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 ◮ co-movements of aggregate variables: y t , c t , n t , i t , y t / n t ⋆ 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 � � � N 1 + ǫ = C 1 − γ − 1 j , t t u C t , { N j , t } j ∈ J − χ 1 + ǫ dj 1 − γ J Flow budget constraint � � P t C t = J W j , t N j , t dj + J Π j , t dj 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 Y j , t = A j , t N 1 − α j , t Island j firms care about u ′ ( C t ) Π j , t P t Realized profits of island j firms Π j , t = P j , t Y j , t − W j , t N i , 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 Y t = θ J Y j , t dj ◮ 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 a t ≡ log A t is such that � � 0, σ 2 a t ∼ N 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 a j , t ≡ log A j , t is such that � � ω t , σ 2 a j , t = a t + ι j , t ι j , t ∼ N objectively ω t = 0. ι ◮ accessible only for island j agents but not for the agents on other islands Ambiguity: agents cannot fully understand ω t . ◮ A common prior belief over the set of possible models ω t ∈ R : � � � 0, e ψ t � ψ , σ 2 ω t ∼ N ψ t ∼ N ψ ◮ ψ t ⇒ the perceived amount of ambiguity ◮ ψ ⇒ the perceived amount of ambiguity at A-SS 1 1 Ambiguous 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 I t, 0 = { ψ t } I j,t, 1 = I t, 0 ∪ { a j,t } I t, 2 = ∪ j I j,t, 1 ∪ { ζ t } �� � Nature generates Island j firms and workers observe a j,t , Household observes j a j,t dj, ζ t a t and { a j,t ; j ∈ (0 , 1) } . and makes consumption decisions C t . and make local labor Ambiguity ψ t 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: � � �� � � N 1 + ǫ C 1 − γ − 1 j , t E ω t t f w � φ − χ 1 + ǫ dj j , t ,1 ( ω t ) d ω t j , t ,1 1 − γ Ω t J � � s.t. P t C t = J W j , t N j , t dj + J Π j , t dj ◮ Smooth model of ambiguity: Klibanoff, Marinacci and Mukerji (2005) ◮ CAAA specification φ ( x ) = − 1 λ e − λ x ⋆ 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 � � �� − χ � N 1 + ǫ C 1 − γ − 1 φ ′ E ω t j , t t 1 + ǫ dj j , t ,0 1 − γ J f w � j , t ,1 ( ω t ) ∝ � � �� f ( a j , t | ω t ) f t ( ω t ) − χ � N 1 + ǫ C 1 − γ � �� � − 1 E ω t φ ′ j , t t 1 + ǫ dj j , t ,1 1 − γ J Bayesian Kernel � �� � Weights ◮ 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: � � �� � C − γ E ω t t f f � φ ( P j , t Y j , t − W j , t N j , t ) j , t ,1 ( ω t ) d ω t j , t ,1 P t Ω t Guangyu PEI (UZH) Impacts of Ambiguity Shocks HKBU, 2017 24 / 55
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