

I

I

asset demand (equity, bonds) ambiguity averse agents asset supply capital structure, credit market frictions uncertainty shocks price volatility / predictability of excess returns

Study dynamics using 1st order approximation I

allows for tractable estimation

Preliminary results: I

uncertainty shocks: dynamics of asset supply and asset pricing



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Solution 1. Find recursive equilibrium 1

Compute the ergodic volatility vector σ

2

Worst-case mean: xi = −

η i σi 1 − ρi

3

Worst-case endogenous variable Y = f (x ) from deterministic FOCs

4

Linearize around Y , σ, η, x and solve a ‘rational expectations’ model under worst-case belief p 0 et = C (ξ t ) + T Y et −1 + Rσ (ξ t −1 ) ε t Y I

time-variation in constant: from first order effect of volatility regime ξ t



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Solution 2. Equilibrium dynamics under econometrician’s law of motion (p ∗ ) 1

Zero-risk (ergodic) steady state Y ∗ I

I

2

Expectations under belief p 0 but shocks set to their ergodic values under p ∗ Y ∗ can be found from linearized solution Y ∗ − Y = T Y ∗ − Y + Rησ

bt = Yt − Y ∗ Dynamics: define Y I

beliefs formed under p 0 but realized innovations under p ∗ bt = C (ξ t ) + T Y bt −1 + Rσ (ξ t −1 ) ε t + R (ηe Y σ (ξ t −1 ) + σe ηt − 1 )



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