Journal of International Money and Finance 41 (2014) 128–145

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Monetary shocks, exchange rates, and the extensive margin of exportsq Dudley Cooke Department of Economics, University of Exeter, Streatham Court, Rennes Drive, Exeter EX4 4PU, United Kingdom

a b s t r a c t JEL classification: E31 E52 F41 Keywords: Exchange rate pass-through Extensive margin of exports Monetary shocks

This paper develops a two-country Dynamic General Equilibrium model to assess the relationship between the real exchange rate and the extensive margin of exports. Exchange rate pass-through to consumer prices governs the relative strength of a demand channel onto the exporting decision of a firm. With incomplete pass-through, a favorable movement in the real exchange rate generates increased export participation and an expansion in the extensive margin of exports. This result is consistent with firmlevel studies, and contributes to an ongoing empirical debate as to the importance of changes in export participation over the business cycle.
2013 Elsevier Ltd. All rights reserved.

1. Introduction Recent empirical studies based on firm-level data have shown that exchange rate movements induce firm entry and exit in export markets. For example, Berman et al. (2012) and Fitzgerald and Haller (2012) find that favorable movements in the real exchange rate generate entry into foreign markets (for French and Irish firms, respectively). However, using product-level data for the US and OECD, Alessandria and Choi (2008) and Kehoe and Rhul (2013), argue that the number of exporters has little correlation with the real exchange rate and the extensive margin of exports is largely invariant to

q I am very grateful to an anonymous referee for constructive suggestions. I also thank participants at the 2011 ESEM in Oslo, the 2011 Anglo-French-Italian Macroeconomics Workshop in Milan, the Bank of Portugal, the Hong Kong Institute for Monetary Research, and the Universities of Cardiff, Lausanne, Leicester, Manchester, and Sussex, as well as Pierre-Richard Agenor, Philippe Bacchetta, Mick Devereux, Ana Fernandes, Alessandro Flamini, Christos Kotsogiannis, Philip Lane, and Michael Wycherley. I received financial support from the Hong Kong Monetary Authority. E-mail address: [email protected]. 0261-5606/$ – see front matter
2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jimonfin.2013.10.003

D. Cooke / Journal of International Money and Finance 41 (2014) 128–145

129

general fluctuations in the business cycle.1 This paper attempts to discriminate between these findings using a two-country Dynamic General Equilibrium model. I start with a standard explanation for real exchange rate movements and business cycle fluctuations: the interaction of monetary shocks with sticky goods prices.2 In this environment I allow for endogenous export participation based on per-period export costs. I show that exchange rate passthrough to consumer prices determines the relative strength of a demand channel onto the export participation decision of a firm. With incomplete exchange rate pass-through, a favorable movement in the exchange rate expands the set of firms that find it profitable to export because increased demand dominates the rising costs of production. This relationship between the exchange rate and extensive margin of exports is consistent with firm-level studies. Although favorable movements in the exchange rate are associated with expansions in the extensive margin of exports, the magnitude of this change depends on the extent of pass-through.3 In this sense, even if pass-through were low, it could still be possible that the extensive margin is only weakly correlated with the business cycle, as suggested by product-level studies. To determine whether this is indeed the case, I calibrate the model and show that the relative strength of the demand channel identified in this paper is quantitatively important. In the low pass-through specification, a 1 percent rise in the money stock (after one year) results in a 0.2 percent expansion in the extensive margin of exports, on impact.4 There are two features of the model that generate the pass-through-based trade-off between demand and costs for firms, and thus strong results with regard to the extensive margin. First, consumed goods undergo two stages of production, with international trade in intermediate inputs, similar to Huang and Liu (2007). Intermediate firms (stage one) use labor as an input, are heterogeneous in productivity, and export subject to a per-period cost. Firms that produce consumer goods (stage two) use domestic and available foreign intermediate goods as inputs and also sell their output in domestic and export markets. The price of consumer goods is sticky in either producer or local currency terms, which limits exchange rate pass-through. The second feature of the model is that firm creation is subject to a sunk entry cost.5 Because firm creation requires resources, the export participation decision of all preexisting intermediate firms is conditional on the mass of new entrants, and greater firm creation, all else equal, leads to fewer firms in the export market. The decision of an intermediate firm to export then depends on both the demand for its output (by firms producing consumer goods) and the mass of new entrants in the domestic market. As such, changes in the extensive margin of exports depend on international relative consumer prices, which affect demand, and the terms-of-labor, which affects costs. The demand channel dominates at low levels of exchange rate pass-through. Ghironi and Melitz (2005) consider an environment in which firms face sunk entry and per-period export costs but focus on technology shocks as the source of business cycle fluctuations.6 They study both a permanent and transitory (with 0.9 persistence) 1 percent increase in home productivity. This results in a 0.55 and 0.21 percent expansion in the extensive margin, on impact, respectively, and positive co-movement between the home and foreign extensive margins. With monetary shocks, nominal rigidities, and incomplete pass-through, the results are comparable, yet the channel is markedly different. Positive international co-movement and pro-cyclical extensive margins are

1

Alessandria et al. (2012) provide evidence on real exchange rates and extensive margins across emerging markets. For example, see Chari et al. (2002) and the multi-sector model of Carvalho and Nechio (2011). Iversen and Soderstrom (2012) discuss the role of non-monetary shocks in sticky-price models. 3 If pass-through has fallen over time, as suggested by Marazzi and Sheets (2007), increased export participation following a favorable movement in the real exchange rate is more likely. 4 Berman et al. (2012) and Fitzgerald and Haller (2012) both estimate linear probability models. In the former (latter), a 10 percent home currency depreciation, generates a 2 (0.5) percentage point increase in the probability of exporting. Berman et al. (2012) also show that larger firms raise export prices and not volumes in response to exchange rate changes (the average exporter raises price by 0.8 percent and volume by 4 percent). 5 The relationship between monetary policy and firm creation is discussed in Bilbiie et al. (2007), Bergin and Corsetti (2008), Lewis (2009), and Lewis and Poilly (2012). 6 See Alessandria and Choi (2007) for an analysis with sunk export costs. 2

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generated by changes in demand driven by fluctuations in real income across countries. Fluctuations in the real exchange rate arise from deviations in the law of one price for traded consumer goods. I also consider how movements in the extensive margin of exports contribute to the response of trade volumes and prices. The extensive margin plays an important role for changes in volumes because, although new exporters are necessarily smaller (and charge higher prices) than preexisting exporters, with a low trade elasticity, they gain a relatively high market share. Since pass-through has implications for the extensive margin, one interpretation is that pass-through may also play a role in the response of trade volumes to exchange rate movements. This possibility complements the work of Gust et al. (2009) who estimate a DSGE model using US data and find similar overall trade adjustment in low and high pass-through environments.7 Finally, this paper adds to a literature focused on the role of monetary uncertainty and endogenous export participation. For example, Russ (2007) analyzes the differential effect of domestic and foreign monetary uncertainty on multinational production (albeit without an exporting decision), Bergin and Lin (2009) consider the role of the exchange rate regime for adjustment along the extensive margin, and Lewis (2011) analyzes the choice to serve a foreign market by exporting or to produce as a multinational.8 Rodríguez-López (2011) presents a model where changes in the extensive margin of exports explain exchange rate disconnect. In this paper, the extent of exchange rate pass-through to consumer prices is given, and I study movements in the extensive margin of exports over the business cycle. Pass-through has important implications for movements in the extensive margin, which in turn affects the overall trade response to changes in the exchange rate. The remainder of the paper is organized as follows. Section 2 develops a two-country model with heterogeneous firms, vertical specialization in production, and sticky-prices. Section 3 provides analytical results and Section 4 computes impulse responses for a quantitative version of the model. Section 5 concludes. 2. The world economy The world consists of a home and foreign economy each populated by a unit mass of identical, infinitely-lived households. Each household supplies labor to firms producing intermediate goods and holds three domestic assets: shares in a mutual fund, a risk-free bond, and money. Households also consume domestic and foreign goods at the final stage of production. Intermediate firms are heterogeneous in productivity and export subject to a per-period cost. Firms producing consumer goods set prices and use home and (available) foreign intermediate goods as inputs. Below, consumption, output, and the nominal price of the home/foreign output are subscripted with an h/f. An asterisk denotes a foreign economy variable. 2.1. Households intratemporal consumption Consumption is an aggregate of z˛(0,1) home and foreign final goods,

gh gf

Ct ¼ GYh;t Yf ;t and Yi;t ¼ g


Z

1 0

 yi;t ðzÞ dz q

1=q

for i ¼ h; f

(1)

g

where Gh1=ghh gf f and ghþgf¼1 and I define sh1/(1q)>1 as the elasticity of substitution between R1 R1 varieties. Households maximize consumption, subject to Pt Ct ¼ 0 ph;t ðzÞyh;t ðzÞdz þ 0 pf ;t ðzÞyf ;t ðzÞdz, choosing yh,t(z) and yf,t(z), and taking prices, ph,t(z) and pf,t(z), as given. There is a downward-sloped demand curve for a variety z,

7 Gust et al. (2009) include distribution services and a variable demand elasticity (alongside local currency pricing) which reduce exchange rate pass-through. 8 Monetary models with nominal rigidities that analyze the role of technology shocks are presented in Naknoi (2008), Cavallari (2010), and Auray et al. (2012).

D. Cooke / Journal of International Money and Finance 41 (2014) 128–145


ydi;t ðzÞ ¼ gi


 pi;t ðzÞ s Pi;t 1 Ct Pt Pi;t

131

(2)

R1 g g where Pi;t ¼ ð 0 pi;t ðzÞ1s dzÞ1=ð1sÞ . The consumer price index is given by, Pt ¼ Ph;th Pf ;tf . 2.2. Consumer-firms production Firms producing consumer goods use home and foreign intermediate goods (nh,t and nf,t, respectively) as inputs. The technology available to these firms is,

0

B q uh uf yh;t ðzÞ þ y+ h;t ðzÞ ¼ UYh;t Yf ;t and Yi;t ¼ @Ni;t

Z

11=q

C yi;t ðz; aÞq daA

(3)

ni;t

y1=q

u

h uf f and uhþuf¼1 and Ni;t hni;t where Uh1=uu controls a variety effect in production. Costs of h R R production are, nh;t ph;t ðaÞyh;t ðz; aÞda þ nf ;t pf ;t ðaÞyf ;t ðz; aÞda, and cost minimization implies the u s1 R 1s h following unit input function, Pt ¼ Pu P f , where Pi;t ¼ ðNi;t daÞ1=ð1sÞ . The demand ni;t pi;t ðaÞ h;t f ;t

schedules that result from cost minimization are,

ydi;t ðaÞ

pi;t ðaÞ ¼ 1s Pi;t Ni;t

ui

!s
 Z i Pi;t 1 1 h yh;t ðzÞ þ y+ h;t ðzÞ dz Pt 0

(4)

Firms compete in a monopolistically competitive market. Accounting for the technology given in (3), the flow profit of firm z can be written as, dt ðzÞ ¼ ðph;t ðzÞ  Pt Þydh;t ðzÞ þ ðet p+ ðzÞ  Pt Þy+d ðzÞ. Each h;t h;t firm maximizes profit, subject to the demand for their product from households, given by (2), and faces a constant probability of a price-adjustment opportunity, denoted 1a. I allow for two possibilities in terms of price setting. Firms can either set the price of output in their own currency only, choosing the P t ~h;t ðzÞ, to maximize N (reset) price p t¼0 a E0 M0;t dt ðzÞ, where M0,t is a discount factor. In this case, the foreign currency price of their output is, p+ ðzÞ ¼ ph;t ðzÞ=et , where et is the nominal exchange rate. h;t ~h;t ðzÞ and Alternatively, firms can set prices in local currency terms and choose both (reset) prices, p 9 ~+ p ðzÞ. In this case, the law of one price fails and exchange rate pass-through is incomplete. h;t 2.3. Intermediate-firms production Firms producing intermediate goods require labor and have a linear technology, yh;t ðaÞ þ y+ ðaÞ ¼ alh;t ðaÞ þ al+ h;t ðaÞhLt , where a is firm-specific. Costs of production are WtLt. Cost h;t minimization implies the unit cost of production for an intermediate firm is, Wt/a, and intermediate firm   profits from domestic and (potential) export sales are, dt ðaÞ ¼ ph;t ðaÞ  Wa t ydh;t ðaÞþ   ðaÞ  Wa t y+d ðaÞ  Wt Fx , where Fx>0 is a fixed cost associated with exporting. Firms maximize et p+ h;t h;t profit, subject to demand, given by (4), and optimal prices are characterized by simple price markup expressions, which, for domestic sales are, ph,t(a)¼Wt/qa, with the corresponding export price, ðaÞ ¼ ph;t ðaÞ=et , where q<1. p+ h;t With fixed costs and a distribution over productivity a subset of firms do not export because they do not earn profit from doing so. I define the zero export profit (threshold) level of productivity as, + a+ hinffa : d+ h;t ðaÞ > 0g, where dh;t ðaÞ are the potential export profits of a firm with productivity level h;t a. Using the first-order conditions from profit maximization, the threshold level of productivity for exporting can be written as,

9 Optimization produces standard Calvo-style pricing formulas in which the reset price is a weighted average over future marginal costs (see Table 1 below).

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D. Cooke / Journal of International Money and Finance 41 (2014) 128–145

a+ h;t

¼

+ P+ t =Ph;t

qN+ h;t

!

Wt e t P+ t

91=ð1sÞ !1=q 8
< 1  u Z 1 h i = h + yh;t ðzÞ þ yh;t ðzÞ dz ; : sFx 0

(5)

The threshold level of productivity depends on the demand for consumer goods, international relative prices, the unit costs of production, and the mass of home intermediate exporting firms. Following Ghironi and Melitz (2005), I write all firm-level variables in averages (denoted by an upper-bar). In any period, there are nh,t intermediate firms producing goods, with an average level of RN productivity, ahð 1 aq1 dGðaÞÞ1=ðq1Þ , where G(a)¼1ak and a>1.10 Because it is possible to earn zero profit from exporting, only a subset of intermediate firms export, and they have average productivity, R N q1 a+ a dGðaÞ=ð1  Gða+ ÞÞg1=ðq1Þ . The term 1  Gða+ Þ is the ex-post probability of successh;t hf½ a+ h;t h;t h;t fully exporting, and relates the ratio of intermediate exporters to all intermediate firms by the following expression, n+ =nh;t ¼ 1  Gða+ Þ. h;t h;t 2.4. Entry and exit The creation of new intermediate firms is subject to a sunk entry cost, denoted Fe>0. New entrants at time t start producing at time tþ1. Prospective intermediate firms are forward looking, and correctly anticipate their future expected profits, as well as the probability of incurring an exit shock, d, at the end of each period, after they produce. Intermediate firms post-entry value is given by the present P t discounted value of expected profits, v0 ¼ E0 M0;1 d1 þ E0 N t¼1 ð1  dÞ M0;tþ1 dtþ1 . New intermediate firms enter as long as they can cover sunk costs, which implies vt  Fe Wt . Finally, the timing of entry and production implies the mass of intermediate firms during period t is, nh,t¼(1d)nh,t1 þ ne,t1, where ne,t1 is the mass of intermediate entrants. 2.5. Households The representative household consumes Ct units of goods, supplies Lt units of labor, holds real money balances, mthMt/Pt, shares in a mutual fund of domestic intermediate firms, St, and a domestic risk-free bond, Bt. The household’s intertemporal utility function is,

U0 ¼ E0

N X t¼0



bt lnðCt Þ þ nlnðmt Þ 




f

  h L1þ t

1þh

(6)

where b˛(0,1) is a subjective discount factor and 1/h is the Frisch elasticity of labor supply. Utility is maximized subject to,

  Btþ1 þ nt Stþ1 vtþ1 þ Pt Ct þ Mt ¼ Bt It þ Wt Lt þ nh;t St dt þ vt þ dt þ Mt1  Tt

(7)

where nthnh,tþne,t is the mass of intermediate firms prior to the exit shock, and is comprised of nh,t preexisting firms, and ne,t entrants. The variable vt is the average firm value, It is the gross nominal interest rate, Wt is the nominal wage, dt and dt are firm profits, and Tt is a lump-sum tax. The following conditions are associated with the household’s optimization problem over shares, labor supply, money, and bonds, respectively,

h i Ct Pt h and wt ¼ fCt Lt ð1  dÞvtþ1 þ dtþ1 Ctþ1 Ptþ1


vt ¼ bEt

(8)

10 The assumption that productivity is Pareto distributed is a common assumption and matches well with micro data on firm size distribution.

D. Cooke / Journal of International Money and Finance 41 (2014) 128–145


mt ¼ nCt It =ðIt  1Þ and 1=It ¼ bEt

Ct Pt Ctþ1 Ptþ1

133

 (9)

where wthWt/Pt is the real wage.

2.6. Foreign economy and equilibrium Foreign firms producing consumer goods choose prices – p+ ðzÞ, or p+ ðzÞ and pf,t(z), depending f ;t f ;t on the possibility of international price discrimination – to maximize profits, taking input prices – p+ ðaÞ and p+ ðaÞ – as given. Foreign intermediate firms choose prices – p+ ðaÞ and pf ;t ðaÞ – to h;t f ;t f ;t maximize profits, with the input price, Wt+ , taken as given. In the foreign economy, there are n+ f ;t intermediate firms, with average productivity a. Of these firms, nf,t also serve the export market, with average productivity af ;t . Potential intermediate firms enter the domestic market if they can cover a sunk cost, and produce with a one period lag, subject to being hit by an exit shock. This PN + t + + + + + + + implies, v+ t¼1 ð1  dÞ M0;tþ1 dtþ1 , vt  Fe Wt , and nf ;t ¼ ð1  dÞnf ;t1 þ ne;t1 , 0 ¼ E0 M0;1 dtþ1 þ E0 characterize the entry decision of intermediate firms in the foreign economy. Aggregating across home households, imposing St¼1 and Bt¼0, and using the government budget constraint, Tt¼Mt1Mt, equilibrium requires that a resource constraint is satisfied,

Wt Lt þ nh;t dt þ dt ¼ Pt Ct þ ne;t vt

(10)

with an analogous condition for the foreign economy. The right-hand side of (10) represents expenditure – on consumption and investment in new intermediate firms – and the left-hand side income – from labor and firm profits. In each economy, the labor market clears, with labor used for domestic production, export production, exporting costs, and domestic entry (firm creation). In the home economy, for example, Lt ¼ ðnh;t þ n+ Þl þ n+ F þ ne;t Fe . The free entry condition holds with h;t t h;t x equality. There are also two sector specific net export equations that capture world trade in goods, + + + + nxt ¼ n+ h;t et ph;t yh;t  nf ;t pf ;t yf ;t and nxt ¼ et ph;t yh;t  pf ;t yf ;t

(11)

Given demand functions (see again (2) and (4)), the first equation in (11) shows how trade in intermediate goods alters overall levels of trade. The second equation shows how exchange rate passthrough is linked with the extensive margin of exports. Note that absent trade in intermediates – when nxt ¼ 0 – the model reduces to one with entry over the business cycle, where input costs for firms producing consumer goods are determined by the wages of domestic intermediates. Finally, balanced trade imposes nxt þ nxt ¼ 0.

2.7. Solution for given monetary policy Table 1 presents the equilibrium condition for the home economy, where I define home money growth as mthMt/Mt1 and zthmt/Ct is a composite variable that determines the dynamics of monetary variables. The equation “Monetary dynamics” in Table 1 is a combination of the consumption Euler equation and money demand function using these definitions. With the inclusion of all foreign conditions, there are 51 equations that, given mt and m+ t , solve for consumption and labor supply, Ct, + + + + + + Ct+ , Lt, L+ t , sector-specific output, yh,t, yh;t , yf ;t , yf,t, yh;t , yh;t , yf ;t , yf ;t , the mass of firms, ne,t, ne;t , nh,t, nh;t , r

+r

r

+r

+r

r

r , average exporter productivity, a+ nf,t, n+ h;t and af ;t , sector-specific profits, dt , dt , dh;t , dh;t , df ;t , df ;t , dt , f ;t r d+r t (an ‘r’ denotes a variable scaled by the country-specific consumer price index), firm values, vt and + +r + + + + + ~h;t , vt , along with consumer, firm, and reset prices, Pt, ph,t, pf,t, Pt , ph;t , pf ;t , Pt , ph;t , pf ;t , Pt , ph;t , pf ;t , p + + ~+ ~+ ~ p h;t , pf ;t , pf ;t , real wages, wt and wt , the monetary variables, zt and zt , and the nominal exchange

rate, et.

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D. Cooke / Journal of International Money and Finance 41 (2014) 128–145

Table 1 Model equations (home economy). Description

Equation

Price indexes Sector (int. and cons.) Output

y Þu ðp n1y Þ1u and P ¼ p p1 Pt ¼ ðph;t n1 t f ;t f ;t h;t f ;t
h;t  1 Pi;t + Þ and y ¼g (P /P )1C for i¼h,f yi;t ¼ nuyi ðy þ y i,t i i,t t t h;t Pt h;t i;t  

w  + ¼ P t t ph;t ¼ Pt w and ep t + h;t qa

Pricing: int-firms (h and f-sales)

g

g

qah;t

Entrants and free entry Exporting firms and cut-off

nh;t ¼ ð1  dÞnh;t1 þ ne;t1 and vrt ¼ Fe wt

Average productivity

a+ h;t

Intermediate-firms profit – Pricing: cons-firms (h-sales) Pricing: cons-firms (f-sales)

+r

s1 k ¼ ða=a+  1Þwt F n+ h;t Þ nh;t and dh;t ¼ ða h;t

¼ a  a+ where a ¼ fk=½k  ðs  1Þg1=ðs1Þ h;t
+ n r r +r dt ¼ dh;t þ nh;t dh;t h;t
     r +r et P+ u t dh;t ¼ snuh;t PPtt yh;t þ y+ Þ ; dh;t h s1 þ yf ;t Þ  wt F y+ Pt h;t f ;t n+ h;t ~  PN t ph;t s s ¼ ap+1s þ ð1  aÞp ~ 1 E0 t¼0 a M0;t Pt  1q yh;t ¼ 0; p1 h;t h;t h;t1 e p~+  PN t t h;t s s ¼ ap+1s þ ð1  aÞp ~ +1 E0 t¼0 a M0;t P  1 y+ ¼ 0; p+1 h;t h;t h;t h;t1 t

Consumption-firm profits

q

 Pt Þy+ drt Pt ¼ ðph;t  Pt Þyh;t þ ðet p+ h;t h;t

Monetary dynamics Labor supply Shares Euler equation Resources

zt ¼ ðzt1  nÞ mbt w/C ¼ cLh h r t vrt ¼ bEt CCtþ1 dtþ1 þ ð1  dÞvrtþ1 

Trade account

p+ y+  nf ;t pf ;t yf ;t þ et p+ y+  pf ;t yf ;t 0 ¼ et n+ h;t h;t h;t h;t h;t

r

Ct ¼ dt nh;t þ drt þ wt Lt  vrt ne;t

3. Analytical results In this section I show how the extensive margin of exports depends on exchange rate pass-through and discuss how the extensive margin contributes to changes in trade volumes and prices. To generate analytical results I make the following simplifications (all of which are relaxed in the quantitative analysis). Firms producing consumer goods can reset their price each period and there is no variety effect in production, all intermediate firms are hit by a death shock immediately after they produce, and home and foreign outputs are used equally in production and consumption. I also focus on a permanent and unanticipated shock to the home money supply in period t¼0 – equivalent to a one period change in rate of money growth. I denote a variable linearized around its steady-state value with b and D M b hM b t ¼ 0 for t  1.11 a caret, which implies, D M 0 3.1. Reduced-form for the extensive margin of exports I start by deriving a reduced-form expression for the extensive margin of exports in the home economy. The export participation decision of an individual firm is driven by its productivity level, a, and only firms with productivity above the threshold, a+ , as determined in (5), enter the export h;0 market. Average productivity (across exporting firms) changes with the proportion of firms that decide to export, and since there is a time-to-build lag in production, the extensive margin and average b+ b+ productivity are linked by, n h;0 ¼ k a h;0 . Accounting for export demand in the productivity threshold,

bW b+ n h;0 ¼ C 0 þ





  b +  1 Tb W  w b+ b b0  P q0  P 0 0 0 2

(12)

11 Given the structure of the model, these assumptions imply that, in periods t1, all real variables reach their long-run levels, monetary shocks are neutral, and there are no nominal exchange rate dynamics (neither are there dynamics in zt and z+ t ). As a result, I focus on the impact effect of the shock. I discuss the details of this in the Appendix, including a characterization of the steady-state.

D. Cooke / Journal of International Money and Finance 41 (2014) 128–145

b + hP b+ T 0 f ;0

b+ P h;0

135

b+ P 0

b hP b P b where T  are international relative consumer prices, b q 0 hb e0 þ  0 f ;0 h;0 and b P 0 is the real exchange rate, and the super-script ‘W’ denotes a world variable such that, W + b x 0 hðb x0 þ b x 0 Þ=2, for any home variable, b x 0 . Based on this reduced-form, movements in the extensive margin can be decomposed into changes in, (i), global aggregate demand, (ii), international relative prices, and (iii), the costs of production, for firms in both sectors. All else equal, a rise in global demand, b W , expands the home extensive margin of exports. Favorable movements in the real exchange rate C 0 also expand the extensive margin, but only when prices are preset in local currency terms. When consumer prices are preset in the currency of the producer, the term in square brackets is zero. b + Þ, introduce a role for the terms-of-labor, defined as, b0  P Input costs, captured by ð w 0 R R + c hw b0  b b 0 hw b0  w b 0 is the relative real wage. When the home real wage rises, all else tol q 0 , where w 0 equal, the extensive margin contracts, consistent with higher export costs. Once the pricing equations b + , the extensive margin can also be written as a for foreign intermediate firms are used to eliminate P 0 12 function of the terms-of-labor. Thus, although higher home intermediate firm input costs reduce the home extensive margin of exports, higher foreign intermediate firm input costs expand the home extensive margin. In this setting, therefore, both international relative prices and the terms-of-labor play a role in determining the response of the extensive margin to shocks. Finally, since sunk costs are labor intensive, the terms-of-labor depend on the extent of firm creation across countries. Firms enter their domestic market until costs rise above the presented discounted value of total expected profits. When firms produce for one period, the average value of the firm is given by the future (i.e., t¼1) level of profits, which are consistent with flexible prices, discounted by the current real interest rate. Imposing free entry, firm value and future b C b þb bW  n b e;0 , respectively. These expressions generate the profits are, b v0 ¼ C d 1 and b d1 ¼ C 0 1 1 following relationship between the terms-of-labor, the relative mass of entrants, and real interest rates.

 c ¼  n b Re;0 þ br R0 þ b tol q0 0

(13)

b + in equation (12), a higher relative real wage led to a contraction in the Recall that by eliminating P 0 home extensive margin of exports. This is appealing because it reflects higher relative costs for home intermediate firms. However, using (13), the same negative relationship holds for new entrants, which implies a positive relationship between relative home firm creation and the home extensive margin. b f ;0 , are Since (13) holds for both economies, relative firm creation and the foreign extensive margin, n also negatively related. In this case, we conclude that relatively more new entrants at home (abroad) leads to an expansion in the home (foreign) extensive margin of exports. 3.2. Analysis of the extensive margin I now provide an explicit solution for the home and foreign extensive margin of exports. I start by imposing pricing restrictions. When firms engage in local currency pricing, consumer price indexes do not react to shocks, and there is zero exchange rate pass-through. When firms engage in producer currency pricing, own-country consumer prices do not react to shocks, there is full exchange rate passb b+ through, and the foreign local-currency price of traded goods is given by, P e 0 .13 I then f ;0 ¼  P h;0 ¼ b apply short-run money demand to solve for monetary shocks. With full pass-through, consumption is b + . Absent b + and raises C positively correlated across countries, since a nominal depreciation lowers P 0 0 + b exchange rate pass-through, consumption is uncorrelated across countries, and C 0 ¼ 0. Table 2 presents expressions for home and foreign extensive margins in the two cases in terms of b Re;0 . the exchange rate and relative domestic entry across the two economies, n +

12 b is the input cost for foreign firms producing consumer goods and is determined by the terms-of-labor and The variable P 0 the extensive margin of exports. Temporarily ignoring the feedback onto the extensive margin from a change in unit costs, it is possible to write the combined cost in terms of the relative real wage. 13 I consider polar cases for simplicity. A reduced-form way to index pass-through is to follow Betts and Devereux (2000) and parameterize the proportion of firms that set prices in local currency. This point is less important when I introduce staggered pricing and perform a quantitative analysis.

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Table 2 Extensive margin of exports. Pricing currency

b+ Home export margin – n h;0

Local

c bR b 2 ð n e;0 þ e 0 Þ

Producer

cbR

2 n e;0

b f ;0 Foreign export margin – n h

1 R i b b e;0 þ b c M  2n e0   R b  1n b c M 2 e;0

In Table 2, I define the parameter chk/[k  (1/2)], where k controls the dispersion of firm-level productivity. To determine the impact of shocks, it is necessary to account for economy-wide resources and the exchange rate, using (10), its foreign counterpart, and balanced trade. I show in the Appendix that, when there is incomplete exchange rate pass-through, a monetary expansion generates an equal response in domestic entry across the two economies. Using the conditions in Table 2, this b b+ bW implies an identical response of extensive margins, and n h;0 ¼ n 0 ¼ ðc=2Þ M > 0. With full passthrough, there is a drop in relative domestic entry across the two economies, the home extensive b+ bR margin contracts, with n h;0 ¼ ðc=2Þ n e;0 , and home and foreign extensive margins are negatively correlated. The general point is that a currency depreciation is only consistent with firm entry into the export market when exchange rate pass-through to consumer prices in incomplete. The reason for the contraction in the home extensive margin under high pass-through is that a home currency depreciation is consistent with increased (decreased) competitiveness of home (foreign) consumer goods. A relative increase in the production of home consumer goods requires more home and foreign intermediate inputs, and whilst home firms have access to all home inputs, they only access a subset of foreign inputs. The result is a rise in the number of foreign firms entering the home economy. The number of home exporters falls for a similar reason – there is less demand from foreign firms. Notice that this point does not account for the deterioration in the terms-of-labor, which has a further negative effect on the export participation of home intermediate firms. There is also an important quantitative implication for the response of extensive margins as passthrough varies. When pass-through is incomplete, the response of the extensive margin only depends on the parameter k. As k rises, productivity is less dispersed, and pre-shock, there are more firms in the export market. With more firms exporting, there is less profit available for new exporters, and so the impact of the shock on the extensive margin is reduced. When pass-through is high, this result still holds, but the response of the margin also falls with s>1. In this class of model, the standard deviation of output is given by [k(s1)]1, so that a higher k means less dispersion in productivity (and therefore output). A higher value of s means the same dispersion in productivity, but less dispersion in output. 3.3. Export volumes and prices I now consider export volumes and prices. In a low pass-through environment, a home monetary expansion leads to a rise in overall home consumption, but no change in foreign consumption. Home +1=2 + exports of consumer goods, y+ ¼ ð1=2ÞTt Ct , are unchanged, and higher export earnings (et p+ rises) h;t h;t pay for an increase in home imports of foreign consumer goods. In a high pass-through environment, both Ct+ and Tt+ rise, providing a boost to home exports. Imports fall because they become more expensive (et p+ is now fixed and pf,t rises). In general, even if one observes a similar trade adjustment in each case, h;t the mechanism is different, with more adjustment via real trade flows as pass-through rises. Trade adjustment in consumer goods is key to understanding the response of the intermediate sector to shocks. Recall that the net export condition for intermediates is given by, nxt ¼ n+ e p+ y+  nf ;t pf ;t yf ;t . Applying firm demands using equation (4), the home intermediate h;t t h;t h;t export volume can be written as, xt hn+ y+ ¼ ð1=2Þðp+ =p+ Þ1=2 ðy+ þ yf ;t Þ, where I have already h;t h;t f ;t h;t f ;t solved for n+ . Using consumer demands, I re-write the export volume for period t¼0 as, h;t

b x0 ¼




b W  1 Tb W C 0 2 0

 


 1 c 1 + b h;0 tol 0 þ n k 2

(14)

where the first term reflects consumer demand, and the second is the terms-of-labor, adjusted for changes in the average productivity of exporters, expressed as a function of the export margin.

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Solving for the volume in terms of the shock, in a low pass-through environment, equation (14) b whereas in a high pass-through environment, b b Re;0 < 0, implies, b x 0 ¼ ½1  ðc=2Þ M, x 0 ¼ ½1  ðc=2Þ n so that extensive margins and volumes move together. The most direct interpretation of the volume response is through the demand for intermediate inputs. With high pass-through, there is a switch toward home consumer goods, home firms import more foreign inputs, and the use of home inputs by foreign firms drops (foreign firms are not competitive in the consumer market and use less intermediates, in general). With low pass-through, foreign firms need more inputs to produce goods for home consumers. Home firms also use more foreign intermediate inputs since overall domestic consumption has risen. This is the same explanation for why home and foreign export margins are positively correlated with low exchange rate pass-through. To gauge the role of the extensive margin in the volume adjustment, note that when all firms export, the qualitative response of the export volume is unchanged. However, the scale of adjustment is smaller (larger) with low (high) pass-through. Put differently, with an extensive margin, the volume of intermediate exports rises by less and falls by more across price setting regimes.14 This result is surprising, because by ignoring the extensive margin, movements in the export volume should be smaller. However, this does not account for the fact that weaker firms sell less, on average, and their entry into the export market affects the market share of more productive firms. With a low elasticity, weaker firms gain a relatively large market share, which explains why an expansion in the extensive margin leads to a muted change in the export volume. The mechanism described above can also be seen in the response of the local currency export price – + b Þ þ ½2ðc  1Þ=c n b þP b + – across price setting regimes. A simple way to see given by b e þb p ¼ ðw 0

h;0

0

0

h;0

+

+

b+ bR how export prices change is to instead use the relative price, b p h;0  b p f ;0 ¼ ½2ðc  1Þ=c n h;0  n e;0 , combined with the results above. Overall, with low pass-through, even though weaker firms enter the export market and push the average price up, the export price rises by less than when pass-through is high. Taken together, the fact that firms enter the export market in response to favorable exchange rate movements (with low pass-through) has important consequences. Volumes rise, but are relatively less sensitive to changes in the exchange rate, and prices rise, but by less than when pass-through is high. Lewis (2012) has recently discussed trade volume and price responses to exogenous changes in the exchange rate using models that feature competing short-run pricing frictions – a Calvo assumption versus a menu cost specification/selection effect – and argued that despite the introduction of these frictions the overall trade response is too strong compared to the data (neither can these models account for asymmetries between export and import responses). He concludes that other frictions are needed to bring models closer to the data. In light of the firm-level evidence in Berman et al. (2012), and given the simple results of this section, one possibility to overcome such issues could be to allow selection into exporting alongside endogenous markups similar to the DSGE model of Gust et al. (2009).15 4. Quantitative example In this Section I analyze a quantitative version of the model. I relax all of the restrictions made in Section 3 and calculate impulse response functions for an exogenous home monetary shock.16 4.1. Dynamics in the extensive margin of exports I assume the change in money growth follows a first-order autoregressive process,

b t ¼ rD M b DM t1 þ εt , where 0r<1. Dynamics in the extensive margin of exports are generated

14 I calculate volumes and prices without an extensive margin by dropping the cut-off equation, where Fx¼0. Analogous b and b b Re;0 , where n b Re;0 < 0 is smaller in absolute value in the latter expressions to those in the text are, b x 0 ¼ ð1=2Þ M x 0 ¼ ð1=2Þ n case than with a margin. I make the same steps in the quantitative analysis of Section 4 where I also determine foreign export volumes and prices. 15 Berman et al. (2012) do discuss a model with endogenous markups in an Appendix to their paper. The development of a fully-specified sticky-price DSGE model with extensive margins and endogenous markups (tailored to address volume and price responses to exchange rate movements) is beyond the scope of this paper. 16 The Appendix contains details of the systems I use to solve the model in the cases I consider below.

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through two main channels: domestic firm creation and price setting. Consider the following expression for the home extensive margin,

b+ n h;t ¼

   

1 bW 1 ct b R  1 u n þð1 yÞn+ 2gð1 gÞ Tb W  u tol Ct þ g C h;t t t f ;t k x 2

(15)

where xh1(1y)[(1u) þ 1/k] and u or g¼1 indicate the intermediate or consumer sector is closed to trade. In general, the response of the extensive margin to shocks depends on world aggregate demand, as above, but also relative demand, when gs1=2. The extensive margin also depends on the creation of new firms, where,

b h;t1 þ d n b h;t ¼ ð1  dÞ n b e;t1 n

(16)

This condition replaces the standard law of motion for capital (investment at the intensive margin) for home firms. The creation of new foreign firms affects the home extensive margin of exports to the extent that there is a variety effect in production, and ys1. Finally, there are movements in relative c t . The extent to b W , and for intermediate firms, through tol prices, both at the consumer level, through T t which relative prices affect the extensive margin depends on the openness of the respective sector. When firms engage in producer currency pricing, two dynamic price equations determine the extent of global price dynamics at the consumer level,





+  b b+ b+ b+ bt  P b D Pb h;t ¼ bEt D Pb h;t1 þ 9 P h;t and D P f ;t ¼ bEt D P f ;tþ1 þ 9 P t  P f ;t

(17)

where 9hð1  aÞð1  abÞ=ab and D denotes the first difference of a variable. The consumer price inb t ¼ gP b+ þ b b þ ð1  gÞð P dexes in the home and foreign economy are, P e t Þ and h;t f ;t + + b b b e t Þ þ g P f ;t , where b e t is the nominal exchange rate. When firms engage in local P t ¼ ð1  gÞð P h;t  b currency pricing, the law of one price fails to hold, and I map price dynamics into four composite b i and D T b i , for i¼h,f, whose driving variables are as in (17).17 variables, D P t t I also depart from the balanced trade assumption made in Section 3 and allow a standard asymmetry in the financial market structure. I follow Benigno and Thoenissen (2008) and suppose home agents have access to foreign currency bonds but face a transaction cost that is increasing in the home economy’s net foreign asset position. Foreign agents receive profits from foreign-owned intermediaries who apply a spread over the risk-free rate of interest when lending to home agents in foreign currency. This assumption leads to a standard arbitrage condition in financial markets, adjusted for the trans+ action cost. In linear terms, Et Db b t , where Et Db e tþ1 ¼ bi t  bi t þ 4b b e tþ1 is the expected change in the exchange rate, and 4b>0 captures the spread of the domestic interest rate on foreign assets over the foreign rate.18 4.2. Calibration Although the model features firm creation and endogenous export participation, it is consistent with a large class of open economy models that feature a fixed number of traded varieties and physical capital, such as Kollmann (2001) and Chari et al. (2002). This allows for a standard calibration of parameter values. Table 3 presents the parameter values used in the quantitative analysis. I interpret a time period in the model as a quarter and set b¼0.99. This implies an annualized interest rate of 4 percent. Following Rotemberg and Woodford (1997), I assume the (inverse) Frisch elasticity of labor supply is h ¼ 0:47. The parameters for production are calibrated as follows. I match the exit shock with a 10 percent rate of job destruction per year, which implies d¼0.025, and as in Ghironi and Melitz (2005), I assume a price markup of 35 percent, which implies q¼3.8. I then match the standard deviation of log US plant

17 b bW bR bW bR Any price can be converted into these composite variables. For example, P h;t ¼ P t þ ð1=2Þ P t  ð1  gÞ½ T t þ ð1=2Þ T t , b t  ð1  gÞ T bt . which is also equal to P 18 The transaction cost also renders the model stationary. See Schmitt-Grohe and Uribe (2003) for a general discussion.

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Table 3 Parameters value for quantitative analysis. Parameter

Description

Value

b h d q y k a g

Subjective discount factor Inverse Frisch elasticity of labor supply Firm exit shock Elasticity of substitution between goods Variety effect Productivity dispersion Duration of price contracts Import penetration Bond transaction cost Autoregressive parameter for money growth

0.99 0.47 0.025 3.8 1.36 3.4 0.67 0.8 0.003 0.68

4b

r

sales of 1.67 by setting the parameter that determines the curvature of the Pareto distribution for firmlevel productivity at k¼3.4. I assume market power and the variety effect coincide in the production of consumer goods, which implies y¼1.36, and that the average length of a price contract is 3 quarters, which implies a¼0.67. Finally, I set g¼u¼0.8, which implies an equal rate of import penetration across sectors. The two remaining parameters relate to the specification of incomplete international financial markets and the shock process. I assume a 30 basis point spread on domestic holdings of net foreign assets, which implies setting 4b¼0.003. I follow Chari et al. (2002) in setting r¼0.68 for the persistence of money growth. As I consider a one-off shock to money growth, εt¼0 for t1, where ε0¼(1r)/ (1r4)¼0.41, such that the home money stock rises by 1 percent four quarters after the shock. 4.3. Results Fig. 1 plots the response of home and foreign variables to a monetary shock under the assumption of producer currency pricing (full exchange rate pass-through). The solid lines in Fig. 1 track the change in the money supply. Lines with >/q represent the home/ foreign economy response of endogenous variables. In general, the impulse responses confirm the analytical results. A favorable movement in the real exchange rate is consistent with a contraction in the home extensive margin of exports and intermediate export volume, and a rise in the intermediate export price, defined as p+ =p+ , following Section 3.19 From a quantitative perspective, there is a 0.3 h f percent fall (1 percent rise) in the home (foreign) extensive margin on impact, given a 1 percent rise in the home money supply after four quarters. The impulse responses also show that, whilst traded variety rises at a global level, the indirect effect of a home monetary stimulus on foreign exported varieties is larger than the direct negative impact on home firms. This is a result of changes in the termsof-labor in a high pass-through environment. Although I focus on exports, new domestic entrants in each economy also embody investment by households and the total stock of firms represents accumulated capital. In IRBC and sticky-price models, it is more common to consider international co-movement rather than country-level responses. In this model, there are strong positive spillovers onto the foreign economy, with positive international co-movement at the extensive margin of investment – measured as the real value of household investment in new firms. Investment is also pro-cyclical. This is broadly similar to results produced by sticky-price models of the business cycle for investment at the intensive margin. Consumption and the real interest rate also respond as they would do in a standard sticky-price model. Consumption rises in both the home and foreign economy and the real interest rate falls. Once local currency pricing is assumed, the international relative price and real interest rate channels of macroeconomic interdependence are weakened (Kollmann, 2001). This leads to a muted

19 I have not plotted the response of consumer prices, but the reaction of home and foreign prices is standard (as are consumer export volumes). Consumer prices rise by less in the foreign economy than in the home economy which gives rise to expenditure switching.

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Consumption

Investment

0.8

Real Interest Rate

0.8 Home Variable Foreign Variable

0.6

0.6

0.6

0.4

0.4

0.2

0.2

0

0

0.4 0.2

−0.2

0

5

10

15

20

−0.2

0

0

Extensive Margin of Exports

5

10

15

20

−0.2

0

Intermediate Export Volume

1

1

0.5

0.5

5

10

15

20

Intermediate Export Price 0.6 0.4 0.2

0

0 0

−0.5

0

5

10

15

20

−0.5

0

Real Wage

5

10

15

20

−0.2

0

Consumer Export Volume

0.8 0.6

5

10

15

20

Exchange Rate and Net Assets

1.5

0.6

1

0.4

0.5

0.2

0

0

Exchange Rate NFAs

0.4 0.2 0 −0.2

0

5

10

15

20

−0.5

0

5

10

15

20

−0.2

0

5

10

15

20

Fig. 1. Impulse responses with producer currency pricing.

response of foreign macro-variables to home monetary shocks and quantitatively small international spillovers. In the analytical version of the model the producer/local currency pricing distinction was also important for the extensive margin of exports. Fig. 2 plots the response of home and foreign variables to a home monetary shock under local currency pricing (incomplete exchange rate passthrough). It is immediate from the impulse responses that international spillovers from home monetary shocks onto foreign consumption and investment (at the extensive margin) are relatively weak. However, this is not the case for the extensive margin of exports and intermediate trade volume. Both home and foreign extensive margins expand as a result of the shock, with an impact effect on the home extensive margin of around 0.2 percent. The differential response of margins is a result of home-bias at b R > 0, the monetary shock the consumer level. Consider equation (15) with g>1/2, and note that since C t causes a contraction in the extensive margin, all else equal. However, under local currency pricing, changes in exports are driven by global movements in demand, with only a limited change in the terms-of-labor to drive differences in the home and foreign extensive margin of exports, relative to producer currency pricing. To see this point, note that irrespective of pass-through, the home real wage rises in response to the home monetary shock – although with local currency pricing the foreign real wage is less sensitive to the shock. Recall also that the relative real wage can be expressed as the sum of the terms-of-labor and c þb b R0 ¼ tol real exchange rate, w q 0 , and that the real exchange rate is more sensitive to monetary 0

D. Cooke / Journal of International Money and Finance 41 (2014) 128–145

Consumption

Investment

0.8

Real Interest Rate

0.8

0.6

0.6

0.4

0.4

0.4

0.2

0.2

0.2

0

0

0

−0.2

Home Variable Foreign Variable

0.6

−0.2

0

5

10

15

20

−0.2

0

Extensive Margin of Exports

5

10

15

20

−0.4

0.6

0.4

0.4

0.4

0.2

0.2

0.2

0

0

0

5

10

15

20

−0.2

0

Real Wage

5

10

15

20

−0.2

Consumer Export Volume

1

5

0

5

20

10

15

20

1 Exchange Rate NFAs

0.6 0.5

0.4 0.2

0

15

Exchange Rate and Net Assets

0.8

0.5

10

Intermediate Export Price

0.6

0

0

Intermediate Export Volume

0.6

−0.2

141

0

0 −0.5

0

5

10

15

20

−0.2

0

5

10

15

20

−0.5

0

5

10

15

20

Fig. 2. Impulse responses with local currency pricing.

shocks under local currency pricing. Therefore, under producer (local) currency pricing, the terms-oflabor exerts a strong (weak) effect on intermediate firms. This generates negative (under producer currency pricing) or positive (under local currency pricing) co-movement in the extensive margin of exports. The global impact on traded variety is similar across the two price-setting regimes. Thus, when the home extensive margin of exports expands with a home currency depreciation, the rise in foreign imported varieties into the home economy falls in magnitude, consistent with a traditional expenditure switching effect. I now consider the role of the extensive margin in driving the response of the export volume by calculating the response of volumes without a margin.20 In a low pass-through environment, the inclusion of an extensive margin works to reduce the total effect of the shock on the export volume, after four quarters, from 0.40 to 0.26 percent. Recall, the home export volume is given by, +1y ðP+ =P+ Þ1 ðy+ þ y Þ, where changes in the term y+ þ y depend on consumption x+ f ;t f ;t t t ¼ ð1  uÞnh;t h;t f ;t f ;t patterns, y controls the variety effect in production, and u controls openness to trade in intermediate u + inputs. Note also that the firm price ratio can be expressed as, ½ðqt w+ t =wt Þðah;t =af ;t Þ , so that, in general,

20

Again, as with the analytical results, the export price rises, but by less than when exchange rate pass-through is high.

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there are offsetting effects. The productivity term exerts a negative effect, which rises in magnitude with u. In contrast, the variety effect can be positive or negative. In the calibration, productivity and variety work in the same direction, and this explains why the volume adjustment is muted. The results for the extensive margin of exports and export volume highlight an important channel at work. Pass-through to consumer prices is a key determinant in generating expenditure switching in macro models of the open economy. Export volumes can exhibit large or near zero movements, given changes in the exchange rate. In a similar way, in this model, extensive margins and volumes can behave quite differently depending on the extent of pass-through. At low pass-through – the empirically more plausible case – margins and volumes in the home economy expand in response to a home currency depreciation. As pass-through rises, there are stronger effects in the consumer sector but smaller (and possibly negative) effects in the intermediate sector.

5. Conclusion This paper develops a two-country Dynamic General Equilibrium model to understand changes in the extensive margin of exports over the business cycle – which is subject to an ongoing empirical debate. Exchange rate pass-through to consumer prices is shown to play a key role in determining a trade-off (between the demand for a product and the costs of production) for firms when deciding to export. With incomplete pass-though, a favorable movement in the exchange rate generates firm entry and an expansion in the extensive margin of exports, as firm-level studies suggest. A second finding is that the extensive margin also plays a role in muting the overall trade response to changes in the exchange rate.

Appendix A1. Steady-State Solution Consider the equations in Table 1 and drop time subscripts. The trade account reads, en+ p+ y+ þ nf pf yf ¼ ep+ y+  pf yf . Converting intermediate trade into consumption using demand h h h h h schedules, and noting ph ¼ ep+ and pf ¼ ep+ holds in the consumer sector, and that the pricing h f equations reduce to, ph¼P/q, ep+ ¼ P, ð1=eÞpf ¼ P+ =q, and p+ ¼ P+ =q, h f

 0 ¼ ½ð1  2gÞð1  uÞq  ð1  gÞ PC  eP + C +

(18)

where u¼uh, so that the consumer-based real exchange rate, qheP + =P, is equal to relative consumption, q ¼ C=C + . Consumer firm profits, pricing equations, and demands, can be written as,  PÞy+ , where ph¼Ph and p+ ¼ Ph+ . Given (18), profits can be re-written as, dr P ¼ ðph  PÞyh þ ðep+ h h h

dr ¼ ð1  qÞ½gC þ ð1  gÞqC +  ¼ ð1  qÞC. In a similar way, total intermediate firm profits are, +

+r

r

d ¼ dh þ ðn+ =nh Þdh , where dh ¼ qð1  qÞðu=nh ÞC and dh h recall

that

the

export

cut-off

is, r r dh =d

+r dh

¼ qð1  qÞ½ð1  uÞ=n+ C  wFx . Finally, h

¼ ðas1  1ÞwFx ,

which

implies,

nh d ¼ qð1  qÞfu þ ½ðs  1Þ=kð1  uÞgC and ¼ u=fu þ ½ðs  1Þ=kð1  uÞg. This term is equal across countries and measures the relative weight of profit in domestic and export markets. Using the steady-state shares Euler equation and law of motion for intermediate firms, v ¼ fb=½1  r r bð1  dÞgd and nh¼(1/d)ne, we arrive at, nh d =ne vr ¼ 1  bð1  dÞ=bd, which is a standard condition for models with firm entry. I denote Yh1=f1 þ ½ðs  1Þ=kg and use the aggregate accounting r constraint, C ¼ d nh þ dr þ wL  vr ne , to generate the following steady-state ratio, r dr =vr ne ¼ ðnh d =ne vr Þ=qf½ð1  uÞ=Y  1 þ 2ug, and expression for labor supply,

1=ð1  qÞ 1  bð1  dÞ 1 bd ½ð1  uÞ=Y  ð1  2uÞ



cL1þh ¼ 1 þ

(19)

where I have used, w=C ¼ cLh . Since balanced trade implies qC+¼C, and from (19) we know L¼L+, we must necessarily have, qw+¼w. Note that the ratio of marginal costs affects international trade in

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143

intermediate inputs. This ratio can be related to q using consumer based price indexes as, q ¼ ðeP+ =PÞ2g1 ; and is determined by,

 1u  u y =a+ y n+1 = n1 h h h eP+ =P ¼  1u  u y y =a n1 = n+1 f f f

(20)

1=k + 1=k and a + where a+ . Without impediments to trade we have eP+¼ P f ;t ¼ aðnf ;t =nf ;t Þ h;t ¼ aðnh;t =nh;t Þ and q¼1. Finally, to solve for export participation, note that the export cut-off and the ratio of domestic r to export profits imply, dh ¼ ðn+ =nh Þ½u=ð1  uÞfk=½k  ðs  1ÞgwFx . In combination with the shares h r Euler and free entry equations, Fe w ¼ fb=½1  bð1  dÞgd , I find,

nh ¼ n+ h



b=½1  bð1  dÞ




1 1u

Fe =Fx







k 1 k  ðs  1Þ

(21)

for k>(s1). I can then use Fe/F to match an export participation rate. When all firms export, I drop the cut-off condition, and find the following expression for the mass of firms, nh ¼ bqð1  qÞ=Fe ½1  bð1  dÞcLh , where labor supply is defined by (19). A2. Analytical Results I make the following restrictions. Labor is supplied inelastically, home and foreign outputs are used equally in production and consumption, all intermediate firms are hit by a death shock after they produce, there is no variety effect in the production of consumer goods, and all firms can reset their price each period. I consider a permanent and unanticipated shock to the home money supply in period t¼0 and solve the model using a linear approximation of the conditions in Table 1. A caret denotes the deviation of a variable from its steady-state value. The strategy I use to solve the model is to show how monetary shocks affect domestic entry in each economy using the respective resource constraints. In periods t>0, prices are set consistent with their flexible price levels, and the law of one price holds. In the home economy, firm profits in each sector are, r r W + R + b b W and b b W (for a variable b b d þn ¼ C d ¼ C x I use b x hðb x þb x Þ=2 and b x hb x b x ). Using free entry t

h;t

t

t

t

t

t

t

t

t

t

t

b e;t ¼ 0, so there is no addition entry induced by b h;tþ1 ¼ n and the shares Euler equation, this implies, n b R ¼ 0. the monetary shock after period t¼0. Also note that C t In period t¼0, using free entry, the home shares Euler equation can be written as, r b þ ðC bW  C b Þn b n b b h;1 ¼ C b e;0 ¼ w b 0 . As a result, period t¼0 relative resources and profit v0 ¼ C 0 1 0 1 equations are,

b Re;0 ¼ n 

r R

b d0



wL v r ne

1 


r

d nh vr ne



r b d0

R

þ



dr vr ne



r R b d0 




r

d nh vr ne

 r

þ vdr n

e

bR C 0



W  bR bR  P ¼ 2ð1  YÞ b q 0 þ ð2Y  1Þ Tb 0 þ P 0 0

(22)



b r R  b R  Tb W d0 ¼ b q 0 þ ðs  1Þ b e0  P 0 0 b Re;0 h n b e;0  n b+ where Y>1/2 is defined above and n e;0 is relative firm entry into respective domestic markets. Using the cut-off threshold for profits, eliminating wages and intermediate price indexes/ marginal costs for firms producing consumer goods, the extensive margin of exports in each country b Re;0 in the following way, can be written as a function of n

   



R  R  b+ þ 1 b b 1 b bW þ n bW þ n b b b+ b c c C C ¼  T ¼  T n and n q q 0 f ;0 0 0 0 h;0 e;0 e;0 2 0 2 0

(23)

144

D. Cooke / Journal of International Money and Finance 41 (2014) 128–145

b ¼ P b P b b+ b+ b + 21 When firms use local currency pricing, where chk/[k(1/2)], T 0 f ;0 h;0 and T 0 h P f ;0  P h;0 . b W ¼ 0. Using the conditions in (22), and accounting for relative intermediate marginal b q0 ¼ b e 0 and T 0 R

+

b ¼ 0, it is immediate that the response of b , we have, n b e;0 ¼ 0. Since money demand implies C costs, P 0 0 R

b bW b+ margins to shocks is identical across countries, where n h;0 ¼ n 0 ¼ ðc=2Þ M. When firms use producer b b + ¼ b e 0 and P e 0 . In this case, b q 0 ¼ 0 and currency pricing the law of one price implies, P f ;0 ¼ b h;0 bW ¼ b e 0 . Applying these conditions to (22) we find, T 0

1  ð2Ys þ b  1Þð2k  1Þ b b Re;0 ¼ 2k 1 þ n M 2Yð1  sÞ  1

In this case, relative domestic entry falls in response to a home monetary shock. Applying the pricing restrictions to (23) there is now a differential response of extensive margins to shocks, where b  ð1=2Þ n b R and n b b R . b + ¼ ðc=2Þ n ¼ c½ M n h;0

e;0

f ;0

e;0

A3. Solution for Quantitative Example b b+ When consumer firms use producer currency pricing and the law of one price holds ( P et h;t ¼ +P h;t þ b + b ¼ P b þb b b and P e t ), price dynamics are determined by Phillips curves in P f ;t h;t and P f ;t alone. f ;t The remaining conditions are transformed into a system of world and relative equations. This system of 2 þ 16þ1 equations can be written as, Z t ¼ AZ t1 þ BZ tþ1 þ Fut , where h i j bj P b b+ w b t , for j¼R,W and ut is the exogenous Z ¼ C bj b b jt n b jt b b +j b jt P bt DM m et b dt n P h;t t f ;t t t monetary shock. When firms use local currency pricing the law of one price no longer holds and price b i . In this case, I have a system of b i and T dynamics are mapped explicitly into four composite variables, P t t h i j j j j +j j b 4 þ 17þ1 equations, where Z t ¼ C bj P bj w b b t and b j br t b b b b b bt DM qt b nt dt nt mt T t P t t t t +

b P b t . In both cases, I solve for country-level variables by applying the definitions for b br t hb et þ P x t and t R

W b x t , where appropriate.

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21

The reduced-form expressions presented in the text can also be used to generate the conditions in (23).

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