Monetary Policy and Exchange Rate Volatility in a Small Open Economy by Jordi Galí and Tommaso Monacelli March 2005
Motivation The new Keynesian model for the closed economy - equilibrium dynamics: simple three-equation representation - optimal monetary policy design: optimality of in ation targeting How does the introduction of open economy elements a ect that analysis and prescriptions? What role should the exchange rate play in the design of policy? What is the optimal degree of exchange rate volatility? ) main nding: equivalence result (for a benchmark model)
A New Keynesian Model of a Small Open Economy Households subject to Z 0 P H;t (j)c H;t (j) dj+ max E 0 Z Z 0 0 X t=0 t " Ct # N +' t + ' P i;t (j)c i;t (j) dj di +E t fq t;t+ D t+ g D t +W t N t +T t C t = i h( ) CH;t + CF;t Z C H;t = ( C H;t (j) " " " di) " 0 C F;t Z 0 (C i;t ) di ; C i;t Z 0 " C i;t (j) " " " dj
Firms Y t (i) = A t N t (i) a t = a t + u t Law of One Price p i;t (j) = e i;t + p i i;t(j) ) p F;t = e t + p t
Some Identities and De nitions Terms of Trade CPI s t p F;t p H;t p t ( ) p H;t + p F;t = p H;t + s t CPI In ation vs. Domestic In ation: Real Exchange Rate and the Terms of Trade t = H;t + s t q t (e t + p t ) p t = s t + (p H;t p t ) = ( ) s t
Optimal Intratemporal Allocation of Expenditures: - within each category: c H;t (i) = " (p H;t (i) p H;t ) + c H;t c F;t (i) = (p F;t (i) p F;t ) + c F;t - between categories: c H;t = (p H;t p t ) + c t c F;t = (p F;t p t ) + c t Other Optimality Conditions: w t c t = E t fc t+ g p t = c t + ' n t (r t E t f t+ g )
International Risk Sharing (Complete Markets) C i t+ C i t Ct+ C t Pt P t+ P i t E i t Pt+ i E i t+ = Q t;t+ = Q t;t+ Combining domestic and world foc s: C t = # i C i t Q i;t Log-linearizing (after # i = ): c t = c t + q t = c t + s t
Uncovered Interest Parity Complete markets: E t fq t;t+ [R t Rt i (E i;t+ =E i;t )]g = 0 Log-linearizing and aggregating over i: r t r t = E t fe t+ g Combined with the de nition of the terms of trade: s t = (rt E t f t+g) (r t E t f H;t+ g) + E t fs t+ g Integrating forward, and using lim T! E t fs T g = 0 : s t = E t ( X k=0 [(r t+k t+k+) (r t+k H;t+k+ )] )
Equilibrium Dynamics in the SOE: A Canonical Representation H;t = E t f H;t+ g + ey t ey t = E t fey t+ g (r t E t f H;t+ g rr t ) where ey t = y t y t y t = + a t + yt rr t ( a ) a t + ( + ) E t fyt+g ( + ') ; ( ) +! ; + ' + ' ; + '
Aggregate Demand and Output Determination World Market Clearing (WMC) Domestic Market Clearing (DMC) y t = c t y t = c t + s t + = c t +! where! + ( ) ( ). Combining DMC and WMC with IRS we obtain: s t q t where ( )+! > 0. y t = y t + s t ()
Finally, combining DMC with the Euler equation: y t = E t fy t+ g = E t fy t+ g = E t fy t+ g (r! t E t f t+ g ) E tfs t+ g (r t E t f H;t+ g ) E tfs t+ g (r t E t f H;t+ g ) + E t fy t+g where ( ) + ( )( ) =! and ( )+!. Letting ey t = y t y t ; ey t = E t fey t+ g (r t E t f H;t+ g rr t ) where rr t + (y t+ + E t fy t+g)
The New Keynesian Phillips Curve in the Small Open Economy Domestic Price Dynamics: p H;t p H;t + ( ) p H;t Optimal Price Setting: p H;t = + ( ) X () k E t fmc t+k + p H;t g k=0 Domestic In ation Dynamics H;t = E t f H;t+ g + cmc t (2) where ( )( )
Marginal Cost and the Output Gap mc t = + (w t p H;t ) a t = + (w t p t ) + (p t p H;t ) a t = + c t + ' n t + s t a t = + yt + ' y t + s t ( + ') a t Substituting for s t using (): mc t = + ( + ') y t + ( ) yt ( + ') a t Under exible prices, = + ( + ') y t + ( ) yt ( + ') a t Thus, Also y t = + a t + y t which combined with (2) yields: cmc t = ( + ') ey t H;t = E t f H;t+ g + ey t
Optimal Monetary Policy Background and Strategy A Special Case = = = ) C t = Yt (Yt ) (3) Optimal Allocation: subject to Optimality condition: max log C t C t = Y t (Y t ) N +' t + ' = (A t N t ) (Y t ) N = ( ) +'
Flexible Price Equilibrium " = MC t Optimality of Flexible Price Equilibrium: = ( ) A t S t ( ) Y t = N ' t A t C t = ( ) N +' t U N (C t ; N t ) U C (C t ; N t ) C t ( )( ) = " Implied Monetary Policy Objectives for all t. y t = y H;t = 0
Implementation where ( ) + ( ) x > 0: Other Macroeconomic Implications Terms of Trade where +' +' > 0. Special case r t = rr t + H;t + x x t s t = (y t y t ) = + a t y t s t = a t y t Exchange Rate CPI e t = s t p t p t = (e t + p t ) = s t
Consequences of Suboptimal Policies Welfare Losses (special case) W = ( ) 2 X h " i t 2 H;t + ( + ') x 2 t t=0 Taking unconditional expectations and letting!, V = ( ) 2 h " var( H;t) + ( + ') var(x t )i
Three Simple Rules Domestic in ation-based Taylor rule (DITR) r t = + H;t CPI in ation-based Taylor rule (CITR): r t = + t Exchange rate peg (PEG) e t = 0
Concluding Remarks small open economy version of the new Keynesian model under baseline assumptions (complete markets, full pass-through), equilibrium dynamics equivalent to the closed economy in a special (but not implausible) case: same optimal policy implications as in the closed economy (domestic in ation targeting). optimal policy associated with large uctuations in nominal exchange rate. extensions: - sticky wages - limited pass-through - incomplete markets. - scal policy - optimal policy design in a monetary union