A Structural Investigation of Monetary Policy Shifts Yoosoon Chang - PowerPoint PPT Presentation

A Structural Investigation of Monetary Policy Shifts Yoosoon Chang I NDIANA U NIVERSITY B LOOMINGTON Joint with Fei Tan, Xin Wei Workshop on Nonlinear Models in Macroeconomics and Finance for an Unstable World Norges Bank, Oslo, Norway January 26-27, 2018

Fed Funds Rate and Taylor Rule: 1954-Present Clear time variation (regime changes) in monetary policy intervention. What are the drivers?

What Is the Paper About? This work introduces threshold-type switching with endogenous feedback into DSGE models ◮ how agents form expectations on future regime change ◮ shed empirical light on how & why policy regime shifts Substantive finding ◮ post-WWII U.S. monetary policy shifts have been largely driven by non-policy shocks Methodological contribution ◮ derive analytical solution for endogenous switching Fisherian model ◮ develop an endogenous switching Kalman filter

Main Results Endogenous switching in Fisherian model ◮ structural shocks drive regime change through endogenous feedback mechanism ◮ endogenous feedback induces expectational effect, which helps stabilize price level Endogenous switching in a New Keynesian model ◮ we show empirically that U.S. monetary policy shifts are mainly driven by non-policy shocks ◮ in particular, the markup shocks associated with oil crises were the main driver of monetary policy in 70’s, and preference shocks indicating the strong economic recovery in early 80’s drove monetary policy regime back to active.

Endogenous Switching in Fisherian Model

Model Fisher equation: i t = E t π t + 1 + E t r t + 1 Real rate process: r t = ρ r r t − 1 + σ r ǫ r t Monetary policy with endogenous feedback: i t = α ( s t ) π t + σ e ǫ e t s t = 1 { w t ≥ τ } w t + 1 = φ w t + v t + 1 , � � � � 1 �� ǫ e ρ t = d iid N 0 , ρ v t + 1 1 as considered in Chang, Choi and Park (2017).

Information Structure ◮ Agents don’t observe the level of latent regime factor w t , but observe whether or not it crosses the threshold, as reflected in s t = 1 { w t ≥ τ } . ◮ Agents form expectations on future inflation as F t = { i u , π u , r u , ǫ r u , ǫ e u , s u } t E t π t + 1 = E ( π t + 1 | F t ) , u = 0 ◮ Monetary authority observes all information in F t and also the history of policy regime factor ( w t ) .

Endogenous Feedback Mechanism To see the endogenous feedback mechanism, rewrite � w t + 1 = φ w t + ρǫ e 1 − ρ 2 η t + 1 t + , η t + 1 ∼ i . i . d . N ( 0 , 1 ) � �� � v t + 1 From variance decomposition, we see that ρ 2 is the contribution of past intervention to regime change ◮ ρ = 0 : fully driven by exogenous non-structural shock w t + 1 = φ w t + η t + 1 ◮ | ρ | = 1 : fully driven by past monetary policy shock w t + 1 = φ w t + ǫ e t

Time-Varying Transition Probabilities Agents infer TVTP by integrating out the latent factor w t using its invariant distribution, N ( 0 , 1 / ( 1 − φ 2 )) , and obtain � τ √ � � 1 − φ 2 φ x 1 − φ 2 − ρǫ e Φ ρ τ − � ϕ ( x ) dx t −∞ p 00 ( ǫ e t ) = � 1 − φ 2 ) Φ( τ � � � ∞ φ x 1 − φ 2 − ρǫ e 1 − φ 2 Φ ρ τ − � ϕ ( x ) dx τ √ t p 10 ( ǫ e t ) = � 1 − φ 2 ) 1 − Φ( τ � where Φ ρ ( x ) = Φ( x / 1 − ρ 2 ) .

Time-Varying Transition Probabilities ◮ If ρ = 0 , reduce to exogenous switching model ◮ ρ governs the fluctuation of transition probabilities

Analytical Solution We solve the system of expectational nonlinear difference equations using the guess and verify method. Davig and Leeper (2006) show that the analytical solution for the model with fixed regime monetary policy process is π t + 1 = a 1 r t + 1 + a 2 ǫ e t + 1 with some constants a 1 and a 2 . Motivated by this, we start with the following guess π t + 1 = a 1 ( s t + 1 , p s t + 1 , 0 ( ǫ e t + 1 )) r t + 1 + a 2 ( s t + 1 ) ǫ e t + 1

Analytical Solution ◮ Solution derivation � α 0 � ( α 1 − α 0 ) p s t + 1 , 0 ( ǫ e − E p 00 ( ǫ e + α 0 E p 10 ( ǫ e t + 1 ) + α 1 t + 1 ) t + 1 ) ρ r ρ r π t + 1 = � α 0 r t + 1 � α ( s t + 1 ) − E p 00 ( ǫ e + ( α 0 − ρ r ) E p 10 ( ǫ e ( α 1 − ρ r ) t + 1 ) t + 1 ) ρ r � �� � a 1 ( s t + 1 , p st + 1 , 0 ( ǫ e t + 1 )) σ e ǫ e − t + 1 α ( s t + 1 ) � �� � a 2 ( s t + 1 ) ◮ Limiting case 1: exogenous switching solution ( ρ = 0 ) � α 0 � ( α 1 − α 0 )¯ p s t + 1 , 0 + α 1 − ¯ + α 0 ¯ p 00 p 10 ρ r ρ r σ e ǫ e π t + 1 = � α 0 r t + 1 − � t + 1 α ( s t + 1 ) α ( s t + 1 ) ( α 1 − ρ r ) − ¯ + ( α 0 − ρ r )¯ p 00 p 10 � �� � ρ r a 2 ( s t + 1 ) � �� � a 1 ( s t + 1 )

Analytical Solution ◮ Solution derivation � α 0 � ( α 1 − α 0 ) p s t + 1 , 0 ( ǫ e − E p 00 ( ǫ e + α 0 E p 10 ( ǫ e t + 1 ) + α 1 t + 1 ) t + 1 ) ρ r ρ r π t + 1 = � α 0 r t + 1 � α ( s t + 1 ) − E p 00 ( ǫ e + ( α 0 − ρ r ) E p 10 ( ǫ e ( α 1 − ρ r ) t + 1 ) t + 1 ) ρ r � �� � a 1 ( s t + 1 , p st + 1 , 0 ( ǫ e t + 1 )) σ e ǫ e − t + 1 α ( s t + 1 ) � �� � a 2 ( s t + 1 ) ◮ Limiting case 2: fixed-regime solution ( α 1 = α 0 ) ρ r r t + 1 − σ e ǫ e π t + 1 = t + 1 α − ρ r α ���� � �� � a 2 a 1

Macro Effects of Policy Intervention Monetary authority sets future policy intervention ǫ e ǫ e ǫ e I t = { ˜ t + 1 , ˜ t + 2 , . . . , ˜ t + K } and evaluates its effect on future inflation. To illustrate, consider a contractionary intervention as in Leeper and Zha (2003): I T = { 4 % , . . . , 4 % , 0 , . . . , 0 } with K = 16 , s T = 0 � �� � � �� � 8 periods 8 periods ◮ Baseline = E ( π T + K | F T , s t = s T , t = T + 1 , . . . , T + K ) ◮ Direct Effects = E ( π T + K | I T , F T , s t = s T , t = T + 1 , . . . , T + K ) - Baseline ◮ Total Effects = E ( π T + K | I T , F T ) - Baseline ◮ Expectations Formation Effects = Total Effects - Direct Effects

Impulse Response Function ρ> 0 ◮ ǫ T + 1 > 0 − − → w T + 2 ↑ , s T + 2 ր 1 → more aggressive ◮ endogenous mechanism helps explain price stabilization

Expectations Formation Effect ρ> 0 ◮ ǫ T + 1 > 0 − − → w T + 2 ↑ , s T + 2 ր 1 → more likely to switch ◮ price stabilized b/c agents adjust their beliefs on future regimes ◮ black dot signifies period T + 2 total effect;

Endogenous Switching in New Keynesian Model

Households and Firms Households: � ( C t + s / A t + s ) 1 − ǫ � ∞ � β s ξ t + s − N t + s max E t 1 − ǫ { C t + s , N t + s , B t + s } ∞ s = 0 s = 0 s.t. P t C t + B t + T t = R t − 1 B t − 1 + P t W t N t + P t D t Firms: ∞ � β s ξ t + s Q t + s | t D jt + s max E t { N jt + s , P jt + s } ∞ s = 0 s = 0 � � 2 − W t N jt − φ s.t. D jt = P jt Y jt P jt − 1 Y jt Π ∗ P t 2 s t P jt − 1 � �� � real price-adjustment cost Y jt = A t N jt (Production) � P jt � − θ t Y jt = Y t (Dixit-Stiglitz aggregation) P t

Policy and Shocks Monetary and Fiscal Policy: � � ρ R ( s t ) �� Π t � ψ y ( s t ) � 1 − ρ R ( s t ) � ψ π ( s t ) � Y t R t R t − 1 = e t R ∗ R ∗ Π ∗ Y ∗ t s t s t − 1 s t s t = 1 { w t ≥ τ } w t = α w t − 1 + v t P t G t + R t − 1 B t − 1 = T t + B t Shocks: technology: ln A t = ln γ + ln A t − 1 + ln a t ln a t = ρ a ln a t − 1 + σ a ε a t preference: ln ξ t = ρ ξ ln ξ t − 1 + σ ξ ε ξ t markup: ln u t = ( 1 − ρ u ) ln u + ρ u ln u t − 1 + σ u ε u t MP: ln e t = σ e ε e t FP: ln g t = ( 1 − ρ g ) ln g + ρ g ln g t − 1 + σ g ε g t

Endogenous Feedback Mechanism       ε a ρ av 1 0 0 0 0 t ρ ξ v ε ξ 0 1 0 0 0       t     ρ uv   ε u 0 0 1 0 0  , ρ ′ ρ < 1    ∼ N  0 ,     t 0 0 0 1 0 ρ ev ε e    t ρ gv 0 0 0 0 1 ε g t ρ av ρ ξ v ρ uv ρ ev ρ gv 1 v t + 1 � i.e. w t + 1 = α w t + ρ ′ ε t + 1 − ρ ′ ρ η t + 1 . � �� � v t + 1 Variance decomposition: h � α 2 ( h − j ) FEV ( w t , h ) = j = 1 � � 5 h h 5 � � � � ρ 2 k α 2 ( h − j ) ρ 2 α 2 ( h − j ) = + 1 − k k = 1 j = 1 j = 1 k = 1 � �� � � �� � k -th structural non-structural

Equilibrium Conditions � β R t � ǫ � A t � � � ξ t + 1 �� C t / A t = 1 Euler: E t Π t + 1 C t + 1 / A t + 1 A t + 1 ξ t � Π t � Π t � ǫ � C t � �� u t � + u t NKPC: u t − φ − 1 2 − 1 Π ∗ Π ∗ A t 2 s t s t � � − ǫ Π t + 1 � �� � ξ t + 1 Y t + 1 / A t + 1 C t + 1 / A t + 1 Π t + 1 + βφ ( u t − 1 ) E t st + 1 − 1 = 1 ξ t Y t / A t C t / A t Π ∗ Π ∗ st + 1 � Π t � 2 Mkt Clear: Y t = C t + G t + φ − 1 Y t Π ∗ 2 s t � ρ R ( s t ) �� Π t � ψ π ( s t ) � Y t � ψ y ( s t ) � 1 − ρ R ( s t ) � R t R t − 1 MP: = e t Π ∗ R ∗ R ∗ Y ∗ s t s t − 1 s t t � τ √ 1 − α 2 � � α x 1 − α 2 − ρ ′ ε t Φ ρ τ − ϕ ( x ) dx √ −∞ TVTP1: p 00 ( ε t ) = √ Φ( τ 1 − α 2 ) � ∞ � � α x 1 − α 2 − ρ ′ ε t 1 − α 2 Φ ρ τ − ϕ ( x ) dx √ τ √ TVTP2: p 10 ( ε t ) = √ 1 − Φ( τ 1 − α 2 )