The Origins and Effects of Macroeconomic Uncertainty Francesco Bianchi, Howard Kung, and Mikhail Tirskikh Duke University, London Business School, and London Business School Bianchi, Kung, and Tirskikh
Motivation Growing literature studying the role of uncertainty using general equilibrium models Most of these papers tend to find modest effects of uncertainty These papers typically... only use macroeconomic data 1 consider only one source of uncertainty 2 rely on a two-step procedure in which uncertainty is separately estimated 3 Bianchi, Kung, and Tirskikh
This paper We study the joint behavior of the macroeconomy and the term structure taking into account the origins and effects of uncertainty We construct a general-equilibrium model with an endogenous term premium and solve the model with a risk-adjusted loglinearization We introduce a novel analytical decomposition of the effects of uncertainty into risk propagation channels We conduct a structural estimation of the model in which we... employ both macroeconomic and term structure data 1 distinguish between demand-side (preferences) and supply-side (TFP) uncertainty 2 jointly estimate the process for uncertainty and its effects 3 Bianchi, Kung, and Tirskikh
Main results Both supply-side and demand-side uncertainty generate sizable business cycle fluctuations in consumption, investment, and term premia. But,... Supply-side uncertainty has larger effects on inflation and investment Analysis of the five risk propagation channels accounts for these differences The investment risk premium channel amplifies the response of investment to 1 supply-side uncertainty: Investment in capital becomes relatively riskier The nominal pricing bias channel accounts for the different inflation responses: 2 Demand-side uncertainty ⇒ inflation uncertainty ⇒ inflationary pressure The precautionary savings channel cannot account for these differences 3 Good fit of the term structure, with realistic nominal and real term premia Bianchi, Kung, and Tirskikh
The Model: Households The representative household has recursive preferences: � � 1 � � �� 1 − 1 / ψ 1 − 1 / ψ ( 1 − β t ) u ( C t , L t ) 1 − 1 / ψ + β t V 1 − γ 1 − γ = V t E t t + 1 L 1 + τ t u ( C t , L t ) = ( C t − hC t − 1 ) exp ( − τ 0 1 + τ ) where γ is the coefficient of risk aversion, ψ is the elasticity of intertemporal substitution, � � − 1 , where ˜ β exp ( ˜ 1 + ˆ and β t = b t ) b t is a preference shock b t = ρ β ˜ ˜ b t − 1 + σ β , ξ D t ε β , t , ε β , t ∼ N ( 0 , 1 ) t follows a Markov-switching process with transition matrix H D and The variable ξ D determines the volatility regime of preference shocks at time t . Bianchi, Kung, and Tirskikh
The Model: Firms Final good representative firm uses a continuum of differentiated intermediate goods as input in a CES production technology Representative intermediate firm faces: Monopolistic competition Sticky prices (Quadratic adjustment cost) Rental rate for capital (owned by households) Changes in the volatility of TFP shocks Z t = e n t , ∆ n t = µ + x t x t = ρ x x t − 1 + σ x , ξ S t ε x , t , ε x , t ∼ N ( 0 , 1 ) t follows a Markov-switching process with transition matrix H S and The variable ξ S determines the volatility regime of TFP shocks at time t . Bianchi, Kung, and Tirskikh
The Model: Policy makers The central bank follows a Taylor rule � R t � � R t − 1 � = ρ r ln + ln R ∗ R ∗ � � � �� � Π t � Y t +( 1 − ρ r ) + ρ y ln + σ m ε m , t ρ π ln � Π ∗ Y ∗ ss Fiscal authority keeps debt on a stable path Bianchi, Kung, and Tirskikh
Propagation channels of uncertainty Precautionary savings channel - consumption Euler equation � � � � � � x t − 1 + 1 r f , t + ( 1 − βρ β ) ˜ 2 ( 1 − γ ) 2 Var t ˜ ˜ − � b t + ρ x � � v t + 1 + � c t = E t c t + 1 2 Var t m t + 1 ˜ x t + 1 � �� � Precautionary savings motive Investment risk premium channel - asset pricing equation for investment return r i , t + 1 ] − 1 E t [ � r i , t + 1 − � r f , t ] = − Cov t [ � m t + 1 ; � 2 Var t [ � r i , t + 1 ] � �� � Investment Risk Premium Inflation risk premium channel - asset pricing equation for nominal short term rate � � � � � � − 1 r t = � � r f , t + E t � + Cov t m t + 1 ; � � 2 Var t � π t + 1 π t + 1 π t + 1 � �� � Inflation Risk Premium Bianchi, Kung, and Tirskikh
Propagation channels of uncertainty Nominal pricing bias channel - Phillips curve w t + ˜ π t = β E t [ ˜ π t + 1 ] + κ R ( ˜ y t ) + ˜ l t − ˜ ∗ � � � � �� 1 ˜ y t + 1 + � 2 β 2 Cov t m t + 1 + ˜ x t + 1 ; ˜ π t + 1 + 3 Var t π t + 1 ˜ � �� � Nominal Pricing Bias Investment adjustment channel - firm’s investment decision � � � � � � � � + 5 q t − ϕ I e 2 µ ∆ i t + ϕ I e 2 µ β � m t + 1 + � � E t ∆ i t + 1 + Cov t q t + 1 ; ∆ i t + 1 2 Var t ∆ i t + 1 = 0 � �� � Investment adjustment Bianchi, Kung, and Tirskikh
Capturing the effects of Uncertainty Our approximation method is based on the following two key ideas Expectational equations are approximated assuming log-normality. The approximate 1 solution indeed satisfies this condition Uncertainty is regime dependent: V t [ x t + 1 ] = V ξ t [ x t + 1 ] 2 These two ideas allow us to write the risk-adjusted linearized system of equations as Γ 0 S t = Γ 1 S t − 1 + Γ σ Q ξ t ε t + Γ η η t + Γ c , ξ t (1) However, we need to know how the economy reacts to the exogenous shocks in order to compute the uncertainty terms in Γ c , ξ t ⇒ iterative procedure. The solution can be characterized as a MS-VAR: C ( ξ t , θ v , θ p , H ) + T ( θ p ) S t − 1 + R ( θ p ) Q ( ξ t , θ v ) ε t S t = (2) � �� � � �� � Endogenous uncertainty Exogenous uncertainty Bianchi, Kung, and Tirskikh
Parameter estimates We estimate the model with Bayesian methods over the sample 1984:Q2-2015:Q4 using macro variables and yields with maturity from 1 year to 5 year. Preference 0.8 0.6 0.4 0.2 0 1985 1990 1995 2000 2005 2010 2015 TFP growth 0.8 0.6 0.4 0.2 0 1985 1990 1995 2000 2005 2010 2015 Probability of high uncertainty regimes Bianchi, Kung, and Tirskikh
The Effects of Uncertainty Bianchi, Kung, and Tirskikh
Effects of Uncertainty Bianchi, Kung, and Tirskikh
Channels of Uncertainty - Demand side Consumption Investment GDP 5 0 0 -0.5 -0.5 % % 0 % -1 -1 -5 0 10 20 0 10 20 0 10 20 Inflation FFR Slope 0.5 0.5 0.4 0 Total Prec. Sav. % % % 0 0.2 Inv. Risk Prem. -0.5 Nom. Pric. Bias Inv. Adj. 0 -1 Infl. Risk Prem. -0.5 0 10 20 0 10 20 0 10 20 Response to an increase in demand uncertainty Bianchi, Kung, and Tirskikh
Channels of Uncertainty - Supply side Consumption Investment GDP 0 0 0 -0.5 -0.5 -2 % % % -4 -1 -1 -6 0 10 20 0 10 20 0 10 20 Inflation FFR Slope 0 0 0.4 Total Prec. Sav. % % -0.5 % -0.2 Inv. Risk Prem. 0.2 Nom. Pric. Bias Inv. Adj. 0 Infl. Risk Prem. -1 -0.4 0 10 20 0 10 20 0 10 20 Response to an increase in supply side uncertainty Bianchi, Kung, and Tirskikh
Fit of term structure Upward slope of nominal and real term structure: Yields Term Premium 1Q 1Y 2Y 3Y 4Y 5Y Total Risk Liquidity Only Pref. Only TFP Nominal 2.77 2.88 3.08 3.31 3.53 3.72 0.95 0.89 0.06 0.63 0.41 Real 0.57 0.58 0.71 0.89 1.06 1.21 0.63 0.63 - 0.22 0.43 Cochrane-Piazzesi regressions: Model Data Maturity 2Y 3Y 4Y 5Y 2Y 3Y 4Y 5Y β ( n ) 0.41 0.83 1.21 1.56 0.45 0.81 1.24 1.50 (2.91) (3.35) (3.49) (3.49) (3.65) (3.56) (3.99) (4.03) R 2 0.12 0.16 0.17 0.18 0.23 0.21 0.24 0.23 N obs 127 127 127 127 127 127 127 127 Bianchi, Kung, and Tirskikh
Term Premium Bianchi, Kung, and Tirskikh
Conclusions In this paper: An estimated general equilibrium model with endogenous term premia and supply-side and demand-side uncertainty Novel decomposition into risk propagation channels to study the effects of uncertainty in a conditionally linear framework Uncertainty emerges as an important driver of the business cycle and premia Supply-side uncertainty has larger effects on investment, inflation, and real premia Risk channels explain differences between demand-side and supply-side uncertainty Bianchi, Kung, and Tirskikh
Recommend
More recommend
