Monetary Policy and Trade Globalization∗ by po9383

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									Monetary Policy and Trade Globalization
Dudley Cooke† Trinity College Dublin

∗

Abstract: I develop a two country general equilibrium model with heterogeneous price-setting firms to understand how shocks to monetary policy and aggregate labor productivity impact trade integration, which I capture through the average productivity of exporting firms. A contractionary shock to the domestic interest rate raises the average productivity of domestic exporting firms but lowers the average productivity of foreign exporting firms. The magnitude of these changes is greater when governments target domestic price inflation as opposed to consumer price inflation. A positive shock to domestic labor productivity generates only modest (positive) changes in average productivity for both sets of exporting firms when consumer prices are targeted. However, when domestic prices are targeted, the shock causes a fall in the average productivity of domestic exporting firms, and a far larger rise in the productivity of foreign exporting firms. JEL Classification: E31, E52, F41. Keywords: Monetary Policy, Heterogeneous Firms, Trade Globalization.

∗

Financial support from the Hong Kong Institute for Monetary Research (HKIMR) is gratefully acknowledged. First

draft: September 2009. † Department of Economics, Trinity College Dublin, College Green, Dublin, Ireland. Email: dcooke@tcd.ie

I. Introduction

The connection between deepening economic integration and the fall of world-wide inflation has generated considerable debate. One idea is that the recent process of globalization has led to increased levels of competition and a reduction in prices. This helped lower inflation, at least in the short to medium run (Rogoff, 2004), and in the most open economies resulted in global excess capacity being the main driver of inflation dynamics (Rogoff, 2007). An alternative argument is that trade integration per se had little impact on inflation (Ball, 2006).1 Inflation fell instead because of a shift in policy

at central banks. This paper develops a two country dynamic stochastic general equilibrium model to shed some light on this debate. The model I develop combines two key features. Each country is associated with an industry in

which a differentiated good is produced by monopolistically competitive price-setting firms that are heterogeneous in productivity. Because exporting is subject to fixed costs, some varieties of each good are not traded. For traded goods, the law of one price fails because when a firm decides to export it sets the local currency price of it’s product in advance. This eliminates exchange rate pass through. Governments use the short-term nominal interest rate to target an inflation index. Because output price inflation generates resource costs, the allocation of resources within an industry depends on the inflation target set by the central bank. I consider interest rate policy regimes. One in which consumer price inflation - which includes imported varieties of the foreign good - is targeted, and another in which domestic prices are targeted.2 By specifying interest rate rules, the dynamics of inflation, the response of monetary policy, and trade integration - captured through variations in the size of the non-traded sector and average productivity of exporting firms - are jointly determined. I consider two sources of uncertainty; exogenous shocks to domestic monetary policy and domestic aggregate labor productivity. An exogenous rise in the domestic interest rate generates a ‘cleansing out’ effect for the domestic economy. Specifically, entry falls and the average productivity of domestic exporting firms rises as resources are reallocated across the industry (the average productivity of foreign
1

This has been dubbed the “globalization-inflation hypothesis”. See Borio and Filardo (2007) and Ihrig et al. (2007),

who find conflicting evidence based on reduced form analysis of Phillips curves. 2 See Svensson (2000) for a discussion of the different implications of each policy regime.

1

exporting firms falls).

If entry costs are modeled as labor costs and prices are sticky, in the closed

economy, a contractionary monetary policy shock raises firm entry. However, the evidence suggests the opposite (Bergin and Corsetti, 2008). My model generates a result in line with the data because firms need to pay additional fixed labor costs to export. This is also the source of the endogenously determined non-traded sector and the extent of trade integration. This result holds in both the

consumer price and domestic price inflation targeting regimes, although it is magnified in the latter. The initial change in average productivity is also greater the more persistent is the shock. A rise in labor productivity generates only modest (positive) changes in average productivity for both sets of exporting firms when consumer price inflation is targeted. However, when domestic price

inflation is targeted the shock causes a fall in the average productivity of home firms, and a far larger rise in the productivity of foreign firms. The reason for the differential response is that changes in

domestic labor productivity have a direct impact on all domestic firm’s pricing decisions. In particular, each firm lowers it’s price in response to the fall in marginal costs. Lower marginal costs induce entry and exporting by preexisting firms. When consumer price inflation is targeted the foreign government alters it’s policy to account for this change directly. When domestic price inflation is targeted each government is only concerned with domestically produced goods. In the latter case, the rise in home labor productivity then results in a shift of resources away from exporting to domestic production and a fall in the productivity of domestic exporting firms. A by-product of the analysis is that when each government targets consumer price inflation the real exchange rate is not independent of technology shocks. When the number of varieties are fixed and firms set prices in local currency (and the cost of adjustment in prices is equal within and across countries) the real exchange rate is independent of technology shocks (Benigno, 2004). Once firms

make entry decisions, the result no longer holds because entry depends on fluctuations in relative prices. In particular, the total average profits of firms depends on relative prices, both through domestic sales (which compete with foreign exports and are imperfectly substitutable for consumers) and export sales, the volume of which depends on a zero profit export cutoff. That is, fluctuations in relative prices

also determine entry into export markets, and entry determines the number of varieties of a product available to consumers. 2

There is a growing literature on heterogenous firms in international trade which are related to this paper. The seminal paper of Melitz (2003) considers the impact of a reduction in trade costs on Along similar lines, Bernard et al. (2007)

heterogeneous firms’ decisions to enter, exit and export.

study comparative advantage when firms are heterogeneous. More recently, however, there has been interest in heterogeneous firms and macroeconomic dynamics. Ghironi and Melitz (2005) study a

dynamic version of Melitz’s framework, Atkeson and Burnside (2009) consider the impact of a reduction in trade costs and the associated impact on aggregate productivity. DiGiovanni and Levchenko (2009) use a model in which firms are subject to idiosyncratic shocks to study the link between trade openness and macroeconomic volatility, focusing on the role of large exporters. Finally, Zlate (2008) studies

offshore production and business cycles with heterogeneous firms in a DSGE setting and Neiman (2009) shows that intrafirm trades are less sticky, less synchronized, and exhibit higher exchange rate passthrough, suggesting that firm boundaries also play a role in business cycle dynamics. This paper is the first to consider the role of monetary policy and macroeconomic dynamics alongside heterogenous firms in international trade. There is also a large literature on real exchange rate persistence and technology shocks in DSGE models. Analysis such as Chari et al. (2002) has had some success at replicating real exchange rate movements in the data. However, more recently, Dotsey and Duarte (2008) argue that nontraded

goods are also important for international relative price movements and Carvalho and Necchio (2008) use a sticky-price model which generates sectoral real exchange rate dynamics in the presence of local currency pricing. Finally, Steinsson and Nakamura (2009) provide related empirical evidence on the role of product replacement bias and pricing-to-market. In my model, technology shocks hit all firms symmetrically, the non-traded sector of the economy arises endogenously, and when firms decide to export they price in local currency. The remainder of the paper is organized as follows. In section two I describe the world economy. In section three I derive the linearized conditions and provide some intuition for the main mechanism in the model. Section four presents the simulation results for the different policy regimes and shocks.

Section five concludes. II. The World Economy 3

The world economy consists of a home and foreign economy each populated by a unit mass of atomistic households. Households consume home and foreign produced goods, supply labor and hold assets in terms of a mutual fund and non state-contingent domestic and foreign currency bonds. Firms are

heterogenous in their productivity. Each firm faces a sunk cost of entry and a fixed (per-period) cost of exporting.

A. Domestic Households Intratemporal Consumption Choices

The representative household’s utility function for overall consumption takes the CES form,
θ θ Ct = a1−θ Ch,t + a1−θ Cf,t h f 1/θ

(1)

where Ch,t and Cf,t are bundles of varieties of the home and foreign good and 1/ (1 − θ) is the elasticity of substitution between home and foreign goods. When θ = 0, the upper-tier utility function is CobbDouglas and the elasticity of substitution between the two bundles is one. The consumption of each bundle of varieties depends on relative prices. Ch,t = ah Pt Ph,t
1/(1−θ)

Ct
θ/(θ−1)

; Cf,t = af
θ/(θ−1)

Pt Pf,t

1/(1−θ)

Ct

(2)

where Pt = ah Ph,t

+ af Pf,t

(θ−1)/θ

is the welfare-based CPI. The household’s consumption The lower tier of

of varieties of each good are defined over a continuum, Ωh and Ω∗ , respectively. f consumption is also of CES form,
σ/(σ−1) σ/(σ−1)

Ch,t =
ω∈Ωh

ch,t (ω)

(σ−1)/σ

dω

; Cf,t =

ω ∗ ∈Ω∗ f

ch,t (ω )

∗ (σ−1)/σ

dω

∗

(3)

where σ > 1 is the elasticity between varieties of goods.

In any period, only a subset of varieties

are available; ω ∈ Ωh,t ∈ Ωh and ω ∗ ∈ Ω∗ ∈ Ω∗ , for home and foreign goods respectively. Denoting f,t f ph,t (ω) as the home currency price of a variety of the domestic good and pf,t (ω ∗ ) as the home currency price of a variety of the foreign good, I write the demand for these varieties in the following way, ch,t (ω) = ph,t (ω) Ph,t
−σ

Ch,t

; cf,t (ω ) =

∗

pf,t (ω ∗ ) Pf,t 4

−σ

Cf,t

(4)

where Ph,t =

ω∈Ωh,t

ph,t (ω)1−σ dω

1/(1−σ)

and Pf,t =

ω∈Ω∗ f,t

pf,t (ω ∗ )1−σ dω ∗

1/(1−σ)

. From here on, I

will make the assumption that σ > 1/ (1 − θ), so that the elasticity of substitution between varieties of a particular good is always higher than the elasticity of substitution between (home and foreign) bundles. B. Domestic Firms Pricing and Export Decisions Firms technology is linear in labor, with At indexing aggregate labor productivity, and ϕh indexing relative productivity such that a firm with relative productivity ϕh produces ϕh At units of output per unit of labor employed. Prior to entry, firms are identical, and face a sunk entry cost, fe , equal to wt fe /At units of the domestic consumption good. Upon entry, domestic firms draw their productivity level ϕh from a common distribution, G(ϕh ). Firms can serve the domestic and export market and because there are no fixed production costs all firms produce in every period until they are hit with a shock, which is assumed independent of the firm’s productivity level. Firms also face nominal rigidity in the form of a quadratic cost of adjusting prices in the currency of the market being supplied. This cost is assumed to be proportional to the real revenue from output sales in that market. In period t, there is a mass nh,t of domestic firms producing and setting prices in the domestic economy. Of these, a fraction n∗ also serve the export market. When a firm sets the price of it’s output (in either h,t market) for the first time it does so to be consistent with the average product price in the market it serves.3 For an individual firm, indexed ϕh , I decompose total profit, dt (ϕh ), into portions earned from domestic sales, dh,t (ϕh ), and from potential export sales, d∗ (ϕh ). Thus, total profits in period t are given by h,t dt (ϕh ) = dh,t (ϕh ) + d∗ (ϕh ). Because production is linear, I separate the profit maximization problem h,t for firms into the two markets they serve. Profits from domestic sales are, dh,t (ϕh ) = ρh,t (ϕh ) yh,t (ϕh ) − wt lh,t (ϕh ) −
3

Ph,t Pt

· ξh,t (ϕh )

; yh,t (ϕh ) = ϕh At lh,t (ϕh )
Here, this price is an average

As in Bilbiie et al. (2007), entrants inherit the same price as pre-existing firms.

(discussed below), associated with each market. Bilbiie et al. (2007) extend their framework and allow firms to enter with flexible prices and then set the price for the first time in the second period. This appears to have little importance for their quantitative results.

5

where ρh,t (ϕh ) ≡ ph,t (ϕh ) /Pt , ξh,t (ϕh ) represents the cost of adjusting prices, and wt ≡ Wt /Pt is the real wage (in consumption units). The total demand for the output of firm ϕh is then, yh,t (ϕh ) = ph,t (ϕh ) Ph,t
−σ

Yh,t

; Yh,t ≡ Ch,t +
nh,t

ξh,t (ϕh ) The real cost of movements in output-price

where Yh,t is the output of domestic sales consumed. inflation around a zero steady state level of inflation is, ξh ξh,t (ϕh ) ≡ 2 ph,t (ϕh ) −1 ph,t−1 (ϕh )
2

ph,t (ϕh ) yh,t (ϕh ) Ph,t

Under this formulation of nominal rigidity, the demand for output comes from two sources - consumers and firms; that is, inflation reduces the level of output households access since firms also demand output to pay adjustment costs. Because these costs are deducted from profits, and are proportional to squared output price inflation, this is equivalent to assuming there is a tax on production. This tax distorts that allocation of resources and therefore product creation (firm entry) versus pre-existing firms. At time t, firm ϕh chooses lh,t (ϕh ) and ρh,t (ϕh ) to maximize dh,t (ϕh ) + υh,t (ϕh ) - where,
∞

υh,t (ϕh ) ≡ Et
s=t+1

Mt,s dh,t (ϕh )

and Mt,s is the stochastic discount factor applied by households to future profits, adjusted for a constant probability δ of being hit by a death shock - subject to the demand for it’s product, taking wt , Ph,t , Pt and Yh,t as given. Profit maximization results in the following pricing equation, ρh,t (ϕh ) = µh,t (ϕh ) wt At ϕ ; µh,t (ϕh ) = (σ − 1) 1 − ph,t (ϕh ) ph,t−1 (ϕh )
ξh 2

σ
ph,t (ϕh ) ph,t−1 (ϕh )

−1

2

; + ξh Ωh,t (ϕh )

Ωh,t (ϕh ) ≡

ph,t (ϕh ) −1 ph,t−1 (ϕh )

− Gh,t (ϕh ) ;
2

Mt,t+1 Pt Gh,t (ϕh ) ≡ Pt+1

ph,t+1 (ϕh ) −1 ph,t (ϕh )

ph,t+1 (ϕh ) ph,t (ϕh )

yh,t+1 (ϕh ) yh,t (ϕh )

(5)

where µh,t (ϕh ) is a markup associated with the domestic sales of home firms and wt /At ϕh are real marginal costs. When the cost of adjusting prices is zero (ξh = 0), the markup is constant, and equal to σ/ (σ − 1) > 1. When ξh > 0 price adjustment is sluggish. Again, it it this parameter that affects the entry decision of firms on the competitive fringe of the domestic market. 6

In a similar fashion, firms ϕh ’s potential profits from export sales, are, d∗ h,t (ϕh ) = Qt ρ∗ h,t
∗ (ϕh ) yh,t

(ϕh ) −

∗ wt lh,t

∗ Ph,t Wt ∗ ∗ (ϕh ) − ∗ Qt ξh,t (ϕh ) − f Pt At h

∗ ∗ ; yh,t (ϕh ) = ϕAt lh,t (ϕh )

where Qt = et Pt∗ /Pt is the welfare based consumer price real exchange rate and ρ∗ (ϕh ) ≡ p∗ (ϕh ) /Pt∗ . h,t h,t Again, total demand for the product comes from two sources - foreign consumers and domestic firms and is given by the following.
∗ yh,t

(ϕh ) =

p∗ (ϕh ) h,t ∗ Ph,t

−σ ∗ Yh,t

;

∗ ξh,t

ξ∗ (ϕh ) ≡ h 2

p∗ (ϕh ) h,t −1 p∗ h,t−1 (ϕh )

2

p∗ (ϕh ) ∗ h,t yh,t (ϕh ) ∗ Ph,t

∗ ∗ where Yh,t ≡ Ch,t +

n∗ h,t

∗ ξh,t (ϕh ). Optimization results in a similar dynamic pricing equation to (5),

∗ ∗ with parameter ξh determining the extent of price adjustment. If we assume ξh = ξh , then the cost of

adjusting prices is different in the domestic and export markets. In this case, there are two reasons why firms change different prices. First, exporting firms will be, on average, more productive, and hence
∗ face lower marginal costs. Second, it is simply less expensive to export when, for example, ξh < ξh , all

else equal. This can give rise to local currency pricing, as emphasized in Benigno’s (2004) analysis of the real exchange rate, A firm will choose export if and only if it earns non-negative profit from doing so, which will only be the case if productivity ϕh is above a cut-off level ϕ∗ = inf{ϕ : d∗ (ϕh ) > 0}. I assume the lower bound h,t h,t to productivity is such that ϕ∗ > ϕh , and, in this case, there exists an endogenously determined non h,t traded sector, where firms with productivity levels between ϕh and ϕ∗ only produce for the domestic h,t market. This set of firms fluctuates over time with changes in the profitability of the export market, inducing changes in the productivity cutoff level. For simplicity, and following Ghironi and Melitz

(2005), I do not assume fixed costs to producing for the domestic market, and all firms that enter produce.

C. Domestic Firm Averages, and Firm Entry and Exit

Each period a mass of nh,t firms produce in the domestic economy. I assume firms are distributed with a Pareto distribution over productivity levels, with shape parameter κ, such that G (ϕh ) = 1 − 7
ϕh ϕh κ

.

As κ increases dispersion decreases and firm productivity levels are increasingly concentrated toward their lower bound, ϕh . Average productivity levels are then defined as,
∞ 1/(σ−1)

ϕh ≡

(1/ϕh )
ϕ

1−σ

dG (ϕh )

;

ϕ∗ h,t

ϕ∗ h,t

1 ≡ 1 − G ϕ∗ h,t

∞ ϕ∗ t

1/(σ−1)

(1/ϕh )

1−σ

dG (ϕh )

This assumption provides the following relationships between minimum and average productivity and the productivity of the average export firm with a typical firm, ϕh = νϕh ; ϕ∗ = νϕ∗ h,t h,t This is interpreted such that the nh,t

where ν ≡ [κ/ (κ − σ)]1/σ (see Appendix for a derivation). level ϕ∗ export to the foreign market. h,t is, n∗ /nh,t = 1 − G (ϕh,t ) = h,t
∗

firms with productivity level ϕh produce in the home country and n∗ ∈ nh,t firms with productivity h,t Given this, we know the share of home exporting firms
κ

νϕh /ϕh,t

.

Total average profits for firm ϕh are then given by,

dt = dh,t + n∗ /nh,t dh,t , where the productivity averages ϕh and ϕ∗ are constructed in such a way h,t h,t that dh,t ≡ dh,t (ϕh ) represents the average firm profit earned from domestic sales for all home producers and dh,t ≡ d∗ (ϕ∗ ) represents the average firm export profits for all home exporters. h,t h,t dt = dh,t + 1 − G ϕ∗ h,t
∗ dh,t ∗

In this case,

represents the average total profits of home firms, since 1 − G(ϕ∗ ) h,t

represents the proportion of home firms that export and earn export profits. Alongside preexisting firms, in every period there is an unbounded mass of forward-looking prospective entrants (a competitive fringe). They correctly anticipate future expected profits in every period, as well as the probability of incurring an exit-inducing shock. Entrants at time t start producing at time t + 1 and the exogenous exit shock occurs after production, entry and price setting decisions are made. Prospective home entrants in period t compute their expected post-entry value which is given by the present discounted value of their expected stream of profits. Using firm averages, we can express the value of the average firm in the following way.
∞

v t = Et
s=t+1

Mt,s ds

(6)

Since both new entrants and incumbents face the same probability of survival and v t also represents the average value of incumbent firms after production has occurred. Entry occurs until the average firm 8

value is equalized with the entry cost, leading to the free entry condition, v t = wt fe,t /At . This condition holds so long as the mass of new entrants, ne,t , is positive. Finally, the timing of entry and production implies that the number of home-producing firms during period t is given by nd,t = (1−δ)(nh,t−1 +ne,t−1 ), where ne,t−1 is the mass of new entrants in period t. D. Domestic Household Intertemporal Choices The representative household holds two types of assets: shares (in a mutual fund) and non statecontingent (domestic and foreign currency) bonds. Let st be the share of firms held by the repre-

sentative household entering period t. The mutual fund pays a total profit in each period (in units of home currency) equal to the average total profit of all home firms that produce in that period, Pt dt nh,t . During period t, the representative home household buys st+1 shares of nh,t + ne,t firms.

Only nh,t+1 ≡ (1 − δ) (nh,t + ne,t ) firms will produce and pay dividends at time t + 1. Since the household does not know which firms will be hit by the exit shock at the very end of period t, it finances the continuing operation of all pre-existing home firms and all new entrants during period t. The date t price (in units of home currency) of a claim to the future profit stream of the mutual fund of nh,t + ne,t firms is equal to the average nominal price of claims to future profits of home firms, Pt v t . Af,t . Only foreign bonds are traded internationally. The household maximizes expected intertemporal utility, U0 = E0 subject to a period budget constraint, Ah,t − Ah,t−1 + et 1 + it Af,t − Af,t−1 1 + i∗ t = st Pt dt + v t nh,t + Wt Lt − st+1 Pt v t (nh,t + ne,t ) − Pt Ct
∞ t=0

Finally,

domestic residents issue bonds, Ah,t , in domestic currency, and have access to foreign current bonds,

β t ln (Ct ) −

ψ L1+ησl 1+η t

, where

β ∈ (0, 1) is the subjective discount factor and σl is the inverse of the Frisch elasticity of substitution,

where it and i∗ are the net nominal interest rates. The following are optimality conditions associated t with the domestic households problem. Pt = (1 + it ) βEt Ct et Pt = (1 + i∗ ) βEt t Ct Pt+1 Ct+1 et+1 Pt+1 Ct+1 9 (7) (8)

v t = (1 − δ) βEt Wt = ψCt Lσl t Pt

Pt Ct Pt+1 Ct+1

v t+1 + dt+1

(9) (10)

Equation (7) is the consumption Euler equation, (8) is an uncovered interest rate parity (UIP) condition, (9) is a shares Euler equation, and (10) is labor supply.

E. Foreign Economy

∗θ ∗θ Foreign economic agents have CES preferences; i.e., Ct∗ = a∗1−θ Ch,t + a∗1−θ Cf,t h f

1/θ

. The consumption

allocation satisfies, c∗ h,t (ϕ) = a∗ h p∗ (ϕ) h,t ∗ Ph,t
−σ

Pt∗ ∗ Ph,t

1/(1−θ)

Ct

;

c∗ f,t

(ϕ) =

a∗ f

p∗ (ϕ) f,t ∗ Pf,t

−σ

Pt∗ ∗ Pf,t

1/(1−θ)

Ct∗

Foreign firms set the price of their good in the foreign and domestic markets in each currency and face sunk entry costs to the domestic market and fixed per-period entry costs to the export market. The
∗ ∗ parameters ξf and ξf = ξf determine price adjustment costs. Again, it is possible to generate local

currency pricing when within a country price rigidities are the same for imported and domestically
∗ ∗ produced goods; this requires ξf = ξh and ξh = ξf . Firm relative productivity is drawn from a Pareto

distribution, with dispersion parameter κ∗ , such that, G ϕ∗ = 1 − f

ϕ∗ f ϕ∗ f

κ∗

, .

Foreign agents have The foreign

access to n∗ varieties of the foreign good and n∗ ∈ nh,t varieties of the home good. f,t h,t wage rate Wt∗ .

household also supplies L∗ units of labor in each period in the foreign labor market at the nominal t

F. Equilibrium

The demand for labor is determined by the following condition.
∗ Lt = Lh,t + L∗ + n∗ fh + ne,t fe /At h,t h,t

lh,t

dh,t + (Ph,t /Pt ) ξ h,t = (µh,t − 1) wt

;

∗ lh,t

=

∗ ∗ dh,t + et Ph,t /Pt ξ h,t + fh wt /At

∗

∗

µ∗ − 1 wt h,t 10

(11)

Total labor used for production in the domestic and export markets is Lh,t ≡ nh,t lh,t and L∗ ≡ n∗ lh,t , h,t h,t respectively. In addition, new entrants hire fe units of labor to cover the sunk entry cost and each
∗ exporter hires fh units of labor to cover the fixed export cost. The total amount of labor hired to cover ∗ the costs associated with the creation of new products and their export is therefore n∗ fh + ne,t fe /At . h,t

∗

Analogous conditions hold in the foreign economy. Aggregating the household budget constraint (across symmetric agents) and imposing the equilibrium conditions (Ah,t = Ah,t+1 = 0 and st = st+1 = 1) yields the national budget constraint for the domestic economy. et Af,t − Af,t−1 1 + i∗ t = Wt Lt + Pt dt nh,t − Pt (Ct + v t ne,t ) (12)

Equation (12) can be interpreted as usual; plus wage income plus profits, minus consumption and investment. Let
t

be the domestic economy’s trade balance. We know average total profits of do∗

mestic firms are, dt = dh,t + n∗ /nh,t dh,t , and that the free entry requirement equates the value h,t of the firm with wages and the sunk costs of entry; Pt v t = fe Wt /At . If we use labor demand
t

and eliminate profits from domestic and foreign sales, it is possible to derive the following,
∗ ∗ Ch,t = a∗ Pt∗ /Ph,t h ∗ Ph,t Pt∗ 1/(1−θ)

≡

∗ ∗ (Ph,t /Pt ) Ch,t + et Ph,t /Pt Ch,t − Ct . Using the upper tier demands (Ch,t = ah (Pt /Ph,t )1/(1−θ) Ct and

Ct∗ ) and the CPI we can write the trade balance, in units of consumption as, − (1 − ah ) Pf,t Pt
θ/(θ−1)

θ/(θ−1)

t

=

a∗ h

Qt Ct∗

Ct

(13)

The right-hand side of (13) are exports, and the left-hand side imports. Although this appears to be a somewhat standard expression, it should be clear that I have also used, Pf,t Pt
θ/(θ−1)

=

θ/(θ−1) n1+Φ ρf,t f,t

;

∗ Ph,t Pt∗

θ/(θ−1)

= n∗1+Φ ρh,t h,t

∗θ/(θ−1)

where Φ ≡ [σ (θ − 1) + 1] / (σ − 1) (1 − θ). Using this definition, note that when θ = 0, the upper tier of utility is Cobb-Douglas, Φ = −1. When the elasticity of substitution across varieties and is the

same as across the two goods produced by each industry, then, Φ = 0. Finally, also note that domestic resources used in production are, y h,t = ah 1 − ξh 2 π 2 h,t
−1

nΦ ρh,t h,t

1/(θ−1)

Ct

; y ∗ = ah 1 − h,t 11

∗ ξh ∗2 π 2 h,t

−1

n∗Φ ρh,t h,t

∗1/(θ−1)

τt Ct∗

respectively for the domestic and export market. Again, there are analogous conditions for the foreign economy.

III. Inflation Dynamics and Firm Heterogeneity

To simplify the exposition, I assume the distribution of firms size is the same in each country (κ = κ∗ ), the parameters governing costs of price adjustment are identical across and within countries (ξh =
∗ ∗ ξh = ξf = ξh ≡ ξ), the upper tier of utility is Cobb-Douglas (θ = 0) and symmetric across countries

(ah = a∗ = 1/2) and there is financial autarky (Af,t = 0). h

A. Inflation and Relative Price Dynamics

I begin by deriving expressions for the paths of inflation and relative prices. To do so, I focus on a linear approximation of the model around the steady state (see Appendix). For example, the deviation of a variable, say xt , from it’s steady state value is denoted xt . I characterize the supply side of the world economy using (5) along, with the equivalent expression for domestic exported goods, and their foreign counterparts. These expression tie down the dynamic paths of output price inflation, given a process for the markups. However, it is necessary to convert these expressions into dynamic equations in
1 relative and world welfare-based consumer price inflation; that is, ΠR ≡ Πt − Π∗ and ΠW ≡ 1 Πt + 2 Π∗ , t t t t 2 1 and consumer based relative prices; that is TtR ≡ Tt − Tt∗ and TtW ≡ 2 Tt + 1 Tt∗ , where Tt ≡ Pf,t − Ph,t and 2 ∗ ∗ Tt∗ ≡ Pf,t − Ph,t . An important part of constructing these equations therefore also lies in the adjustment

for the number products/product quality. It is also worth noting at this point that without entry and heterogeneity pinning down the path of relative prices is not always necessary - it depends on asset markets and consumer preferences. However, when there is entry into export markets relative prices play a dual role - they affect consumer decisions on consumption and firms decisions on entry and exporting. In the case of relative inflation (and relative variables, in general), we need only account for the relative average productivity of export firms in each economy, defined below as ϕt ≡ ϕh,t − ϕf,t . In particular, 12
R ∗

and because κ = κ∗ , we have, ΠR = π t − t where π t =
R R

1 1 + ν 1−σ
1 2 R

∆ϕt
R

R

;
R

1 + ν 1−σ
R

−1

= κ/ (σ − 1) > 1

;

σ>1

π h,t + π f,t

and π h,t and π f,t are relative (domestic consumption versus foreign con-

sumption) inflation rates in producer price terms of the home and foreign countries, in home and foreign currencies. Given this result, the path of welfare-based relative CPI inflation is given by the following: ΠR + t 1/2 1 + ν 1−σ
R R

∆ϕt = βEt ΠR + t+1
R R

R

β/2 1 + ν 1−σ

Et ∆ϕt+1 + ξQt + ξ ϕt

R

R

(14)
R

where ∆ϕt ≡ ϕt − ϕt−1 and ξ ϕt

indicates that the forcing term is a function of ϕt , dependent also

on steady state parameters. Note that aggregate labor productivity shifters (At and A∗ ) do not enter t this expression. In constructing (14), I have used the labor demands of firms, and taken advantage
∗ of the fact that 2Qt = Ψh,t + Ψf,t , where Ψh,t and Ψf,t are LOP-gaps (ex: Ψh,t ≡ et + Ph,t − Ph,t ), 1 1+ν 1−σ R

as in Monacelli (2004), unadjusted for product quality (or, 2Qt = ψ h,t + ψ f,t −

ϕt ).

This

formulation shows that absent heterogeneity, the path of relative inflation is the same as it would be in an economy without varieties. That is, because the two economies are identical, and they would produce the same number of goods. Here, entry of firms into the export market is also an important source of inertia to the dynamic adjustment of inflation as lag relative average productivity terms enter. Finally, note the special case, when ν 1−σ → 0. This is equivalent to assuming κ → (σ − 1), which In my model, as

is consistent with the ‘granular’ economy of DiGiovanni and Levchecnko (2009). path of ΠR , all else equal. t

ν 1−σ → 0, then the inertial terms on average productivity exert a relatively strong influence over the

In a similar way, the path of world welfare-based CPI inflation is given by the following: ΠW − t 1 1 + ν 1−σ ∆ϕt −
W

∆nW t κ

= βEt ΠW − t+1
W

β 1 + ν 1−σ

Et ∆ϕt+1 −

W

∆nW t+1 κ (15)

W +ξ nW , ϕt , wt ; At , A∗ t t

where ∂ ξ (·) /∂ At < 0 and ∂ ξ (·) /∂ A∗ < 0. t

In this case, world inflation is affected not only by

the extent of firm heterogeneity, but also by the number of products in the global economy; i.e., nh + n∗ . Moreover, unlike relative inflation, which is driven to a large extent by movements in the f,t 13

real exchange rate, world inflation also depends on conditions in the labor market explicitly. In this case, wages (essentially marginal costs) can be accounted for by individuals labor supply decisions (and the marginal product of labor) when wages are assumed to be instantaneously adjusted in response to a shock. With entry and firm heterogeneity, labor supply is shifted between sectors (creation of new firms, domestic supply from preexisting firms, exports by preexisting firms, see (11)) when there is a shock, and is linked to the resource constraint of the economy. I discuss this in more detail below. Using a similar approach there are two equations that determine the path of relative prices. In relative terms, ∆TtR −
R

2 1 + ν 1−σ

R ∆ϕt = βEt ∆Tt+1 − W

W

2β 1 + ν 1−σ

Et ∆ϕt+1 + ξ TtR , ϕt

W

W

(16)

where tt = TtR − ∆TtW + 1 1 + ν 1−σ

2 1+ν 1−σ

ϕt , and in world terms,
R

∆ϕt ∆nR t − 2 κ

=

W βEt ∆Tt+1

+

β 1 + ν 1−σ
R

Et

∆ϕt+1 ∆nR t+1 − 2 κ (17)

R

R +ξ TtW , Qt , nR , ϕt , wt ; At , A∗ t t

where tt = TtW +

W

1 1+ν 1−σ

ϕt 2

R

−

nR t κ

and ∂ ξ (·) /∂ At > 0 and ∂ ξ (·) /∂ A∗ < 0. These dynamic equat

tions share similar feature with those for inflation but there are some important differences. Because of the way in which relative prices have been defined, the combined world average export productivity variable affects the path of home versus foreign relative prices. In the same way, a world weighted

average of relative prices is, in part, determined by differences in the average export productivity and the number of products between the two economies. The equivalent expression for inflation depends on the weighted average number of products, not the difference between them. Finally, it is worth stressing that even in this simple case, fluctuations in world-relative prices play an important role in determining firm behavior. Whereas relative welfare-based CPI inflation also plays a role in determining the relative patterns of consumption, relative prices affect firm profits in each economy, both for domestic sales and export sales, the latter through a zero-profit export cutoff. Note that if we were to drop the identical preferences assumption, made for simplicity, this result no longer holds, and world relative prices would also play a role in determining world consumption patterns (this can be easily shown in an economy with a fixed number of varieties. 14

B. Firm Heterogeneity

To determine (17).

ΠR , ΠW , TtR , TtW t t

I need only pin-down the paths of variables in ξ (·)-terms in (14)That is, I solve a

To do so, I take advantage of a relative and world system of equations.

system in which, for any variable xt , xR ≡ xt − x∗ and xW ≡ 1 xt + 1 x∗ . t t t 2 2 t

In each economy, there

are dynamic equations that determine the evolution of the value of the average firm (a shares Euler equation) and a law of motion/transition equation for the number of products available. There are also static equations for resources (accounting for total labor supplied), total firm average profits and a zero export-profit cutoff. These are exactly as they would be in an environment of flexible prices. That is, if we temporarily assume ξ = 0, then these equations determine the evolution of the number of firms, average productivity and other endogenous variables. However, when prices are sticky, total average profits and the zero export-profit cutoff depend on markups, which are endogenous. These

can be accounted for in exactly the same was as (14)-(17); that is, by using the pricing equations. A full list of these equilibrium conditions is given in the Appendix. Here I focus on total average profits and wages shed some light on how relative prices affect the two profit terms. Differences in total average profits across the two economies, can be expressed in the following way: dt = Ψ Qt − nR + (σ − 1) µh,t − µf,t t
domestic sales R ∗ R + (1 − Ψ) wt − AR − κϕt t export sales R

(18)

where Ψ ≡ {κ + [κ − (σ − 1)]} /κ ∈ (0, 1). Again, note that the only difference between this expression and that with flexible prices is a markup gap, specifically, µh,t − µf,t . Likewise, a weighted average of total firm profits, dt , depends on weighted average of the same endogenous variables as in (18), and a weighted average of the same markups, µh,t and µf,t . Both of these markups - and the relative and world composites- refer to domestic sales, for the home and foreign firms respectively. Given the pricing equations (see 5), it then becomes clear that dt must be a function of TtW , and dt is a function of TtR . The second step is to use the zero-profit export cutoffs to determine wages. In relative terms, I find,
R wt = Qt − nR + κϕt + (σ − 1) µh,t − µf,t + AR t t R ∗ R W ∗ W ∗

(19)

15

Again, the key point is that a relative markup term, µh,t − µf,t , enters, and this means that relative price fluctuations, specifically, TtW , affect the cut-off. Equally, there are an equivalent equations for the world cut-off, which depends on the relative price TtR . Finally, these static solutions for wages are
j connected to the free entry condition, which in linear term is, v t = wt − Aj , and, in turn, the path of t j

∗

wages is pined down through a shares Euler equation. In particular,
j v t = Ctj − Ct+1 + β (1 − δ) v t+1 + [1 − β (1 − δ)] dt+1 j j j

(20)

where j ∈ {R, W }. These conditions generate a link between the price of shares and bonds which also appear in the Phillips curves, (14)-(17), derived above. This channel also plays an important role in the closed economy model of Bilbiie et al. (2005) because it restores the Taylor Principle - with this particular form of capital accumulation - and gives rise to a secondary channel for the transmission of monetary policy. With heterogeneous firms, this channel is augmented because there is an additional demand for labor - from the export sector.

C. Monetary Policy

I focus on two monetary policy regimes: welfare-based consumer price inflation - which includes all imported varieties of the foreign good - targeting and domestic price inflation targeting. Although it seems clear that the government cannot observe welfare based prices, this seems a natural benchmark. Consider the first policy regime, in which each government targets welfare based consumer prices, with the same weight. Consistent with the discussion above, the relative and world interest rates are, iR = φΠ ΠR + νtR t t ; iW = φΠ ΠW + νtW t t

Because each agent (home and foreign) only has access to a non-traded risk free bond denominated in domestic currency we can simply plug these equations into the relative and world consumption Euler equations to determine the path of CtR = Qt and CtW . When the governments follow a rule targeting domestic price inflation (Πh,t and Π∗ , for the domestic f,t and foreign governments respectively), I rewrite the interest rate rules to reflect changes in relative 16

prices that the governments account for versus the case in which they target the welfare based CPI.4 In particular, we have, iR = φΠ ΠR − ∆TtW + νtR t t 1 ; iW = φΠ ΠW − ∆TtR t t 4 + νtW

On thing is immediately clear from these expressions. Suppose that the number of varieties is fixed. If we use labor supply to eliminate wages in the dynamic equations for ΠW and TtW (I show the details t of this in the Appendix) the latter is self-contained. Moreover, when the number of varieties is fixed, it is immediate from (16) and (17) that TtW and TtR are orthogonal to the interest rate shocks. That is, TtW and TtW only depend on their own lagged and lead values, as neither additional endogenous variables nor the shocks to the monetary rules enter. As such, a shock to the monetary policy rules will have the same effect under each policy rule, i.e., whether the governments target the GDP deflator or the CPI (the former is simply the latter adjusted by variables which are independent from the more general system). When firms make entry decisions, subject to sunk costs, and export decisions, subject to period fixed costs, this result breaks down, for the reasons discussed above. IV. Quantitative Analysis In this section I analyze the quantitative implications of the model through simulations. I describe the parametrization and present the quantitative results for the baseline specification above. The shocks to domestic labor productivity and monetary policy are given by the following, At = ρA At−1 + εA,t ; νt = ρν νt−1 + εν,t

2 2 where εA,t and εν,t are i.i.d. normal innovations with mean zero and variance σεA and σεν .

A. Calibration Because of the assumption of Cobb-Douglas preferences, many of the steady state parameters do not influence the dynamic behavior of the model near the zero inflation steady state. Table 1 presents the baseline parameters for the calibration.
4 R That is, iR = φΠ Πh,t − Π∗ + νt and iW = t t f,t φΠ 2 W Πh,t + Π∗ + νt . f,t

17

Table 1 Here I interpret periods as quarters and set β = 0.99. The size of the exogenous firm exit shock δ = 0.025 to match the U. S. empirical level of 10% job destruction per year. We use the value of from Bernard et al. (2003) and set σ = 3.8, which was calibrated to fit U. S. plant and macro trade data. Given the standard deviation of log U.S. plant sales reported in Bernard et al. (2003) σ = 3.8 implies that κ = 3.4 (this also satisfies the requirement k > σ − 1. The Frisch elasticity of labor supply is σl = 2. The Rotemberg adjustment cost parameter is set at ξ = 77, as in Bilbiie et al. (2007). The parameter on inflation in the interest rate rule is set at φΠ = 1.5. Finally, the persistence parameters for the

monetary policy and labor productivity shocks are set at ρν = 0.3 and ρA = 0.979, respectively. To simulate the model, I use the method outlined in Binder and Pesaran (1996), which, in this case, transforms the system of equations into the following lead and lag system. AZt = BZt−1 + CEt Zt+1 + DXt where the vector Zt = [.....] contains the endogenous variables of the model and the vector Xt contains the monetary policy and aggregate labor productivity shocks. of exogenous variables can be reduced to Zt = Turning off the shocks, the vector
R W

Qt CtW ΠR ΠW TtR TtW nR nW ϕt t t t t q t , π t , π t , tt , tt
R W R W

ϕt

1 where we again note that, for example, a domestic economy variable is given by, xt = xW + 2 xR . Note t t

also that this system can be transformed easily into one containing

because such
R W

a transformation only involves variables already in the system, specifically, nR , nW , ϕt , ϕt t t

.

B. Monetary Policy Shocks

Consider the situation in which each government targets consumer price inflation. A contractionary domestic monetary policy shock (i.e., εν,t > 0) generates a fall in consumption in both economies. Home consumer price inflation falls as the nominal interest rate rises whilst foreign consumer price inflation rises. This is the standard result in the fixed varieties New Keynesian model. Here, the monetary shock lowers (home and foreign) firm entry into their respective domestic markets, increases the average productivity of domestic exporting firms (note: this productivity is ϕh,t = nh,t − n∗ /κ > 0 and h,t 18
∗

determines the fraction of exported products) but reduces the average productivity of foreign exporting firms. This is shown in figure 2, where the dashed line are the responses of the foreign economy’

endogenous variables to the shock and the bold lines represent the home economy variables. Figure 2 Here The result that a contractionary shock lowers firm entry is in line with empirical evidence, such as that presented in Bergin and Corsetti (2008). However, many closed economy models with free entry and sticky prices fail to generate such a correlation. The reason is the following: the free entry condition implies the price of equity (value of the firm) enters the NKPC (via wages). A no-arbitrage condition links bonds and equities. When the nominal interest rate rises so does the real return on bonds,

generating an increase in the expected return on equity. This is equivalent to a rise in the expected return on investing in product creation, and implies that the value of the firm falls, today, relative to tomorrow. As such, the cost of creating new firms falls. When firms are heterogeneous in productivity, the link between wages and the value of the firms is unchanged. Rather, there is an extra dimension to average firms profits - i.e., potential export profits - which is driven by the average level of firm productivity and there is an additional source of labor demand. When there is a contractionary monetary policy shock, real wages fall, which induces entry, but since marginal costs are higher more firms also decide to export. To export, firms need to pay

additional labor costs per period and as firms enter the export market, this increases real wages. That is, in a sticky price model with firm heterogeneity, a contractionary shock induces a fall in entry - there is a fall in the real wage, which generates entry but there is also a countervailing rise in wages from firms wishing to export their product to earn extra profits overall (as shown in figure two). The net result is that there is a cleansing effect of a contractionary shock to monetary policy, forcing smaller firms out of the export market. I now consider the alternative regime in which each government targets domestic prices. It is common in open economy New Keynesian analysis to consider such a possibility (see, for example, Clarida et al. (2002) and Monacelli (2004)) because, for certain specification over preferences and specific shocks optimal policy is consistent with targeting zero domestic price inflation. Here, and mostly as 19

a comparison, I study the impulse responses of average productivity in both regimes when the shock to interest rates has an autoregressive parameter of ρν = 0.8. There is some debate about the value this parameter should take. For example, Smets and Wouters (2007) estimate of a value of 0.12 for the US (which they assume is a closed economy). However, they also document a significant amount of interest rate smoothing; one lag weighted at 0.81. Steinsson (2008) and Carvalho and Necchio

(2009) work with calibrated two country models and both assume a persistence parameter closer to one. Figure 3 presents two sets of impulse responses. The dotted lines correspond to consumer price inflation targeting regime and the dashed lines are the domestic price inflation targeting regime. Figure 3 Here It is clear that adding persistence to the shock adds persistence productivity process. It also increases the magnitude of the initial reaction of average productivity in both countries. Targeting domestic

price inflation creates a larger initial reaction from productivity than targeting consumer price inflation but the persistence of the change in average productivity is less. When thinking about these differences it is important to recall that the costs associated with price changes arise from output price inflation. For example, the average home firm selling in the domestic market pays a cost in terms of π h,t . The home government is targeting domestic consumer prices, which are, Πh,t = π h,t −
1 1−σ

∆nh,t . That

is, once we account for the number/quality of products in the domestic economy - and all firms that produce sell in the domestic market - the government is using a rule that aims to reduce the level of inflation consistent with the costs of the average firm. When the government targets consumer prices, it is explicitly concerned with the price of imported goods, which represent only a fraction of the goods sold in the foreign economy by foreign firms. This target then implicitly accounts for the heterogeneity of foreign firms.

C. Labor Productivity Shocks

I now briefly consider a shock to domestic aggregate labor productivity - similar to the RBC literature - and how they impact the average productivity of exporting firms in the two countries. I consider a relatively persistent shock consistent with most of these studies. The important point to note is that 20

an exogenous rise in labor productivity has a direct impact on the firm’s pricing decision and it directly affects all domestic firms marginal costs. Specifically, each firm will lower its price in response to the fall in marginal costs. As the number of producers (and also the relative price t) is predetermined, this results in a drop in the aggregate price level. The real wage rises as the price level falls. In my model, the reduction in marginal costs induces entry into the domestic market, but as firms also wish to export, the associated rise in the real wage also forces some firms out of the export market. However, overall, when consumer prices are targeted, the average productivity of both home and foreign exporting firms rises, albeit modestly. Figure 4 presents impulse response for the average productivity response of

domestic and foreign exporting firms for the two regimes. As above, the dotted lines correspond to consumer price inflation targeting regime and the dashed lines are the domestic price inflation targeting regime. Figure 4 Here It is clear that there is a large difference across regimes. When governments target consumer prices there is an increase in the average productivity of exporting firms. However, when each government targets domestic prices, and there is a shock in the labor productivity shock in the home economy there is a larger (and still positive) effect on average productivity of foreign exporter but a fall in the average productivity of domestic exporters. This result is related to the fact that the shock directly hits firms marginal costs. The transmission of the shock therefore differs across the two regimes and is compounded by the fact that exporting firms price to market. When the governments target domestic prices there are, in effect, neglecting the price of imported goods, despite that fact that there are set in local currency terms. This situation creates a larger spillover effect, via labor markets, from the

domestic sales sector to the export sector amongst preexisting firms.

V. Conclusion

I have developed a two country general equilibrium model with heterogeneous price-setting firms to understand how shocks to monetary policy and aggregate labor productivity impact macroeconomic interdependence. A contractionary shock to the domestic interest rate raises the average productivity 21

of domestic exporting firms but lowers the productivity of foreign exporting firms - a cleansing out effect. The magnitude of these changes is greater when governments target domestic price inflation as opposed to consumer price inflation. A positive shock to domestic labor productivity generates

only modest (positive) changes in average productivity for both sets of exporting firms when consumer prices are targeted. However, when domestic price inflation is targeted, the shock causes a fall in the average productivity of home exporting firms, and a larger rise in the average productivity of foreign exporting firms.

22

References

Alessandria and Choi, 2007. Do Sunk Costs of Exporting Matter for Net Export Dynamics? Quarterly Journal of Economics 122, 289-33. Backus, D., Kehoe, P., and Kydland, F., 1992. Political Economy 101, 745-775. Ball, L., 2006. Has Globalization Changed Inflation? NBER Working Paper 12687. Bernard, A. S. Redding and P. Schott., 2007. Review of Economic Studies 73, 31-66. Benigno, G., 2004. Real Exchange Rate Persistence and Monetary Policy Rules, Journal of Monetary Economics 51, 473-502. Benigno, P., 2009. Price Stability with Imperfect Financial Integration, Journal of Money, Credit, and Banking, forthcoming. Bergin, P. and Corsetti, G., 2008. The Extensive Margin and Monetary Policy, Journal of Monetary Economics 55, 1222-1237. Bergin, P., 2003. Putting the New Open Economy Macroeconomics to a Test, Journal of International Economics 60, 3-34. Bergin, P., 2006. How Well Can the New Open Economy Macroeconomics Explain the Exchange Rate and Current Account, Journal of International Money and Finance 25, 675-701. Betts, C., Devereux, M., 2000. Exchange Rate Dynamics in a Model of Pricing to Market, Journal of International Economics 50, 214-244. Bilbiie, F., Ghironi, F., Melitz, M., 2007. Monetary Policy and Business Cycles with Endogenous Comparative Advantage and Heterogeneous Firms, International Real Business Cycles, Journal of

Entry and Product Variety, NBER Macroeconomics Annual, MIT Press. Binder, M., Pesaran, H., 1996. Multivariate Rational Expectations Models and Macroeconomic Modelling: A Review and Some New Results, in Handbook of Applied Econometrics: Macroeconomics, Pesaran, H., Wickens, M. (eds.), Blackwell. 23

Binyamini, A., Razin, A., 2007.

Flattened Inflation-Output Tradeoff and Enhanced Anti-Inflation

Policy as an Equilibrium Outcome of Globalization, HKIMR working paper 23/2007. Borio, C., Filardo, A., 2007. Globalization and Inflation: New Cross-Country Evidence on the Global Determinants of Domestic Inflation, BIS working paper 227. Broda, C., Weinstein, D., 2006. Globalization and the Gains from Variety, Quarterly Journal of Economics 121, 541-585. ——-, ——-, 2007. working paper 13041. Carvalho., C., Necchio, F., 2008. Princeton University. Chaney, T., 2008. Distorted Gravity: The Intensive and Extensive Margins of International Trade, Aggregation and the PPP Puzzle in Sticky-Price Models, mimeo, Product Creation and Destruction: Evidence and Price Implications, NBER

American Economic Review 98, 1707-1721. Chari, V., Kehoe, P., McGratten, E., 2002. Can Sticky Price Models Generate Volatile and Persistant Real Exchange Rates, Review of Economic Studies 69, 533-563. Chen, N., Imbs, J., Scott, A., 2008/9. The Dynamics of Trade and Competition, Journal of International Economics 77, 50-62. Corsetti, G, Martin, P., Pesenti, P., 2007. Productivity, Terms of Trade and the ‘Home Market Effect’, Journal of International Economics 73, 99-127. Devereux, M., Engel, C., 2002. Exchange Rate Pass-Through, Exchange Rate Volatility, and Exchange Rate Disconnect, Journal of Monetary Economics.49, 913-940. Ghironi, F., Melitz, M., 2005. International Trade and Macroeconomic Dynamics with Heterogeneous Firms, Quarterly Journal of Economics 120, 865-915. Ihrig, J., Kamin, S., Lindner, D., Marquez, J., 2007. Some Simple Tests if the Globalization and

Inflation Hypothesis, Board of Governors International Finance Discussion Papers Number 891. Kollmann, R., 2001. The Exchange Rate in a Dynamic Optimizing Business Cycle Model with Nominal Rigidities: A Quantitative Investigation, Journal of International Economics 55, 243-262. 24

Melitz, M., 2003. The Impact of Trade on Aggregate Industry Productivity and Intra-Industry Reallocations, Econometrica 71, 1695-1726. Rogoff, K., 2004. Globalization and Global Disinflation, Monetary Policy and Uncertainty: Adapting to a Changing Economy, Federal Reserve Bank of Kansas City. ——-, 2007. Impact of Globalization on Monetary Policy, The New Economic Geography: Effects and Policy Implications, in Federal Reserve Bank of Kansas City. Sbordone, A., 2007. Globalization and Inflation Dynamics: The Impact of Increased Competition, NBER working paper 13556. Schmitt-Grohe, S., and Uribe, M., 2003. Closing Small Open Economy Models, Journal of International Economics 61, 163-185. Steinsson, J., 2008. The Dynamic Behavior of the Real Exchange Rate in Sticky-Price Models,

American Economic Review 98, 519-533. Svensson, L., 2000. Open-Economy Inflation Targeting, Journal of International Economics 50, 155-183. Woodford, M., 2007. Globalization and Monetary Control, mimeo, Columbia University.

25

Appendix A: Productivity Averages

Define the following cutoffs for the level of productivity of domestic firms as, ϕ∗ = inf ϕ : d∗ (ϕ) ≥ 0 t h,t where ϕ ≡ ϕ∗ = ϕf . Define two average levels of productivity; one for all domestic firms and one for h all domestic exporters, as,
∞ 1/(σ−1)

ϕ≡
ϕ

(1/ϕ)

1−σ

dG (ϕ)
∞ ϕ∗ t 1/(σ−1)

1 ϕ∗ (ϕ∗ ) ≡ t t 1 − G (ϕ∗ ) t

(1/ϕ)

1−σ

dG (ϕ)

Note that ϕ does not vary over time and so has no time subscript. However, ϕ∗ does vary over time. t We will also assume that ϕ has a Pareto distribution, G (ϕ) = 1 −
ϕ ϕ κ

, where κ > 0. Note that this

implies, ϕ = ϕ [1 − G (ϕ)]−1/κ . Also note, G ϕ = 0 and G (∞) = 1. In this case,
∞ 1/(σ−1)

ϕ=ϕ
ϕ

[1 − G (ϕ)]

(1−σ)/κ

dG (ϕ)

and so,
∞ ϕ

[1 − G (ϕ)]

(1−σ)/κ

dG (ϕ) =

1−σ − 1+ κ 1+ 1−σ κ
−1

−1

∞

[1 − G (ϕ)]

1+[(1−σ)/κ]

+ const.
ϕh

= In this case, κ ϕ = νϕ ; ν ≡ κ − (σ − 1)

=

κ κ − (σ − 1)

1/(σ−1)

I perform the same analysis for ϕ∗ . Specifically, t ϕ∗ = ϕ t 1 1 − G (ϕ∗ ) t
∞ ϕt

[1 − G (ϕ)](1−σ)/κ dG (ϕ)

1/(σ−1)

26

and,
∞ ϕx,t

[1 − G (ϕ)]

(1−σ)/κ

dG (ϕ) = =

1−σ − 1+ κ 1+ 1−σ κ
−1

−1

∞

[1 − G (ϕ)]

1+[(1−σ)/κ] ϕx,t

[1 − G (ϕ∗ )]1+[(1−σ)/κ] t

which implies, ϕ∗ = ϕν · [1 − G (ϕ∗ )]−1/κ ,and as such, t t ϕ∗ = νϕ∗ t t ; κ κ − (σ − 1)
1/(σ−1)

Since ϕ∗ is proportional to ϕ∗ we can study changes in either variable when analyzing the dynamics h,t h,t of the model.

27

Appendix B: Equilibrium

The demand for labor is determined by the following condition.
∗ Lt = Lh,t + L∗ + n∗ fh + nEh,t fE /At h,t h,t

lh,t

dh,t + (Ph,t /Pt ) ξ h,t = (µh,t − 1) wt

;

∗ lh,t

=

∗ ∗ dh,t + et Ph,t /Pt ξ h,t + fh wt /At

∗

∗

µ∗ − 1 wt h,t

∗ Total labor used for production in the domestic and export markets is Lh,t ≡ nh,t lh,t and L∗ ≡ n∗ lh,t . h,t h,t ∗ In addition, new entrants hire fE units of labor to cover the entry cost and each exporter hires fh to

cover the fixed export cost in each period. The total amount of labor hired to cover fixed export costs
∗ and new entrants is therefore n∗ fh + nEh,t fE /At . We therefore have, h,t

Lt

n∗ nh,t ∗ ∗ h,t ∗ ∗ = dh,t + (Ph,t /Pt ) ξ h,t + ∗ dh,t + et Ph,t /Pt ξ h,t + fh wt /At (µh,t − 1) wt µh,t − 1 wt 1 + n∗ f ∗ + nEh,t fE At h,t h

Aggregating the household budget constraint (across symmetric agents) and imposing the equilibrium conditions (Ah,t = Ah,t+1 = 0 and st = st+1 = 1 and ng,t ≡ nh,t + ne,t ) yields, et Af,t − Af,t−1 = Wt Lt + Pt dt nh,t − Pt (Ct + v t ne,t ) (1 + i∗ ) t
n∗ h,t ∗ d , nh,t h,t

Now now eliminate profits. We know average total profits of domestic firms are, dt = dh,t + entry; Pt v t = fe Wt /At . defined as,
t

and that the free entry requirement equates the value of the firm with wages and the sunk costs of Once we impose labour demand, the trade account (in real terms) can be

≡ +

µh,t µh,t − 1

nh,t dh,t +

µ∗ h,t µ∗ − 1 h,t

∗ n∗ dh,t + fh h,t

∗

wt At
∗

− Ct

n∗ nh,t h,t (Ph,t /Pt ) ξ h,t + ∗ µh,t − 1 µh,t − 1

∗ Qt Ph,t /Pt∗ ξ h,t

where Qt = et Pt∗ /Pt . Note also that for domestic sales, average profits, in terms of consumption, are, Pt dh,t = ph,t y h,t − Wt lh,t − Ph,t ξ h,t ⇔ dh,t = µh,t − 1 µh,t ρh,t nh,t ; y h,t = Ch,t − ph,t Ph,t
−σ

Ch,t + nh,t ξ h,t

σ/(1−σ)

1 1/(1−σ) ρ n ξ h,t µh,t h,t h,t 28

where ρh,t ≡ ph,t /Pt , and for foreign sales, average profits, again in terms of consumption, are,
∗ Pt dh,t

= =

et p∗ y ∗ h,t h,t

−

∗ Wt lh,t

−

∗ ∗ et Ph,t ξ h,t

−

∗ fh Wt /At

;

y∗ h,t

=

p∗ h,t ∗ Ph,t

−σ ∗ Ch,t + n∗ ξ h,t h,t ∗

∗ dh,t

µ∗ − 1 h,t µ∗ h,t

Qt ρ∗ nh,t h,t

∗σ/(1−σ)

∗ Ch,t −

1 ∗1/(1−σ) ∗ ∗ Qt ρ∗ nh,t ξ h,t − fh wt /At h,t ∗ µh,t

where ρ∗ ≡ p∗ /Pt∗ . These imply, h,t h,t tier demands and the CPI,
t

t

∗ ∗ ≡ (Ph,t /Pt ) Ch,t + et Ph,t /Pt Ch,t − Ct . Finally, using the upper

= ah

∗ Ph,t Pt∗

θ/(θ−1)

Qt Ct∗

− (1 − ah )

Pf,t Pt

θ/(θ−1)

Ct

where the right-hand side is exports, and the left-hand side imports.

29

Appendix C: Steady State
∗ ∗ In the steady state there is balanced trade and zero inflation. In addition, fe = fe , fx = fx , τ = τ ∗

and A = A∗ = 1. Under these assumptions, the steady state of the model is symmetric, and Q = 1 and C = C ∗ . From the pricing equations, ρh = µh w/ϕ ; ρ∗ = µ∗ τ w/ϕ∗ h h ; µh = µ∗ = h σ >1 σ−1
1/(1−σ)

where ph /P ≡ ρh and p∗ /P ∗ ≡ ρ∗ . The CES price indexes reduce to, Ph = nh h h
∗ Ph = nh ∗1/(1−σ) ∗ ph , 1/(θ−1)

ph , Pf = nf

1/(1−σ)

pf ,

and consumption of products are, C ; cf = (1 − ah ) nΦ ρf f
1/(θ−1)

ch = a h nΦ ρh h

C

; c∗ = (1 − ah ) n∗Φ ρh h h

∗1/(θ−1)

C

where Φ ≡ [σ (θ − 1) + 1] / (σ − 1) (1 − θ). mestic goods is defined as sh ≡ ah n1+Φ ρh h

The expenditure share of domestic consumption on do. Note, when the elasticity of substitution is the same

θ/(θ−1)

between goods and brands, σ = 1/ (1 − θ) ⇔ Φ = 0, and so, sh ≡ ah nh ρ1−σ ; when the upper tier of h utility is Cobb-Douglas, θ = 0 ⇔ Φ = −1, and, sh ≡ ah . In each case, the respective CPI is, 1 = a h nh 1 = nh
1/(1−σ) θ/(θ−1) θ/(θ−1)

ρh
ah

+ af nf ρf
af

1/(1−σ)

ρf

:θ>0

1/(1−σ)

ρh

nf

1/(1−σ)

:θ=0

And note, y h = ch and y ∗ = τ c∗ . Total profits, the value of the firm, in terms of total profit, and the h h free entry condition are, dt = dh + n∗ h nh dh
∗

; v=

(1 − δ) β d ; v = wfe 1 − (1 − δ) β

Profits from domestic and export sales, and the zero-profit export cutoff are, dh = ρh y h − wlh ; dh =
∗

1 ∗ ∗ ρh y ∗ − wlh − fh w h τ

∗ ; dh = ν σ−1 − 1 fh w

∗

where ν ≡ {κ/ [κ − (σ − 1)]}1/(σ−1) . The share of exporting firms and number of firms are, n∗ h = nh ϕ ϕ∗
κ

; nh =

1−δ δ

ne

and finally, labor demand, labor supply, and balanced trade are given by,
∗ ∗ L = nh lh + n∗ lh + n∗ fh + ne fe h h

; w = φCLϕ

; C = wL + dnh − vne 30

I first determine the zero-profit export productivity level, ϕ∗ . First, total profits, the value of the firm and the free entry condition imply, dh + n∗ h nh dh =
∗

1 − (1 − δ) β wfe (1 − δ) β

Second, profits from domestic and export sales - by apply the pricing equations to eliminate wages can be expressed in terms of consumption as, w σ w ah Φ θ/(θ−1) C y h ; ρh = ⇒ dh = nh ρh ϕ σ−1ϕ σ 1 w σ τw ah ∗Φ ∗θ/(θ−1) ∗ ∗ ∗ ∗ C dh + fh w = ρh y ∗ − ∗ y ∗ ; ρ∗ = nh ρh h h h ∗ ⇒ dh + fh w = τ ϕ σ−1 ϕ σ dh = ρh y h −
∗ If we also use the zero-profit export cutoff, dh = (ν σ−1 − 1) fh w, we find an expression for profits from ∗

domestic sales only, dh = nh n∗ h
Φ

ρh ρ∗ h

θ/(θ−1) ∗ ν σ−1 fh w

where ν is defined above. Now use this condition, the expression for total profits and the zero-profit export cut off (again) to eliminate profits and wages. 1 − (1 − δ) β fe = ∗ (1 − δ) β fh ρ∗ h ρh
θ/(1−θ)

n∗ h nh

−Φ

ν σ−1 +

n∗ h nh

ν σ−1 − 1

Finally, the pricing equations and share of exporting firms are, τ νϕ ρ∗ h = ∗ ρh ϕ ; n∗ h = nh νϕ ϕ∗
κ

where we have also used, ϕ = νϕ. Finally, we can determine ϕ∗ through the following equation, ξ1 ϕ∗θ/(θ−1)+κΦ + ξ2 ϕ∗−κ = ξ3 where, ξ1 ≡ τ θ/(1−θ) ϕθ/(1−θ)−Φκ ν σ−1+θ/(1−θ)−Φκ ξ2 ≡ ϕκ ν σ−1 − 1 ν κ ; ξ3 ≡ 1 − (1 − δ) β fe ∗ (1 − δ) β fh

This derivation does not rely on the CPI. 31

I now determine the expenditure share when preferences are CES; that is sh = ah n1+Φ ρh h

θ/(θ−1)

. Since

I consider a symmetric steady state in which nf = n∗ - that is, foreign varieties sold in the domestic h economy are equal in number to domestic varieties sold in the foreign economy - and ρf = ρ∗ , the CPI h can be re-expressed as, 1 = ah n1+Φ ρh h is given by the following. sh = ah τ νϕ ϕ∗
θ/(1−θ) θ/(θ−1)

+ (1 − ah ) n∗1+Φ ρh h

∗θ/(θ−1)

, and the expenditure share variable

ah

τ νϕ ϕ∗

θ/(1−θ)

+ (1 − ah )
κ

νϕ ϕ∗

κ(1+Φ) −1

as ρ∗ /ρh = τ νϕ/ϕ∗ and n∗ /nh = νϕ/ϕ∗ . When the upper tier of utility is Cobb-Douglas, h h ρh nh
1/(1−σ)

=

τ νϕ ϕ∗

ah −1

νϕ ϕ∗

κ(1−ah )(σ−1)

Once we have determined expenditure shares, we can use this to determine other variables.

For

labor supply, start from the aggregate accounting condition, but now use the shares Euler equation to eliminate v instead of d (we do not use the free entry condition), C = wL + nh d − vne ⇒ C = wL + ; ne = δ 1−δ nh ; v=d (1 − δ) β 1 − (1 − δ) β

1−β n∗ ∗ nh d ; d = dh + h dh 1 − (1 − δ) β nh

We also have profits from domestic sales and profits from export sales (incorporating the cutoff for zero export profits). nh dh = sh s∗ 1 ∗ h C ; n∗ dh = 1 − σ−1 C h σ σ ν 1−β sh s∗ w h = 1− + ⇒ C 1 − (1 − δ) β σ σ r r+δ
(r+δ)σ−r ψ(r+δ)σ

1−

1 ν σ−1

1 L

Finally, we have, ψL1/η = w/C, and so, L(1+η)/η = 1− sh + σ
η/(1+η)

s∗ h σ .

1−

1 ν σ−1

1 ψ

Notice also that if we set sh = 1, then s∗ = 0 (the closed economy), and we have a more familiar h expression, L =

Finally, I determine the relative price, ρh . Given the definition of expenditure shares, this also determines the number of varieties in the economy. First, given the definition of sh , we have, ρ1−σ = h ah sh
1/(1+Φ)

nh 32

where I have used θ/ (θ − 1) (1 + Φ) = σ − 1. Second, use the trade balance, the number of firms, the value of the average firm (as a function of total profits) and the free entry condition. These imply, 1−β C =L+ fe n h w (1 − δ) β ; L= C φ w
−1/ϕ

⇒

1−β C =L+ fe n h w (1 − δ) β

where L has already been determined. Second, export profits and the zero-profit export cutoff (using n∗ = nh ϕν/ϕ∗ ) also yield a linear equation in the consumption-wages ratio, as used above. h C nh = ∗ w sh ϕ ϕ∗
κ ∗ σν κ+σ−1 fh κ

Eliminating the consumption-wage ratio, we find, nh = 1 s∗ h ϕ ϕ∗
κ ∗ σν κ+σ−1 fh +

1−β fe L−1 (1 − δ) β

which determines the number of varieties produced and the relative price, ρh , given labor supply, L.

33

Appendix D: Fixed Varieties System

When the number of varieties is fixed and all goods are exported we can simply use labor supply and
R W the goods market clearing conditions to eliminate wt and wt in the dynamic equations for ΠW and t

TtW . This gives, ΠW = βEt ΠW + t+1 t 1+β+ (1 + σl ) (1 − σ) ξ TtW − CtW − AW t (1 + σl ) (1 − σ) W W AR = Tt−1 + βEt Tt+1 t ξ

(1 + σl ) (1 − σ) ξ

The remaining equations are as in the main text. That is, ΠR = βEt ΠR + t t+1 (1 + β) + and, Qt+1 − Qt = iR − Et ΠR t t+1 where,
W iR = φΠ ΠR − TtW − Tt−1 t t

1−σ ξ

Qt

1−σ ξ

R R TtR = Tt−1 + βEt Tt+1

;

W Ct+1 − CtW = iW − Et ΠW t t+1

+ νtR

;

iW = φΠ ΠW − t t

1 R TtR − Tt−1 4

+ νtW

are the interest rate rules when each government targets GDP deflator inflation. These eight equations determine the path of Qt , CtW , iR , iW , ΠR , ΠW , TtR , TtW , for shocks to At and νt ; that is aggregate t t t t
R It is worth noting that if we take relative output is, yt = TtW .

labor productivity and the nominal interest rate, that follow, At = ρA At−1 + εA,t and νt = ρν νt−1 + εν,t , where εA,t and εν,t are i.i.d. That means, suppose we assume each country targets their CPI and GDP, say with parameter, φy > 0. Then, ignoring the monetary policy shocks, we must have, iR = φΠ ΠR + φy TtW and iW = φΠ ΠW + φy CtW . t t t t Such a policy does not add any inertia to policy rules. When there is firm entry some of this simplicity breaks down because we need to differentiate output that is consumed from that which is invested.

34

Appendix E: Heterogeneous Firms System

Recall that for any variable, say xt , I defined ∆xt ≡ xt − xt−1 , xR ≡ xt − x∗ and xW ≡ 1 xt + 1 x∗ . t t t 2 2 t Assuming that each government targets welfare-based CPI inflation, I have the following system of ten dynamic equations that determine Qt , CtW , nR , nW , ΠR , ΠW , TtR , TtW , ϕt , ϕt t t t t Qt + φΠ ΠR + νt = Qt+1 + Et ΠR t t+1 nR = (1 − δ) nR + δnR t t−1 e,t−1
R R W

.

;

1 CtW + φΠ ΠW + νt t 2

W = Ct+1 + Et ΠW t+1

;

nW = (1 − δ) nW + δnW t t−1 e,t−1 κβ κ R R Et ϕt+1 + ϕt−1 2 2
W

−ξ Qt + ΠR + A2 ϕt = βEt ΠR + t t+1

W ΠW − ξ wt − AW + A1 nW − A2 ϕt t t t

= βEt ΠW + t+1 +
W

1 σ−1

1 κ W nW − ϕt+1 t+1 σ−1 2 κ W nW − ϕt−1 t−1 2
W W

R R (σ − 1) A1 TtR − 2κ 1 + β − ξ (1 − κ) ϕt = βEt Tt+1 − 2κϕt+1 + Tt−1 − 2κϕt−1

R −ξ Qt + (σ − 1) A1 TtW + ξ wt − AR − A1 nR + A2 ϕt t t

R

W = βEt Tt+1 − W +Tt−1 −

1 σ−1

1 σ−1

κ R nR + ϕt+1 t+1 2 κ R nR + ϕt−1 t−1 2

R −Qt + wt − AR = −Qt+1 + t W W −CtW + wt − AW = −Ct+1 + t

1−δ 1+r 1−δ 1+r

R wt+1 − AR + t+1 W wt+1 − AW + t+1

r+δ 1+r r+δ 1+r

dt+1 dt+1
W

R

These are consumption Euler equations, laws of motion for products, relative CPI, world CPI, relative and world relative price Phillips curves and shares Euler equations. The following six static conditions,
R A4 Qt − A3 wt + nR − e,t

nd d nE v nd d nE v

nR − t nW − t
R

nd d nE v nd d nE v

dt − AR = 0 t dt − AW = 0 t
R W

R

W A4 CtW − A3 wt + nW − e,t

R −ΨQt + Ψ (σ − 1) TtW + A5 wt + dt − [κ − (σ − 1)] κϕt − A5 AR = 0 t

35

−ΨCtW + Ψ

σ−1 4

W TtR + A5 wt + dt − [κ − (σ − 1)] κϕt − R

W

W

A5 2

AW = 0 t

R − [1 + (σ − 1) 2] Qt + (σ − 1) TtW + σ wt − (σ − 1) ϕt − σ AR = 0 t

−CtW − determine

σ−1 4

W TtR + σ wt − (σ − 1) ϕt − σ AW = 0 t R W

W

R W wt , wt , nR , nW , dt , dt e,t e,t

. These are the resource constraints, total (average) firm profits,

and zero-profit export cutoffs.

The terms Ai , for i = 1..9, are constants and determined by the

underlying structural parameters of the model - see Appendix C.

36

Table 1: Baseline Calibration

Calibration of Parameters Parameter Description σ κ σl φΠ β ξ δ ρν ρA U. S. plant and macro-trade data Dispersion of firms Intertemporal elasticity of labor supply Coefficient on inflation in interest rate rule Subjective discount factor Rotemberg weight/cost of price changes Exogenous firm exit shock Autoregressive parameter for monetary shock Base Value 3.8 3.4 2 1.5 0.96 0.77 0.025 0.3

Autoregressive parameter for labor productivity shock 0.979

37

Figure 2: Impulse Response Functions - Monetary Policy Shock

Consumption 0.2 0 −0.2 −0.4 −0.6 −0.8 0.2 0 −0.2 −0.4 −0.6 −0.8

Inflation 0.5

Entry

0

−0.5

0

10 Profits

20

0

10 Av. Productivity

20

−1

0

10 Shock

20

2.5 2 1.5 1 0.5 0 −0.5 0 10 20

0.1 0 −0.1 −0.2 −0.3 −0.4

1 0.8 0.6 0.4 0.2 0

0

10

20

0

10

20

38

Figure 3: Av. Productivity IRFs for two Policy Regimes - Monetary Policy Shock

Domestic Average Productivity 0.6 0.4 0.2 0 −0.2

0

2

4

6

8

10

12

14

16

Foreign Average Productivity 0.5 0 −0.5 −1 −1.5

0

2

4

6

8

10

12

14

16

39

Figure 4: Av. Productivity IRFs for two Policy Regimes - Labor Productivity Shock

Domestic Average Productivity 0.1 0.05 0 −0.05 −0.1

0

2

4

6

8

10

12

14

16

Foreign Average Productivity 0.2 0.15 0.1 0.05 0

0

2

4

6

8

10

12

14

16

40


								
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