Introduction Model Asset Prices Discussion Conclusions A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt Eric T. Swanson University of California, Irvine Conference on Nonlinear Models in Macroeconomics and Finance Norges Bank January 26, 2018
Introduction Model Asset Prices Discussion Conclusions Motivation Goal: Show that a simple macroeconomic model (with Epstein-Zin preferences) is consistent with a wide variety of asset pricing facts equity premium puzzle long-term bond premium puzzle (nominal and real) credit spread puzzle
Introduction Model Asset Prices Discussion Conclusions Motivation Goal: Show that a simple macroeconomic model (with Epstein-Zin preferences) is consistent with a wide variety of asset pricing facts equity premium puzzle long-term bond premium puzzle (nominal and real) credit spread puzzle Reduces separate puzzles in finance to a single, unifying puzzle: Why does risk aversion and/or risk in model need to be so high?
Introduction Model Asset Prices Discussion Conclusions Motivation Goal: Show that a simple macroeconomic model (with Epstein-Zin preferences) is consistent with a wide variety of asset pricing facts equity premium puzzle long-term bond premium puzzle (nominal and real) credit spread puzzle Reduces separate puzzles in finance to a single, unifying puzzle: Why does risk aversion and/or risk in model need to be so high? uncertainty: Weitzman (2007), Barillas-Hansen-Sargent (2010), et al. rare disasters: Rietz (1988), Barro (2006), et al. long-run risks: Bansal-Yaron (2004) et al.
Introduction Model Asset Prices Discussion Conclusions Motivation Goal: Show that a simple macroeconomic model (with Epstein-Zin preferences) is consistent with a wide variety of asset pricing facts equity premium puzzle long-term bond premium puzzle (nominal and real) credit spread puzzle Reduces separate puzzles in finance to a single, unifying puzzle: Why does risk aversion and/or risk in model need to be so high? uncertainty: Weitzman (2007), Barillas-Hansen-Sargent (2010), et al. rare disasters: Rietz (1988), Barro (2006), et al. long-run risks: Bansal-Yaron (2004) et al. heterogeneous agents: Mankiw-Zeldes (1991), Guvenen (2009), Schmidt (2015), et al. financial intermediaries: Adrian-Etula-Muir (2013)
Introduction Model Asset Prices Discussion Conclusions Motivation Implications for Finance: unifying explanation for asset pricing puzzles structural model of asset prices (provides intuition, robustness to breaks and policy interventions)
Introduction Model Asset Prices Discussion Conclusions Motivation Implications for Finance: unifying explanation for asset pricing puzzles structural model of asset prices (provides intuition, robustness to breaks and policy interventions) Implications for Macro: show how to match risk premia in DSGE framework start to endogenize asset price–macroeconomy feedback
Introduction Model Asset Prices Discussion Conclusions Motivation Implications for Finance: unifying explanation for asset pricing puzzles structural model of asset prices (provides intuition, robustness to breaks and policy interventions) Implications for Macro: show how to match risk premia in DSGE framework start to endogenize asset price–macroeconomy feedback Secondary theme: Keep the model as simple as possible
Introduction Model Asset Prices Discussion Conclusions Motivation Implications for Finance: unifying explanation for asset pricing puzzles structural model of asset prices (provides intuition, robustness to breaks and policy interventions) Implications for Macro: show how to match risk premia in DSGE framework start to endogenize asset price–macroeconomy feedback Secondary theme: Keep the model as simple as possible Two key ingredients: Epstein-Zin preferences nominal rigidities
Introduction Model Asset Prices Discussion Conclusions Households Period utility function: l 1 + χ t u ( c t , l t ) ≡ log c t − η 1 + χ additive separability between c and l SDF comparable to finance literature log preferences for balanced growth, simplicity Flow budget constraint: a t + 1 = e i t a t + w t l t + d t − c t
Introduction Model Asset Prices Discussion Conclusions Households Period utility function: l 1 + χ t u ( c t , l t ) ≡ log c t − η 1 + χ additive separability between c and l SDF comparable to finance literature log preferences for balanced growth, simplicity Flow budget constraint: a t + 1 = e i t a t + w t l t + d t − c t Calibration: (IES = 1), χ = 3, l = 1 ( η = . 54)
Introduction Model Asset Prices Discussion Conclusions Generalized Recursive Preferences Household chooses state-contingent { ( c t , l t ) } to maximize ( c t , l t ) u ( c t , l t ) − βα − 1 log [ E t exp( V ( a t ; θ t ) = max − α V ( a t + 1 ; θ t + 1 ))]
Introduction Model Asset Prices Discussion Conclusions Generalized Recursive Preferences Household chooses state-contingent { ( c t , l t ) } to maximize ( c t , l t ) u ( c t , l t ) − βα − 1 log [ E t exp( V ( a t ; θ t ) = max − α V ( a t + 1 ; θ t + 1 ))] Calibration: β = . 992, RRA ( R c ) = 60 ( α = 59 . 15)
Introduction Model Asset Prices Discussion Conclusions Firms Firms are very standard: continuum of monopolistic firms (gross markup λ ) Calvo price setting (probability 1 − ξ ) Cobb-Douglas production functions, y t ( f ) = A t k 1 − θ l t ( f ) θ fixed firm-specific capital stocks k Random walk technology: log A t = log A t − 1 + ε t simplicity comparability to finance literature helps match equity premium
Introduction Model Asset Prices Discussion Conclusions Firms Firms are very standard: continuum of monopolistic firms (gross markup λ ) Calvo price setting (probability 1 − ξ ) Cobb-Douglas production functions, y t ( f ) = A t k 1 − θ l t ( f ) θ fixed firm-specific capital stocks k Random walk technology: log A t = log A t − 1 + ε t simplicity comparability to finance literature helps match equity premium k Calibration: λ = 1 . 1, ξ = 0 . 8, θ = 0 . 6, σ A = . 007, ( ρ A = 1), 4 Y = 2 . 5
Introduction Model Asset Prices Discussion Conclusions Fiscal and Monetary Policy No government purchases or investment: Y t = C t
Introduction Model Asset Prices Discussion Conclusions Fiscal and Monetary Policy No government purchases or investment: Y t = C t Taylor-type monetary policy rule: i t = r + π t + φ π ( π t − π ) + φ y ( y t − y t )
Introduction Model Asset Prices Discussion Conclusions Fiscal and Monetary Policy No government purchases or investment: Y t = C t Taylor-type monetary policy rule: i t = r + π t + φ π ( π t − π ) + φ y ( y t − y t ) “Output gap” ( y t − y t ) defined relative to moving average: y t ≡ ρ ¯ y y t − 1 + ( 1 − ρ ¯ y ) y t
Introduction Model Asset Prices Discussion Conclusions Fiscal and Monetary Policy No government purchases or investment: Y t = C t Taylor-type monetary policy rule: i t = r + π t + φ π ( π t − π ) + φ y ( y t − y t ) “Output gap” ( y t − y t ) defined relative to moving average: y t ≡ ρ ¯ y y t − 1 + ( 1 − ρ ¯ y ) y t Rule has no inertia: simplicity Rudebusch (2002, 2006)
Introduction Model Asset Prices Discussion Conclusions Fiscal and Monetary Policy No government purchases or investment: Y t = C t Taylor-type monetary policy rule: i t = r + π t + φ π ( π t − π ) + φ y ( y t − y t ) “Output gap” ( y t − y t ) defined relative to moving average: y t ≡ ρ ¯ y y t − 1 + ( 1 − ρ ¯ y ) y t Rule has no inertia: simplicity Rudebusch (2002, 2006) Calibration: φ π = 0 . 5, φ y = 0 . 75, π = . 008, ρ ¯ y = 0 . 9
Introduction Model Asset Prices Discussion Conclusions Solution Method Write equations of the model in recursive form Divide nonstationary variables ( Y t , C t , w t , etc.) by A t Solve using perturbation methods around nonstoch. steady state
Introduction Model Asset Prices Discussion Conclusions Solution Method Write equations of the model in recursive form Divide nonstationary variables ( Y t , C t , w t , etc.) by A t Solve using perturbation methods around nonstoch. steady state first-order: no risk premia second-order: risk premia are constant third-order: time-varying risk premia higher-order: more accurate over larger region Model has 2 state variables ( ¯ y t , ∆ t ), one shock ( ε t )
Introduction Model Asset Prices Discussion Conclusions Impulse Responses Technology A t percent 1.0 0.8 0.6 0.4 0.2 0.0 0 10 20 30 40 50
Introduction Model Asset Prices Discussion Conclusions Impulse Responses Consumption C t percent 1.0 0.8 0.6 0.4 0.2 0.0 0 10 20 30 40 50
Introduction Model Asset Prices Discussion Conclusions Impulse Responses Inflation π t ann. pct. 0.0 10 20 30 40 50 - 0.2 - 0.4 - 0.6 - 0.8 - 1.0
Introduction Model Asset Prices Discussion Conclusions Impulse Responses Short - term nominal interest rate i t ann. pct. 0.0 10 20 30 40 50 - 0.1 - 0.2 - 0.3 - 0.4 - 0.5
Introduction Model Asset Prices Discussion Conclusions Impulse Responses Short - term real interest rate r t ann. pct. 0.5 0.4 0.3 0.2 0.1 0.0 0 10 20 30 40 50
Introduction Model Asset Prices Discussion Conclusions Impulse Responses Labor L t percent 0.4 0.2 0.0 10 20 30 40 50 - 0.2 - 0.4
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