Wall Street and Silicon Valley: A Delicate Interaction George-Marios Angeletos Guido Lorenzoni Alessandro Pavan June 2019
Motivation “Technological revolutions and financial bubbles seem to go hand in hand” — The Economist, September 21, 2000 Arrival of new, unfamiliar, investment opportunities “Internet craze”late 1990s “biotech revolution”early 1980s “new financial instruments”mid 2000s ⇒ high uncertainty, abnormal real and financial activity (Pastor and Veronesi, 2009) Financial markets look at real sector for clues and vice versa co-movements in real investment and financial prices Do such co-movements reflect efficient response to available information? Or could they be product of excessive waves of optimism and pessimism?
This Paper Positive and normative implications of information spillovers between real and financial sector? Information spillovers from financial mkts to real economy quite well studied Information spillovers from real to financial sector largely under-explored Source of non-fundamental volatility dampen response to fundamental shocks amplify response to noise and higher-order-uncertainty Symptoms of (constrained) inefficiency policy interventions Mechanism: collective signaling (from real to financial sector) source of endogenous complementarities micro-foundation for ” beauty-contests”and ” irrational-exuberance”
Plan Model 1 Equilibrium 2 Positive Analysis 3 4 Welfare Analysis 5 Policy 6 Robustness and Extensions
Model
Model: Actors Two types of agents: entrepreneurs financial investors Two project phases: start-up : entrepreneurs decide whether to start new project of unknown profitability IPO stage : entrepreneurs expand project using IPO proceeds
Model: Technology Starting a project ( t = 1) 1 unit of perishable good Subsequent expansion ( t = 2) k ∈ R + : period-2 expansion Output at t = 3: q = Θ k α Θ: underlying fundamental
Model: Timing At t = 1, each entrepreneur endowed with 1 unit of perishable good consume ( n i = 0) invest to start project ( n i = 1) At t = 2, profile ( n i ) i ∈ [0 , 1] of start-up activity publicly observed Entrepreneurs who did not initiate project at t = 1 no other source of income no further action Entrepreneurs who initiated project receive no income at t = 2 finance project expansion k i by selling shares in IPO mkt Budget constraint k i = p i s i , At t = 3, fundamental Θ publicly revealed Entrepreneurs receive (1 − s i )Θ k α i Investors receive s i Θ k α i
Model: Information 0 , π − 1 � � θ ≡ log Θ with θ ∼ N θ Entrepreneurs observe 0 , π − 1 ξ i ∼ N � � x i = θ + ξ i , x 0 , π − 1 ε ∼ N � � y = θ + ε, y “Representative”investor observes 0 , π − 1 w = θ + η , with η ∼ N � � ω Investor’s information at beginning of t = 2: I = { ω, ( n j ) j ∈ [0 , 1] } Entrepreneur i ’s information at beginning of t = 2: J i = { x i , y , ( n j ) j ∈ [0 , 1] } Market-generated information: M ≡ ( p i , s i , k i ) i ∈ [0 , N ]
Model: Financial Market Microstructure Similar to Kyle (1985) Each entrepreneur i submits supply correspondence S s p j ) j ∈ [0 , N ] , (˜ i ((˜ k j ) j ∈ [0 , N ] \ i |J i ) � S d � Representative investor submits demand correspondences i ( ·|I ) i ∈ [0 , N ] , one for each active IPO i ∈ [0 , N ], with each p j ) j ∈ [0 , N ] , (˜ S d i ((˜ k j ) j ∈ [0 , N ] |I ) Auctioneer selects triples ( p i , s i , k i ) i ∈ [0 , N ] so that each mkt clears each expansion funded with IPO proceeds ( k i = p i · s i ) Two differences wrt Kyle (1985): endogenous dividend (depends on k i ) entrepreneurs do not have mkt power
Model: Payoffs Entrepreneurs’ lifetime utility: U i = c i 1 + β c i 2 + β 2 c i 3 , c i 1 = 1 − n i c i 2 = 0 c i 3 = 0 if n i = 0 and c i 3 = (1 − s i )Θ k α otherwise. i At t = 2, representative investor can produce consumption good out of labor, l , at one-to-one rate perfectly elastic supply of external funds Consumption levels of representative investor � � s i Θ k α c 2 = l − p i s i di and c 3 = i di , i ∈ [0 , N ] i ∈ [0 , N ] Investor’s lifetime utility: � [ β Θ k α i − p i ] s i di V = i ∈ [0 , N ]
Plan Model 1 Equilibrium 2 Positive Analysis 3 4 Welfare Analysis 5 Policy 6 Robustness and Extensions
Equilibrium
Equilibrium PBE satisfying following restrictions/refinements: p i depends only on mkt information (standard) representative investor’s posterior about θ is normal with mean ˆ θ ≡ E [ θ |I ] normally distributed (known variances) Each entrepreneur“informationally small” investor’s posterior about aggregate TFP θ invariant to ( n i , p i , s i , k i ) ...function of cross-sectional distribution ( n j , p j , s j , k j ) j ∈ [0 , N ]
Equilibrium: IPO Stage Representative investor’s demand in IPO mkt i perfectly elastic at p = β ˆ Θ k α where I ′ = { ω, ( n j ) j ∈ [0 , 1] } ∪ { ( p j , s j , k j ) j ∈ [0 , N ] } Θ ≡ E [Θ |I ′ ] ˆ and
Equilibrium: IPO Stage “Relaxed”problem in which entrepreneur i can condition his supply on ˆ Θ For every ˆ Θ, entrepreneur chooses ( p , s , k ) that maximize his utility s.t. k = p · s p = β ˆ Θ k α To invest k , entrepreneur must sell k s = β ˆ Θ k α Entrepreneur’s payoff (1 − s )Θ k α = Θ Θ k α − k � � β ˆ β ˆ Θ thus maximized by 1 1 K (ˆ Θ) = ( αβ ˆ P (ˆ 1 − α ( β ˆ α S (ˆ 1 − α , 1 − α , Θ) Θ) = α Θ) Θ) = α
Equilibrium: IPO Stage Because p = P (ˆ Θ) is invertible, solution to relaxed problem can be implemented by submitting supply schedule S s i (( p j ) j ∈ [0 , N ] , ( k j ) j ∈ [0 , N ] \ i |J i ) = K ( P − 1 ( p i )) / p i . Because each ( p i , s i , k i ) depends only on ˆ Θ, representative investor does not update his beliefs about Θ after observing mkt outcomes: Θ ≡ E [Θ |I ′ ] = E [Θ |I ] . ˆ Remark: same conclusions if each entrepreneur submits mkt order instead of limit order
Equilibrium: Start-up Stage Each entrepreneur i finds it optimal to start project iff β 2 E i [(1 − s i )Θ k α i ] ≥ 1 Using normality of ˆ θ ≡ E [ θ |I ′ ] and of θ |I , (1 − α ) E i [ θ ] + α E i [ˆ n i = 1 ⇔ θ ] ≥ C First direction of feedback mechanism : higher ˆ θ ⇒ higher IPO price ⇒ higher startup activity, N
Equilibrium: Market valuation Using Normality n i = 1 ⇔ (1 − b ) x i + by ≥ c Aggregate level of startup activity: � √ π x (1 − b ) θ + by − c � N = Pr ((1 − b ) x i + by ≥ c | θ, y ) = Φ 1 − b Observation of N conveys same information as“ endogenous ”signal z ≡ (1 − b ) θ + by = θ + b ε π z = π y / b 2 Investors cannot tell apart whether high N driven by high θ or correlated error, ε , in entrepreneurs’ beliefs Hence, Θ = E [Θ |I ′ ] = E [Θ | ω, N ] = E [Θ | ω, z ] ˆ Second direction of feedback mechanism : higher startup activity N ⇒ higher ˆ Θ ⇒ higher IPO prices
Equilibrium: Fixed Point Using θ = E [ θ | ω, z ] = π ω π ω + π z ˆ π z , θ ] = π ω + π z (1 − b ) E i [ θ ] + π z E i [ˆ π by π where E i [ θ ] = δ x x i + δ y y with π x π y δ x ≡ and δ y ≡ π θ + π x + π y π θ + π x + π y Hence, each entrepreneur finds it optimal to start project iff (1 − b ′ ) x i + b ′ y ≥ c ′ There exist functions Γ : R → R and Λ : R → R s.t. if b ∗ is fixed point of Γ and c ∗ = Λ( b ∗ ) , then there exists eq. in which each entrepreneur starts a project iff (1 − b ∗ ) x i + b ∗ y ≥ c ∗ Proposition 1 (i) There always exists eq. in which b ∗ ∈ (0 , 1). (iii) Such eq. unique for all α ≤ ¯ α . (iv) For α > ¯ α , multiple equilibria
Plan Model 1 Equilibrium 2 Positive Analysis 3 4 Welfare Analysis 5 Policy 6 Robustness and Extensions
Positive Analysis
Role of information spillovers Suppose investors do not learn from N ˆ θ is linear function of exogenous signal ω = θ + η Since entrepreneurs do not possess any information about η , E i [ˆ θ ] is linear transformation of E i [ θ ] In this case, E i [ θ ] ≥ ˆ n i = 1 ⇔ C Equivalently, n i = 1 ⇔ (1 − δ ) x i + δ y ≥ ˆ c where π x π y δ x ≡ and δ y ≡ π θ + π x + π y π θ + π x + π y With information spillovers: b ∗ > δ Proposition 2 Informational spillovers from real to financial sector amplify contribution of noise to aggregate volatility: ∂ N /∂ε ∂ N /∂θ = b ∗ > δ
Mispricing and speculation Entrepreneurs’ startup rule: E i [ θ ] + α E i [ˆ ⇔ θ − θ ] ≥ C n i = 1 Mispricing: θ − θ = π ω π η + π z ˆ π b ∗ ε Higher p ⇒ lower cost of capital ⇒ higher return to startup activity Reminiscent of dot-com bubble: when entrepreneurs expect financial mkt to “overvalue”their businesses ⇒ higher startup activity (Pastor and Veronesi, 2009) E i [ η ] = 0 whereas E i [ ε ] = y − E i [ θ ] = (1 − δ y ) y − δ x x Because higher y contributes to both higher E i [ θ ] and higher E i [ˆ θ − θ ], relative sensitivity of startup activity to sources with correlated noise higher than what warranted by informativeness of such sources Spillover from entrepreneurs’ collective optimism to exuberance in financial mkt crowds out private information and amplifies non-fundamental volatility
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