Monetary Policy and the Uncovered Interest Rate Parity Puzzle Dave - PowerPoint PPT Presentation

Monetary Policy and the Uncovered Interest Rate Parity Puzzle Dave Backus, Federico Gavazzoni, Chris Telmer and Stan Zin – 1

� � � � � � � � USD/EUR Interest Rate Differential Eonia Less Fed Funds Interest Rate Spread Question ⊲ Rate Spread Question Findings Overview Model Bilson-Fama Regression Main Result Intuition Calibration Conclusions Extra Slides – 2

Question Question Rate Spread Why do countries with high-interest-rate policies have ⊲ Question Findings currencies that tend to appreciate? Overview Model Bilson-Fama Regression Main Result � When the Fed decides to tighten vis-a-vis the ECB, Intuition why does USD get anointed as the risky currency? Calibration Conclusions Extra Slides – 3

... More Specifically Domestic and foreign Taylor Rules: Question Rate Spread ⊲ Question Findings Overview i t = τ + τ π π t + τ x x t ¯ Model Bilson-Fama Regression Main Result τ ∗ + τ ∗ Intuition i ∗ = ¯ π π ∗ t + τ ∗ x x ∗ t t Calibration Conclusions Extra Slides � How are these policies reflected in exchange rates? � Does the answer have anything to do with currency risk? – 4

Findings Question Rate Spread Question ⊲ Findings � A relatively tight domestic monetary policy, τ π > τ ∗ π , Overview makes the foreign currency risk premium larger . Model Bilson-Fama Regression Main Result Intuition � Empirical application based on U.S. - Australia Calibration Conclusions – Qualitative predications of model confirmed Extra Slides – Quantitatively, risk premiums too small – 5

Question ⊲ Overview FX Risk Lucas Equation Method Basic Approach Taylor Rules Model Background and Overview Bilson-Fama Regression Main Result Intuition Calibration Conclusions Extra Slides – 6

Two Points Question Overview FX Risk 1. Currency risk = difference in volatility. Lucas Equation Method Basic Approach Taylor Rules Model Bilson-Fama Regression 2. Overview of what we do: Main Result Intuition � Take Lucas (1982). Calibration Conclusions � Replace money with Taylor rules Extra Slides – 7

Currency Risk in Log-Normal Models High volatility implies low currency risk: Question Overview ⊲ FX Risk Lucas Equation � � � � Method Var t m t +1 − Var t m ∗ E t s t +1 − f t = / 2 Basic Approach t +1 Taylor Rules Model Bilson-Fama Regression where, Main Result Intuition � m = nominal MRS of U.S. representative agent Calibration � m ∗ = nominal MRS of European representative agent Conclusions Extra Slides � s t = log spot rate (price of EUR) � f t = log forward rate � � � E t s t +1 − f t = expected excess return on EUR – 8

(continued) Implications: Question Overview ⊲ FX Risk � Time-varying volatility is necessary Lucas Equation Method Basic Approach � For monetary policy to matter, it must either generate Taylor Rules volatility or respond to it. Model Bilson-Fama Regression � Our model: volatility arises from real shocks ... Taylor Main Result rule responds: Intuition Calibration Conclusions Extra Slides � � x t , σ 2 i t = τ + τ π π t ¯ + τ x x t t – 9

Lucas Equation � Lucas (1982) equation: Question Overview FX Risk ⊲ Lucas Equation Method u ′ ( c ∗ t +1 ) P ∗ Basic Approach t S t +1 u ′ ( c ∗ t ) P ∗ Taylor Rules t +1 = u ′ ( c t +1 ) Model S t P t u ′ ( c t ) P t +1 Bilson-Fama Regression Main Result Intuition Calibration Conclusions Extra Slides – 10

Lucas Equation � Lucas (1982) equation: Question Overview FX Risk ⊲ Lucas Equation Method u ′ ( c ∗ t +1 ) P ∗ Basic Approach t S t +1 u ′ ( c ∗ t ) P ∗ Taylor Rules t +1 = u ′ ( c t +1 ) Model S t P t u ′ ( c t ) P t +1 Bilson-Fama Regression t +1 e − π ∗ n ∗ Main Result t +1 = Intuition n t +1 e − π t +1 Calibration Conclusions Extra Slides – 10

Lucas Equation � Lucas (1982) equation: Question Overview FX Risk ⊲ Lucas Equation Method u ′ ( c ∗ t +1 ) P ∗ Basic Approach t S t +1 u ′ ( c ∗ t ) P ∗ Taylor Rules t +1 = u ′ ( c t +1 ) Model S t P t u ′ ( c t ) P t +1 Bilson-Fama Regression t +1 e − π ∗ n ∗ Main Result t +1 = Intuition n t +1 e − π t +1 Calibration m ∗ Conclusions t +1 = Extra Slides m t +1 – 10

Method Question � Previous work on monetary policy and the UIP puzzle: Overview FX Risk Alvarez, Atkeson, and Kehoe (2007), Backus, Gregory, Lucas Equation ⊲ Method and Telmer (1993), Bekaert (1994), Burnside, Basic Approach Eichenbaum, Kleshchelski, and Rebelo (2006), Canova Taylor Rules Model and Marrinan (1993), Dutton (1993), Grilli and Roubini Bilson-Fama (1992), Lucas (1982), Macklem (1991), Marshall Regression (1992), McCallum (1994) and Schlagenhauf and Wrase Main Result Intuition (1995) Calibration Conclusions Extra Slides � Most feature explicit models of money . � We replace money with Taylor rules – 11

Basic Approach � Usual set-up (private sector behavior): Question Overview i t = − log E t n t +1 e − π t +1 FX Risk Lucas Equation Method � Monetary policy is a Taylor rule: ⊲ Basic Approach Taylor Rules i t = τ + τ π π t + τ x x t ¯ Model Bilson-Fama Regression � Endogenous inflation (Gallmeyer, Hollifield, Palomino, and Zin Main Result (2007)) Intuition π t = − 1 � τ + τ x x t + log E t n t +1 e − π t +1 � Calibration ¯ τ π Conclusions Extra Slides � Do the same for foreign country, use Lucas equation to solve for exchange rate: t +1 e − π ∗ t +1 ( τ ) ( τ, τ ∗ ) = n ∗ S t +1 n t +1 e − π t +1 ( τ ∗ ) S t – 12

Different Taylor Rules � Can evaluate different Taylor rules: Question – Baseline, with/without shocks/asymmetries: Overview FX Risk Lucas Equation i t = τ + τ π π t + τ x x t + z t ¯ Method τ ∗ + τ ∗ i ∗ = π π ∗ t + τ ∗ x x ∗ t + z ∗ Basic Approach ⊲ Taylor Rules t t Model – Asymmetric w.r.t. exchange rate: Bilson-Fama Regression i t = τ + τ π π t + τ x x t + z t ¯ Main Result τ ∗ + τ ∗ i ∗ = π π ∗ t + τ ∗ x x ∗ t + τ ∗ 3 log( S t +1 /S t ) + z ∗ Intuition t t Calibration Conclusions – Interest rate smoothing (McCallum (1994)): Extra Slides i t = τ + τ π π t + τ x x t + τ 4 i t − 1 + z t ¯ τ ∗ + τ ∗ i ∗ = π π ∗ t + τ ∗ x x ∗ t + τ ∗ 4 i ∗ t − 1 + z ∗ t t � Important identification issues (Cochrane (2007)) – 13

Question Overview ⊲ Model Setting Preferences Consumption Taylor Rule Inflation Solution Model Pricing Kernel Foreign Economy Bilson-Fama Regression Main Result Intuition Calibration Conclusions Extra Slides – 14

Setting Question Overview U ′ ( c ∗ t +1 ) /U ′ ( c ∗ t ) S t +1 P t � � � � τ = τ Model ⊲ Setting S t U ′ ( c t +1 ) /U ′ ( c t ) P t +1 Preferences � �� � Consumption Real FX Rate Taylor Rule Inflation Solution � Complete markets Pricing Kernel Foreign Economy Bilson-Fama Regression � Recursive preferences Main Result Intuition � Exogenous domestic and foreign consumption ( c ∗ t , c t ) Calibration Conclusions Extra Slides – No feedback from policy to allocations � Taylor rules ( τ , τ ∗ ) – 15

Preferences � Recursive preferences for representative agent: Question Overview Model U t = [(1 − β ) c ρ t + βµ t ( U t +1 ) ρ ] 1 /ρ Setting ⊲ Preferences Consumption Taylor Rule Inflation Solution µ t ( U t +1 ) ≡ E t [ U α t +1 ] 1 /α Pricing Kernel Foreign Economy Bilson-Fama Regression � Real pricing kernel: Main Result Intuition � c t +1 � ρ − 1 � � α − ρ Calibration U t +1 n t +1 = β . Conclusions c t µ t ( U t +1 ) Extra Slides � Hansen, Heaton, and Li (2005) linearization – 16

Consumption Question Consumption growth: Overview Model Setting Preferences ⊲ Consumption (1 − ϕ x ) θ x + ϕ x x t + √ u t ǫ x x t +1 = t +1 Taylor Rule Inflation Solution Pricing Kernel Foreign Economy Volatility: Bilson-Fama Regression (1 − ϕ u ) θ u + ϕ u u t + σ u ǫ u Main Result u t +1 = t +1 Intuition Calibration Conclusions Extra Slides – 17

Taylor Rule Question Overview Model i t = ¯ τ + τ π π t + τ x x t Setting Preferences Consumption ⊲ Taylor Rule Inflation Solution Pricing Kernel Foreign Economy Bilson-Fama Regression Main Result Intuition Calibration Conclusions Extra Slides – 18

Solution: Domestic Inflation Question π t = − 1 � τ + τ x x t + log E t n t +1 e − π t +1 � ¯ Overview τ π Model Setting Preferences Consumption � Solution: Taylor Rule ⊲ Inflation Solution Pricing Kernel π t = a + a x x t + a u u t Foreign Economy Bilson-Fama Regression Main Result � Coefficients Intuition (1 − ρ ) ϕ x − τ x Calibration a x = Conclusions τ π − ϕ x Extra Slides � � 2 α 2 ( α − ρ )( ω x + 1) 2 − 1 (1 − α ) − ( α − ρ ) ω x + a x 2 a u = τ π − ϕ u – 19