Reputation for Quality Simon Board, Moritz Meyer-ter-Vehn UCLA - - PowerPoint PPT Presentation

Introduction Model Equilibrium Analysis Good News Bad News Imperfect Learning Moreover Reputation for Quality Simon Board, Moritz Meyer-ter-Vehn UCLA - Department of Economics March 2011

Introduction Model Equilibrium Analysis Good News Bad News Imperfect Learning Moreover Overview Investment and Reputation � “Firm” can invest into future quality � Moral hazard due to imperfect observability � Reputation gives …rm incentive to invest Modeling Innovation � Persistent quality: function of past investments � Reputation: belief over endogenous state variable Project Analyzes � Reputational investment incentives � Reputational dynamics

Introduction Model Equilibrium Analysis Good News Bad News Imperfect Learning Moreover Learning Processes Perfect Good News - Labor markets � Market discovers high quality via “breakthroughs” � Work-Shirk Equilibrium & Ergodic Dynamics Perfect Bad News - Computer industry � Market discovers low quality via “breakdowns” � Shirk-Work Equilibria & Non-ergodic Dynamics Imperfect Learning - Automotive � Gradual market learning through consumer reports � Work-Shirk Equilibrium & Ergodic Dynamics ...

Introduction Model Equilibrium Analysis Good News Bad News Imperfect Learning Moreover Literature - Reputation Theory � Moral Hazard: Kreps (1990), ... � Adverse Selection: Bar-Isaac (2003), ... � Combination: � Kreps, Wilson (1982) � Holmstrom (1999) � Mailath, Samuelson (2001), ... Empirical � eBay: Cabral, Hortacsu (2008); Resneck et al. (2006) � Airlines: Bosch et al. (1998); Chalk (1987) � Restaurant Hygiene: Jin, Leslie (2009)

Introduction Model Equilibrium Analysis Good News Bad News Imperfect Learning Moreover Outline 1. Introduction 2. Model 3. Equilibrium Analysis 4. Perfect Good News 5. Perfect Bad News 6. Imperfect Learning 7. Quality Choice

Introduction Model Equilibrium Analysis Good News Bad News Imperfect Learning Moreover Bare-Bones Model Players: One long-lived …rm, many short-lived consumers Timing: Continuous time t 2 [ 0 , ∞ ) , discount rate r � Quality θ t 2 f L = 0 , H = 1 g � Invest η t 2 [ 0 , 1 ] at marginal cost c � Expected consumption utility θ t � Reputation x t = E [ θ t ] MPE: Beliefs e η = e η ( x ) , strategies η = η ( θ , x ) with (1) η ( x t , θ t ) maximizes value V θ ( x ) = R e � rt E [ x t � c η t ] dt (2) Correct beliefs: e η ( x ) = E [ η ( θ , x ) j x ]

Introduction Model Equilibrium Analysis Good News Bad News Imperfect Learning Moreover Fleshing out the Model Technology: Poisson shocks with intensity λ � At shock, e¤ort determines quality Pr ( θ t = H ) = η t � Otherwise, quality is constant θ t = θ t � dt Z t 0 e λ ( s � t ) λη s ds + e � λ t Pr ( θ 0 = H ) Pr ( θ t = H ) = Information: Consumers update reputation x t : (1) Poisson signal with arrival rate µ L , µ H (2) Believed e¤ort e η t dx t = “ Bayes ” + λ ( e η t � x t ) dt

Introduction Model Equilibrium Analysis Good News Bad News Imperfect Learning Moreover Bayesian Learning from Poisson Signals Perfect Good News: Product breakthrough with probability θ t dt � Breakthrough: x t jumps to 1 � Otherwise: dx = � x ( 1 � x ) dt Perfect Bad News: Product breakdown with prob. ( 1 � θ t ) dt � Breakdown: x t jumps to 0 � Otherwise: dx = x ( 1 � x ) dt Imperfect News: Signal with net arrival rate µ = µ H � µ L � Arrival: x t jumps to j ( x ) = x + µ x ( 1 � x ) ( � � � ) � Otherwise: dx = � µ x ( 1 � x ) dt

Introduction Model Equilibrium Analysis Good News Bad News Imperfect Learning Moreover First-Best E¤ort Lemma: First-best e¤ort η 2 [ 0 , 1 ] satis…es � 1 λ if c < λ + r η ( x ) = λ 0 if c > λ + r Proof: Social bene…t of e¤ort is: � ... social bene…t of high quality 1, times � ... probability ot technology shock λ dt , annuitized by � ... e¤ective discount rate r + λ . λ Always assume that e¤ort is socially bene…cial, i.e. c < λ + r .

Introduction Model Equilibrium Analysis Good News Bad News Imperfect Learning Moreover Equilibrium Characterization Lemma: Optimal e¤ort η ( x ) is: � Independent of quality θ , � Bang-bang in reputation: � 1 if c < λ ∆ ( x ) , η ( x ) = 0 if c > λ ∆ ( x ) , where ∆ ( x ) : = V H ( x ) � V L ( x ) is value of quality. Proof: � Probability of technology shock: λ dt � Bene…t in case of shock: ∆ ( x )

Introduction Model Equilibrium Analysis Good News Bad News Imperfect Learning Moreover Asset Value of Quality ∆ ( x ) = V H ( x ) � V L ( x ) Theorem: In any MPE, ∆ is present value of D H ( x t ) : Z ∞ e � ( r + λ ) t E θ � t = L [ D H ( x t )] dt . ∆ ( x 0 ) = 0 D H ( x ) = V H ( 1 ) � V H ( x ) (Good) Speci…cally D L ( x ) = V L ( x ) � V L ( 0 ) (Bad) D H ( x ) = µ ( V H ( j ( x )) � V H ( x )) (Imperfect)

Introduction Model Equilibrium Analysis Good News Bad News Imperfect Learning Moreover Asset Value of Quality ∆ ( x ) =( 1 � ( r + λ ) dt ) E [ V H ( x + d H x ) � V L ( x + d L x )] Theorem: In any MPE, ∆ is present value of D H ( x t ) : Z ∞ e � ( r + λ ) t E θ � t = L [ D H ( x t )] dt . ∆ ( x 0 ) = 0 D H ( x ) = V H ( 1 ) � V H ( x ) (Good) Speci…cally D L ( x ) = V L ( x ) � V L ( 0 ) (Bad) D H ( x ) = µ ( V H ( j ( x )) � V H ( x )) (Imperfect)

Introduction Model Equilibrium Analysis Good News Bad News Imperfect Learning Moreover Asset Value of Quality ∆ ( x ) =( 1 � ( r + λ ) dt ) E [ V H ( x + d H x ) � V H ( x + d L x )] + ( 1 � ( r + λ ) dt ) E [ V H ( x + d L x ) � V L ( x + d L x )] Theorem: In any MPE, ∆ is present value of D H ( x t ) : Z ∞ e � ( r + λ ) t E θ � t = L [ D H ( x t )] dt . ∆ ( x 0 ) = 0 D H ( x ) = V H ( 1 ) � V H ( x ) (Good) Speci…cally D L ( x ) = V L ( x ) � V L ( 0 ) (Bad) D H ( x ) = µ ( V H ( j ( x )) � V H ( x )) (Imperfect)

Introduction Model Equilibrium Analysis Good News Bad News Imperfect Learning Moreover Asset Value of Quality ∆ ( x ) =( 1 � ( r + λ ) dt ) E [ V H ( x + d H x ) � V H ( x + d L x )] + ( 1 � ( r + λ ) dt ) E [ ∆ ( x + d L x )] Theorem: In any MPE, ∆ is present value of D H ( x t ) : Z ∞ e � ( r + λ ) t E θ � t = L [ D H ( x t )] dt . ∆ ( x 0 ) = 0 D H ( x ) = V H ( 1 ) � V H ( x ) (Good) Speci…cally D L ( x ) = V L ( x ) � V L ( 0 ) (Bad) D H ( x ) = µ ( V H ( j ( x )) � V H ( x )) (Imperfect)

Introduction Model Equilibrium Analysis Good News Bad News Imperfect Learning Moreover Asset Value of Quality ∆ ( x ) =( 1 � ( r + λ ) dt ) E [ V H ( x + d H x ) � V H ( x + d L x )] + ( 1 � ( r + λ ) dt ) E [ ∆ ( x + d L x )] = Reputational Dividend + Cont Value Theorem: In any MPE, ∆ is present value of D H ( x t ) : Z ∞ e � ( r + λ ) t E θ � t = L [ D H ( x t )] dt . ∆ ( x 0 ) = 0 D H ( x ) = V H ( 1 ) � V H ( x ) (Good) Speci…cally D L ( x ) = V L ( x ) � V L ( 0 ) (Bad) D H ( x ) = µ ( V H ( j ( x )) � V H ( x )) (Imperfect)

Introduction Model Equilibrium Analysis Good News Bad News Imperfect Learning Moreover Asset Value of Reputation Reputation x has asset value: � Current revenue x � Future revenue x t j x 0 = x Lemma: In MPE …rm value V θ ( x ) is strictly increasing in x . Proof: � Firm x 0 > x can mimick x � Same e¤ort & quality ) x 0 t � x t for all t � In MPE …rm x 0 does at least as good

Introduction Model Equilibrium Analysis Good News Bad News Imperfect Learning Moreover Perfect Good News

Introduction Model Equilibrium Analysis Good News Bad News Imperfect Learning Moreover Updating & Dynamics Reputational Updating: Breakthrough at rate µ = 1 if θ = H � Breakthrough: x t jumps to 1 � Otherwise: dx = λ ( e η ( x ) � x ) dt � x ( 1 � x ) dt “Work-Shirk” pro…le with cut-o¤ x � : � 1 for x < x � η ( x ) = for x > x � 0 dx= λ dt dx=0 dx=- λ dt x=0 x* x=1

Introduction Model Equilibrium Analysis Good News Bad News Imperfect Learning Moreover Work-Shirk Proposition: Every equilibrium is work-shirk. Proof : Z e � ( r + λ ) t D H ( x t ) dt ∆ ( x 0 ) = � Dividend D H ( x ) = V H ( 1 ) � V H ( x ) decreasing in x � Future reputation x t increasing in x 0 (conditional on θ � t = L ) � ∆ ( x ) decreasing in x Corollary: Dynamics x t are ergodic.

Introduction Model Equilibrium Analysis Good News Bad News Imperfect Learning Moreover Unique Equilibrium Proposition: Equilibrium is unique, if λ > 1. Proof : Consider two cuto¤s x and x x x x � ∆ x ( x ) > ∆ x ( x ) : Value of quality increasing in reputation � ∆ x ( x ) > ∆ x ( x ) : x has more to gain if he can drift further

Introduction Model Equilibrium Analysis Good News Bad News Imperfect Learning Moreover Perfect Bad News

Introduction Model Equilibrium Analysis Good News Bad News Imperfect Learning Moreover Updating & Dynamics Reputational Updating: Breakdown with arrival rate µ L = 1 � Breakdown: x t jumps to 0 � Otherwise: dx = λ ( e η ( x ) � x ) dt + x ( 1 � x ) dt "Shirk-Work” pro…le with cut-o¤ x � : � 0 for x < x � η ( x ) = for x > x � 1 dx= λ dt x* dx=0 x=1 x=0