Journal of International Economics 78 (2009) 60–71

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Journal of International Economics j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / j i e

Expectations and exchange rate dynamics: A state-dependent pricing approach☆ Anthony Landry ⁎ Federal Reserve Bank of Dallas, 2200 North Pearl Street, Dallas, Texas, 75201, United States

a r t i c l e

i n f o

Article history: Received 13 June 2007 Received in revised form 12 January 2009 Accepted 15 January 2009 Keywords: State-dependent pricing Variable demand elasticity International business cycle transmission Exchange rate dynamics JEL classification: F41 F42

a b s t r a c t This paper presents a two-country DSGE model with state-dependent pricing as in Dotsey et al. [Dotsey, M., King, R.G., and Wolman, A.L., 1999. State-dependent pricing and the general equilibrium dynamics of money and output. Quarterly Journal of Economics 114, 655–690] and variable demand elasticity as in Kimball [Kimball, M.S., 1995. The quantitative analytics of the basis neomonetarist model. Journal of Money, Credit, and Banking 27, 1241–1277]. Following a domestic monetary expansion, the model predicts: (i) positive hump-shaped responses of domestic output and consumption, (ii) positive spillover effects on foreign output and consumption, (iii) a high international output correlation relative to consumption correlation, (iv) a delayed increase in domestic and foreign inflation, (v) a delayed nominal exchange rate overshooting, (vi) a deterioration in the terms of trade, and (vii) a J-curve in the trade balance. The model matches the impulse responses from an identified VAR more closely than an otherwise identical model with time-dependent pricing.

© 2009 Elsevier B.V. All rights reserved.

1. Introduction What are the implications of monetary policy shocks in open economies? The New Open Economy Macroeconomics literature aims to provide a framework to answer this question. The unifying feature of this literature is the introduction of nominal rigidities and market imperfections into a dynamic general equilibrium model to explain movements in exchange rates, terms of trade, trade balances, and other macroeconomic variables. However, a much criticized but standard element of this literature is an exogenously imposed timing of the opportunity firms have for nominal price adjustments.1 I address this critique by developing a two-country version of the dynamic general equilibrium model with state-dependent pricing

☆ First and foremost, I would like to thank Marianne Baxter and Robert G. King for continuous guidance and support. I also gratefully acknowledge comments and suggestions from two anonymous referees and Giancarlo Corsetti, Russell Cooper, Mario Crucini, Jon Faust, Simon Gilchrist, Dale Henderson, Sylvain Leduc, John Rogers, Tatsuma Wada, and seminar participants at the American Economic Association 2006 Annual Meeting, the Bank of Canada, Boston University, the Canadian Economic Association2005 Annual Meeting, the Computing in Economics and Finance Conference 2005, the Conference on International Macroeconomics 2006, FRB-Boston, FRB-Dallas, the Federal Reserve Board, Georgetown University, HEC Montreal, North Carolina State University, the Society for Economic Dynamics 2006 Annual Meeting, the University of Colorado-Boulder, and Universite de Montreal. The views expressed in this paper do not necessarily reflect those of the Federal Reserve Bank of Dallas or the Federal Reserve System. ⁎ Tel.: +1 214 922 5831; fax: +1 214 922 5194. E-mail address: [email protected]. 1 See Chari et al. (2002), Lane (2001), and Sarno (2001). 0022-1996/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jinteco.2009.01.010

(SDP) due to Dotsey et al. (1999). In addition, I highlight the role of complementarity in price-setting by adding variable demand elasticity as in Kimball (1995). Following a domestic monetary expansion, the model predicts: (i) positive hump-shaped responses of domestic output and consumption, (ii) positive spillover effects on foreign output and consumption, (iii) a high international output correlation relative to consumption correlation, (iv) a delayed increase in domestic and foreign inflation, (v) a delayed nominal exchange rate overshooting, (vi) a deterioration in the terms of trade, and (vii) a Jcurve in the trade balance. To estimate and evaluate the model, I pursue a limited information strategy along the lines of Christiano et al. (2005). First, I estimate the dynamic response of key macroeconomic and international variables conditional on a U.S. monetary policy expansion using an identified vector autoregression (VAR). Second, I select a set of structural parameters to minimize the distance between the empirical impulseresponse functions and the SDP model's impulse-response functions. I do the same with an otherwise identical model with time-dependent pricing (TDP). Overall, the SDP model's predictions match the impulse responses in the identified VAR more closely than the predictions of the TDP model. The key to the model's success is the combination of SDP and complementarity in price-setting. In contrast to the time-dependent approach, in which the timing of price adjustment is fixed, SDP and variable demand elasticity increase the interaction between firms: Variable demand elasticity makes it desirable for firms to keep their prices similar to those of others, while SDP makes it feasible for them to do so. At the microeconomic level, this combination leads domestic

A. Landry / Journal of International Economics 78 (2009) 60–71

price-adjusting firms to react slowly to a monetary expansion. On one hand, firms would prefer to raise prices in light of increased demand. On the other hand, they have the option to reset prices at any time in the future and would rather do so than lose market share by pricing high relative to competitors. Over time, the firms' cumulative actions feed into the aggregate price level and lead prices to overshoot their new long-run value. In the aggregate, the overshooting in domestic prices is mirrored by the price level and the nominal exchange rate. Nominal exchange rate overshooting is important in explaining international economic fluctuations. In fact, the logic of the model places pricing at the center of the domestic and international transmission mechanisms. Following a monetary expansion, slow price responses increase domestic and import demand, causing a short-run worsening of the trade balance. Improvement in the trade balance arises as domestic prices and the nominal exchange rate overshoot their long-run values, contracting domestic and import demand. With complementarity between domestic and foreign goods, demand movements cause a Jcurve in the domestic trade balance. Together, relative price movements lead to fluctuations in output, consumption, and trade balances that are similar to those observed in the data. This paper builds a two-country version of Dotsey et al. (1999) and Dotsey and King (2005), who introduced SDP into a dynamic general equilibrium model. It is also related to the development of other recent closed-economy SDP models, such as Burstein (2006), Devereux and Siu (2007), Gertler and Leahy (2008), and Golosov and Lucas (2007). In open-economy, Floden and Wilander (2006), and

61

Midrigan (2007), use a SDP framework to study the behavior of prices in response to exchange rate innovations. Floden and Wilander focus on exchange rate pass-through and the volatility of import prices, while Midrigan analyzes the relationship between real and nominal exchange rate volatility. Closer to this paper is Hernandez (2006), who develops a small-open-economy SDP model to study the output and consumption dynamics associated with exchange-rate and monetary disinflation programs. In contrast to other open-economy SDP work, I develop a twocountry dynamic general equilibrium model to study international business-cycle transmission and exchange rate dynamics following a monetary expansion. The introduction of SDP and variable demand elasticity implies a gradual transmission of monetary policy shocks to aggregate economic activity. The resulting movements in relative prices and real macroeconomic aggregates mimic fluctuations observed in the data. Section 2 of this paper highlights the properties of international economic fluctuations conditional on a U.S. monetary expansion. Section 3 describes the open-economy SDP model, while Section 4 presents the model's solution and estimation. Section 5 discusses the model's implications. In this Section, I analyze the endogenous evolution of price distributions in response to a monetary expansion, describe the way these distributions influence international economic activity, and contrast the implications of the SDP model with a corresponding TDP model which is used as a reference case because of its popularity in the current literature. Finally, Section 6 concludes.

Fig. 1. Domestic response to a U.S. monetary expansion. Note: The left column displays VAR impulse-response functions. The right column displays SDP (red) and TDP (blue) impulseresponse functions. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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A. Landry / Journal of International Economics 78 (2009) 60–71

2. International fluctuations conditional on a U.S. monetary expansion Several features drive international trade and prices following a U.S. monetary expansion. I use an aggregate of Japan, Germany, France, and the U.K., which form the economy called Foreign, to discuss the effects of a U.S. monetary expansion abroad. The U.S. data are from the Bureau of Economic Analysis. The Japanese, German, French, and British data are from OECD Economic Outlook. The quarterly data cover the period 1974Q1 to 2005Q4 and are expressed in 2000 U.S. dollars at purchasing power parity when necessary. Appendix A describes the data sources and aggregation. I follow the recursive VAR framework of Eichenbaum and Evans (1995) and Christiano et al. (2005) and consider the dynamic responses of key macroeconomic and international variables to a U.S. monetary expansion. The characterization of U.S. monetary policy is given in Eq. (1), where FFRt represents the monetary instrument, f is a linear function, Υt is an information set, and εt represents the monetary policy shock. The identifying assumption relies on εt being orthogonal to the elements of Υt. Let Yt denote the vector of variables included in Υt. FFRt = f ðΥt Þ + et

ð1Þ V

Yt = ½Y1t ; FFRt ; Y2t  :

ð2Þ

The recursive causal ordering assumes that the vector Y1t contains variables whose values at time t do not respond contemporaneously to a monetary policy shock, while its counterpart Y2t consists of all other variables included in Υt. The variables in Y1t are per capita U.S. real gross domestic product (GDP), per capita U.S. real personal expenditure, per capita Foreign real GDP, per capita Foreign real personal expenditure, U.S. personal expenditure deflator, Foreign personal expenditure deflator, and per capita U.S. real trade balance with the Foreign economy. The variables in Y2t are the growth rate of per capita U.S. real M1, the nominal exchange rate, and U.S. terms of trade. The nominal exchange rate is the dollar price of one unit of Foreign currency. The U.S. terms of trade is the ratio of import to export prices. The decision to include aggregates of output, consumption, inflation, and the trade balance in Y1t reflects a long-standing view that those macroeconomic variables do not respond contemporaneously to monetary policy shocks. Finally, the monetary instrument is the Federal Funds Rate (FFRt), which is the preferred policy instrument of Bernanke and Blinder (1992), Bernanke and Mihov (1998), and Christiano et al. (1999, 2005). The VAR contains two lags of each variable. To compare the empirical estimates with the business-cycle model described below, variables in Yt are logged and filtered using a one-sided approximate band-pass business-cycle filter, which admits frequency components between 6 and 32 quarters (see Baxter and King, 1999). The VAR takes the following representation: Yt = A0 + A1 Yt − 1 + A2 Yt − 2 + Cet ;

confidence intervals. Following a U.S. monetary expansion, the VAR predicts: (i) positive hump-shaped responses of U.S. output and consumption, (ii) positive spillover effects on Foreign output and consumption, (iii) a delayed increase in U.S. and Foreign inflation, (iv) a delayed nominal exchange rate overshooting, (v) a deterioration of U.S. terms of trade, and (vi) a J-curve in U.S. trade balance. Although the uncertainty surrounding the empirical results is large, the VAR responses are consistent with other work. For example, the output, consumption, and inflation responses are typical to VAR studies such as Kim (2001): A U.S. monetary expansion initially increases U.S. and Foreign output and consumption. Eventually, U.S. and Foreign output and consumption decline because prices adjust. Kim also finds a J-curve in U.S. trade balance following a domestic monetary expansion. As well, the dynamic response of the nominal exchange rate mimics the delayed overshooting result of Eichenbaum and Evans (1995) and, more recently, Scholl and Uhlig (2008). 3. The model The world economy consists of two countries, each having (i) a representative infinitely lived household, (ii) a continuum of firms indexed on the unit interval, and (iii) a monetary authority. In what follows, each variable is represented by a country-specific subscript (i.e., i = 1, 2 for Country 1 (U.S.) and Country 2 (Foreign)). When three subscripts are attached to a single variable, the first subscript denotes the country of production, the second denotes the country of consumption, and the third denotes time. 3.1. Households Households in both countries maximize a time separable objective function defined over consumption goods (ci,t) and leisure (1 − ni,t), where σi governs the intertemporal elasticity of substitution and ηi governs the elasticity of labor supply: ∞ X

E0 t =0

β

t



1 χ 1 − σi 1 + ηi c − n 1 − σ i i;t 1 + ηi i;t

for i = 1; 2:

ð4Þ

Country 1 and Country 2 aggregate consumptions are defined as c1;t =

c2;t =

!

1 γ1 −1 γ1 γ1

1 γ1 −1 γ1 γ1

1 γ2 −1 γ2 γ2

1 γ2 −1 γ2 γ2

ð1− θ1 Þ c1;1;t + θ1 c2;1;t

ð1− θ2 Þ c2;2;t + θ2 c1;2;t

γ1 γ 1 −1

!

ð5Þ

γ2 γ2 −1

:

The following equations define the optimal allocations between domestic and imported consumption: P

c1;1;t = ð1 − θ1 Þ

ð3Þ

where C is an 11 × 11 lower triangular matrix, and et is an 11 × 1 vector of zero-mean serially uncorrelated shocks. I estimate the parameters A0, A1, A2, C, and the variance of the elements of et using ordinary least-squares. Using these estimates, I compute the dynamic path of Yt. To maintain consistency with the model presented below, I consider an innovation in the Federal Funds Rate that corresponds to a 1% increase in the growth rate of the monetary aggregate. Chari et al. (2002), and Christiano et al. (2005) support this process as a good approximation to an interest rate rule. The left columns of Figs. 1 and 2 display the U.S. and Foreign impulse-response functions. The solid lines correspond to the estimated averages, while the shaded areas represent 90% Bootstrap



c2;2;t = ð1 − θ2 Þ

P1;t

!− γ1

C P1;t P P2;t C P2;t

P

c1;t

c2;1;t = θ1

c2;t

c1;2;t = θ2

!− γ2

St P2;t

!− γ1 c1;t

C P1;t P P1;t C St P2;t

ð6Þ

!− γ2 c2;t ;

which depend on domestic and foreign aggregate consumption; producer price indices (hereafter PPIs), denoted by Pi,tP; consumer price indices (hereafter CPIs), denoted by Pi,tC; and the nominal exchange rate Si,t, defined as the dollar price of one unit of Foreign currency. Households are identical across countries except for the local bias introduced in consumption. (1 − θi) determines the degree of home bias in the steady-state, and γi determines the elasticity of substitution between domestic and imported goods. This specification implies that following a decline in imported goods prices, households do not fully substitute domestic for imported goods in their

A. Landry / Journal of International Economics 78 (2009) 60–71

63

Fig. 2. Foreign response to a U.S. monetary expansion. Note: The left column displays VAR impulse-response functions. The right column displays SDP (red) and TDP (blue) impulseresponse functions. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

consumption basket. Instead, households consume a relatively fixed basket, with a fraction (1 − θi) of domestic goods and the remaining fraction θi of foreign goods. This is consistent with the data because the ratios of imports to consumption are relatively stable in the long run. The benchmark economy features complete risk pooling to isolate the role of SDP.2 This implies that households can freely reallocate risk through a complete set of state-contingent nominal bonds bi,t and corresponding stochastic discount factor Dt, such that Et [Dt + 1bi,t + 1] = Σst + 1ρ(st + 1|st)D(st + 1|st)bi(st + 1), where ρ(st + 1|st) denotes the probability of the state of nature st + 1 given st. The households also receive nominal wages Wi,t from labor services, and a series of dividend payments Zi,t from firms. The sequence of intertemporal budget constraints can be represented in terms of aggregates as h C Pi;t ci;t + Et Dt

+ 1 bi;t + 1

i

V bi;t + Wi;t ni;t + Zi;t for i = 1; 2:

ð7Þ

The problem for households is then to choose consumption, labor, and portfolio holdings to maximize lifetime utility (4) subject to a sequence of intertemporal budget constraints (7) and allocation of time. The maximization problem implies that the ratios of marginal utilities of consumption λi,t are equalized across countries. That is, qt =κ·λ2,t /λ1,t, with the real exchange rate defined as qt =Std (PC2,t /PC1,t) and a constant κ reflecting initial wealth differences. Deviations in the real exchange rate are allowed by the local consumption bias introduced in preferences. 2

A single uncontingent nominal bond can easily be introduced and does not change the general results.

Prices are set in the currency of the producer so that the law of one price holds. Finally, the level of nominal aggregate demand is governed by a cash-in-advance constraint Mi,t / Pi,tC = ci,t for i = 1, 2, along with money supply rules. 3.2. Modeling complementarity in price setting As in Dotsey and King (2005) and as in the open-economy literature of Bouakez (2005) and Gust et al. (2006), I introduce complementarity in price setting by allowing for variable demand elasticity following the work of Kimball (1995). In contrast to the Dixit–Stiglitz demand, variable demand elasticity makes it more costly for adjusting firms to get their prices out of line with prices set by other firms. However, as opposed to the literature in which the timing of price adjustment is fixed, SDP and variable demand elasticity increase the interaction between firms as they opt to keep their prices in line with average product prices. 3.2.1. Firms' relative demand Consider the following expenditure minimization problem for each country: Z 1  Z 1  min Pi;t ðzÞdi;t ðzÞdz subject to C di;t ðzÞ = di;t dz = 1 for i = 1; 2; di;t ðzÞ

0

0

ð8Þ where di,t represents aggregate demand in country i and is defined by a demand aggregator Γ such that an aggregate producer price index Pi,tP holds. Each firm produces a differentiated product such that Pi,t(z)

64

A. Landry / Journal of International Economics 78 (2009) 60–71

identifies the price of the good charged by an individual firm z, with corresponding relative demand di,t(z) /di,t. The demand aggregator Γ is an increasing and concave function reflecting diminishing demand elasticity and is defined over the parameters φi and ϱi, which govern the curvature of the demand function. The parameter ϱi determines the elasticity of demand at average product prices, while φi determines the curvature of the demand function. A nice property of this specification is that the Dixit–Stiglitz aggregator is a special case represented by φi = 0.   C di;t ðzÞ = di;t =

 h   i%  1 1 i ð1 + ’i Þ di;t ðzÞ=di;t − ’i − 1 + for i = 1; 2: ð1 + ’i Þ%i ð1 + ’i Þ%i

ð9Þ The demand aggregator defines firms' relative demand as a function of individual and aggregate prices, and curvature parameters of the demand function di;t ðzÞ Pi;t ðzÞ =f ; ’i ; %i P di;t Pi;t

! for i = 1; 2:

3.2.2. Price indices PPIs are given as a weighted sum of prices over individual firm demand ratios P

Z

Pi;t =

1 0

  Pi;t ðzÞ di;t ðzÞ = di;t dz for i = 1; 2;

ð10Þ

and CPIs follow a weighted sum of domestic and imported goods prices

C P1;t =

C

P2;t =

  1 − γ  1 − 1 P P ð1− θ1 Þ P1;t + θ1 St P2;t   1 − P ð1 − θ2 Þ P2;t

γ2

γ1

 1 − P + θ2 P1;t = St



1 1 − γ1

γ2

ð11Þ



1 1− γ2

:

As in standard open-economy models, the expenditure-switching effect arises as movements in the nominal exchange rate alter the price of imports and the composition of CPIs. 3.3. Firms A continuum of monopolistically competitive firms is located on the unit interval and indexed by z in each country. At any date t, a firm is identified by its current price Pi,t(z) and its current menu cost of price adjustment ξi,t(z) ∈ [0, B ̅]. The menu cost is denominated in labor hours and drawn from a time-invariant distribution G(ξi,t) common across all firms in country i. Since the indices z are uncorrelated over time, and there are no other state variables attached to individual firms, price-adjusting firms in the same country find it optimal to charge a common price P ̂i,t. I restrict the analysis to positive steady-state inflation rates so that the benefit of price adjustment becomes infinitely large as the number of periods for which the price has been fixed grows. Given that the support of the distribution G(ξi,t) is finite, there is a finite fraction of vintages in each country Ji, a vintage being a measure of firms with a common price. 3.3.1. Production and demand Labor used for price adjustment is denoted ni,ta (z) and labor used for production is denoted ni,ty (z). Total labor employed by a firm is thus ni,ta (z) + ni,ty (z) = ni,t (z). Technology is linear in labor, and production by an individual firm is represented by yi,t(z) = ni,ty (z). Using Eq. (6), Country 1 aggregate demand d1,t is the sum of domestic c1,1,t and exported c1,2,t consumption of home-produced goods d1,t =c1,1,t +c1,2,t. Similarly, Country 2 aggregate demand is d2,t =

c2,2,t +c2,1,t. Supply is demand driven, and production by an individual firm satisfies a fraction of its country's aggregate demand Pi;t ðzÞ

yi;t ðzÞ = f

P Pi;t

!  di;t for i = 1; 2:

; ’i ; %i

ð12Þ

Eq. (12) illustrates that production by an individual firm depends on its price relative to other domestic firms (PPI) and on aggregate demand in each country. 3.3.2. Pricing policy In both SDP and TDP frameworks, the firms' optimal decision can be represented using a dynamic programming approach: Given the level of demand, the current menu cost of price adjustment, the current real price, and the prevailing real wage rate, individual firms decide whether or not to adjust their prices with respect to a state vector st. Accordingly, each firm z that has changed its price j periods ago has a real value function of the form 8 < max :v

i;0;t

  v pCj;t ; i;t ðzÞ j st =     9 C C = vi;j;t = π pi;j;t j st + βEt Λ i;t;t + 1 v pi;j + 1;t + 1 ; i;t + 1 ðzÞ j st + 1 ;     C C = maxpˆ C π pˆ i;t jst + βEt Λ i;t;t + 1 v pˆ i;t + 1 ; i;t + 1 ðzÞ jst + 1 − wi;t i;t ðzÞ ; t

for i = 1; 2;

ð13Þ with the value if the individual firm does (vi,0,t) or does not (vi,j,t) adjust, C C real profits π(pi,j,t |st) = (pi,j,t −ψi,t)yi,j,t, and the optimal price chosen by C adjusting firms p̂i,t. Both the optimal p̂iC,t and current real price pi,tC are C relative to domestic CPI such that p̂iC,t =p̂i,t/Pi,tC and pj,i,t =Pj,i,t/Pi,tC, which are the appropriate prices in firms' decisionmaking, Λi,t,t + 1 =λi,t + 1 /λi,t denotes the ratio of future to current marginal utility and is the appropriate discount factor for future real profits, and ψi,t denotes real marginal cost, which is equal to ψi,t =wi,t. Eq. (13) shows that the firm must weigh the current and future benefits of adjusting its price against the status quo. Price-adjusting firms set prices optimally and choose cost-minimizing levels of input. Firms that decide not to adjust prices satisfy demand while choosing inputs to minimize costs. In this environment, the fraction of firms in country i that choose to adjust is αi,j,t. These fractions are determined by the menu cost ξi,t(z) of marginal firms being just equal to the value gained such that3   vi;0;t ðst Þ − vi;j;t ðst Þ for i = 1; 2:  α i;j;t = wi;t ðst Þ

ð14Þ

Finally, the dynamic program (13) implies that the optimal price satisfies a first-order equation balancing pricing effects on current and expected future profits. As part of an optimal plan, price-adjusting firms choose prices that satisfy    3 2 Aπ pˆ Ci;t jst Av pˆ Ci;t ; i;t + 1 jst + 1 5for i = 1; 2: 0= + βEt 4Λ i;t;t + 1  AˆpCi;t AˆpCi;t ð15Þ Iterating the first-order Eq. (15) forward, firms' nominal optimal prices P ̂ can be expressed as an explicit function of current and expected future variables

PJ Pˆ i;t =

PJ

i − 1 j β Et j = 0

h Xi;j;t;t

h i − 1 j β Et Xi;j;t;t j = 0

+ j

+ j

i P + j  i;j;t + j  ψi;t + j  Pi;t + j  di;j;t + j     P C + j  i;j;t + j − 1  Pi;t + j = Pi;t + j  di;j;t

 Λ i;t;t

 Λ i;t;t

i for i = 1; 2; + j

ð16Þ

3 These are continuous functions on the unit interval 0 ≤ αi,j,t ≤ 1 such that the real labor cost of a marginal firm is ξ(αi,j,t) if the fraction of firms αi,j,t are adjusting prices. Thus, Eq. (14) describes the endogenous fractions of price-adjusting firms in each country.

A. Landry / Journal of International Economics 78 (2009) 60–71

where Ωi,j,t,t + j represents the probability of nonadjustment from t to t + j and  i,j,t + j denotes the elasticity of demand for the individual firm. Accordingly, the optimal price is a fixed markup over real marginal cost if the demand elasticity, real marginal cost, and aggregate prices are expected to be constant over time. The optimal pricing rule (16) is a generalization of the types derived in open-economy TDP models (i.e., with exogenous probabilities of price adjustment). It also represents an open-economy version of the SDP rule of Dotsey et al. (1999), and Dotsey and King (2005). However, in contrast to its closed-economy counterpart, export demand and the nominal exchange rate enter the decision of the value-maximizing firms and hence influence adjustment probabilities. 3.4. Monetary policies Money supply growth is exogenous and follows an autoregressive process in each country: ΔMi;t = ρi ΔMi;t − 1 + mi;t for i = 1; 2;

3.5. General equilibrium The aggregate state of the economy at time t is a vector st =(M1,t, M2,t, Θ1,t, Θ2,t), where Mi,t represents the exogenous state variables and Θi,t represents the period t distribution of producer prices in country i. Given the aggregate state, a general equilibrium for the economy is a collection of functions satisfying a set of equilibrium conditions: a collection of allocations for consumers c1, n1, b1 and c2, n2, b2; a collection of allocations and prices for firms y1(z), n1(z), P1(z) and y2(z), n2(z), P2(z); and a collection of prices P P1, P C1 , W1, D1 and P P2, P C2, W2 , D2 such that (i) households maximize their utilities, (ii) firms maximize their values, and (iii) aggregate consistency conditions hold. These aggregate consistency conditions include market-clearing conditions in the goods and labor markets, and in the time-varying distributions of firms in each country. 4. Solution and estimation 4.1. Solution I use numerical methods to solve the model. First, I compute the steady-state equilibrium by imposing trade account balance to the Table 1 Calibrated and estimated parameter values. State-dependent pricing model

Estimated parameters σ Intertemporal elasticity of substitution η

Elasticity of labor supply

γ Elasticity of substitution between domestic and imported goods ϕ Demand curvature ϱ

Elasticity of demand

ρ

Money growth autocorrelation

Table 2 SDP model's adjustment hazard and vintage fractions. Quarter(s) since last adjustment 0

1

2

3

4

5

6

Adjustment hazard Vintage fractions

N/A 0.246

0.035 0.238

0.111 0.212

0.219 0.165

0.379 0.103

0.643 0.037

1 N/A

Foreign αj Adjustment hazard ωj Vintage fractions

N/A 0.242

0.033 0.234

0.107 0.209

0.210 0.165

0.360 0.106

0.599 0.043

1 N/A

U.S. αj ωj

model's long-run behavior. The steady-state equilibrium for this economy involves the minimum number of vintages that generates unconditional adjustment by all firms in each country. Second, I take a linear approximation of the behavioral equations around the steadystate equilibrium and compute the resulting linear rational expectations equilibrium using the algorithm developed by King and Watson (1998).

ð17Þ

where ρi describes the coefficients of autocorrelation and vi,t describes independently and identically distributed zero-mean disturbances.

Calibrated parameters β Discount rate n Fraction of time working θ Degree of home bias μ Steady-state money growth rate

65

Time-dependent pricing model

4.2. Calibration I calibrate and estimate the model to replicate the central features of international fluctuations conditional on a U.S. monetary expansion as described in Section 2. The first two columns of Table 1 present the calibrated parameters for the benchmark economy. The estimation of the remaining parameters is described below. The length of a time period is one quarter. The subjective discount factor β is 0.99 and implies an annual real rate of returns of 4.1%. Households devote 20% of their time endowment to work. The U.S. is characterized by a degree of home bias of 3.7% and represents half of the world's output. The former corresponds to the average share of U.S. exports to GDP traded with Foreign over the sample period, while the latter corresponds to the ratio of U.S. to Foreign GDP. Finally, the steady-state money growth rate represents an annual inflation rate of 4% in the U.S. and 3.8% in Foreign, which correspond to the average inflation rates observed in these countries over the sample period. 4.3. Minimum-distance estimation of the structural parameters Following the open-economy macroeconomic literature, the experiment consists of a U.S. monetary expansion: a 1% increase in the money stock. The estimation approach sets the remaining parameters to minimize the distance between the empirical impulse-response functions and the SDP model's impulse-response functions of U.S. output, U.S. consumption, U.S. CPI inflation, the nominal exchange rate, U.S. terms of trade, U.S. trade balance, Foreign output, Foreign consumption, and Foreign CPI inflation. The set of structural parameters ψ = (ρ1, φ1, φ2, 1, 2, σ1, σ2, η1, η2, γ1, γ2) is estimated as the solution to

½

 ½ V



U.S.

Foreign U.S.

Foreign

ˆ ðψÞ W Ψˆ − Ψ ðψÞ ; J = min Ψ−Ψ

0.990 0.200 0.037 0.010

0.990 0.200 0.037 0.010

0.990 0.200 0.037 0.010

0.990 0.200 0.037 0.010

0.209 (0.007) 0.040 (0.014) 0.810 (0.257) 1.020 (0.001) 7.098 (0.094) 0.596 (0.006)

0.262 (0.131) 0.058 (0.023) 0.819 (0.257) 1.020 (0.028) 9.992 (0.207) N/A

0.296 (0.009) 0.060 (0.001) 0.737 (0.205) 1.020 (0.001) 9.995 (0.001) 0.533 (0.007)

0.193 (0.244) 0.060 (0.022) 0.703 (0.205) 1.020 (0.031) 7.000 (0.035) N/A

where Ψ̂ represents the empirical impulse-response functions and Ψ(ψ) represents the model's impulse-response functions. W is a diagonal matrix with the inverse of each impulse-response's variances along the diagonal. This weighting matrix accounts for the fact that some points of the impulse-response functions are less precisely estimated than others and hence guarantees that Ψ(ψ) lies as much as possible inside the confidence intervals. I utilize the first 16 time periods of the impulseresponse functions and discard the first empirical point estimate from the estimation procedure to minimize the impact of the VAR identification strategy in the estimation of the model.4 The estimated parameters

ψ

ð18Þ

4 The VAR identification is inconsistent with our theoretical model: the VAR assumes that the variables contained in the vector Y1t do not immediately react to the monetary expansion while in the theoretical model, firms begin to adjust prices on impact altering output and consumption responses immediately after the shock.

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A. Landry / Journal of International Economics 78 (2009) 60–71

Fig. 3. Firms' reactions to a U.S. monetary expansion. Note: SDP (red) and TDP (blue) impulse-response functions. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

and standard errors are shown in the first two columns of Table 1.5 Following Ireland (2004), standard errors are the square root of the diagonal elements of V≡([∂g(ψ)/∂ψ]′W [∂g(ψ)/∂ψ])− 1 /T, where g(ψ)= (Ψ̂ −Ψ(ψ)) and T is the total number of observations used in the estimation. The preference parameters imply an elasticity of marginal cost with respect to output of approximately 0.25 for the U.S. and 0.32 for Foreign.6 The elasticity of substitution between domestic and imported consumption goods is 0.81 for the U.S. and 0.82 for Foreign—although the unit value often used in the literature cannot be rejected. The demand function parameters are estimated such that the steady-state elasticity of demand  i holds at di(z) / di = 1 for each country. Together with the values of φi, they imply that a 1% increase in prices decreases demand by 9% in the U.S. and 13% in Foreign. The parameter governing the U.S. autocorrelation of money growth of 0.60 is in line with Christiano et al. (2005). The remaining parameters involve the adjustment-cost distributions which, along with the demand functions, determine the timing and distribution of prices. Table 2 presents the steady-state adjustment hazards and vintage fractions of adjusting firms for each country. The adjustment-cost structure is consistent with microeco5 A substantial part of the parameter space cannot be solved according to the criteria of Blanchard and Kahn (1980). To avoid nonexistence or multiplicity of equilibriums, the structural parameters ψ are in the neighborhood of the parameter value explored by Dotsey and King (2005). 6 Given that the households efficiency condition is wt = cσt nη, and that consumption and labor are approximately equal to output, the elasticity of marginal cost is approximately equal to σ + η.

nomic data on price adjustment that suggest that steady-state adjustment hazards are quadratic in log relative price deviations (Caballero and Engle, 1993).7 The estimated parameters imply an average age of prices of 1.75 quarters for the U.S. and 1.79 quarters for Foreign. The corresponding expected price duration is 4.06 quarters for U.S. and 4.13 quarters for Foreign. Together, the demand and adjustment-cost specifications provide a reasonable approximation of the main features governing the pattern of price adjustments and pricing policies observed in empirical studies such as Bils and Klenow (2004) and Nakamura and Steinsson (2008). 5. Findings The SDP pricing structure implies that the degree of price rigidity depends on the state of the economy. Over the business cycle, the nature of the pricing structure generates discrete and occasional price adjustment by firms in light of variation in demand and cost conditions. Those changes in economic environment affect not only the intensive margin—the level of price adjustment undertaken by price-adjusting firms—but also the extensive margin—the fraction of firms actively engaged in price adjustment. Relative to similar experiments in the open-economy TDP literature, the novel feature

7 I adopt the cost structure used in Dotsey and King (2005) and set the maximum adjustment cost to 7.5% of households production time. This implies that the resources ^ spent adjusting prices relative to sales average 0.8% of firms' revenues in the steady ^ state, in line with Levy et al. (1997).

A. Landry / Journal of International Economics 78 (2009) 60–71

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Fig. 4. Nominal exchange rate and terms of trade responses to a U.S. monetary expansion. Note: SDP (red) and TDP (blue) impulse-response functions. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

of the model is the interplay between the intensive and extensive margins across countries. First, I discuss the SDP model's responses to the 1% increase in the U.S. money stock and contrast these responses with those from a TDP models for which the fractions of price-adjusting firms are held fixed at steady-state values. In contrast to the flat adjustment hazards of Calvo (1983), the TDP adjustment hazards are similar to Levin (1991), in which the adjustment probabilities are conditional on the amount of time elapsed since a firm's last price adjustment. To get a better understanding of the mechanism through which money affects international economic activity, I start by exploring the reactions of individual firms to a U.S. monetary expansion in Section 5.1. Then, I turn to the aggregate implications in Section 5.2. Finally, I estimate the TDP model and assess the relative empirical performance of the SDP and TDP models in Section 5.3. 5.1. Firms' reactions to a monetary expansion Fig. 3 displays the firms' reactions to a U.S. monetary expansion. The top row displays the fractions of price-adjusting firms under the Dixit–Stiglitz demand (φi = 0), while the middle row displays the fractions of price-adjusting firms under the estimated Kimball demand. The bottom row displays the optimal prices chosen by price-adjusting firms under the different demand specifications and pricing structures. The Dixit–Stiglitz demand does not generates inertia in firms' reactions following a U.S. monetary expansion. In the TDP model, the

optimal price set by domestic firms increases by more than one-forone with the money stock. This is possible because only a fraction of firms adjust prices. In the SDP model, the optimal price and adjusting fractions jump on impact and display oscillatory dynamics that translate into the price level, output, and other macroeconomic variables (see Dotsey and King, 2005).8 I do not carry the analysis of the Dixit–Stiglitz demand further because the macroeconomic dynamics induced by this demand specification are different from those estimated by VARs. In contrast, the Kimball demand generates inertia in firms' reactions following a U.S. monetary expansion. In the TDP model, firms adjust prices on the intensive margin. Therefore, the Kimball demand generates inertia only in optimal prices. In this environment, price-adjusting firms do not have any control over the timing of price adjustments and must therefore incorporate this inability to reset prices in their pricing policy. This leads the domestic optimal price to jump on impact and then to slowly converge to its new long-run value. In the SDP model, firms adjust prices on the intensive and extensive margins, and the Kimball demand generates inertia in optimal prices and in firms' adjustment fractions. SDP means that firms can make smaller adjustments in prices now knowing that they can choose to increase them later when it is more valuable to do so. Combined with the Kimball demand, this leads U.S. price-adjusting firms to react slowly to the monetary expansion because they do not 8 In a companion paper available upon request, I explore in more detail the Dixit– ^ Stiglitz demand implications (Landry, 2003).

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Table 3 TDP model's adjustment hazard and vintage fractions. Quarter(s) since last adjustment 0

1

2

3

4

5

6

U.S. αj Adjustment hazard ωj Vintage fractions

N/A 0.249

0.035 0.240

0.113 0.213

0.224 0.165

0.389 0.101

0.667 0.034

1 N/A

Foreign αj Adjustment hazard ωj Vintage fractions

N/A 0.240

0.032 0.232

0.104 0.208

0.204 0.166

0.348 0.108

0.576 0.046

1 N/A

want to lose profit by raising price too aggressively. Over time, the increase in domestic demand raises the value of price-adjusting firms and induces more firms to adjust prices. This becomes obvious six quarters after the monetary expansion as the adjusting fraction and optimal price deviate further from their long-run values. Ultimately, the collective action of price-adjusting firms feeds into the aggregate price level, and the piling up of prices and actions leads to an overshooting of the optimal price. The U.S. monetary expansion is transmitted to Foreign by a depreciation of the U.S. dollar. The U.S. dollar depreciation initially decreases the demand for Foreign goods and lowers the value of Foreign firms. Foreign firms react by playing on the intensive and extensive margins: To compete against U.S. goods, some firms delay their price adjustment, while others decrease their prices. Over time, demand builds back up and the adjusting fraction and optimal price rise. Together, SDP and variable demand elasticity generate smooth movements in firms' pricing behavior—the intensive and extensive margins. In turn, firms' pricing behavior heavily influences aggregate prices and is responsible for the novel response of aggregate economic activity. In particular, the overshooting of the domestic optimal price, absent in the TDP model, is important in explaining international economic fluctuations. 5.2. Aggregate implications to a monetary expansion 5.2.1. U.S. aggregates The right column of Fig. 1 displays the models' U.S. impulse-response functions following a U.S. monetary expansion. The SDP model generates positive hump-shaped responses of output and consumption followed by a real contraction. The real contraction of economic activity arises as prices overshoot long-run values. Although the output contraction lasts for a substantial amount of time, it does not undo the initial stimulation generated by the monetary expansion. An important strength of the SDP model relative to the TDP model is its ability to generate initial price inertia and a delayed response in CPI inflation. In the SDP model, the U.S. monetary expansion induces a significant and persistent depreciation in U.S. currency. The model also displays the delayed overshooting emphasized by Eichenbaum and Evans (1995) in their empirical study on the effects of U.S. monetary policy shocks on nominal exchange rates. In the SDP and TDP models, the nominal exchange rate is best understood by looking at the dynamics of its components: the real exchange rate, and the U.S. and Foreign consumer price levels. The top row of Fig. 4 displays the components of the nominal exchange rate, while the middle row displays their relative contributions. Short-term responses of the nominal exchange rate are mostly in the real exchange rate: these are relative price changes that affect demand composition. At longer horizons, the domestic price level mainly affects the nominal exchange rate in a close to neutral manner. The SDP nominal exchange rate overshooting explanation differs from Dornbusch (1976) and Obstfeld and Rogoff (1996). In Dornbusch, the overshooting results from a simple TDP rule combined with instantaneous adjustment in asset markets. In Obstfeld and Rogoff, the overshooting results from the interaction between flexible prices in

traded goods and TDP in nontradable goods. In the SDP model, all goods are traded and the overshooting results from the optimal pricing response of domestic firms following a monetary expansion. A well-documented fact in international economics is the strong positive comovement between real and nominal exchange rates (see Chari et al., 2002). A shortcoming of the SDP model is the implication of a negative comovement between real and nominal exchange rates: The real exchange rate is determined by the ratio of marginal utilities of consumption between the two countries. In the SDP model, the monetary expansion generates oscillations in the nominal exchange rate that are negatively correlated with relative consumption, and the real exchange rate (i.e., the overshooting of the nominal exchange rate corresponds to an appreciation in the real exchange rate). In contrast, the monetary expansion generates persistent fluctuations in relative consumption, and in real and nominal exchange rates that are essentially monotonic in the TDP model. In addition, the middle row of Fig. 4 points toward a larger role for prices in the determination of nominal exchange rate in the SDP model (shown by the combined yellow and red areas being larger in the SDP model). This is consistent with the idea that SDP models generate more aggressive price movements following a monetary shock because of the additional effect of endogenous price responses. The last two panels of the right column of Fig. 1 display U.S. terms of trade and U.S. trade balance. The bottom row of Fig. 4 displays the components of U.S. terms of trade, namely import and export prices. In the SDP model, depreciation in the nominal exchange rate feeds into import prices, while export prices remain stable because of slow-moving domestic prices. After 10 quarters, U.S. terms of trade starts to improve as export prices mimic domestic prices overshooting. In contrast, deterioration of U.S. terms of trade is persistent in the TDP model. Finally, U.S. trade balance displays a J-curve following a domestic monetary expansion: it worsens within a year, then starts to improve and becomes positive after 10 quarters. The trade improvement is persistent, peaking after 15 quarters. On impact, the positive response of consumption raises import demand and explains the short-run worsening of the trade balance. Improvement in the trade balance arises as domestic prices overshoot their long-run values and contract consumption. With an estimated high degree of complementarity between domestic and foreign goods, the contraction in consumption causes an expenditure-switching effect in the trade balance.9 5.2.2. Foreign aggregates The right column of Fig. 2 displays the models' Foreign impulseresponse functions. Note that the scales are different from the Foreign country empirical impulse-response functions (i.e., the left column of Fig. 2). The current framework generates small movements in Foreign output, consumption, and CPI inflation following a U.S. monetary expansion.10 These small movements are consistent with the fact that Foreign output, consumption, and CPI inflation are insignificant in the VAR impulse response functions. Following a U.S. monetary expansion, the SDP model generates positive hump-shaped responses of Foreign output and consumption followed by real contractions. Although Foreign output peaks roughly at the same time as U.S. output, consumption peaks with a delay. This delayed response of Foreign consumption gives rise to a high international output correlation relative to consumption correlation, as discussed in Section 5.3.

9 The high degree of complementarity between domestic and foreign goods is key to deliver the J-curve dynamics. For a degree of elasticity of substitution between domestic and imported goods (γ) higher than 2, domestic import demand falls, Foreign output falls, and the trade balance dynamics changes (i.e., expenditureswitching effect first) following a U.S. monetary expansion. 10 An increase in trade would increases the effect of a U.S. monetary expansion abroad through its impact on Foreign firms' reaction and ultimately on Foreign real aggregates. The qualitative results are not altered by an increase in trade.

A. Landry / Journal of International Economics 78 (2009) 60–71

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Fig. 5. VAR against SDP and TDP model responses to a U.S. monetary expansion. Note: VAR alongside SDP (red) and TDP (blue) impulse-response functions. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

To better understand Foreign economic activity, I decompose Foreign output and consumption into their domestic and foreign components. The expansion of Foreign output arises in two phases. First, increasing export demand from the U.S. stimulates output. Then, low domestic producer prices (see Fig. 3) raise domestic consumption, which further propels output. The expansion of Foreign consumption arises in two phases as well. First, nominal exchange rate depreciation generates an expenditure-switching effect in favor of U.S. goods. In turn, this increases the level of competition among Foreign firms and leads to lower domestic producer prices, which further propels consumption.

The previous subsection contrasts the aggregate implications of the SDP model with those of an otherwise identical TDP model. Since the parameter values are identical, the different dynamic responses are attributable to whether the adjustment fractions vary following a monetary expansion. In this subsection, I evaluate the empirical performance of the SDP model alongside the TDP model. To do so, I estimate the TDP model according to the method described in Section 4.3 and compare its predictions with the SDP model.11

The TDP parameters and standard errors are presented in the right columns of Table 1. The preference parameters generate an elasticity of marginal cost with respect to output of 0.36 for the U.S. and 0.25 for Foreign. The elasticity of substitution between domestic and imported consumption goods is 0.74 for the U.S. and 0.70 for Foreign. The demand function parameters imply that a 1% increase in prices decreases demand by 13% in the U.S. and 9% in Foreign. Finally, the coefficient governing the U.S. autocorrelation of money growth is 0.53. Table 3 presents the steady-state adjustment hazards and vintage fractions of adjusting firms for each country. The estimated parameters imply an average age of prices of 1.73 quarters for the U.S. and 1.81 quarters for Foreign. The expected price duration is 4.02 quarters for U.S. and 4.16 quarters for Foreign. Fig. 5 displays the estimated SDP and TDP models' impulseresponse functions alongside the VAR impulse-response functions. In line with empirical estimates, the SDP model replicates key patterns found in the VAR. Following a domestic monetary expansion, the SDP model predicts: positive hump-shaped responses of U.S. output and consumption, positive spillover effects on Foreign output and consumption, a delayed increase in U.S. and Foreign inflation, a delayed nominal exchange rate overshooting,12 a deterioration in U.S. terms of trade, and a J-curve in U.S. trade balance. The major points

11 The TDP model steady-state computation is similar to the SDP model: the steadystate equilibrium involves the lowest value of vintage fractions that generates unconditional adjustment by all firms in each country. The dynamic computation and estimation are done keeping adjustment fractions fixed at steady-state values.

12 The SDP and TDP long-run nominal exchange rate movements are distant from the VAR estimates because of the long-run multipliers implied by the rational expectation approach.

5.3. Empirical Performance of the Models

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Table 4 Minimum-distance estimation metrics. Series

State-dependent pricing model

Time-dependent pricing model

U.S. output U.S. consumption U.S. CPI inflation Nominal exchange rate U.S. terms of trade U.S. trade balance Foreign output Foreign consumption Foreign CPI inflation Total

4.40 6.96 8.14 5.20 18.32 3.88 6.06 6.16 5.63 64.75

9.30 6.95 7.74 3.47 10.83 10.89 11.84 6.04 5.80 72.84

prices and the nominal exchange rate leads to real exchange rate and terms-of-trade movements that are inconsistent with the empirical literature. An important direction for future work will be to introduce frictions to generate plausible movements in real exchange rate and terms of trade. For example, one could introduce complementarity in price-setting using a mechanism that leads to goods market segmentation, as in Burstein et al. (2007) who combine Kimball demand specification with domestic distribution costs. As well, Corsetti and Dedola (2005) and Corsetti et al. (2008a,b) stress the interaction between upstream producers and distributors using local inputs. It will be interesting to see whether some form of goods market segmentation can address this issue. Appendix A. Data

missed by the TDP model are related to the SDP core mechanism: a delayed overshooting in prices and in the nominal exchange rate, a fall in output and consumption, and an expenditure-switching effect in U.S. trade balance (second part of the J-curve). Table 4 presents the minimum-distance estimation metrics for each impulse-response function and for the minimized sums. The SDP model does better than the TDP model at minimizing the sum of impulse-response functions. With respect to individual impulseresponse functions, the SDP model does particularly well matching U.S. output and U.S. trade balance. In contrast, the TDP model more closely matches U.S. terms of trade because of its high persistence. Finally, a well-documented characteristic of international business cycles is the high international output correlation relative to consumption correlation (see Backus et al., 1992; Baxter, 1995). Ambler et al. (2004) note that replicating the international correlations of consumption relative to output remains a significant challenge for dynamic stochastic general equilibrium models, especially when those models assume a high degree of international risk sharing. In the data, the international output correlation conditional on a U.S. monetary expansion is 0.60, while the international consumption correlation is 0.42 at business-cycle frequencies. In the SDP model, the delayed response of Foreign consumption generates an international output correlation of 0.93, while the international consumption correlation is 0.69.13 This result arises with international risk-sharing and without goods market segmentation. In the TDP model, the international output correlation is 0.98, while the international consumption correlation is 0.88. 6. Conclusion This paper presents an open-economy macroeconomic model consistent with many empirical aspects of international economic fluctuations. In contrast with previous open-economy macroeconomic work, the introduction of SDP and complementarity in price-setting implies a gradual transmission of monetary policy shocks to aggregate economic activity. The resulting movements in relative prices and real macroeconomic aggregates mimic fluctuations observed in the data. By replicating key fluctuations in real and nominal economic activity, the model therefore offers a new framework in which to address questions in international finance. Unfortunately, the current framework is unable to replicate the dynamics of international real prices. The near coincidence between 13 A large body of research relies on goods market segmentation to generate a high international output correlation relative to consumption correlation following monetary policy shocks. Betts and Devereux (2000) assume goods market segmentation for a fraction of firms and show how this specification can be used to attain the observed international output and consumption correlations. Chari et al. (2002) impose goods market segmentation for all firms. In their model, international goods market segmentation is necessary to cleave the relationship between output and consumption, while cross-correlated monetary shocks are needed to provide a consumption expansion abroad.

This appendix describes the data used in the paper. Data from the Bureau of Economic Analysis are quarterly U.S. real gross domestic product; quarterly U.S. real personal consumption expenditure; quarterly U.S. personal consumption expenditure price deflator; quarterly U.S. exports price index; quarterly U.S. imports price index; quarterly U.S. working-age population; monthly effective Federal Funds rate; monthly U.S. M1 money stock; monthly U.S. trade weighted exchange rate index—major currencies; monthly U.S. exports/imports to/from Japan; monthly U.S. exports/imports to/ from Germany; monthly U.S. exports/imports to/from France; monthly U.S. exports/imports to/from the U.K. Data from OECD Economic Outlook are quarterly nominal gross domestic product for Japan, Germany, France, and the U.K.; quarterly nominal private final consumption expenditure for Japan, Germany, France, and the U.K.; quarterly gross domestic product deflator for Japan, Germany, France, and the U.K.; quarterly private final consumption expenditure deflator for Japan, Germany, France, and the U.K.; quarterly working-age population for Japan, Germany, France, and the U.K.; and annual purchasing power parity in U.S. dollars for Japan, Germany, France, and the U.K. To construct Foreign aggregates, I convert the series in 2000 U.S. dollars using year 2000 PPP values. Then, I aggregate the series using working-age population weights.

References Ambler, S., Cardia, E., Zimmermann, C., 2004. International business cycles: what are the facts? Journal of Monetary Economics 51, 257–276. Backus, D.K., Kehoe, P.J., Kydland, F.E., 1992. International real business cycles. Journal of Political Economy 100, 745–775. Baxter, M., 1995. International trade and business cycles. In: Grossman, G.M., Rogoff, K. (Eds.), Handbook of International Economics, North Holland, pp. 1801–1864. Baxter, M., King, R.G., 1999. Measuring business cycles: approximate band-pass filters for macroeconomic time series. Review of Economics and Statistics 81, 575–593. Bernanke, B.S., Blinder, A.S., 1992. The federal funds rate and the channels of monetary policy transmission. American Economic Review 82, 901–921. Bernanke, B.S., Mihov, I., 1998. Measuring monetary policy. Quarterly Journal of Economics 113, 869–902. Betts, C., Devereux, M.B., 2000. Exchange rate dynamics in a model of pricing-tomarket. Journal of International Economics 50, 215–244. Bils, M., Klenow, P., 2004. Some evidence on the importance of sticky prices. Journal of Political Economy 112, 947–985. Blanchard, O.J., Kahn, C.M., 1980. The solution of linear difference models under rational expectations. Econometrica 48, 1305–1311. Bouakez, H., 2005. Nominal rigidity, desired markup variations, and real exchange rate persistence. Journal of International Economics 66, 49–74. Burstein, A., 2006. Inflation and output dynamics with state-dependent pricing decisions. Journal of Monetary Economics 53, 1235–1257. Burstein, A., Eichenbaum, M., Rebelo, S., 2007. Modeling exchange rate passthrough after large devaluation. Journal of Monetary Economics 54, 346–368. Caballero, R., Engle, E., 1993. Microeconomics rigidities and aggregate price dynamics. European Economic Review 37, 697–717. Calvo, G., 1983. Staggered prices in a utility-maximizing framework. Journal of Monetary Economics 12, 383–398. Chari, V.V., Kehoe, P.J., McGrattan, E.R., 2002. Can sticky price models generate volatile and persistent real exchange rates? Review of Economic Studies 69, 533–564. Christiano, L.J., Eichenbaum, M.S., Evans, C.L., 1999. Monetary policy shocks: what have we learned and to what end? In: Taylor, J., Woodford, M. (Eds.), Handbook of Macroeconomics, North Holland, pp. 65–148.

A. Landry / Journal of International Economics 78 (2009) 60–71 Christiano, L.J., Eichenbaum, M.S., Evans, C.L., 2005. Nominal rigidities and the dynamic effects of a shock to monetary policy. Journal of Political Economy 113, 1–45. Corsetti, G., Dedola, L., 2005. A macroeconomic model of international price discrimination. Journal of International Economics 67, 129–155. Corsetti, G., Dedola, L., Leduc, S., 2008a. International risk sharing and the transmission of produictivity shocks. Review of Economic Studies 75, 443–473. Corsetti, G., Dedola, L., Leduc, S., 2008b. High exchange-rate volatility and low passthrough. Journal of Monetary Economics 55 (6), 1113–1128. Devereux, M.B., Siu, H.E., 2007. State-dependent pricing and business cycle asymmetries. International Economic Review 48, 281–310. Dornbusch, R., 1976. Expectations and exchange rate dynamics. Journal of Political Economy 84, 1161–1176. Dotsey, M., King, R.G., 2005. Implication of state-dependent pricing for dynamic macroeconomic models. Journal of Monetary Economics—Carnegie-Rochester Series on Public Policy 52, 213–242. Dotsey, M., King, R.G., Wolman, A.L., 1999. State-dependent pricing and the general equilibrium dynamics of money and output. Quarterly Journal of Economics 114, 655–690. Eichenbaum, M.S., Evans, C.L., 1995. Some empirical evidence on the effects of monetary policy shocks on exchange rates. Quarterly Journal of Economics 110, 975–1010. Floden, M., Wilander, F., 2006. State-dependent pricing, invoicing currency, and exchange rate pass-through. Journal of International Economics 70, 178–196. Gertler, M., Leahy, J., 2008. A Phillips curve with an Ss foundation. Journal of Political Economy 116, 533–572. Golosov, M., Lucas, R.E., 2007. Menu costs and Phillips curves. Journal of Political Economy 2007, 171–199. Gust, C., Leduc, S., Vigfusson, R.J., 2006. Trade integration, competition, and the decline in exchange-rate pass-through. International Finance Discussion Papers 864. Hernandez, K., 2006. State-dependent Nominal Rigidities and Disinflation Programs in Small Open Economies. University of Delaware. Manuscript.

71

Ireland, P., 2004. A method for taking models to the data. Journal of Economic Dynamics and Control 28, 1205–1226. Kim, S., 2001. International transmission of U.S. monetary policy shocks: evidence from VARs. Journal of Monetary Economics 48, 339–372. Kimball, M.S., 1995. The quantitative analytics of the basis neomonetarist model. Journal of Money, Credit, and Banking 27, 1241–1277. King, R.G., Watson, M.W., 1998. The solution of singular linear difference systems under rational expectations. International Economic Review 39, 1015–1026. Landry, A., 2003. What Does State-dependent Pricing Imply for Exchange Rates? Boston University. Manuscript. Lane, P.R., 2001. The new open-economy macroeconomics: a survey. Journal of International Economics 54, 235–266. Levin, A., 1991. The macroeconomic significance of nominal wage contract duration. Discussion Paper 08–91., University of California at San Diego. Levy, D., Bergen, M., Dutta, S., Venable, S., 1997. The magnitude of menu costs: direct evidence from a large U.S. supermarket chain. Quarterly Journal of Economics 112, 791–825. Midrigan, V., 2007. International price dispersion in state-dependent pricing models. Journal of Monetary Economics 54, 2231–2250. Nakamura, E., Steinsson, J., 2008. Five facts about prices: a reevaluation of the menu cost models. Quarterly Journal of Economics 123 (4), 1415–1464. Obstfeld, M., Rogoff, K., 1996. Foundations of International Macroeconomics. The MIT Press. Sarno, L., 2001. Toward a new paradigm in open economy modeling: where do we stand? Federal Reserve Bank of St. Louis Review 83–3, 21–36. Scholl, A., Uhlig, H., 2008. New evidence on the puzzle: results from an agnostic identification on monetary policy and exchange rates. Journal of International Economics 76 (1), 1–13.