Does the Exchange Rate Belong in Monetary Policy Rules?

Transcription

1 Does the Exchange Rate Belong in Monetary Policy Rules? Michael Kumhof International Monetary Fund Douglas Laxton International Monetary Fund Kanda Naknoi Purdue University July 27

2 1 Introduction The Question Should the (real) exchange rate enter the monetary policy rule? Under the following specic conditions: 1. Producer currency pricing. 2. Endogenous tradability of goods. 3. Real trade frictions.

3 The Literature Monetary policy need not pay attention to the exchange rate: Gali and Monacelli (25), Benigno and Benigno (23) and Obstfeld and Rogo (22). Common set of assumptions: 1. Producer currency pricing and perfect exchange rate pass-through. 2. Exogenous preference and technology shares of imported goods. 3. No real trade rigidities. Alternative 1: Local currency pricing. =) Signicant role for the exchange rate in the monetary policy rule: Smets and Wouters (22), Devereux and Engel (23) and Corsetti and Pesenti (25). Alternative 2: Endogenous tradability plus real trade rigidities. This paper.

4 2 The Global Endogenous Trade Model (GETM) Households: { Consume (habit persistence). { Supply Labor (sticky wages). { Accumulate Capital (investment adjustment costs). Primary Producers: Dier by productivity. Choose between three modes: 1. Produce for both exports and domestic market. 2. Produce only for domestic market. 3. Quit production.

5 Intermediates and Final Goods Producers: { Combine domestic and foreign goods. { Sell them domestically or abroad. Trade Frictions: 1. Iceberg trading cost. 2. Costly to become an exporter. 3. Costly and time-consuming to vary the import volume. Government: 1. Ricardian scal policy. 2. Optimizes a monetary policy rule.

6 Time to Build Capital G J t G * t t J * t C Sticky Prices t Final Output O Time to O t Build Markets V Z t,f Z * t,h C t * Time to Build Markets Sticky Prices O t * V * Time to Build Capital Z t,h Z t,f * D t,n Time to Time to D Intermediates D t D * Build Build t Markets D t,h D t,f D * t,h Markets D * t,f D * t,n Y t,n Y t,h Y t,f * Y t,n * y tn (z) y th (z) Primary Varieties y(z) Y t f* (z) Y t n* (z) K t L t Sticky Wages L t * K t * Sticky Wages Goods and Factor Flows in the Model Economy

7 2.1 Households Preferences: Max E 1 X t= t 8 < : (C t C t 1 ) ( L t) n (m t ) = ; Time-to-Build Capital: K t+1 = (1 )K t + I t 5 J t = 5 j=! ji t j (investment spending) Adjustment costs: (i) Investment. (ii) Wages. (iii) Net foreign assets. Standard FOC.

8 2.2 Primary Producers Technology for variety z 2 [; 1]: { `, k = Labor and Capital. { x t = TFP. y t (z) = a(z) t x t`t(z) k t (z) (1 ) { a(z) t = Firm-Specic Productivity.

9 Firm-Specic Productivity: 1. Declining relative productivity a(z): a(z) = Ne nz 2. Cost of becoming an exporter t : l t = 1 zl t z l t 1 z l t 1 1 A z l t is the marginal Home export variety Optimality: P = MC p t (z) = mc t x t a(z) t

10 z range where Home can compete with Foreign (assume x = x = 1): P t (z) S tp t (z) (1 ) =)=)=) mc t Ne nz 5 mc t s t (1 ) h t Home marginal cost < Foreign competitor's marginal cost. Foreign cost includes two hurdles: 1. Trading cost. 2. Export adjustment cost h t.

11 a(z) Comparative Advantage when x=x * =1 and a * (z)=1 Export Hurdle for Home mc / (1 t)x l mc*s mc mc*s mc (mc*s) / (1 t)x h Home Exports & Produces for Home Nontraded Goods Foreign Exports & Produces for Foreign Export Hurdle for Foreign z 1 z l z h Comparative Advantage

12 2.3 Intermediates Producers Technology combines primary varieties z: D t = 2 Z 1 4 y t(z) D 1 D dz 3 5 D D 1 = CES(Dt;H ; D t;n ; D t;f ) TIME to build import markets: (D = stock of import orders, O = new import orders) D t;f = (1 df )D t 1;F + Ot DF 2 COST to build import markets: DF t = df 2 ODF t Ot DF D t Ot DF 1 1 D t 1 12 C A

13 Solution for imports: t p t;f q DF t = t+1 p t+1;f q DF t+1 (1 df )+ t 2 6 4p D t (1 zt h)d! 1 t D t;f D p t;f df t p t;f Ot DF D t Ot DF 1 1 D t 1 1 C A O DF t D t O DF t 1 D t 1 1 C A = T t+2 p t+2;f q DF t+2 Shadow price of import orders q DF demand shock. t turns positive after a positive import =)=) new orders O =)=) higher order stock D after 2 quarters. Delayed and gradual response of import volumes to shocks.

14 2.4 Final Output Producers Tradables Composite T t combines Home and Foreign intermediates. { Time to build import markets technology again. Final output t adds the nontradable xed factor V. Price Setting - sticky price ination as in Ireland (21).

15 2.5 Government Ricardian Fiscal Policy: T x t + M t M t 1 = G t Taylor (1993) rule that allows for real exchange rate feedback term: i t = (i t 1 ) i! 1 i 4;t gdp t gdp T t! y s t Output Gap: gdp T = 2-sided centered moving average of GDP with weights taken from the Hodrick-Prescott (HP) lter. =) at end of sample use MODEL PREDICTIONS to measure trend level of output. Real Exchange Rate Gap: s constructed like gdp T. s t! s

16 3 Calibration Home = 25 percent of the world economy. Intertemporal elasticity of substitution: :5. Habit persistence: :85. Frisch elasticity of labor supply: 1. Markups Home/Foreign: { Labor Market: 3%/16%. { Goods Market: 35%/23%. Elasticities of substitution: { Home and Foreign traded goods: 1:5. { Traded and exogenously nontraded goods: :8.

17 Time to build capital: 6 quarters. Time to build import markets: 2 quarters. Steady state Home exports/gdp = 2%, imports/gdp = 2%. Trading costs = :15. Shocks: Wage and price markups, consumption and investment demand (correlated), uip shocks.

18 Home Economy Responses to a 1 Basis Point Interest Rate Hike 1.5 Interest Rate.2 Y O Y Inflation Real GDP Consumption Investment 1 Government Consumption Exports.5 Imports.5 Real Exchange Rate

19 4 Results Comparative Statics Showing the Eects of Trading Costs Optimal Simple Policy Rules

20 Long-Run Eects of Reducing Trading Costs Base-Case Results - Part I 1 Home GDP (Percent deviation from taubar=.15) 1 2 Foreign GDP (Percent deviation from taubar=.15) Home Exports/GDP Ratio (Percentage point deviation from taubar=.15) 5 2 Foreign Exports/GDP Ratio (Percentage point deviation from taubar=.15) Home Utility (Level difference from taubar=.15).6.2 Foreign Utility (Level difference from taubar=.15) Home Consumption (Percent deviation from taubar=.15) 15 2 Foreign Consumption (Percent deviation from taubar=.15)

21 Long-Run Eects of Reducing Trading Costs Base-Case Results - Part II 5 Home Labor (Percent deviation from taubar=.15) 5.5 Foreign Labor (Percent deviation from taubar=.15) Home Investment (Percent deviation from taubar=.15) Foreign Investment (Percent deviation from taubar=.15) Home Real Exchange Rate (Percent deviation from taubar=.15).5 1. Foreign Real Exchange Rate (Percent deviation from taubar=.15)

22 Generalized Taylor Reaction Function i t = i i t 1! 1 i gdpt gdp T t! ygap s t s T t! sgap { lagged interest rate term (i i t 1 ) { equilibrium nominal interest rate { output gap gdpt gdp T t { real exchange rate gap st s T t

23 HP 2-Sided Moving Average of the Output Gap Z = TX (y i i ) 2 + TX 2 i=1 i=1 [( i+2 i+1 ) ( i+1 i )] 2 A = y = A 1 y

24 :

25 Hodrick-Prescott Filter Weights

26 Loss Function L = L 1 var( 4 ) + L 2 var(ygap) + L 3 var(xgap)

27 Optimal Simple Rules Under Dierent Loss Functions: Baseline Loss i ygap sgap ygap xgap sgap Ination Nutter Dierence Output Gapper Dierence Output-Export Gapper Dierence

28 Optimal Simple Rules Under Dierent Loss Functions: Exogenous Tradability Loss i ygap sgap ygap xgap sgap Ination Nutter Dierence Output Gapper Dierence Output-Export Gapper Dierence

29 Optimal Simple Rules Under Dierent Loss Functions: tau =.1 Loss i ygap sgap ygap xgap sgap Ination Nutter Dierence Output Gapper Dierence Output-Export Gapper Dierence

30 Optimal Simple Rules Under Dierent Loss Functions: Demand Shocks Only Loss i ygap sgap ygap xgap sgap Ination Nutter Dierence Output Gapper Dierence Output-Export Gapper Dierence

31 Optimal Simple Rules Under Dierent Loss Functions: Markup Shocks Only Loss i ygap sgap ygap xgap sgap Ination Nutter Dierence Output Gapper Dierence Output-Export Gapper Dierence

32 Optimal Simple Rules Under Dierent Loss Functions: UIP Shocks Only Loss i ygap sgap ygap xgap sgap Ination Nutter Dierence Output Gapper Dierence Output-Export Gapper Dierence

33 Optimal Simple Rules Under Dierent Loss Functions: Ination in the Rule Four Quarter Ahead Loss i ygap sgap ygap xgap sgap Ination Nutter Dierence Output Gapper Dierence Output-Export Gapper Dierence

34 Optimal Simple Rules Under Dierent Loss Functions: Equal 5% Final Goods Exports Loss i ygap sgap ygap xgap sgap Ination Nutter Dierence Output Gapper Dierence Output-Export Gapper Dierence

35 Optimal Simple Rules Under Dierent Loss Functions: Intermeditate Goods Exports Share = 3% and Steeper Comparative Advantage Schedule Loss i ygap sgap ygap xgap sgap Ination Nutter Dierence Output Gapper Dierence Output-Export Gapper Dierence

36 Impulse Response Functions Without Endogenous Tradability.6 Interest Rate.3 GDP.5 Real Exchange Rate Y O Y Inflation.4 Consumption.2 Exports Real Interest Rate.3 Investment.6 Imports

37 Impulse Response Functions With Endogenous Tradability.6 Interest Rate.6 GDP.5 Real Exchange Rate Y O Y Inflation.6 Consumption.5 Exports Real Interest Rate.6 Investment 1 Imports

38 5 Conclusions Old Question: Should the exchange rate optimally enter the monetary rule under producer currency pricing? Old Answer: No. New Model: { Standard: Monetary DSGE model with real and nominal rigidities, incl. producer currency pricing. { New: Endogenous tradability of goods. { New: Export and import adjustment costs and lags. Results: { Conrmed: No role for the exchange rate under exogenous tradability and no trade frictions. { New: With endogenous tradability and trade frictions real exchange rate optimally enters the rule.