Leads, Lags, and Logs: Asset Prices in Business Cycle Analysis

Transcription

1 Leads, Lags, and Logs: Asset Prices in Business Cycle Analysis David Backus (NYU), Bryan Routledge (CMU), and Stanley Zin (CMU) Society for Economic Dynamics, July 2006 This version: July 11, 2006 Backus, Routledge, and Zin () Leads, lags, and logs 1 / 20

2 Overview Leads and lags in business cycles (Almost) the usual equations Loglinear approximation Properties of the model Extensions Backus, Routledge, and Zin () Leads, lags, and logs 1 / 20

3 Leads and lags Leads and lags Cross-correlation functions of GDP with Stock price indexes Interest rates and spreads Consumption and employment US data, quarterly, 1960 to present Quarterly growth rates (first difference of logs), except Interest rates and spreads Occasional year-on-year comparisons (y t+2 y t 2 ) Backus, Routledge, and Zin () Leads, lags, and logs 2 / 20

4 Leads and lags Stock prices and GDP Leads GDP S&P 500 Lags GDP Backus, Routledge, and Zin () Leads, lags, and logs 3 / 20

5 Leads and lags Stock prices and GDP (year-on-year) S&P 500 (yoy) Backus, Routledge, and Zin () Leads, lags, and logs 4 / 20

6 Leads and lags Stock prices and GDP Leads GDP S&P 500 Lags GDP S&P 500 minus Short Rate NYSE Composite Nasdaq Composite Backus, Routledge, and Zin () Leads, lags, and logs 5 / 20

7 Leads and lags Interest rates and GDP Yield Spread (10y 3m) Yield Spread (GDP yoy) Short Rate (3m) Real Rate Backus, Routledge, and Zin () Leads, lags, and logs 6 / 20

8 Leads and lags Consumption and GDP Consumption Services Nondurables Durables Backus, Routledge, and Zin () Leads, lags, and logs 7 / 20

9 Leads and lags Investment and GDP Investment Structures Equipment and Software Residential Backus, Routledge, and Zin () Leads, lags, and logs 8 / 20

10 Leads and lags Employment and GDP Employment (Nonfarm Payroll) Employment (Household Survey) Avg Weekly Hours (All) Avg Weekly Hours (Manuf) Backus, Routledge, and Zin () Leads, lags, and logs 9 / 20

11 Leads and lags Lead/lag summary Things that lead GDP Stock prices Yield curve and short rate Consumption (a little) Things that lag GDP Employment Backus, Routledge, and Zin () Leads, lags, and logs 10 / 20

12 The usual equations (Almost) the usual equations Basic real business cycle model except Recursive preferences (Kreps-Porteus/Epstein-Zin-Weil) CES production More complex shock process (predictable component in productivity) Backus, Routledge, and Zin () Leads, lags, and logs 11 / 20

13 The usual equations Preferences Equations U t = V [u t, µ t (U t+1 )] u t = ct γ (1 n t ) 1 γ V (a, b) = [(1 β)a ρ + βb ρ ] 1/ρ µ t (U t+1 ) = ( E t U α t+1 ) 1/α Interpretation IES = 1/(1 ρ) CRRA = 1 α α = ρ additive preferences Backus, Routledge, and Zin () Leads, lags, and logs 12 / 20

14 The usual equations Technology Equations y t = f (k t, z t n t ) = [ωkt ν + (1 ω)(z t n t ) ν ] 1/ν y t = c t + i t k t+1 = (1 δ)k t + i t Interpretation Elast of Subst = 1/(1 ν) Capital Share = ω(y/k) ν Backus, Routledge, and Zin () Leads, lags, and logs 13 / 20

15 The usual equations Productivity process Equation log z t+1 log z t = ḡ + χ j ε t+1 j j=0 Interpretation Moving average allows predictable component Backus, Routledge, and Zin () Leads, lags, and logs 14 / 20

16 Logs Loglinear decision rules We re looking for decision rules of the form ĉ = h ck ˆk + h cj ε t j j=0 ˆn = h nk ˆk + h nj ε t j j=0 Backus, Routledge, and Zin () Leads, lags, and logs 15 / 20

17 Logs Loglinear decision rules Traditional methods Dependence of decisions on capital independent of shocks Scale by z for stationarity Decision rules follow from loglinear approximation of derivatives of value function With recursive preferences Dependence of decisions on capital independent of shocks Scale by z for stationarity We need the value function, not just its derivatives Tallarini: logquadratic value function Us: loglinear value function Impact: risk aversion has no impact on quantities Backus, Routledge, and Zin () Leads, lags, and logs 16 / 20

18 Properties of the model Asset prices Pricing kernel m t+1 = β (c t+1 /c t ) ρ 1 [U t+1 /µ t (U t+1 )] α ρ Short rate r t = log E t m t+1 Backus, Routledge, and Zin () Leads, lags, and logs 17 / 20

19 Properties of the model Impulse response of short rate Backus, Routledge, and Zin () Leads, lags, and logs 18 / 20

20 Bottom line Bottom line Asset prices contain information about business cycles Specifically: they lead the cycle Not true of traditional business cycle models We add recursive preferences predictable component to productivity Lots left to do equity macro-based bond pricing stochastic volatility Backus, Routledge, and Zin () Leads, lags, and logs 19 / 20

21 Related work Related work Leads and lags Ang-Piazzesi-Wei, Beaudry-Portier, Jaimovich-Rebelo, Stock-Watson Predictable component Bansal-Yaron Computation with recursive preferences Hansen-Sargent, Tallarini, Uhlig Kreps-Porteus pricing kernel Hansen-Heaton-Li, Weil Backus, Routledge, and Zin () Leads, lags, and logs 20 / 20