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

High Ambiguity Low Ambiguity

Agg. Fundamental

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 9 / 55 Introduction Results Results: RBC Extension

Impulse response functions I co-movements of aggregate variables: yt , ct , nt , it , yt /nt F akin to conﬁdence shock Angeletos, Collard and Dellas (2016), Huo and Takayama (2015), Ilut and Saijo (2016) I counter-cyclical higher-order uncertainty F 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

I near zero correlation between output and productivity I signiﬁcant negative correlation between hours and productivity I 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

I salient features of the data, in both ﬁrst- and second- moment statistics Linkages to games of incomplete information with ambiguity averse preference

I 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

I model setup I equilibrium characterization I game theoretic interpretation I analytical results RBC Extension

I impulse response functions I 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 ∈ 2 I a continuum of ﬁrms, indexed by (i, j) I J = [0, 1] ∈ × F producing island commodity j 2 I a continuum of workers, indexed by (i, j) I J = [0, 1] ∈ × I island-speciﬁc competitive labor market A mainland that contains

I a large number of final good producers I a continuum of households indexed by h H = [0, 1], each of which ∈ F connects to workers (h, j) : j J and firms (h, j) : j J { ∈ } { ∈ } I 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

1 γ N1+e Ct − 1 j,t u Ct , Nj,t j J = − χ dj { } ∈ 1 γ − J 1 + e − Z Flow budget constraint

Pt Ct = Wj,t Nj,t dj + Πj,t dj ZJ ZJ

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

1 α Yj,t = Aj,t Nj,−t Island j ﬁrms care about

u0 (Ct ) Πj,t Pt Realized proﬁts of island j ﬁrms

Πj,t = Pj,t Yj,t Wj,t Ni,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

θ θ 1 θ 1 −θ − Yt = Yj,t dj ZJ

I 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 ≡ 2 at N 0, σ ∼ 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 ≡ 2 aj,t = at + ιj,t ιj,t N ωt , σ objectively ωt = 0. ∼ ι

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

Ambiguity: agents cannot fully understand ωt . I A common prior belief over the set of possible models ωt : ∈ R ψ 2 ωt N 0, e t ψt N ψ, σ ∼ ∼ ψ I ψt the perceived amount of ambiguity ⇒ 1 I ψ the perceived amount of ambiguity at A-SS ⇒

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 Stage 1 Stage 2 = ψ = a = ζ It,0 { t} Ij,t,1 It,0 ∪{ j,t} It,2 ∪j Ij,t,1 ∪{ t}

Nature generates Island j ﬁrms and workers observe aj,t, Household observes j aj,tdj, ζt at and aj,t; j (0, 1) . and make local labor and makes consumptionn decisionsoCt. { ∈ } R Ambiguity ψt realizes. supply and demand decisions. 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:

1 γ N1+e ωt Ct − 1 j,t w φ Ej,t,1 − χ dj fj,t,1 (ωt ) dωt Ω 1 γ − J 1 + e Z t " − Z #! e s.t. Pt Ct = Wj,t Nj,t dj + Πj,t dj ZJ ZJ

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

1 λx φ (x) = e− − λ

F 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

1 γ 1+e ω C − 1 Nj,t φ E t t − χ dj 0 j,t,0 1 γ − J 1+e f w (ω ) ∝ − f (a ω ) f (ω ) j,t,1 t 1 γ 1+e j,t t t t ω C − 1 R Nj,t | φ E t t − χ dj 0 j,t,1 1 γ − J 1+e Bayesian Kernel e − Weights R | {z } | {z } I 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:

γ C − φ E ωt t (P Y W N ) f f (ω ) dω j,t,1 P j,t j,t j,t j,t j,t,1 t t ZΩt " t − #! e

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

1 γ 1+e ω C − 1 Nj,t φ E t t − χ dj 0 j,t,0 1 γ − J 1+e f f (ω ) ∝ − f (a ω ) f (ω ) j,t,1 t γ j,t t t t ωt Ct− R | φ E (Pj,t Yj,t Wj,t Nj,t ) 0 j,t,1 Pt − Bayesian Kernel e Weights | {z } | {z } I 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

θ Pj,t − Y = Y j,t P t t Price index

1 1 θ 1 θ − Pt = Pj,−t dj = 1 Zj 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

1 γ 1 Y e  ωt θ θ   j,t  χNj,t = Ej,t,1 Yt − Yj−,t fj,t,1 (ωt ) dωt (1 α) − Nj,t ZR        marginal utility of islandej commodity  marginal productivity         with distorted| posterior belief over{z possible models} at Stage| 1: {z }

1 γ N1+e ωt Ct − 1 j,t fj,t,1 (ωt ) ∝ φ0 Ej,t,0 − χ dj f (aj,t ωt ) ft (ωt ) 1 γ J 1 + e " − Z #! | − Bayesian Kernel e Belief Distortion | {z } Assume that 1 | 1 > 0, i.e. complementarity{z in production} across islands θ −

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

I 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 =κya (ψt , λ) aj,t + hy (ψt , λ) ≡ −   j · Ambiguous SS Use of Private Info. Impact of Amb. Shock b   b | {z } | {z } | {z } y ln Y y h , a dj h , t t  ∗ + y ψ  =κyaj (ψt λ) j,t + y (ψt λ) ≡ − · ZJ Ambiguous SS Impact of Amb. Shock   Use of Private Info. b   b | {z } | {z } | {z } where hy (ψt ; λ) denotes the impact of ambiguity shocks on island and aggregate output satisfying b hy ψ, λ = 0 b 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

1+e 1 γ y 1 α a θ E y j,t = 1+e − 1 j,t + 1+e − 1 j,t [ t ] 1 α 1 + θ ! 1 α 1 + θ ! − − − − κa κy (0, 1) ∈ The distorted information| {z structure} is given| by {z }

2 aj,t = at + ιj,t , ιj,t N 0, σ ∼ ι 2 ψt at N g (ψt , λ), σ + e + g (ψt , λ) e ∼ e µe e ζ σ e

Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 31 / 55 A Simple Static Model without Capital Equilibrium Characterization Game Theoretic Interpretation (Cont.)

High Ambiguity Low Ambiguity

Agg. Fundamental

2 ψt at N g (ψt , λ), σ + e + g (ψt , λ) ∼ µ ζ σ ψt ∂ e + gσ (ψt , λ) ∂gµ (ψt , λ) e < 0, < 0 ∂ψt ∂ψt

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

∂h (ψ , λ) y t < 0 ∂ψt b 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,

2 FDt (ψt ) Ej,t [yt ] Ej,t [yt ] dj dj ≡ J − J Z Z FD is increasing in the amount of ambiguity ψ , i.e., ∂ t (ψt ) > 0. t ∂ψt

Aggregate output forecast of ambiguity neutral professional forecasters λ = 0:

2 ψt σζ + e Ej,t [yt ] = y ∗ + hy ψ + κya (ψt , λ) aj,t + hy (ψt , λ) . j 2 ψt 2 σζ + e + σι ! b

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

1+e 1 γ y 1 α a θ E y j,t = 1+e − 1 j,t + 1+e − 1 j,t [ t ] 1 α 1 + θ ! 1 α 1 + θ ! − − − − κa κy (0, 1) ∈ The distorted information| {z structure} is given| by {z }

2 aj,t = at + ιj,t , ιj,t N 0, σ ∼ ι 2 ψt at N g (ψt , λ), σ + e + g (ψt , λ) e ∼ e µe e ζ σ e

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

h ( , ) ∂ ∂ y ψt λ ∂ψt 0 b < ∂κy

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

Micro Macro Micro εInc,Amb (∆, ψt ) = ε + π (∆, ψt ) ε ε − 2 σζ where ∆ = 2 2 (0, 1) and ψt measures the amount of ambiguity. Here the σζ +σι ∈ function π (∆, ψt ) satisﬁes the followings:

π (0, ψt ) = 0 π (1, ψt ) = 1 π (∆, ∞) (0, 1) π (∆, +∞) = 1 − ∈ and ∂π (∆, ψ ) ∂π (∆, ψ ) t > 0 t > 0 ∂∆ ∂ψt

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

I aggregate ﬂuctuations I counter-cyclical Higher-Order uncertainty Game theoretic interpretation

I 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 ≡ 2 at = ρat 1 + ζt with ζt N 0, σζ − ∼

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 ≡ 2 aj,t = at + ιj,t ιj,t N ωt , σ objectively ωt = 0 for t. ∼ ι ∀

I 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 { + ∀ ≥ } I period t prior belief over possible models At t : ∈ A

ψt,t+k k k ωt k i.i.d N 0, e k 0, ψt,t k = 1 ρ ψ + ρ ψt + ∼ ∀ ≥ + − ψ ψ I Amount of ambiguity ψt follows an AR(1) process

2 ψt ψ = ρψ ψt 1 ψ + τt with τt N 0, στ − − − ∼ F 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 Stage 1 Stage 2

t,0 = t 1,2 ψt j,t,1 = t,0 xj,t t,2 = j j,t,1 ζt I I − ∪{ } I I ∪{ } I ∪ I ∪{ }

Nature generates Island j ﬁrms and worker observe xj,t, Consumer observes z , ζ and { t t} at and aj,t; j (0, 1) . and make local factors makes consumption decisions Ct { ∈ } Ambiguity shock τ realizes, supply and demand decisions, and saves in the form of Kj,t+1 ∞ . t { }j=1 hence ψt. where capital supply Kj,t is pre-determined. Final goods producers produce.

xj,t = ζt + ιj,t zt = xj,t dj = ζt + ωt ZJ

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 ≡ − 1+e Nj,t b Jt = max u (Ct ) χ dj Ct , Kj,t+1 − j 1 + e { } Z 1 ωt+1 + βφ− φ Et,2 [Jt+1] ft,2 (ωt+1) dωt+1 ZR Utility Equivalent of the Ambiguous Continuation Value

s.t. Pt Ct + Pt |Ij,t dj = Wj,t Nj,t dj{z+ Rj,t Kj,t dj + Πj},t dj ZJ ZJ ZJ ZJ Kj,t 1 = (1 δ) Kj,t + Ij,t + −

I Klibanoﬀ, Marinacci and Mukerji (2009): Bayesian posterior ft,2 (ωt+1) Log-exponential speciﬁcation:

1 λx u (Ct ) = ln (Ct ) φ (x) = e− . − λ

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

ωt φ E [Jt ] w 0 j,t,0 f (ωt ) ∝ f (aj,t ωt ) ft (ωt ) j,t,1 N1+e ωt j,t | φ E ln (Ct ) χ dj 0 j,t,1 − J 1+e Bayesian Kernel e Weights R | {z }

Interim beliefs of island| j ﬁrms {z }

ωt φ E [Jt ] f 0 j,t,0 fj,t,1 (ωt ) ∝ f (aj,t ωt ) ft (ωt ) ωt 1 | φ0 E (Pj,t Yj,t Wj,t Nj,t ) j,t,1 Ct Pt − Bayesian Kernel e h i Weights | {z } | {z }

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 + κyk kt + κyaat 1 + κyx (ψt ) xj,t + hy (ψt ) − Amb. SS Semi-linear Components Non-linear Func. b b ct =c|∗ +{zhc ψ} + κck kt + κcaat 1 + κcz (|ψt ) z{zt + κc}ζ (ψt ) ζt + | {zhc (}ψt ) − Amb. SS Semi-linear Components Non-linear Func. b b | {z } Approximation| {z of} belief distortion | {z }

ωt λE [Jt ] ωt 1 2 Mt (ωt ) = e− t,0 E [Jt ] constantt + κJz ωt + κJzz ω t,0 ≈ 2 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 e 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: I 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

Output Consumption Hours 0 0 0

-0.2 -0.05 -0.5 -0.1 -0.4

-0.15 -0.6 -1 -0.2 -0.8 -0.25 -1.5

-1 -0.3 -2 -1.2 -0.35

-1.4 -0.4 -2.5 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20

Investment Productivity Total Labor Wedge 0.8 2.5 0

0.7 -0.5 2 0.6 -1 0.5 -1.5 1.5 0.4 -2 0.3 1 -2.5 0.2

-3 0.1 0.5

-3.5 0

-4 -0.1 0 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20

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

2 sj,t = xj,t dj + ξj,t with ξj,t N 0, σξ J ∼ Z 2 I Calibration of σξ : 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

I ambiguity shock as aggregate demand shock I counter-cyclical higher-order uncertainty I match salient features of the data, in both ﬁrst- and second- moment statistics

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