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 333 News Shock: Barsky and Sims (2009), Sims (2009) 377 Jaimovich and Rebelo (2009) Noise Shock: Angeletos and La'O (2009), Lorenzoni (2009) 377 Confidence Shock: Angeletos and La'O (2013), 377 Angeletos, Collard and Dellas (2016), Huo and Takayama (2015) Ambiguity shock: Ilut and Schneider (2014) 373 Misspecification shock: Bhandari, Borovicka and Ho (2016) 373 Uncertainty Shock: Bloom (2009), Bloom et.al (2016) 3 ? 7 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 2 I a continuum of firms, indexed by (i, j) I J = [0, 1] 2 × F producing island commodity j 2 I a continuum of workers, indexed by (i, j) I J = [0, 1] 2 × 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 2 F connects to workers (h, j) : j J and firms (h, j) : j J f 2 g f 2 g 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 g N1+e Ct − 1 j,t u Ct , Nj,t j J = − c dj f g 2 1 g − J 1 + e − Z Flow budget constraint Pt Ct = Wj,t Nj,t dj + Pj,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 a Yj,t = Aj,t Nj,−t Island j firms care about u0 (Ct ) Pj,t Pt Realized profits of island j firms Pj,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 q q 1 q 1 −q − Yt = Yj,t dj ZJ I q 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, s ∼ z 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 + ij,t ij,t N wt , s objectively wt = 0. ∼ i I accessible only for island j agents but not for the agents on other islands Ambiguity: agents cannot fully understand wt . I A common prior belief over the set of possible models wt : 2 R y 2 wt N 0, e t yt N y, s ∼ ∼ y I yt the perceived amount of ambiguity ) 1 I y 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 g N1+e wt Ct − 1 j,t w f Ej,t,1 − c dj fj,t,1 (wt ) dwt W 1 g − J 1 + e Z t " − Z #! e s.t. Pt Ct = Wj,t Nj,t dj + Pj,t dj ZJ ZJ I Smooth model of ambiguity: Klibanoff, Marinacci and Mukerji (2005) I CAAA specification 1 lx f (x) = e− − l F l 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 g 1+e w C − 1 Nj,t f E t t − c dj 0 j,t,0 1 g − J 1+e f w (w ) ∝ − f (a w ) f (w ) j,t,1 t 1 g 1+e j,t t t t w C − 1 R Nj,t j f E t t − c dj 0 j,t,1 1 g − 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: g C − f E wt t (P Y W N ) f f (w ) dw j,t,1 P j,t j,t j,t j,t j,t,1 t t ZWt " 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 g 1+e w C − 1 Nj,t f E t t − c dj 0 j,t,0 1 g − J 1+e f f (w ) ∝ − f (a w ) f (w ) j,t,1 t g j,t t t t wt Ct− R j f 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 q Pj,t − Y = Y j,t P t t Price index 1 1 q 1 q − 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 g 1 Y e 0 wt q q 1 0 j,t 1 cNj,t = Ej,t,1 Yt − Yj−,t fj,t,1 (wt ) dwt (1 a) − Nj,t ZR B C B C B C B marginal utility of islandej commodity C Bmarginal productivityC B C B C @ A @ A with distorted| posterior belief over{z possible models} at Stage| 1: {z } 1 g N1+e wt Ct − 1 j,t fj,t,1 (wt ) ∝ f0 Ej,t,0 − c dj f (aj,t wt ) ft (wt ) 1 g J 1 + e " − Z #! j − Bayesian Kernel e Belief Distortion | {z } Assume that 1 | 1 > 0, i.e.