The Tail that Wags the Economy: Belief-driven Business Cycles and Persistent Stagnation

The Tail that Wags the Economy: Belief-driven Business Cycles and Persistent Stagnation Julian Kozlowski Laura Veldkamp Venky Venkateswaran NYU NYU Stern NYU Stern June 215 1 / 27

Introduction The Great Recession spawned two major lines of business cycle research Belief shocks: News, sentiments, disaster risk, uncertainty... Secular stagnation: Long-lived adverse effects from large shocks 2 / 27

Introduction The Great Recession spawned two major lines of business cycle research Belief shocks: News, sentiments, disaster risk, uncertainty... Secular stagnation: Long-lived adverse effects from large shocks These two agendas have largely remained separate Most belief-driven theories have no internal propagation Effects only as persistent as exogenous persistence of belief shocks Cannot explain why some cycles are more persistent than others. 2 / 27

Introduction The Great Recession spawned two major lines of business cycle research Belief shocks: News, sentiments, disaster risk, uncertainty... Secular stagnation: Long-lived adverse effects from large shocks These two agendas have largely remained separate Most belief-driven theories have no internal propagation Effects only as persistent as exogenous persistence of belief shocks Cannot explain why some cycles are more persistent than others. Can belief changes explain persistent responses to transitory shocks? Yes, when agents are learning about distributions (as opposed to hidden states) 2 / 27

This paper A new approach to beliefs in business cycles Agents estimate the distribution of aggregate shocks using real time data Empirical discipline on belief formation Delivers large, persistent responses to transitory shocks 3 / 27

This paper A new approach to beliefs in business cycles Agents estimate the distribution of aggregate shocks using real time data Empirical discipline on belief formation Delivers large, persistent responses to transitory shocks Results: Tail events have a large, permanent effect on beliefs Leverage amplifies belief revisions from left-tail shocks A calibrated model predicts a permanent 13% drop in US GDP 3 / 27

Contribution to the Literature Secular stagnation: Summers (214), Eggertsson and Mehrotra (214), Gordon (215) We add : new mechanism, acting through belief revisions Belief-driven business cycles Belief shocks: Gourio (212), Angeletos and La O (213), Bloom (29)... We add: endogenous belief revisions, persistence Learning models: Johannes et. al. (212), Cogley and Sargent (25)... We add: production, flexible non-parametric distributions Endogenous uncertainty: Fajgelbaum et.al. (214), Straub and Ulbricht (213)... We add: empirical discipline, larger effects 4 / 27

Model Preferences: U t = Representative household [ (1 β) ) 1 ψ ( (C t ζ L1+γ t + βe t 1 + γ U 1 η t+1 ] 1 ) 1 ψ 1 ψ 1 η M t+1 ( ) 1 du t du t dc t dc t+1 : Stochastic discount factor 5 / 27

Model Preferences: U t = Representative household [ (1 β) ) 1 ψ ( (C t ζ L1+γ t + βe t 1 + γ U 1 η t+1 ] 1 ) 1 ψ 1 ψ 1 η M t+1 Technology: ( ) 1 du t du t dc t dc t+1 : Stochastic discount factor A continuum of firms, indexed by i Production: y it = Ak α it l 1 α it Aggregate capital quality shocks: k it = φ t ˆkit φ t G ( ) iid Idiosyncratic shocks, Π it = v it [y it + (1 δ)k it ] v it F ( ), common knowledge, iid v it di = 1 5 / 27

Model Preferences: U t = Representative household [ (1 β) ) 1 ψ ( (C t ζ L1+γ t + βe t 1 + γ U 1 η t+1 ] 1 ) 1 ψ 1 ψ 1 η M t+1 Technology: ( ) 1 du t du t dc t dc t+1 : Stochastic discount factor A continuum of firms, indexed by i Production: y it = Ak α it l 1 α it Aggregate capital quality shocks: k it = φ t ˆkit φ t G ( ) iid Idiosyncratic shocks, Π it = v it [y it + (1 δ)k it ] v it F ( ), common knowledge, iid v it di = 1 Beliefs: E t ( ) E [ I t] : More on I t later 5 / 27

Model Labor markets Hired in advance, i.e. before observing aggregate/idiosyncratic shocks Non-contingent wages workers subject to default risk Economy-wide wage rate (in period t consumption ) W t ( du t dc t ) 1 dut dl t+1 6 / 27

Model Labor markets Hired in advance, i.e. before observing aggregate/idiosyncratic shocks Non-contingent wages workers subject to default risk Economy-wide wage rate (in period t consumption ) W t Credit markets ( du t dc t ) 1 Competitive lenders offer price schedules q( ) for 1-period bonds Total proceeds: χqb it+1 where χ > 1 reflects tax advantage of debt dut dl t+1 6 / 27

Model Labor markets Hired in advance, i.e. before observing aggregate/idiosyncratic shocks Non-contingent wages workers subject to default risk Economy-wide wage rate (in period t consumption ) W t Credit markets ( du t dc t ) 1 Competitive lenders offer price schedules q( ) for 1-period bonds Total proceeds: χqb it+1 where χ > 1 reflects tax advantage of debt Default Firm assets sold to a identical new firm at a discount of 1 θ Proceeds distributed pro-rata among bondholders and workers dut dl t+1 6 / 27

The firm s problem V (Π it, B it, S t) = max [, max d it,ˆk it+1,b it+1,w it+1,l it+1 d it + E tm t+1v (Π it+1, B it+1, S t+1) ] Dividends: d it Π it B it ˆk it+1 + χq it b it+1 ) Discounted wages: W t w it+1 q (ˆkit+1, l it+1, B it+1, S t Future obligations: B it+1 = b it+1 + w it+1 l it+1 [ ] Resources: Π it+1 = v it+1 A(φ t+1 ˆk it+1 ) α l 1 α it+1 + (1 δ)φ t+1 ˆk it+1 ) [ ] Bond price: q (ˆkit+1, l it+1, B it+1, S t = E tm t+1 r it+1 + (1 r it+1 ) θṽit+1 B it+1 Dividends d it can be negative, i.e. no financing constraints Default policy r it+1 {, 1} and value Ṽ it+1 V (Π it,, S t) Aggregate state: S t (includes information) 7 / 27

Information and learning Distribution G of aggregate shocks unknown to agents I t: (Finite) History of aggregate variables {φ t s } T s= Agents construct an estimate Ĝt from observed data Use a standard Gaussian kernel density estimator 8 / 27

Information and learning Distribution G of aggregate shocks unknown to agents I t: (Finite) History of aggregate variables {φ t s } T s= Agents construct an estimate Ĝt from observed data Use a standard Gaussian kernel density estimator Equilibrium concept: anticipated utility Agents myopic with respect to belief changes, but otherwise rational 8 / 27

The mechanism max ˆk t+1,l t+1,lev t+1 ˆk t+1 χw tl t+1 + E t [M t+1π t+1] }{{} Output + Undep capital + (χ 1) q t lev t+1 ˆk t+1 }{{} Tax advantage of debt (1 θ) E t [M t+1(1 r t+1)π t+1] }{{} Cost of default 9 / 27

The mechanism max ˆk t+1,l t+1,lev t+1 ˆk t+1 χw tl t+1 + E t [M t+1π t+1] }{{} Output + Undep capital + (χ 1) q t lev t+1 ˆk t+1 }{{} Tax advantage of debt (1 θ) E t [M t+1(1 r t+1)π t+1] }{{} Cost of default A negative shock More pessimistic beliefs E t [M t+1π t+1] declines (also present without debt) Tax advantage goes down (because q t declines) Default costs rise Lower incentives to invest and hire 9 / 27

Calibration Strategy: Match aggregate and cross-sectional moments of the US economy Parameter Value Description β.91 Discount factor η 1 Risk aversion ψ.5 1/Intertemporal elasticity of substitution γ.5 1/Frisch elasticity ζ 1 Labor disutility α.4 Capital share δ.3 Depreciation rate A 1 TFP χ 1.6 Tax advantage of debt θ.7 Recovery rate ˆσ.33 Idiosyncratic volatility lev Target.7 Leverage ratio 1 / 27

Measuring capital quality shocks φ t = Kt value of capital = ˆK t yesterday s capital +investment Observables NFA RC t = Replacement cost of non-financial assets (Flow of Funds) NFA HC t = Historical cost of non-financial assets (Flow of Funds) PINDX k t = Investment price index (BEA) Model objects P k t K t = NFA RC t P k t 1 ˆK t = (1 δ)nfa RC t 1 + P k t 1X t 1 = (1 δ)nfa RC t 1 + NFA HC t (1 δ) NFA HC t 1 ( ) ( Pt k K t PINDX k ) φ t = t 1 Pt 1 k ˆK t PINDXt k 11 / 27

Capital quality shocks Between 195-27, φ t in a relatively tight range around 1 Large negative shocks in 28-9 significant rise in tail risk 1.2 1.15 35 3 27 29 1.1 25 1.5 1.5 1.95.9 Density 2 15 1 1.5.8.85.9.85 5.8 195 196 197 198 199 2 21.8.85.9.95 1 1.5 1.1 12 / 27

Effect of a transitory shock Experiment: Start with beliefs estimated on 195-27 data, add 8 and 9 shocks Simulate aggregate variables, holding beliefs fixed (For now, leverage is also held fixed - relaxed later). 13 / 27

Effect of a transitory shock Experiment: Start with beliefs estimated on 195-27 data, add 8 and 9 shocks Simulate aggregate variables, holding beliefs fixed (For now, leverage is also held fixed - relaxed later). Baseline results: Compare to de-trended data GDP close to the data, overshoot on capital and undershoot on labor 13 / 27

Effect of a transitory shock Experiment: Start with beliefs estimated on 195-27 data, add 8 and 9 shocks Simulate aggregate variables, holding beliefs fixed (For now, leverage is also held fixed - relaxed later). Baseline results: Compare to de-trended data GDP close to the data, overshoot on capital and undershoot on labor Decomposition: Role of shock size: Contrast 28-9 shocks (5σ) to 21 shock (1σ). Small shocks have transitory effects Role of learning: Use distribution implied by full sample throughout Without learning, initial impact similar, but less persistence Role of leverage: Assume no debt (χ = 1, Lev = ) Debt accounts for a third of the long-run effects Role of higher moments: Assume E(φ t) = 1 throughout Higher moments account for more than half of total effect Role of risk-aversion: Assume ψ = η =, i.e. preferecnes are quasi-linear Risk aversion doubles effects, both in the short run and long run 13 / 27

Results: Baseline.5 Capital quality shock.5 GDP.5.5.1.1.15.15.2 21 215 22 225 23 235.2 21 215 22 225 23 235.5 Capital.5 Labor.5.5.1.1.15.15.2 21 215 22 225 23 235.2 21 215 22 225 23 235 A permanent drop in output of 13% 14 / 27

Results: Model vs Data.5 Capital quality shock.5 GDP Model Data.5.5.1.1.15.15.2 21 215 22 225 23 235.2 21 215 22 225 23 235.5 Capital.5 Labor.5.5.1.1.15.15.2 21 215 22 225 23 235.2 21 215 22 225 23 235 Data: Deviations from log-linear, pre-crisis trend 15 / 27

Persistent vs Permanent? What would temper our long-run effects? 16 / 27

Persistent vs Permanent? What would temper our long-run effects? Answer: if long-run beliefs differ significantly from current, e.g. because of New data, e.g. a long period without crises or with very good shocks Agents discount (or forget) past data Agents perceive regime changes (the distribution g changes over time) 16 / 27

Results: Role of shock size.5 Capital quality shock.5 GDP 28 Recession 21 Recession.5.5.1.1.15.15.2 21 215 22 225 23 235.2 21 215 22 225 23 235.5 Capital.5 Labor.5.5.1.1.15.15.2 21 215 22 225 23 235.2 21 215 22 225 23 235 Small shocks small belief revisions negligible long-run effects 17 / 27

Results: Role of learning.5 Capital quality shock.5 GDP Learning No learning.5.5.1.1.15.15.2 21 215 22 225 23 235.2 21 215 22 225 23 235.5 Capital.5 Labor.5.5.1.1.15.15.2 21 215 22 225 23 235.2 21 215 22 225 23 235 No learning effects are transitory 18 / 27

Results: Role of debt.5 Capital quality shock.5 GDP Debt No Debt.5.5.1.1.15.15.2 21 215 22 225 23 235.2 21 215 22 225 23 235.5 Capital.5 Labor.5.5.1.1.15.15.2 21 215 22 225 23 235.2 21 215 22 225 23 235 Debt accounts for one-third of long-run effects 19 / 27

Results: Role of higher moments.5 Capital quality shock.5 GDP Baseline Mean = 1.5.5.1.1.15.15.2 21 215 22 225 23 235.2 21 215 22 225 23 235.5 Capital.5 Labor.5.5.1.1.15.15.2 21 215 22 225 23 235.2 21 215 22 225 23 235 Higher moments account for half of the long-run effects 2 / 27

Results: Role of risk aversion.5 Capital quality shock.5 GDP Epstein Zin Quasi linear.5.5.1.1.15.15.2 21 215 22 225 23 235.2 21 215 22 225 23 235.5 Capital.5 Labor.5.5.1.1.15.15.2 21 215 22 225 23 235.2 21 215 22 225 23 235 Risk aversion amplifies effects of belief revisions 21 / 27

Conclusion A simple, tractable framework of investment and hiring under learning Debt and large belief changes combine to generate significant - and persistent - declines in economic activity A potential explanation for the recent prolonged stagnation? 22 / 27

The quasi-linear case ψ = η = M t+1 = β Isolates the effect of belief revisions on returns Results presented for endogenous leverage 23 / 27

Optimality conditions ( ) χ 1 (1 θ) E t [M t+1vf (v)] = E t [M t+1 (1 F (v))] χ ] 1 = E t [M t+1rt+1j k k l t+1 (v) χw t ( ˆkt+1 ˆk t+1 ) α J l (v)] χw t = E t [M t+1 (1 α) Aφ α t+1 l t+1 where R k t+1 = Aφα t+1 ˆk α t+1l 1 α t+1 + (1 δ)φt+1 ˆk t+1 ˆk t+1 J k (v) = 1 + v (χ 1) (1 F (v)) + (θχ 1) h (v) J l (v) = 1 + h (v) (θχ 1) v 2 f (v) χ (θ 1) Now, χ = 1 v = J k = J l = 1 24 / 27

Variance vs Tail Risk 135 SKEW VIX (Right) 35 13 3 125 25 12 2 115 15 11 199 1995 2 25 21 1 25 / 27

Simulation with belief revisions post-29.5 Capital quality shock GDP -.5 Constant beliefs after 29 Learning after 29 -.5 -.1 -.1 -.15 -.15 -.2 2 21 22 23 24 -.2 2 21 22 23 24 Capital.5 Labor -.5 -.1 -.15 -.5 -.2 -.25 -.1 -.3 2 21 22 23 24 -.15 2 21 22 23 24 26 / 27

With belief revisions post-29 Capital quality shock GDP No debt + Learning Data -.1 -.1 -.2 -.2 -.3 21 215 22 225 23 235 24 -.3 21 215 22 225 23 235 24 Capital Labor -.1 -.1 -.2 -.2 -.3 21 215 22 225 23 235 24 -.3 21 215 22 225 23 235 24 27 / 27