Impacts of Ambiguity Shocks Guangyu PEI University of Zurich HKBU, - - PowerPoint PPT Presentation

Impacts of Ambiguity Shocks

Guangyu PEI University of Zurich HKBU, 2017

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 1 / 55

Introduction Motivation

Motivation

What kind of shocks drive business cycle fluctuations?

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 2 / 55

Introduction Motivation

Aggregate Fluctuations ...

Fact 1: Business cycles disconnected with technology or inflation

• shock to news, noise, confidence, uncertainty ...

This paper: a novel theory of ambiguity-driven business cycles

• aggregate demand shocks
• countercyclical uncertainty

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 3 / 55

Introduction Motivation

Countercyclical Higher-Order Uncertainty. ...

Fact 2: Countercyclical cross-sectional dispersion of output forecast.

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 4 / 55

Introduction This Paper

A Theory of Ambiguity-Driven Business Cycles

Key ingredients:

• 1. aggregate demand externalities
• 2. incomplete and ambiguous information over TFP process
• 3. ambiguity aversion (smooth model of ambiguity)
• 4. ambiguity shocks (shocks to the perceived amount of ambiguity)

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 5 / 55

Introduction Why Ambiguity Aversion?

Why Ambiguity Aversion? Systematic Pessimism ...

Fact 3: Long-lasting “pessimism” for decision makers inside the economy.

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 6 / 55

Introduction Why Ambiguity Aversion?

This Paper

Part 1: Analytical results without capital Part 2: Quantitative evaluation of full model, RBC extension

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 7 / 55

Introduction Results

Results: A Simple Model without Capital

Analytically, a positive ambiguity shock generates

• lower aggregate output if agents are ambiguity averse
• larger higher-order uncertainty ex ante

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 8 / 55

Introduction Results

Key Mechanism: Impacts of Ambiguity Shock

• Agg. Fundamental

Low Ambiguity High Ambiguity

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 9 / 55

Introduction Results

Results: RBC Extension

Impulse response functions

◮ co-movements of aggregate variables: yt, ct, nt, it, yt/nt ⋆ akin to confidence shock Angeletos, Collard and Dellas (2016), Huo and Takayama (2015), Ilut and Saijo (2016) ◮ counter-cyclical higher-order uncertainty ⋆ cross-sectional dispersion of output forecast in SPF Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 10 / 55

Introduction Results

Results: RBC Extension

Quantitative performance: business cycle moments

◮ near zero correlation between output and productivity ◮ significant negative correlation between hours and productivity ◮ negative correlation between output and higher-order uncertainty Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 11 / 55

Introduction Results

Contribution

A theory of ambiguity-driven business cycles capturing

◮ salient features of the data, in both first- and second- moment statistics

Linkages to games of incomplete information with ambiguity averse preference

◮ GE mechanisms Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 12 / 55

Introduction Literature Review

Related Literature: Business Cycles

Fact 1 Fact 2 Fact 3 Business Cycles Disconnected Countercyclical Long-lasting with Technology or Inflation Forecast Dispersion Pessimism This Paper ✓ ✓ ✓ News Shock: Barsky and Sims (2009), Sims (2009) ✓ ✗ ✗ Jaimovich and Rebelo (2009) Noise Shock: Angeletos and La’O (2009), Lorenzoni (2009) ✓ ✗ ✗ Confidence Shock: Angeletos and La’O (2013), ✓ ✗ ✗ Angeletos, Collard and Dellas (2016), Huo and Takayama (2015) Ambiguity shock: Ilut and Schneider (2014) ✓ ✗ ✓ Misspecification shock: Bhandari, Borovicka and Ho (2016) ✓ ✗ ✓ Uncertainty Shock: Bloom (2009), Bloom et.al (2016) ✓ ? ✗ Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 13 / 55

Introduction Roadmap

Roadmap

A simple static model abstracting out capital

◮ model setup ◮ equilibrium characterization ◮ game theoretic interpretation ◮ analytical results

RBC Extension

◮ impulse response functions ◮ business cycle moments: aggregate variables and Higher-Order uncertainty Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 14 / 55

A Simple Static Model without Capital Model Setup

The Model I: Agents and Markets

A continuum of islands indexed by j ∈ J = [0, 1], each contains

◮ a continuum of firms, indexed by (i, j) ∈ I × J = [0, 1]2 ⋆ producing island commodity j ◮ a continuum of workers, indexed by (i, j) ∈ I × J = [0, 1]2 ◮ island-specific competitive labor market

A mainland that contains

◮ a large number of final good producers ◮ a continuum of households indexed by h ∈ H = [0, 1], each of which ⋆ connects to workers {(h, j) : j ∈ J} and firms {(h, j) : j ∈ J} ◮ centralzed markets for differentiated island-commodities and for final good Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 15 / 55

A Simple Static Model without Capital Model Setup

The Model II: Households

Period utility of the representative houshold u

• Ct, {Nj,t}j∈J
• = C1−γ

t

− 1 1 − γ − χ

• J

N1+ǫ

j,t

1 + ǫ dj Flow budget constraint PtCt =

• J Wj,tNj,tdj +
• J Πj,tdj

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 16 / 55

A Simple Static Model without Capital Model Setup

The Model III: Island Firms

Production function of island j firms Yj,t = Aj,tN1−α

j,t

Island j firms care about u′ (Ct) Pt Πj,t Realized profits of island j firms Πj,t = Pj,tYj,t − Wj,tNi,j,t

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 17 / 55

A Simple Static Model without Capital Model Setup

The Model IV: Final Goods Producer

CES production technology for final goods Yt =

• J Y

θ−1 θ

j,t dj

• θ

θ−1

◮ θ controls the strength of aggregate demand externalities Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 18 / 55

A Simple Static Model without Capital Model Setup

The Model V: Productivity and Ambiguity

Aggregate productivity at ≡ log At is such that at ∼ N

• 0, σ2

ζ

• Guangyu PEI (UZH)

Impacts of Ambiguity Shocks HKBU, 2017 19 / 55

A Simple Static Model without Capital Model Setup

The Model V: Productivity and Ambiguity (Cont.)

Island-specific productivity aj,t ≡ log Aj,t is such that aj,t = at + ιj,t ιj,t ∼ N

• ωt, σ2

ι

• bjectively ωt = 0.

◮ accessible only for island j agents but not for the agents on other islands

Ambiguity: agents cannot fully understand ωt.

◮ A common prior belief over the set of possible models ωt ∈ R:

ωt ∼ N

• 0, eψt

ψt ∼ N

• ψ, σ2

ψ

• ◮ ψt ⇒ the perceived amount of ambiguity

◮ ψ ⇒ the perceived amount of ambiguity at A-SS1

1Ambiguous steady state refers to the state the economy converges to in the absence of any

shocks but taking into account of the existence of ambiguity.

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 20 / 55

A Simple Static Model without Capital Model Setup

The Model VI: Timing and Information Sets

Stage 0 It,0 = {ψt} Nature generates at and {aj,t; j ∈ (0, 1)}. Ambiguity ψt realizes. Stage 1 Ij,t,1 = It,0 ∪ {aj,t} Island j firms and workers observe aj,t, and make local labor supply and demand decisions. Stage 2 It,2 = ∪jIj,t,1 ∪ {ζt} Household observes

• j aj,tdj, ζt
• and makes consumption decisions Ct.

Final goods producers produce.

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 21 / 55

A Simple Static Model without Capital Model Setup

The Model VII: Preferences of Island j Workers

Smooth model of ambiguity:

• Ωt

φ

• E ωt

j,t,1

• C1−γ

t

− 1 1 − γ − χ

• J

N1+ǫ

j,t

1 + ǫ dj

• f w

j,t,1 (ωt) dωt

s.t. PtCt =

• J Wj,tNj,tdj +
• J Πj,tdj

◮ Smooth model of ambiguity: Klibanoff, Marinacci and Mukerji (2005) ◮ CAAA specification

φ (x) = − 1 λe−λx

⋆ λ measures degree of ambiguity aversion Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 22 / 55

A Simple Static Model without Capital Model Setup

The Model VII: Preferences of Island j Workers (Cont.)

Smooth rule of updating

• f w

j,t,1 (ωt) ∝

φ′

• E ωt

j,t,0

• C1−γ

t

−1 1−γ

− χ

J N1+ǫ

j,t

1+ǫ dj

• φ′
• E ωt

j,t,1

• C1−γ

t

−1 1−γ

− χ

J N1+ǫ

j,t

1+ǫ dj

• Weights

f (aj,t|ωt) ft (ωt)

• Bayesian Kernel

◮ Hanany and Klibanoff (2009), Hanany, Klibanoff and Mukerji (2016) Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 23 / 55

A Simple Static Model without Capital Model Setup

The Model VIII: Preferences of Island j Firms

Smooth model of ambiguity:

• Ωt

φ

• E ωt

j,t,1

• C −γ

t

Pt (Pj,tYj,t − Wj,tNj,t)

• f f

j,t,1 (ωt) dωt

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 24 / 55

A Simple Static Model without Capital Model Setup

The Model VIII: Preferences Island j Firms (Cont.)

Smooth rule of updating

• f f

j,t,1 (ωt) ∝

φ′

• E ωt

j,t,0

• C1−γ

t

−1 1−γ

− χ

J N1+ǫ

j,t

1+ǫ dj

• φ′
• E ωt

j,t,1

• C −γ

t

Pt (Pj,tYj,t − Wj,tNj,t)

• Weights

f (aj,t|ωt) ft (ωt)

• Bayesian Kernel

◮ DC from the perspective of households Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 25 / 55

A Simple Static Model without Capital Equilibrium Characterization

Roadmap: Equilibrium Characterization

[Step 1]: Optimality conditions [Step 2]: Joint approximation of belief and allocations [Step 3]: Unique estimated symmetric conditional log-normal equilibrium [Step 4]: Game theoretic interpretation

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 26 / 55

A Simple Static Model without Capital Equilibrium Characterization

Equilibrium Characterisation I

Demand for island j commodity Yj,t = Pj,t Pt −θ Yt Price index Pt =

• j P1−θ

j,t dj

• 1

1−θ

= 1 Market clearing of final goods Ct = Yt

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 27 / 55

A Simple Static Model without Capital Equilibrium Characterization

Equilibrium Characterisation II

Equilibrium level of employment is pinned down by χNǫ

j,t =

    

• R E ωt

j,t,1

• Y

1 θ −γ

t

Y − 1

θ

j,t

• fj,t,1 (ωt) dωt
• marginal utility of island j commodity

           (1 − α) Yj,t Nj,t

• marginal productivity

      with distorted posterior belief over possible models at Stage 1:

• fj,t,1 (ωt) ∝ φ′
• E ωt

j,t,0

• C1−γ

t

− 1 1 − γ − χ

• J

N1+ǫ

j,t

1 + ǫ dj

• Belief Distortion

f (aj,t|ωt) ft (ωt)

• Bayesian Kernel

Assume that 1

θ − 1 > 0, i.e. complementarity in production across islands

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 28 / 55

A Simple Static Model without Capital Equilibrium Characterization

Equilibrium Characterisation III

Joint approximation of equilibrium allocation and belief distortion

◮ double fixed point conditions

Justification for Conditional Log-Normal Equilibrium

Definition: Conditional Log-Normal Equilibrium.

An allocation {Yj,t, Yt}j∈J constitutes a conditional log-normal equilibrium if both Yj,t|ψt and Yt|ψt are log-normally distributed.

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 29 / 55

A Simple Static Model without Capital Equilibrium Characterization

Symmetric Conditional Log-Normal Equilibrium

Proposition: Equilibrium Characterization.

There exists a unique approximated symmetric conditional log-normal equilibrium where the allocation {Yj,t, Yt}j∈J is such that

• yj,t ≡ ln Yj,t −

  y∗ + hy

• ψ
• Ambiguous SS

   =κyaj (ψt, λ) · aj,t

• Use of Private Info.

+

• hy (ψt, λ)
• Impact of Amb. Shock
• yt ≡ ln Yt −

  y∗ + hy

• ψ
• Ambiguous SS

   =κyaj (ψt, λ) ·

• J aj,tdj
• Use of Private Info.

+

• hy (ψt, λ)
• Impact of Amb. Shock

where hy (ψt; λ) denotes the impact of ambiguity shocks on island and aggregate

• utput satisfying
• hy
• ψ, λ

= 0

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 30 / 55

A Simple Static Model without Capital Equilibrium Characterization

Game Theoretic Interpretation

Equilibrium allocation is identical to that of a beauty contest such that yj,t =

• 1+ǫ

1−α 1+ǫ 1−α − 1 + 1 θ

• κa

aj,t +

• 1

θ − γ 1+ǫ 1−α − 1 + 1 θ

• κy ∈ (0, 1)

Ej,t [yt] The distorted information structure is given by

• aj,t =

at + ιj,t,

• ιj,t ∼ N
• 0, σ2

ι

• at ∼ N
• gµ (ψt, λ), σ2

ζ + eψt + gσ (ψt, λ)

• Guangyu PEI (UZH)

Impacts of Ambiguity Shocks HKBU, 2017 31 / 55

A Simple Static Model without Capital Equilibrium Characterization

Game Theoretic Interpretation (Cont.)

• Agg. Fundamental

Low Ambiguity High Ambiguity

• at ∼ N
• gµ (ψt, λ), σ2

ζ + eψt + gσ (ψt, λ)

• ∂
• eψt + gσ (ψt, λ)
• ∂ψt

< 0, ∂gµ (ψt, λ) ∂ψt < 0

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 32 / 55

A Simple Static Model without Capital Results

Results: Aggregate Fluctuations

Fact 1: Business cycles disconnected with technology or inflation

Proposition: Ambiguity Driven Business Cycles.

A positive ambiguity shock that increases the amount of ambiguity ψt generates lower aggregate output in the sense that ∂ hy (ψt, λ) ∂ψt < 0 if agents are ambiguity averse, i.e. λ > 0.

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 33 / 55

A Simple Static Model without Capital Results

Results: Use of Private Information

Proposition: Use of Private Information

In equilibrium, use of private information κyaj (ψt, λ) is an increasing function of amount of ambiguity ψt.

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 34 / 55

A Simple Static Model without Capital Results

Results: Higher-Order Uncertainty

Assumption: Ambiguity Neutral Professional Forecasters

Professional forecasters possess ambiguity over the cross-sectional mean of idiosyncratic TFP shocks. However, they are ambiguity neutral, i.e., λ = 0.

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 35 / 55

A Simple Static Model without Capital Results

Results: Higher-Order Uncertainty

Fact 2: Countercyclical cross-sectional dispersion of output forecast.

Corollary: Higher-Order Uncertainty

Higher-order uncertainty, measured by output forecast dispersion ex-ante, FDt (ψt) ≡

• J
• Ej,t [yt] −
• J Ej,t [yt] dj

2 dj is increasing in the amount of ambiguity ψt, i.e., ∂FDt(ψt)

∂ψt

> 0. Aggregate output forecast of ambiguity neutral professional forecasters λ = 0: Ej,t [yt] = y∗ + hy

• ψ

+ κyaj (ψt, λ)

• σ2

ζ + eψt

σ2

ζ + eψt + σ2 ι

• aj,t +

hy (ψt, λ) .

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 36 / 55

A Simple Static Model without Capital Discussion

Game Theoretic Interpretation

Equilibrium allocation is identical to that of a beauty contest such that yj,t =

• 1+ǫ

1−α 1+ǫ 1−α − 1 + 1 θ

• κa

aj,t +

• 1

θ − γ 1+ǫ 1−α − 1 + 1 θ

• κy ∈ (0, 1)

Ej,t [yt] The distorted information structure is given by

• aj,t =

at + ιj,t,

• ιj,t ∼ N
• 0, σ2

ι

• at ∼ N
• gµ (ψt, λ), σ2

ζ + eψt + gσ (ψt, λ)

• Guangyu PEI (UZH)

Impacts of Ambiguity Shocks HKBU, 2017 37 / 55

A Simple Static Model without Capital Discussion

Discussion: General Equilibrium (GE) Mechanism I

Proposition: GE Mechanism and Pessimism

GE mechanism amplifies the impact of ambiguity shocks on aggregate output in the sense that ∂ ∂

hy (ψt,λ) ∂ψt

∂κy < 0

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 38 / 55

A Simple Static Model without Capital Discussion

Discussion: General Equilibrium (GE) Mechanism II

Proposition: Dampening GE

Elasticity of the aggregate TFP shock with the presence of ambiguity under incomplete information, denoted as εInc,Amb, can be expressed into εInc,Amb (∆, ψt) = εMicro + π (∆, ψt)

• εMacro − εMicro

where ∆ =

σ2

ζ

σ2

ζ +σ2 ι ∈ (0, 1) and ψt measures the amount of ambiguity. Here the

function π (∆, ψt) satisfies the followings: π (0, ψt) = 0 π (1, ψt) = 1 π (∆, −∞) ∈ (0, 1) π (∆, +∞) = 1 and ∂π (∆, ψt) ∂∆ > 0 ∂π (∆, ψt) ∂ψt > 0

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 39 / 55

A Simple Static Model without Capital Discussion

Take-home Lesson (so far)

Tractable model of business cycle driven by ambiguity shock

◮ aggregate fluctuations ◮ counter-cyclical Higher-Order uncertainty

Game theoretic interpretation

◮ Discussions about GE mechanism Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 40 / 55

RBC Extension with Capital

RBC Extension: TFP and Ambiguity Processes

Aggregate TFP at ≡ log At follows an AR(1) process at = ρat−1 + ζt with ζt ∼ N

• 0, σ2

ζ

• Guangyu PEI (UZH)

Impacts of Ambiguity Shocks HKBU, 2017 41 / 55

RBC Extension with Capital

RBC Extension: TFP and Ambiguity Processes (Cont.)

Island-specific productivity aj,t ≡ log Aj,t is such that aj,t = at + ιj,t ιj,t ∼ N

• ωt, σ2

ι

• bjectively ωt = 0 for ∀t.

◮ accessible only for island j agents but not for the agents on other islands Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 42 / 55

RBC Extension with Capital

RBC Extension: TFP and Ambiguity Processes (Cont.)

At period t, agents cannot fully understand At = {ωt+k : ∀k ≥ 0}

◮ period t prior belief over possible models At ∈ At:

ωt+k ∼ i.i.d N

• 0, eψt,t+k ∀k ≥ 0,

ψt,t+k =

• 1 − ρk

ψ

• ψ + ρk

ψψt

◮ Amount of ambiguity ψt follows an AR(1) process

ψt − ψ = ρψ

• ψt−1 − ψ

+ τt with τt ∼ N

• 0, σ2

τ

• ⋆ ψ measures the amount of ambiguity at the ambiguous steady state

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 43 / 55

RBC Extension with Capital

RBC Extension: Timing and Information Sets

Stage 0 It,0 = It−1,2 ∪ {ψt} Nature generates at and {aj,t; j ∈ (0, 1)}. Ambiguity shock τt realizes, hence ψt. Stage 1 Ij,t,1 = It,0 ∪ {xj,t} Island j firms and worker observe xj,t, and make local factors supply and demand decisions, where capital supply Kj,t is pre-determined. Stage 2 It,2 = ∪jIj,t,1 ∪ {ζt} Consumer observes {zt, ζt} and makes consumption decisions Ct and saves in the form of {Kj,t+1}∞

j=1.

Final goods producers produce.

xj,t = ζt + ιj,t zt =

• J xj,tdj = ζt + ωt

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 44 / 55

RBC Extension with Capital

RBC Extension: Preferences of Consumers

Recursive smooth model of ambiguity Jt ≡ J

• kt, at−1, zt, ζt, ψt
• Jt =

max

Ct,{Kj,t+1}

u (Ct) − χ

• j

N1+ǫ

j,t

1 + ǫ dj + βφ−1

• R φ
• E ωt+1

t,2

[Jt+1]

• ft,2 (ωt+1) dωt+1
• Utility Equivalent of the Ambiguous Continuation Value

s.t. PtCt + Pt

• J Ij,tdj =
• J Wj,tNj,tdj +
• J Rj,tKj,tdj +
• J Πj,tdj

Kj,t+1 = (1 − δ) Kj,t + Ij,t

◮ Klibanoff, Marinacci and Mukerji (2009): Bayesian posterior ft,2 (ωt+1)

Log-exponential specification: u (Ct) = ln (Ct) φ (x) = − 1 λe−λx.

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 45 / 55

RBC Extension with Capital

RBC Extension: Interim Beliefs of Island j Agents

Interim beliefs of island j workers

• f w

j,t,1 (ωt) ∝

φ′ E ωt

j,t,0 [Jt]

• φ′
• E ωt

j,t,1

• ln (Ct) − χ

J N1+ǫ

j,t

1+ǫ dj

• Weights

f (aj,t|ωt) ft (ωt)

• Bayesian Kernel

Interim beliefs of island j firms

• f f

j,t,1 (ωt) ∝

φ′ E ωt

j,t,0 [Jt]

• φ′
• E ωt

j,t,1

• 1

CtPt (Pj,tYj,t − Wj,tNj,t)

• Weights

f (aj,t|ωt) ft (ωt)

• Bayesian Kernel

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 46 / 55

RBC Extension with Capital Quantitative Evaluation

Quantitative Methodology

Semi-log-linearisation around the ambiguous steady state

yj,t =y∗ + hy

• ψ
• Amb. SS

+ κyk kt + κyaat−1 + κyx (ψt) xj,t

• Semi-linear Components

+

• hy (ψt)

Non-linear Func.

ct =c∗ + hc

• ψ
• Amb. SS

+ κck kt + κcaat−1 + κcz (ψt) zt + κcζ (ψt) ζt

• Semi-linear Components

+

• hc (ψt)

Non-linear Func.

Approximation of belief distortion Mt (ωt) = e−λE ωt

t,0 [Jt]

E ωt

t,0 [Jt] ≈constantt + κJzωt + 1

2κJzzω2

t

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 47 / 55

RBC Extension with Capital Quantitative Evaluation

RBC Extension: Model Parameters

Parameters Value Role β 0.99 discount factor ǫ 0.5 Frisch elasticity=2 α 0.36 capital share δ 0.025 depreciation rate θ 1 Cobb-Douglas aggregation χ 3.75 1/3 hours at D-SS ρ 0.95 persistence of agg. TFP shock ρψ 0.75 persistence of ambiguity shock

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 48 / 55

RBC Extension with Capital Quantitative Evaluation

RBC Extension: Calibrated Model Parameters

Targets of calibration:

◮ stddev(y), stddev(c), stddev(h), stddev(i), and stddev(y/n)

Parameters Value Role 100σζ 0.65

• std. dev. of agg. TFP Shock

σι 0.1

• std. dev. of island TFP shock

στ 0.43

• std. dev. of ambiguity shock

ψ

• 5

amount of ambiguity eψ at A-SS λ 10 Degree of ambiguity aversion

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 49 / 55

RBC Extension with Capital Quantitative Evaluation

IRFs of Ambiguity Shock: Aggregate Variables

5 10 15 20

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

Output

5 10 15 20

• 0.4
• 0.35
• 0.3
• 0.25
• 0.2
• 0.15
• 0.1
• 0.05

Consumption

5 10 15 20

• 2.5
• 2
• 1.5
• 1
• 0.5

Hours

5 10 15 20

• 4
• 3.5
• 3
• 2.5
• 2
• 1.5
• 1
• 0.5

Investment

5 10 15 20

• 0.1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Productivity

5 10 15 20 0.5 1 1.5 2 2.5

Total Labor Wedge Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 50 / 55

RBC Extension with Capital Quantitative Evaluation

Moments of Aggregate Variables

Data(1969Q1-2016Q4) Baseline Model A Only ψ Only Standard Deviations stddev(y) 1.42 1.56 1 1.2 stddev(c) 0.83 0.65 0.34 0.56 stddev(n) 1.71 1.86 0.46 1.83 stddev(i) 5.4 4.5 3.32 3.1 stddev(y/n) 0.83 0.89 0.58 0.67 Correlations corr(c, y) 0.86 0.95 0.94 0.98 corr(n, y) 0.88 0.88 0.99 0.99 corr(i, y) 0.95 0.99 0.99 0.99

• Corr. with Productivity

corr(y, y/n)

• 0.09
• 0.1

0.99

• 0.98

corr(n, y/n)

• 0.56
• 0.56

0.97

• 0.99

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 51 / 55

RBC Extension with Capital Quantitative Evaluation

Labor Wedge

Data(1969Q1-2016Q4) Model Stddev 2.1 2.1 Correlation with y

• 0.73
• 0.72

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 52 / 55

RBC Extension with Capital Quantitative Evaluation

Professional Forecasts

Ambiguity neutral λ = 0. Access to additional private information regarding average productivity sj,t =

• J xj,tdj + ξj,t

with ξj,t ∼ N

• 0, σ2

ξ

• ◮ Calibration of σ2

ξ : long-run average of cross-sectional dispersion in SPF data.

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 53 / 55

RBC Extension with Capital Quantitative Evaluation

Moments of Output Forecast Dispersion

Data(1981Q3-2016Q4) Model Stddev 0.05 0.02 Correlation with y

• 0.41
• 0.72

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 54 / 55

Conclusion

Conclusion

A theory of ambiguity-driven business cycles

◮ ambiguity shock as aggregate demand shock ◮ counter-cyclical higher-order uncertainty ◮ match salient features of the data, in both first- and second- moment statistics Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 55 / 55