Market entry and international propagation of business cycles

Journal of International Economics 56 (2002) 155–175 www.elsevier.com / locate / econbase

Market entry and international propagation of business cycles David Cook* Hong Kong University of Science & Technology, Department of Economics, Clear Water Bay, Kowloon, Hong Kong Received 5 January 1999; received in revised form 20 March 2000; accepted 27 June 2000

Abstract In this paper, pro-cyclical market entry acts as an international transmission mechanism for business cycle shocks. In an imperfectly competitive dynamic equilibrium model, an expansion in one open economy leads to additional business formation in a parallel large open economy through demand spillovers. Business formation causes a decline in markups leading to an expansion in employment, production, and investment in both economies. The modeling of the entry decision is critical. Only when the entry game is modelled as sequential (with incumbents enjoying a first mover advantage) are markups sufficiently elastic to cause international comovement.  2002 Elsevier Science B.V. All rights reserved. Keywords: Counter-cyclical markups; International comovement JEL classification: F4 Macroeconomic Aspects of International Trade and Finance

1. Introduction In the post-Bretton Woods era, OECD countries have displayed cyclical comovement in output and employment. In open economy dynamic general equilibrium models (see Backus et al., 1995), cyclical comovement across countries is weak or negative. When technology shocks cause productivity levels *Corresponding author. Tel.: 1852-2358-7614; fax: 1852-2358-2084. E-mail address: [email protected] (D. Cook). 0022-1996 / 02 / $ – see front matter  2002 Elsevier Science B.V. All rights reserved. PII: S0022-1996( 01 )00112-X

156

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to persistently differ across countries, capital investment flows to the high productivity country; output and employment drop in the low productivity country as the capital stock diminishes due to low investment levels. Baxter (1995) refers to this discrepancy between models and data as the ‘comovement problem’. In this paper, I examine pro-cyclical entry into imperfectly competitive markets as an international business cycle transmission mechanism. Entry makes markets more competitive; markups over marginal cost drop when new firms enter a market. Markups act as distorting taxes which reduce demand for factors of production. If a business cycle expansion in one country leads to additional entry and a drop in markups in a trading partner’s goods markets, capital and employment demand can expand in the latter country. Pro-cyclical market entry leads to counter-cyclical markup offering an additional channel for international comovement. I study equilibrium business cycle comovement in two open economies with final goods markets characterized by Cournot competition with free entry. I model two types of market entry. In the first, following Chatterjee et al. (1993) and Portier (1995), firms enter markets simultaneously. All markets are assumed to have the same number of competitors such that firms make zero profits after fixed costs. As demand for goods increases during a business cycle expansion, more firms are able to sell a quantity of goods sufficient to cover fixed costs. As new firms enter markets, Cournot competition intensifies and markups fall. As each new marginal firm enters a market, the sales of each firm in the market falls. The falling size of sales per firm makes it more difficult for subsequent entrants to sell enough to cover fixed costs. In the second, entry is sequential (see Eaton and Ware, 1987). Goods markets are dominated by incumbents committed to market entry. Entry is restricted only in that marginal entrants take the incumbents’ entry as given. The share of markets in which marginal participants enter is determined such that marginal participants make zero profits. A business cycle expansion leads firms to enter previously less competitive markets and average markups fall. The entry of a marginal firm into a previously less competitive market does not reduce the size of potential sales for subsequent entrants into less competitive markets. This property implies that entry and markups respond more elastically to changes in aggregate demand in the sequential entry equilibrium than in the simultaneous entry equilibrium. The modelling difference is crucial. The simultaneous equilibrium model solves the comovement problem only when steady state markups are implausibly high. Using a conservative parameterization of steady state markups, the markup is sufficiently elastic in the sequential entry model to solve the comovement problem under two important conditions. First, international financial markets are limited to risk-free debt, and second, capital utilization is time varying. Modelling international financial markets as limited to risk free debt (as in Baxter and Crucini, 1995, and Kollmann, 1996) is especially important for matching the cross-country comovements of both employment and consumption. When international financial markets are extended to include a complete set of contingent claims, a productivity

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expansion in one country leads to an increase in income in a partner country through risk sharing. The negative impact of that income on labor supply exacerbates the decline in employment and output in the low productivity country. Moreover, limited capital markets are required to explain the near zero crosscountry correlation of consumption, which should be near 1 under complete risk-sharing. Modelling endogenous capital utilization (as in Greenwood et al., 1988, and Burnside and Eichenbaum, 1996) is especially important for matching the (mildly positive) comovement of investment. When firms are able to vary their rate of capital utilization in the sequential equilibrium model, utilization displays positive cross-country correlation. This comovement leads to comovement in the marginal product of capital increasing comovement in capital formation. In a model with perfect competition, limited financial markets and endogenous capital utilization (together or separately) are unable to explain many aspects of international comovement. However, they are important parts of an imperfect competition model with counter-cyclical markups which can explain many of these aspects. Time varying capital utilization also explains the cross country comovement of measured Solow residuals. Backus et al. (1992) and Zimmerman (1997) display evidence that Solow residuals are positively correlated across countries at business cycle frequencies. Rather than treating this as part of the comovement problem, many papers treat this as part of the solution. Following Backus et al. (1992), international RBC models typically assume technology spillovers are an exogenous source of cyclical comovement 1 . There is reason, however, to be skeptical about technology comovement as a source of business cycle comovement. Costello (1993), after controlling for variation in capital utilization, finds at most weak evidence for international correlation in Solow residuals. There is strong evidence that capital utilization moves pro-cyclically (see Burnside et al., 1995, or Shapiro, 1996). If capital utilization, like output, is correlated across countries, failing to account for this correlation will exaggerate the cross-country correlation of technology movements. In a model with counter-cyclical markups, endogenous capital utilization matches cross country co-movement of the measured Solow residual even with zero exogenous correlation in technology. This paper follows a literature in which imperfect competition acts as a business cycle propagation mechanism. Dynamic equilibrium business formation is a propagation mechanism in the Cournot models of Gali (1995) and Portier (1995) and the love of variety models of Devereux et al. (1996) and Chatterjee and Cooper (1993). Counter-cyclical markups are a propagation mechanism in the cartel models of Rotemberg and Woodford (1991, 1992, 1995). The first paper to examine whether counter-cyclical markups could explain international propagation in a real model was Schmitt-Grohe (1998). In a small open economy model, 1

Boileau (1998) and Beaudry and Devereux (1995) examine endogenous technology transfers through production externalities.

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Schmitt-Grohe (1998) finds that counter-cyclical markups due to equilibrium cartel competition can help explain some, but not all of the transmission of US interest rate and trade shocks to the Canadian economy. This paper differs from SchmittGrohe in that it directly studies technology shocks in a general equilibrium large open economy framework. In a two country model, Ubide (1999) finds that exogenous markup shocks (when correlated across countries) can explain cross country co-movements. This paper offers a theory as to why there might be correlated endogenous movements in business cycles. Head (1997) finds that when love of variety is sufficiently strong, pro-cyclical introduction of new products can lead to cross-country co-movement. Chang and Devereux (1998) find that the inclusion of cartel competition with pricing to market can increase cross-country comovement between output but do not concentrate on their model’s ability to solve the comovement problem. Devereux and Lee (1999) study the effects of trade liberalization in a model in which an increase in cross-country trade reduces markups through additional entry. Several recent papers study aspects of the comovement problem in models with perfectly competitive markets. Ambler et al. (1998) examine the effects of production linkages on international comovement. Canova and Ubide (1998) find that shocks to non-market production contribute to the comovement of market production and employment. Kehoe and Perri (1998) show that endogenously incomplete international capital markets can lead to comovement in investment. Boileau (1999) examines idiosyncratic investment specific technological shocks.

2. The Model Two large, symmetric economies, l 5 USA and EU, trade goods and a risk-free bond.

2.1. Households The household is endowed with initial capital, K l0 , and time, T. The household maximizes utility with respect to consumption, C tl , and leisure, time less labor, H tl :

O b [ln C 1 G lnsT 2 H d] `

t

max Eo

l t

l t

(1)

t 50

l

The household accumulates capital through investment, I t , subject to costs of capital utilization, U tl , and adjustment:

S D l

It l l l K t 11 5s1 2 dtdK t 1 I t 1 d2 ]l 2 D Kt

2 l

Kt

dt 5 d1 (U lt )k

(2)

Labor and capital are rented to domestic firms. Households receive domestic

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159

profits, P lt and pay lump sum taxes, G lt for government consumption. The budget constraint is: B lt 11 1 C lt 1 I lt 1 G lt 5 w lt H lt 1 R ltU lt K lt 1 P lt 1 (1 1 r Bt ) ? B tl l

l

(3)

l

where w t is the wage rate, R t is the capital rental price, B t are risk-free bonds and 1 1 r tB is the risk free rate. Define q tl as the ratio of the shadow values of installed capital and uninstalled capital. An interior solution satisfies the boundary condition lim b t (1 /C lt )Bt 11 5 0 t →` and:

F

S S DD dG s d

I lt l 1 5 q t 1 2 d2 ]l 2 D Kt

1 G ]l ? w lt 5 ]]l Ct T 2 Ht l

Ct B 1 5 Et b ? ]] ?s1 1 r t 11 C lt 11

l

l

(4)

l k 21

l

R t K t 5 q td1 k U t

F H S

K lt

(5)

C tl l q t 5 Et b ? ]] C lt 11 ? q

l t 11

S

I tl 11 I tl 11 ? 1 2 dt11 2 d2 ]] ? ]] 2 D K lt 11 K lt 11

DD

l

l

JG

1 R t11U t11

(6)

2.2. Production 2.2.1. Technology Aggregation. Households purchase aggregate goods from a global, competitive aggregator industry that combines j 5 1,..,2J differentiated final goods, y j,t to produce aggregate output, Yt 2 :

Oy ] 2J

Yt 5 [(2J)f 21

f 1 /f j,t

(7)

j 51

with j # J produced in USA and j . J produced in EU. Aggregator firms maximize profits s.t. (7)implying the inverse demand curve for good j:

Op y ] FO ( p ) 2J

maxPt Yt 2 [

1 /f

j,t

j,t

j 51

2J

5s2Jd (f 21) / f

j,t

j 51

f ] 12 f

S D

pj,t 2Jy j,t ⇒ ] 5 ]] Pt Yt

G

f 21

Pt

( 12 f ) / f

51

(8)

2 The aggregation industry is a notationally simple way of assuming that consumption, investment, and government spending are Dixit and Stiglitz (1977) CES indices of the range of final goods with equivalent elasticities of substitution between goods.

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where pj,t is the price of final good j and Pt is the numeraire aggregate goods price. Final goods. There are n 5 1, . . . ,Nj,t imperfectly competitive firms in final goods industry j at time t. The production of firm n is y nj,t . Final goods are produced using undifferentiated materials purchased from competitive firms in both countries. The production function of each final goods firm displays increasing returns to scale due to a fixed cost, Ft . Nj,t

y j,t 5

Nj,t

O y 5 O sm n j,t

n51

n j,t

2 Ftd 5 m j,t 2 Nj,t Ft

n51

n

where materials purchased by firm n in market j at time t are m j,t and m j,t is the materials purchased by industry j. Materials. In each country, competitive firms produce undifferentiated materials with constant returns to scale Cobb–Douglas technology using labor and capital services rented from households in their own country: M lt 5 A ltsU lt K ltdusH ltd 12u

(9)

where A tl is a country specific technology level. The standard first order conditions specifying factor demand are: pM,t M lt w tl 5s1 2 ud ? ]] H lt

pM,t M lt R tlU tl 5 u ? ]] K lt

(10)

pM,t is the price of materials or the inverse of the aggregate markup.

2.2.2. Industrial structure I consider three industrial structures for the imperfectly competitive final goods sector. They are: (1) PC: Perfect Competition; and (2) SIM: Cournot Competition with Simultaneous Entry; and (3) SEQ: Cournot Competition with Sequential Entry. In all models, the number of goods 2J is fixed. Perfect competition (PC). In this case, final goods are perfect substitutes, f 5 1 and production is constant returns to scale, F 5 0. The materials price, pM,t 5 1. Yt 5 M tU S A 1 M tEU

(11)

Cournot competition with simultaneous entry (SIM). In this case (similar to Gali, 1995, and Portier, 1995), the only deterrent to market entry is the fixed cost F. Potential market entrants chose their entry strategy simultaneously; competition within markets is Cournot, so markups are determined by the number of firms per market. In equilibrium, the number of firms entering is such that final goods firms profits are zero. The profit maximizing markup over marginal cost depends on the number of entrants. I assume the number of firms per industry is symmetric so pM,t , the inverse markup is increasing in the number of firms per market.

D. Cook / Journal of International Economics 56 (2002) 155 – 175

Nj,t Nt 1 f 2 1 pj,t 5 ]]]] ? pM,t ⇒ pM,t 5 ]]] Nj,t 1 f 2 1 Nt

161

(12)

Though the number of firms per market is inherently an integer, it is implausible that a symmetric, integer Nt exists in every period at which firms make zero profits. Instead, I treat Nt as continuous. This approximation seems tenable if the number of firms per market is large. In the SIM case, firms make their entry decision simultaneously which might be thought to represent entry decisions in an industry with a large number of firms unable to observe other firms’ entry decisions. Aggregate output is: Yt 5sM Ut S A 1 M EU t d 2 Nt 2JFt

(13)

Cournot competition with sequential entry (SEQ ). This model describes markets dominated by a number of incumbents. Marginal entry decisions are made by firms that take the presence of incumbents as given 3 . The model described here, dubbed SEQ , differs from SIM in that market entry is sequential rather than simultaneous. The model takes the number of markets as fixed or established. Eaton and Ware (1987), argue sequential entry is the natural way to consider entry into established markets. The SEQ case, unlike the SIM case, imposes the constraint that the number of firms per market is an integer making this a legitimate tool for analyzing markets with a small number of firms. In each final goods industry, there are a countably infinite number of potential market entrants indexed by n 5 1 . . . .`. Market entry occurs sequentially (beginning with potential entrant 1) with each potential entrant committing to play an observable mixed strategy probability of entry s nt . Each entrant takes the entry strategy of the previous potential entrants as given. Following market entry, actual entrants play a simultaneous Cournot quantity such that the markup over marginal cost is: Nj,t pj,t 5 ]]]] ? pM,t Nj,t 1 f 2 1 In symmetric (across industries) perfect foresight Nash equilibrium, there is some N such that the first n 5 1, . . . ,N 2 1 entrants (dubbed incumbents) play s nt 5 1 and the Nth (marginal) entrant enters with probability 0 # s tN # 1 such that marginal entrants are indifferent between entry and non-entry (i.e. profits of marginal 3

Since the Dixit (1979) and Spence (1977) recasting of the Stackelburg framework, microeconomists have realized that an ability of incumbants to commit to market participation can result in a first mover advantage. In much of the literature on sequential entry, incumbants are able to commit to capacity as well as market participation offering greater opportunity to deter entry. Given the emphasis in this paper on variable capital utilization, I restrict examination to the case when first moving firms can only commit to fixed costs rather than variable costs.

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162

entrants are zero). In aggregate, there will be a fraction s Nt of industries with N competitors and 1 2 s tN industries with N 2 1 competitors. In a market with N firms, dubbed the competitive market, all firms make zero profits. However, with positive probability there are only N 2 1 firms in any given market; incumbents make positive profits with positive probability. All entrants make non-negative profits; no non-entrant can make positive profits by entering. At this equilibrium, no firm has any incentive to change their entry strategy given the strategies of the other firms. The number of entrants such that the marginal entrant makes zero profits are given by the size of fixed costs relative to the size of aggregate demand. In equilibrium, no firm will enter a market that already has N firms as long as their is a market available with N 2 1 firms. Thus, given 0 , s Nt , 1, N will be constant. Entry occurs only through variation in s Nt , the entry strategy of marginal entrants. The real price of materials (or the inverse markup) is an increasing function of the entry strategy of marginal firms: M N pM t 5 p (s t )

FS

N 5 s Nt ]]] N211f

D

f / (f 21)

S

D G

N21 1s1 2 s tNd ]]] N221f

f ] f 21

(12 f ) / f

(14)

The aggregate production function is: Yt 5 L(s Nt ) ?fM Ut S A 1 M EU 2 (N 1 s Nt ) ? 2J ? Ftg t

(15)

where L(s t ) is a function of the market entry strategy and reflects the production distortions occurring due to asymmetry across markets (note: L(0) 5 L(1) 5 1, see Cook, 2000, for a derivation of L(s Nt ) with N 5 2).

S S

S S

D D

S S

D D D D

f 1 /f f / ( 12 f ) N21 N ] (1 2 s Nt ) ]]] 1 s Nt ]]] 12 f N221f N211f L(s Nt ) 5 ]]]]]]]]]]]]]]]] 1 1 / (12 f ) N 2 1 N ] (1 2 s Nt ) ]]] 1 s Nt ]]] 12 f N221f N211f

(16)

2.3. Equilibrium conditions Define Ct as the history of shocks to time t. Define allocation functions C lt (Ct ), l I (Ct ), H tl (Ct ), K t11 (Ct ), U tl (Ct ), M tl (Ct ), B tl 11 (Ct ) and price functions p tM (Ct ), l l w t (Ct ), R t (Ct ), rB,t (Ct ). An equilibrium is a collection of allocation and price functions that solve the problem of the household and firms and at which the aggregate goods, materials and bond markets clear: l t

O

l5US A,EU

C lt 1 I lt 1 G lt 5 Yt

O

l 5US A,EU

Om 2J

M lt 5

j 51

l j,t

O

B lt 5 0

(17)

l5US A,EU

in the SIM case, add a number of firms function Nt (Ct ) such that final goods firms

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163

make zero profits; in the SEQ case, add a entry strategy function s t (Ct ) such that marginal final goods firms make zero profits. Define GDP as the value of final goods minus materials imports and net exports NX:

O (p

GDP lt ;

l j,t

l y lj,t 2 pM,t m j,t ) 1 M tl ⇒ NX tl ; GDP tl 2 C tl 2 I tl 2 G tl

j

Define the measured Solow residual as: ln SR lt 5 ln GDP lt 2 u ? ln K lt 2s1 2 ud ? ln H lt Log technologies follow independent, trend stationary AR(1) processes: l

l

l

ln A t 5 (1 2 r ) ? h ? t 1 r ? ln A t 21 1 ´ t

S D S

D

´ EU s2 0 t | N 0, ´tUS A 0 s2

The fixed cost Ft and government spending Gt grow exogenously at rate h.

2.4. Counter cyclical markup elasticities Simultaneous entry. Combine (12) with the no profit condition of individual firm n in market j: Nt 12f n n n ]]] ? p ? y 2 pM,t [y j,t 1 Ft ] 5 0 ⇒ y j,t 5 ]]]] ? Ft Nt 1 f 2 1 M,t j,t Nt 1 (1 2 f ) The output of individual firms falls as the number of firms per market rises. In aggregate, pM,t ?s1 2 fd 12f Yt 5 ]]]] ? 2JFt 5 ]]]] ? 2JFt Nt 1 (1 2 f ) (1 2 pM,t )2

(18)

Define Yˆt and pˆ M,t as log deviations from steady state and pM as steady state materials price. Log-linearize (18): 1 2 pM pˆ M,t . ]]] ? Yˆt (1 1 pM ) The materials price is an increasing function of global demand. As global demand increases, new firms are able to enter and cover fixed costs sufficient to make zero profits. Competition intensifies and markups fall. If we think of the materials price as the inverse of the markup mt ; (1 /pM,t ), the elasticity of the markup with respect to output is e mY 5 (1 2 m ) /(1 1 m ). Sequential entry. The no profit condition under sequential entry is that the Nth marginal entrant make zero profits. Define the price and output of the marginal firm in a competitive market (with N entrants) as pN,t and y Nj,t :

164

D. Cook / Journal of International Economics 56 (2002) 155 – 175

12f pN,t ? y N 2 pM,t ? [y N 1 F ] 5 0 ⇒ y N 5 ]]]] ? Ft N 1 (1 2 f ) The number of firms per competitive industry is constant (local to steady state), only the share of (relatively) competitive industries change. Thus, the production levels of firms in competitive industries is fixed (rising with trend growth in fixed costs). Examining the demand curve of an industry:

S D

2Jy N N pN,t 5 pj,t 5 ]]] ? pM,t 5 ]] N 1f 21 Yt

f 21

⇒ pˆ M,t 5s1 2 fd ? Yˆt

(19)

The elasticity of the materials price with respect to output is 1 2 f and the elasticity of the markup with respect to global demand is e mY 5 f 2 1 , (1 2 m ) / (1 1 m ) , 0. In both models, an increase in demand leads additional marginal firms to enter. Entry continues up to the point where gross profits of a marginal entrant falls to the level of fixed costs. Gross profits of marginal entrants are the product of the output of a marginal entrant times the net markup in the market in which entry occurs. In the simultaneous entry model, a new entrant reduces the output level of individual firms. Any firm that enters will reduce potential output levels of any subsequent entrants and reduce the ability of subsequent entrants to cover fixed costs at a given markup level. In the sequential entry model, the output level of potential entrants remains constant. Thus, an entrant does not reduce the ability of subsequent entrants to meet fixed costs at any given markup level 4 . This property allows entry to respond more elastically to a change in demand in the SEQ case. In other words, in the SIM model, entry reduces both the net markup in the entered market and the output level of a marginal entrant. In the SEQ model, additional market entry reduces only the net markup in the entered market. The output level of marginal entrants stays fixed. Thus, all of the adjustment in gross profits must occur through the net markups in entered markets. The response of the markup to any given increase in demand is larger in the SEQ case. This is somewhat reminiscent of the results of Rogerson (1998) and Hansen (1985) for the wage elasticity of labor supply. Those authors model entry into labor markets occurring on the extensive margin, with each new worker working the same amount of hours as previous labor market entrants. This type of entry leads to more elastic labor supply than the case when entry occurs on the intensive margin, with all workers increasing their work levels simultaneously. Here, the sequential entry model might be described as entry on the extensive margin, with each new marginal entrant producing the same amount of goods as previous

4

Entry does reduce the output level of the incumbents in previously uncompetitive markets. However, the entry strategy of the incumbents is fixed. They enter in either case.

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marginal entrants. The simultaneous entry model might then be described as entry on the intensive margin, in which each entrant produces a smaller number of goods than previous entrants. Entry and markups respond more elastically to an increase in demand when entry occurs on the extensive margin than on the intensive margin.

3. Calibration I solve a linear approximation of this model around steady state using techniques in King and Watson (1995) and Sims (1997). The Benchmark parameterization draws many standard RBC parameters are drawn from Christiano and Eichenbaum (1992) based on a period being of quarterly length. The time discount rate is b 5 1.03 2.25 ; the mean growth rate h 5 0.004; capital share u 5 0.341; G is set so steady state labor is 23% of T; steady state G /GDP50.177. Along the trend growth path, k 5 (rB 1 d /d ) where d is the steady state depreciation rate of capital. I set k so d 5 0.021. The capital adjustment parameters D and d2 are set so steady state adjustment costs are zero and the elasticity of the investment capital ratio with respect to q is 15 as in Baxter and Crucini (1993). As in Baxter (1995), the technology process, r 5 0.995, is persistent but stationary. In the SEQ model, I set f 5 0.7, so the elasticity of the markup with respect to demand, e mY 5 2 0.3. This is within the range of elasticities of the markup used in the equilibrium cartel literature. Rotemberg and Woodford (1992, 1995) use elasticities of e m 5 2 0.19 and e m 5 2 0.39 respectively. Schmitt-Grohe (1998) selects an elasticity e m 5 2 0.35 5 . Rotemberg and Woodford (2000) discuss many of the difficulties in estimating the elasticity of the markup, but argue that under plausible assumptions about technology, elasticities within this range are reasonable. The markups of a monopolist when f 5 0.7 are, 1 /f 5 1.424, with two Cournot competitors the markup 2 /(1 1 f ) 5 1.177; with three competitors 3 /(2 1 f ) 5 1.117; with four 4 /(3 1 f ) 5 1.081; with five 5 /(4 1 f ) 5 1.064, and so forth. I calibrate the market economy so the competitive market has three competitors, N 5 3. For simplicity, I assume that the steady state entry strategy of marginal firms s50.5, so half of markets are competitive. This implies an average markup midway between the markups observed with 2 and 3 competitors m ¯ 1.143. This level of market power is sufficient to demonstrate the effects of imperfect competition while remaining empirically conservative Basu and Fernald (1997) estimate an outer bound of returns to scale for the US economy of 1.26. Given small profits, markups should be of approximately the same size as returns

5

In the cartel literature, markups are determined by current demand relative to permanent profits of being in a cartel.

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D. Cook / Journal of International Economics 56 (2002) 155 – 175

to scale. One property of the sequential entry equilibrium is that the markup elasticity can be as large as that used in Schmitt-Grohe (1998)6 and Rotemberg and Woodford (1995) without implying large average markups. As Rotemberg and Woodford (1992) show, the elasticity of markups with respect to demand in the cartel competition case must be smaller than the net markup. For the elasticity of the markup to be as large as 20.3, the average net markup m 2 1 must be larger than 0.3. Markups of this size seem to be on the outer edge of current estimates of average markups in the US economy (see Schmitt-Grohe, 1997). The PC case assumes no markup over marginal cost. In the SIM case, f is set so the steady state markup is 1.143. The elasticity of the markup with respect to output is e mY 5 (1 2 m ) /(1 1 m ) 5 2 0.066. The elasticity of the markup in the simultaneous entry case would not be as large as 20.3 unless the markup were as large as m 5 1.85. For each case, I generate 5000 repetitions of 84 quarters of Hodrick and Prescott (1997) filtered, simulated data. I set s so the model displays a standard deviation of detrended GDP equal to 1.57% as does US GDP over 1975:1–1995:4. In Table 1, I report cross country correlations of GDP, investment, consumption, employment, and the Solow residual. I also report the correlation of output with net exports and the volatility of employment, consumption and investment relative to output. The calibrated solutions are linearizations of the first order and market clearing conditions. The linearized equations which appear in all models are: (2), (3), (4), (5), (6), (9), (10) and (17). In the PC case, add (11). In the SIM case, add (12), (13) and (18). In the SEQ case, add (14), (15) and (19).

3.1. Data I report empirical moments for the US and European Union economies in Table 1. All series are logged before detrending with the exception of net exports which is reported as a share of output 7 . In each economy, net exports are negatively correlated with output. Employment and consumption have a slightly smaller standard deviation than output while investment has a larger standard deviation. The data demonstrate substantial comovement between the two economies over the sample. GDP and employment are significantly positively correlated. Investment and consumption display minor positive comovement. The Solow residual in each country is also positively correlated which could imply positive comovement in productivity or factor utilization. The relative price of intermediate goods in the US is procyclical being positively correlated with output in the US and the EU. 6

One point of Schmitt-Grohe (1998) was that imperfect competition can explain some but not all of the transmission of shocks from the United States to Canada. Thus, using an outer bound estimate for the effects of counter-cyclical markups is appropriate. 7 See the Data Appendix for further description.

D. Cook / Journal of International Economics 56 (2002) 155 – 175

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Table 1 Empirical moments and model moments from benchmark parameterization Moment Correlation gdp U S , gdp EU h U S , h EU i U S , i EU c U S , c EU sr U S , sr EU nx l , gdp l wU ShU S l ]], y yU S p UMS , y l US EU pM , p M Volatility s gdp

DATA US

EU

PC

SIM

SEQ

20.477

20.474

20.055 20.445 20.548 0.084 0.0176 20.548

0.051 20.341 20.466 0.184 0.124 20.520

0.508 0.898 0.215 0.290 0.184 20.368

20.040

0.048

0

0.000

0.893

0.426

0 NA

0.725 1.000

0.869 1.000

0.348 0.553 0.056 0.082 0.345

0.493 0.401

0.0157

0.0091

0.0157

0.0157

0.0157

0.972

0.988

0.213

0.210

0.593

2.847

2.725

3.049

2.977

3.041

0.821 ...

0.945 ...

0.749 0.0084

0.746 0.0083

0.582 0.0057

h

s ] s gdp si ] s gdp sc ] s gdp s

This measure is also positively correlated with a limited measure of EU relative intermediate goods prices.

3.2. Perfect competition and simultaneous entry The PC case repeats standard open economy RBC models’ success in explaining relative volatilities of consumption, investment, net exports and output. Due to persistent shocks, the model closely matches the correlation between output and net exports (see Backus et al., 1992). However, the model does not capture the business cycle comovement that exists empirically between Europe and the US. In the data, output and employment are positively correlated; in the model, these variables are negatively correlated. Though European and American investment are weakly correlated, the model predicts a strong negative correlation. Employment volatility is small compared to the data. An EU productivity expansion leads to an EU employment expansion. EU output and investment also increase. The high returns to capital in the EU lead to a trade deficit as households in the USA exchange investment goods for EU bonds.

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If high interest rates lead USA households to forego domestic capital accumulation, the USA marginal product of labor and real wages drop sufficiently that equilibrium USA employment contracts. Quantitatively, time varying capital utilization does not lead to cross-country correlation of cyclical aggregates including the measured Solow residual as shown in Table 1. The SIM case repeats the successes of the PC case in replicating the relative volatilities of aggregates and the comovement between net exports and output. In the SIM case, counter-cyclical markups ameliorate the negative comovement in employment and investment observed in the PC case. The market power of final goods firms is a distorting tax that reduces labor and capital demand. During an expansion in global demand, operating profits increase sufficiently that more firms are able to enter markets. Market entry increases competition and reduces markups, effectively increasing capital and labor demand at real factor prices in both countries. However, employment and investment are still negatively correlated across countries. The counter-cyclical response of markups are insufficient to explain cross-country comovement.

3.3. Sequential entry In the SEQ case, there is substantial comovement between the EU and USA following an idiosyncratic shock. A productivity expansion in the EU leads to an increase in EU employment, investment and output. An EU productivity expansion leads to greater global output. At greater output levels, more marginal entrants earn sufficient profits to cover fixed costs; the equilibrium entry probability of marginal entrants increases. In the SEQ case, market entry leads to both an increase in USA labor demand and supply. Due to heightened competition, the relative price of materials increases, increasing USA labor demand. When EU employment and output are expanding; USA output and employment are also expanding. This leads to strong business cycle correlation between output and employment in the two economies. Investment is mildly correlated across countries as the marginal products of capital move more closely than in the PC case. As shown in Table 1, the ordering of the cross-country correlations are similar to those seen in the data; employment shows the strongest correlation, followed by output, followed by consumption, followed by investment. The comovement in capital utilization also leads to a correlation between the measured Solow residual in the USA and EU though technology shocks are independent Why is the comovement so much stronger in the SEQ case? The sequential equilibrium model differs along several dimensions from the simultaneous equilibrium model. First, as shown, the elasticity of the markup is stronger in the SEQ case. Second, in the sequential entry case, market entry results in a loss of profit payments to incumbents that has an income effect on labor supply which increases the comovement of employment (see Hornstein (1993), for an imperfect competition model in which pro-cyclical profits dampen employment volatility).

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Third, changes in the share of markets which are relatively competitive change the parameter L(s t ) which affects output levels through the distortions inherent in asymmetry across markets. In practice, it is the first aspect of the SEQ model that leads to such stronger comovement. Consider an alternative calibration of the SIM model such that the elasticity of markups with respect to the demand are 20.3 as in the benchmark SEQ case. The cross-country correlation of GDP and employment in this high elasticity SIM case are 0.231 and 0.490, respectively; the cross-country correlation of investment and consumption are 0.004 and 0.565. This version of the SIM model solves the ‘comovement problem’. However, for the markup to be this elastic in the SIM case, steady state markups must be m 5 1.85((1 2 1.85) /(1 1 1.85) ¯ 2 0.3), far above any reasonable estimate of markups in the US economy! The cyclical behavior of profits differentiates the two Cournot cases. Profits are counter-cyclical in the SEQ case; profits are always zero in the SIM case. The labor share of income in the SEQ case is strongly procyclical. However, the labor share of income in the US economy over the sample period is approximately acyclical 8 . Measuring the cyclical behavior of the labor share empirically may be difficult if firms earn rents. If economic profits are captured by workers or managers, profits enter income accounts as wage compensation. Counter-cyclical profits would then be consistent with an acyclical or counter-cyclical labor share.

4. Sensitivity analysis and data In Table 2, I report the cross-country correlations of business cycle aggregates for the above parameterizations after a change in one of the underlying assumptions of the model described in Table 1. Two aspects of the benchmark formulation are seen to be key elements of the ability of the SEQ model to solve the comovement problem. Both time varying capital utilization (due to Greenwood et al., 1988), and the modelling of capital markets as being limited to a risk free bond (introduced to large country models by Baxter and Crucini, 1995) are necessary for the sequential equilibrium model to display comovement at conservative estimates of the steady state markup. In Table 2 Section A, I examine the contribution of time varying capital utilization to the ability of the model to explain cross-country comovement. I do this by examining international comovement when capital utilization is fixed. In the PC and SIM models, time varying capital utilization is not a major channel of cross country business cycle transmission. For these models, the cross country correlations in the Fixed Utilization case are not greatly different from the Table 1 case. However, variable capital utilization is clearly a propagation channel for

8

Boldrin and Horvath (1995) find a counter-cyclical labor share over a longer time period.

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Table 2 Alternative parameterizations Correlation

Comovement gdp 0.032 0.096 0.0373

h

i

c

20.412 20.379 0.888

20.751 20.723 20.333

20.112 20.038 20.241

A. Fixed utilization

PC SIM SEQ

B. Complete capital markets

PC SIM SEQ

20.648 20.583 20.143

20.981 20.976 20.312

20.897 20.874 20.544

1.000 1.000 1.000

C. Correlated technology

PC SIM SEQ

0.265 0.279 0.614

20.150 20.118 0.924

20.281 20.263 0.357

0.389 0.398 0.425

D. Alternative firm numbers

SEQ N52 N53 N54 N55

0.513 0.508 0.509 0.503

0.823 0.898 0.921 0.918

0.128 0.215 0.250 0.242

0.368 0.298 0.233 0.244

E. Asymmetric market entry

SEQ

0.521

0.884

0.188

0.284

investment in the SEQ case. The cross-correlation of investment is negative in the SEQ Fixed Utilization case. Time varying capital utilization augments comovement in the marginal product of capital, and thus comovement in investment demand. The comovement in employment, however remains strongly positive even when capital utilization is constant. Given fixed capital utilization, the SEQ case displays positive comovement in output, employment and investment only when f is calibrated at value of 0.55 or lower, indicating a markup elasticity of e mY # 2 0.45 and steady state markups m $ 1.23. Following Backus et al. (1992), many international RBC models are developed with a complete market of contingent claims which allows perfect risk-sharing. In this framework, there is a perfect correlation between the marginal utility of consumption across countries. In Table 2, Section B, I report results under the assumption of complete markets. In the complete markets case, all three models are unable to explain positive comovement between business cycle aggregates. When USA residents have full insurance, an EU productivity expansion will increase the income of USA residents which will have sharply negative impacts on USA labor supply. In all cases, these income effects lead to negative comovement between EU and USA output, employment and investment. The negative comovement is somewhat ameliorated in the SEQ case. In the PC and SIM cases, the negative international comovement in employment and investment is almost

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perfect. Again, given complete financial markets, the SEQ case displays positive comovement in output, employment and investment only when f # 0.55, indicating e mY # 2 0.45 and m $ 1.23. If both capital utilization are fixed and capital markets are complete, the SEQ case displays positive comovement in output, employment and investment only when f # 0.3 indicating e mY # 2 0.7 and m $ 1.41, beyond plausible markup levels. I examine the case when technology shocks are correlated across countries. I assume that in any given period, the shocks to technology are given by:

S D F GS D S D ´ EU a b v EU t t ? USA USA 5 ´t b a vt

v EU t U S A | N(0, I) vt

calibrating a and b such that the standard deviation of detrended output is 0.0157 and the cross country correlation of the detrended Solow residual is 0.35. I report the cross country correlations in Table 2, Section C. Technology spillovers do lead to a correlation of GDP in the PC and SIM cases; however, they do not lead to positive cross-country correlation in employment or investment. In the SEQ case, the Benchmark case produces correlation in the Solow residual close to the data so very little change is observed. In Table 2, Section D., I report comovement for the benchmark (uncorrelated technology, limited financial markets, and time-varying capital utilization) SEQ model under different calibrations of N the number of firms per competitive market for N 5 2, 3, 4, 5. The elasticity of the markup is not determined by the number of firms per market. This leads the choice of N to have relatively little impact on the level of comovement. In the SEQ model, marginal entrants in both economies play the same mixed strategy of entry s t . Since entrants face the same demand curves and marginal costs, symmetry seems a natural choice. However, there are other potential entry equilibrium. Define s Ut S A and s tEU , as the entry strategies of marginal entrants in the USA and EU. For any given level of aggregate demand there is a unique share of competitive industries s t such that s t 5 ]12 s tU S A 1 ]12 s tEU . However, the given strategies of firms across countries is not determined. Further, empirical studies suggest entry in the United States is more closely correlated with the US business cycle than with the EU cycle. A time series index of net business formation in the US has a cyclical correlation of 0.862 with US GDP and a cyclical correlation of 0.312 with EU GDP. To check, the robustness of the model to asymmetric entry strategies, I assume that entry strategies are proportional to relative GDP across countries: US A

st

2 ? GDP Ut S A 5 ]]]]]] ? st A GDP US 1 GDP EU t t

2 ? GDP EU t EU s t 5 ]]]]]] ? st US A GDP t 1 GDP EU t

which satisfies s t 5 ]21 s tUS A 1 ]21 s tEU . In Table 2, Section E., I report the comovement of the major aggregates. The comovement here while slightly less than

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the asymmetric pricing strategy is qualitatively similar. The markup of final goods prices over materials prices leads to comovement between sectors. Markups are determined by the aggregate share of competitive markets, not the share in any particular country.

5. Discussion In an economy characterized by Cournot competition with sequential entry, pro-cyclical market entry generates international trade spillovers sufficient to explain the business cycle comovement observed in large, open economies. This result holds for conservative parameterizations of increasing returns to scale / average markups. Important aspects of the market entry channel are countercyclical markups and counter-cyclical profits. Time varying capital utilization increases the potency of the trade spillover and explains the observed correlation in Solow residuals without technology spillovers. The model of imperfect competition in this paper shares several features with benchmark perfect competition models. First, production firms hire domestic capital and labor and sell an undifferentiated good in a perfectly competitive global market. Second, households in each country purchase an undifferentiated consumption and investment good in a perfectly competitive global market. The assumptions that foreign and domestic materials are perfect substitutes and foreign and domestic final goods are equivalent components in domestic absorption are useful simplifications. These assumptions allow the channels through which imperfect competition leads to comovement to be easily observed. However, these assumptions also imply a constant real exchange rate and no preference toward home goods. Given that real exchange rates are extremely variable and domestically produced goods typically constitute more than 75% of absorption in large open economies, the models here could be extended to allow for imperfect substitution between foreign and domestic goods and a home preference to more realistically match the data.

6. Data appendix The data on output, investment, consumption, net exports and savings were drawn from OECD Main Economic Indicators database for the United States and the European Union. Output is constant dollar gross domestic product (MEI Mnemonic: USARGDPS, E15RGDP); consumption is personal consumption expenditure (USACSMRX, E15CSMRX), and investment is gross capital formation (USAINVTS, E15INVTS). Net exports are exports (USAEXPGS, E15EXPGS)-imports (USAIMPGS, E15IMPGS). Zimmerman (1994) calculates total hours worked and PPP converted output and capital stock for 8 of the 15 EU

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countries (Austria, Denmark, Finland, France, Germany, Great Britain, Greece and Sweden) and the US through mid-1991. This data is used to construct measures of employment and the Solow residual. The labor share of output is from the US business sector (calculated by dividing business sector compensation, Citibase Mnemonic: LBCP7, by business sector average productivity, LBOUT). Business formation is an index of business formation compiled by the BEA with data from Dun and Bradstreet (BUS). The US prices to construct the measure of the real price of materials are from the BLS Producer Price Indices (final goods, PWFSA, and intermediate goods prices less food and energy, PW292A). There was no EU wide series for intermediate goods prices. I construct a LaSpeyres index of input prices from Great Britain and the Netherlands and intermediate goods prices from Denmark and Spain using 1990 as the base year. Real 1990 output from the Penn World Tables data base were used to construct the weights for each index. The implicit GDP deflator from the OECD MEI was used as the price of EU final goods (MEI mnemonic E15DEFLS).

Acknowledgements I wish to thank Michael Devereux, Pierre-Olivier Gourinchas, Rodolfo Manuelli, Stephanie Schmitt-Grohe, Guofu Tan, Yong Wang, Yi Wen, Kafu Wong, ´ Danyang Xie, several anonymous referees, co-editor Carlos Vegh, and participants at seminars at HKUST and CUHK for helpful comments.

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