Reforms and the Real Exchange Rate: The Role of Pricing-to-Market Lise Patureau∗

C´eline Poilly†‡

July 2017

Abstract This paper investigates how fiscal and structural reforms lead to a real exchange rate depreciation. Endogenous pricing-to-market behavior of firms affects the effectiveness of the two reforms through a competition effect and a relative-price effect. A product market dereguation pulls the trigger of a competition effect which reduces domestic markups and magnifies the real exchange rate depreciation observed in the long run. On the opposite, domestic firms take the opportunity of the payroll tax cut to increase their markups, which lessens the exchange rate depreciation. Endogenous pricing-to-market also affects the normative implications of the reforms since welfare gains are larger than under a constant-markup assumption. JEL classification: E32, E52, F41 Keywords: Exchange Rate, Product Market Deregulation, Fiscal reform, Endogenous firm entry, Pricing-to-Market, Endogenous markups.

∗

Corresponding author. Universit´e Paris-Dauphine, PSL Research University, LEDa, France. Place du Mar´echal de Lattre de tassigny, 75016, Paris, France. Email: [email protected] † Aix-Marseille University, CNRS, EHESS, Centrale Marseille, AMSE, France. Email: [email protected] ‡ We would like to thank Philippe Bacchetta, M´ onica Correa-L´ opez, Mick Devereux, Julien Matheron and Carlos Thomas for their comments. We are also grateful to conference participants at RIEF 2015 (Orl´eans), DEGIT Conference 2015 (Geneva), T2M conference 2016 (Paris) and to several seminar participants at the Bank of Spain, the Universit´e Paris-Dauphine, University of Lausanne, Aix-Marseille University, University of Pamplone, University Paris I. This research was funded by the French Agence Nationale de la Recherche (ANR) under grant ANR-11JSH1002 01.

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1

Introduction

The severity of the recession that hit a large number of countries over the last decade forced policymakers and economists to forcefully rethink about stabilization policies. However, there is now wide consensus that the 2007s’ turmoil also acted as a trigger of a more profound crisis that took its roots in the structural fragilities of developed countries that expanded throughout the 2000s. Current account imbalances and sustained real exchange appreciation have notably been pointed out as serious failures for the peripheral euro-zone countries (Lane & Milesi-Ferretti, 2011). Accordingly, the literature attests a renewed interest for studying the effects of fiscal and/or structural policies on external imbalances. Playing on the fiscal tool has thus been studied as a way to depreciate the real exchange rate in the short run (Farhi et al., 2014). Structural reforms on the goods or the labor markets may also help firms compete on the international markets (see Cacciatore et al. (2015a) for a survey). In this paper, we investigate the channels through which fiscal and structural reforms affect the real exchange rate, in both the long- and the short-run perspectives. As pointed out by several empirical studies, the firms’ “pricing-to-market” behavior (PTM hereafter) has key implications on the real exchange rate (see Burstein & Gopinath (2014) for a survey). In this context, it is likely that the ability of a given reform to reduce prices depends on markup adjustments, which differ across destination markets in presence of international markets segmentation. A main contribution of the paper is thus to shed light on the role of endogenous markup adjustments on the effectiveness of the reforms to affect international relative prices. We address this question on theoretical grounds. Precisely, we develop a two-country dynamic model with monopolistic competition and endogenous firm entry featuring international trade costs and sunk entry cost, close to Corsetti et al. (2007). With this simple setup, we capture the two dimensions that have been shown to be key elements in shaping the real exchange rate behavior, the relative price of exported goods and the relative number of exporters (i.e., the extensive margin of trade, see the seminal contribution of Ghironi & M´elitz (2005)). This theoretical framework is enriched with a structure of oligopolistic competition that generates endogenous markups, in a similar way as Atkeson & Burstein (2008). In presence of international trade costs, this implies that firms discriminate across countries by charging different markups specific to the destination market. We show that the markup extracted on each market depends on two elements. First, the “competition effect”, i.e. on the number of competitors in the market: The lower the number of competitors, the lower the price-elasticity of demand for a given variety, hence the higher the markup extracted by its producing firm. Due to the open-economy structure, markups are also determined by the “relative-price effect”: When imported varieties are more expensive than local ones, the price-elasticity of demand for the goods domestically produced reduces, allowing domestic firms to extract higher markups. We then show how these markup adjustments intervene as a major transmission channel of the reforms onto the real exchange rate. Precisely, we study the effects of the Home country carrying out either a reform to alleviate administrative burdens to enter the goods market (i.e. product market deregulation) or to reduce the labor cost by cutting the payroll 2

tax rate (i.e. the fiscal reform), contrasting the cases where markups are constant or endogenously adjust to the economic policy. Within this framework, we provide a careful understanding of the way both reforms operate on the real exchange rate. Two main findings emerge. First, if both the payroll tax cut and the goods market deregulation policy induce a real exchange rate depreciation in the long run, the two reforms work along very distinct channels, that also affect the transitional dynamics of the reforms. Second, we show the important role of the endogenous PTM behavior of firms as a propagation channel of both reforms on international relative prices. If it strengthens the ability of the product market deregulation to depreciate the real exchange rate in the long run, endogenous markup adjustment conversely reduces that of the fiscal policy. Endogenous markup adjustment also matters in the normative implications of the reforms. The underlying transmission mechanisms behind the two reforms can be accounted for as follows. In the long run, the product market deregulation at Home improves the market position of domestic firms, despite the deterioration in their price-competitiveness (the relative price of exports goes up). Through this extensive margin effect, the domestic price index goes down, at the root of the real exchange rate depreciation. On the opposite, the labor tax reform induces a real exchange rate depreciation which mostly channels through a reduction in the relative price of exports, despite the adverse effect on the number of domestic competitors. Taking into account the transition dynamics substantially modifies the picture though. If it depreciates in the long run, the real exchange rate temporarily appreciates after a product market deregulation. By contrast, the payroll tax policy induces an overshooting dynamics of the real exchange rate, as the magnitude of the instantaneous depreciation is larger than in the long run. Here again, the reactions of both the extensive margin of trade and the relative price are key to understand the result. While the unit labor costs (and therefore prices) immediately adjust to the reform, the changes along the number of firms take time to materialize. We thus show that this difference in the adjustment delays is crucial to account for the transitional effects of the two reforms. A key contribution of the paper is to show the importance of the endogenous PTM behavior of firms as a propagation channel of both reforms on international relative prices, and in opposite directions: If this amplifies the depreciation induced by the goods market deregulation, it conversely dampens that of the fiscal policy. The intuition is the following. By reducing the entry cost, product market deregulation pulls the trigger of the competition effect: The larger number of competitors on the domestic market exerts a downward pressure on the markups that can be extracted at Home. This, in turn, magnifies the real exchange depreciation. By contrast, domestic firms take the opportunity of the labor tax cut to increase their markups, in particular on the local market. Under international goods market segmentation, markups extracted at Home increase more than abroad, which lessens the real exchange rate depreciation. Endogenous PTM also has implications in a normative perspective. While both reforms are welfare-improving, the welfare gains are larger when markups endogenously adjust. Following the product market deregulation, the endogenous markup reduction limits firm entry. This, in turn, moderates the need for investment in new firms

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and stimulates consumption by more. The same result obtains for the labor tax policy, although through a distinct channel. As the fiscal reform induces an rise in markups extracted in the reforming country, households expect a higher stream of future dividends and rise consumption on this purpose. Through a different angle, this result confirms our previous findings, pointing out the importance of taking into account the firms’ PTM behavior if willing to correctly evaluate the overall effects of the reforms. Our model allows us to get a clear understanding of the channels through which fiscal and structural reforms play on the real exchange rate. This comes at the price of keeping the model simple by abstracting from several features, although they deserve a discussion. First, in a world of vertically-linked production, some papers have called attention on the importance of deregulating the upstream sector, the competitiveness gains spilling over the downstream sector (Bourl`es et al. (2013), Cacciatore et al., 2016a). While we have excluded this dimension here, our framework could easily be amended to integrate an upstream non-tradable sector. This would mostly change the dynamics of the relative price effect to the product market deregulation, leaving the extensive margin channel which turns to be the main channel of this reform, qualitatively unchanged.1 Second, the absence of the non-tradable sector justifies that we ignore the Balassa-Samuelson effect that stipulates that sectoral TFP differential across countries explains long-run movements of the real exchange rate. We neglect this dimension in order to isolate the dynamics of the number of exporters and of the relative prices to both reforms independently of their reaction to exogenous factors like TFP. Third, we abstract from any nominal rigidity to adopt a purely real modeling approach. Under a standard Dixit & Stiglitz (1977) CES setup, Betts & Devereux (2000) show that PTM has no impact on the exchange rate volatility under flexible prices. In contrast, by combining international trade cost and a production structure ` a la Atkeson & Burstein (2008), we are able to generate real exchange rate movements even under in the absence of nominal rigidities. Fourth, we also discard the productivity heterogeneity dimension, in contrast to e.g., Ghironi & M´elitz (2005). Under firm heterogeneity, a single home firm would compete not only with the foreign firms, but with the other domestic firms. Alongside the impact on the competition effect, this is likely to affect the endogenous markup behavior. Atkeson & Burstein (2008) show that adding heterogeneity in firms’ productivity allows to take into account the heterogeneity in the pricing-to-market behaviors. We choose to leave aside this dimension here, to focus our attention on the combined role of the relative price effect and the competition effect on the markup behavior, hence on the way this shapes the link between the reforms and the real exchange rate. Our paper contributes to the growing recent literature on the effects of fiscal and structural reforms in an open-economy setting. On the fiscal policy side, Chugh & Ghironi (2011) study the effects of a change in the labor tax in a model with endogenous firm entry, but in a closed-economy setting. In 1

Based on Cacciatore et al. (2016a)’s insights, the deregulation of the upstream non-tradable sector would mostly alter the dynamics of the relative price effect, eventually leading to a reduction in the relative price of the domestic downstream sector goods (rather than an increase here). This, in turn, would complement the extensive margin channel (rather than counteracting it) therefore amplifying the long-run real exchange rate depreciation with the product market reform obtained in our model.

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an open-economy framework, Farhi et al. (2014) and Engler et al. (2017) focus on the effects of the so-called “fiscal devaluation” reform (the reduction in payroll taxation being offset by an increase in VAT) on the price competitiveness of the home goods, leaving aside the potential effects on firm entry. Conversely, Auray et al. (ming) point out the importance of also taking into account the effects of this tax policy on the extensive margin of trade. If we share this conclusion with Auray et al. (ming), our contribution is to go deeper in the mechanisms it works through. In particular, we point out how the gains of a labor tax reform are crucially affected, and as a matter of fact, dampened, by the firms’ endogenous markup behavior. Our paper also relates to the literature that investigates the open-economy effects of the structural reforms, in particular on the goods market. Forni et al. (2010), Andr´es et al. (2017) or Eggertsson et al. (2014) investigate the effects of product market deregulation in various open-economy contexts. However, they adopt a “reduced-form approach” by modeling market deregulation by an exogenous markup reduction. Conversely, our paper demonstrates the importance of taking into account the endogeneity of markups adjustment if willing to correctly assess the effects of this structural reform. In this respect, our paper is closer to the series of paper by Cacciatore et al. (2015, 2016), who have extensively studied the open-economy effects of a product market deregulation in interaction with monetary policy. Our contribution to this literature is twofold. First, we focus on the effects of the structural reforms per se, leaving aside the interaction with monetary policy. This is consistent with the view that many countries, in particular in Europe, are currently facing severe structural inefficiencies that require more than a stabilization policy. Second, while the literature has studied either product market deregulation or labor tax policy in a separate manner, we study the two policies in a unified framework. We then provide a deep understanding on the transmission channels they work through. In particular, we show the importance of taking into account the endogenous pricing behavior of firms on internationally segmented markets. Through this dimension, our paper is also related to a second strand of papers that study the role of endogenous markups adjustments in macroeconomic performances. Floetotto & Jaimovich (2008), Colciago & Etro (2010) and Lewis & Poilly (2012) resort to this type of framework in a closed economy. In a two-country context close to ours, Bergin & Feenstra (2001), Corsetti & Dedola (2005) or Atkeson & Burstein (2008) point out the importance of the PTM behavior of firms to account for deviations from the law of one price and the imperfect exchange rate pass-through.2 Our paper differentiates from these papers in two main aspects. First, we explicitly relate endogenous PTM decisions to firm entry in an international setup. In this respect, it bridges a wedge between Atkeson & Burstein (2008) and Floetotto & Jaimovich (2008), to show the importance of both the extent of competition between firms and the relative price effect as key determinants of markups. 2

As surveyed by Burstein & Gopinath (2014), there are a number of ways to introduce pricing-to-market in a real model with international trade costs. Departing from the CES demand is one option (e.g. for instance Bergin & Feenstra (2001), Atkeson & Burstein (2008) or Melitz & Ottaviano, 2008). Alternatively, Corsetti & Dedola (2005) suggest introducing additive distribution costs. In both ways, the price-elasticity of demand is variable and firms adjust their markups across destination. In the paper, we adopt the modeling structure of Atkeson & Burstein (2008) or Floetotto & Jaimovich (2008). As we detail later, one reason is that this competition set-up enables us to retrieve the standard Dixit & Stiglitz (1977) case of a constant markup.

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Second, we confront this to an original question that focuses on how endogenous markups do affect the effects of structural/fiscal reforms. The paper is structured as follows. After laying out the model (Section 2), we analyze the effects of the reforms on the real exchange rate. In Section 3, we study the determinants of the real exchange rate in a partial equilibrium view. Then in Section 4, we evaluate the effects of the reforms on the real exchange rate in a general equilibrium perspective, both over the long run and the short run. In Section 5, we extend the analysis to a larger set of macroeconomic variables and make welfare comparison. Section 6 concludes.

2

The Model

¯ households in the Home country and L ¯∗ We model a world economy made of two countries, with L in the Foreign country.3 We assume a cashless economy with one unit of account common to both countries. As in Corsetti et al. (2007), we will consider the domestic labor as the num´eraire good, with the domestic wage W = 1 accordingly. Firm entry decision is endogenous, and modelled in the spirit of Bilbiie et al. (2012) (among others). Further, we retain a competition structure that induces endogenous markups in the spirit of Atkeson & Burstein (2008) and Floetotto & Jaimovich (2008).4 Precisely, we assume that the production sector features a two-layer production structure. In each country, the final good consumed by the local household is made of a continuum of sectoral goods, according to a standard Dixit-Stiglitz CES aggregator. Sectoral goods are made of intermediate goods both locally produced and imported, given international trade costs. Intermediate goods producers behave like oligopolists within each sector, i.e. taking into account the effect of their pricing decision on the price index of the sector. Ultimately, the price-elasticity of the demand for their variety varies with the market share of firms, at the root of endogenous markups. Importantly, combining endogenous markups with international trade costs allows firms to discriminate across markets’ destination by charging different markups. Describing the model will make this point clearer. Before doing so, let us comment about the two policy instruments under focus. Product market deregulation is modeled by a reduction in the shadow cost of entering the market for firms. This stands in line with the related literature (see the seminal paper by Blanchard & Giavazzi (2003)). As for the fiscal reform, it is conducted through a reduction in the payroll tax rate, financed by an adequate reduction in the lump-sum transfers to balance the government’s budget constraint. In contrast with Chugh & Ghironi (2011) and Auray et al. (ming), we assume that the labor tax cut leaves the firm entry cost unaffected. This enables us to partition the two policies and have a transparent view of the specific channels through which each type of reform affects the economy. 3

All Foreign country’s variables are indexed with a star. Home and Foreign countries are symmetric in the sense that they feature the same preferences and technologies. When the Foreign decisions are identical to the Home one, we describe only the later. 4 Devereux & Lee (2001) investigate the gains of trade with a similar production structure. However, they do not introduce international trade costs, which shuts down a potential pricing-to-market behavior.

6

Additionally, by leaving the indirect tax rate unaffected, we depart from the “fiscal devaluation” scenario studied in Auray et al. (ming) or Farhi et al. (2014) (among others). It follows that the labor tax reform only plays on the unit labor cost, with no other distortionary effect. In this respect, this allows us to study two “pure” supply-side policies (the one playing on the variable cost, the other on the fixed cost to start a business).

2.1

Households

The household decisions can be separated in two steps: Intratemporal decisions (related to the optimal choice of the consumption bundle) and intertemporal choices (related to labor supply, consumption and savings). We start describing the intratemporal program. 2.1.1

Intratemporal Choices

Final goods consumption The final consumption good in the Home country Ct is a bundle of “sectoral goods” denoted by Cst where s ∈ [0, 1] according to a CES aggregator such that: Z Ct = 0

1

θ−1 θ

θ  θ−1

Cst ds

,

R1 where θ > 1 is the elasticity of substitution across sectoral goods. Given Pt Ct = 0 Pst Cst ds, with Pt denoting the consumption price index and Pst the price index of each sectoral good, the optimal demand for sectorial goods and the associated aggregate price index, Ps can be written as:  Cst =

Pst Pt

−θ

Z Ct ,

and

Pt = 0

1 1−θ Pst ds

1  1−θ

.

Anticipating the symmetric equilibrium between sectors, it turns out that Pst = Pt and Cst = Ct . Demand for Intermediate Goods Each good produced in sector s combines differentiated goods produced by domestic and foreign firms. The differentiated goods are indexed by d ∈ ΩD ≡ [0, nt ] when they are produced in the Home country and f ∈ Ωf ≡ [0, n∗t ] in the Foreign one. All goods are produced using only labor. Therefore, nt corresponds to the number of differentiated products in the Home country (n∗t in the Foreign country). Let csxt denote the intermediate good produced in country x (x = h, f ) being used by the Home sector s at time t. Given our assumption of symmetry across sectors (within the same country), csxt = cs0 xt for any sector s, s0 . For the sake of notational clarity, we thus denote cxt ≡ csxt , ∀x = d, f . Therefore, households’ preferences for the type-s sectoral good are such that: Z Cst = 0

nt

Z

σ−1 σ

cdt dd +

0

n∗t

σ−1 σ

cf t df

!

σ σ−1

,

where σ > 1 is the elasticity of substitution between goods within a sector.

7

(1)

The optimal Home demand for differentiated goods produced domestically (cdt ) and abroad (cf t ) in sector s as well as the associated price of the type-s sectoral good Pst have the usual expressions, with pdt and pf t the prices of the local and imported varieties, according to:  cdt =

pdt Pst

−σ

 Cst ,

and

cf t =

pf t Pst

−σ Cst ,

h i 1 ∗ 1−σ 1−σ Pst = nt p1−σ + n p . t ft dt

(2) (3)

Given symmetry across sectors, Equation (3) also yields the expression for the Home CPI Pt . As standard in this literature, due to love-for-variety preferences, with a larger number of firms, the amount to pay in order to get a given utility is lower, such that the welfare-based price index (Pt ) decreases as nt or n∗t increase. Solving a symmetric problem, the optimal demand functions that emanate from the Foreign household for the Home and Foreign differentiated goods (c∗f t and c∗dt , respectively), and the associated CPI (Pt∗ ) (anticipating symmetry across sectors and within a sector, between firms of the same country) are given by:

2.1.2



p∗f t

−σ

Ct∗ ,

c∗dt



p∗dt Pt∗

c∗f t

=

Pt∗

i 1 h
∗ 1−σ 1−σ ∗ ∗ 1−σ + nt (pdt ) = nt p f t .

Pt∗

and

=

−σ

Ct∗ ,

(4) (5)

Intertemporal Choices

For a domestic household, the intertemporal utility function is given by: W=

∞ X

1 1− ψ

β t U(Ct , Ht )

C U(Ct , Ht ) = t 1−

with

t=0

1 ψ

− σH

Ht1+η , 1+η

(6)

with Ct aggregate consumption and Ht total hours worked. 0 < β < 1 is the subjective discount factor, ψ > 0 drives the curvature of the utility function, σH is a scale parameter and η −1 > 0 is the Frisch labor supply elasticity. The household in the Home country maximizes the intertemporal flow of utility (6) subject to the sequence of flow budget constraint, expressed in terms of the final Home good:   ψB Bt+1 2 c = (πt + vt ) Pt nt xt + (1 + it )Bt + Wt Ht + Pt Tt . Pt vt (nt + ne,t ) xt+1 + τt Pt Ct + Bt+1 + Pt 2 Pt (7) In period t, the household’s expenditures are threefold. First, she can consume the Home final good bundle Ct , at the consumption price index Pt and given the gross VAT rate, τtc . Second, she can invest in either existing or startup firms (in numbers nt and net respectively) through the buying of a number of mutual funds share holding xt+1 (per firm), given the value of the firm vt (expressed in terms of the Home good). Third, she can invest in non-contingent stock of nominal bonds Bt+1 issued at the world level. Issuing new bonds is subject to adjustments costs on portfolio, paid to the 8

government and scaled by the parameter ψB , following the modeling of Cacciatore et al. (2016c). On the resources’ side, the households receives labor income with a nominal wage denoted by Wt , as well as the returns from financial assets (1 + it ).5 The household also perceives the returns of past investments xt , equal to the value of the incumbent firms at the beginning of the period (vt ) plus the ¯ dt cdt + L ¯ ∗ p∗ c∗ − τ w Wt hdt (with dividends (profits) perceived from them πt , defined as: Pt πt = Lp t dt dt w τt the gross payroll labor tax rate, that will be the instrument of the fiscal reform). Resources are also made of lump-sum transfers Tt from the government. Solving the household’s intertemporal program with respect Ct , Ht , Bt+1 and xt+1 yields the set of first-order conditions: 1 Wt η ψ (8) = σ H C H t t , τtc Pt   1 cP C ψ Bt+1 τ t t t 1 + ψB = β (1 + it+1 ) , (9) 1 Pt ψ c τt+1 Pt+1 Ct+1   1 cC ψ τ (10) vt = β (1 − δ)  t t 1 (πt+1 + vt+1 ) . ψ c τt+1 Ct+1 Equations (8) represents the intratemporal consumption-leisure arbitrage. Equations (9) and (10) give the intertemporal consumption-saving arbitrage, in international assets and in firm creation respectively. In particular, households invest in new firms such that the cost of investing in new firms is equal to the expected return of the investment, that depends on the expected flows of dividends and profits conditional on the firm not being destroyed (valued in terms of marginal utility of consumption).

2.2

Production of Intermediate Goods

Within a given sector, each individual firm produces a differentiated good using labor domestically supplied, given a CRS production technology. For a domestic firm producing the variety d, it is written as: yt = hdt , (11) where hdt denotes firm’s labor demand used to produce the type-d variety. Each variety is sold on the domestic and the foreign markets, with international trade being subject to iceberg trade costs. Firms are free to enter the market, provided that they pay a fixed cost to start producing, imputed in labor, as e.g. in Corsetti et al. (2007). 2.2.1

Endogenous Entry

The program of the firms may be decomposed in two steps. First, they take the decision to enter the goods market, given the fixed cost of entry (which ultimately determines the number of firms 5

In this setup, the two countries can be viewed as belonging to a monetary union with a common interest rate. In the absence of nominal rigidities, the monetary policy is irrelevant and the interest rate ensures equilibrium in the bond market.

9

in each country). Second, once entered, they maximize the operating profit. We solve the problem backwards. Profit Maximization Once entered, the Home firm maximizes its operational profit πt , given the production function (11) and the good market equilibrium condition: ¯ dt + τ L ¯ ∗ c∗ , yt = Lc dt

(12)

where τ > 1 denotes the international trade costs. Further, in a monopolistic competition setting each firm knows the demand functions for its good that emanates from the final good sector in each country (cd , from Equation (2) and c∗d from (4)). International trade costs give rise to market segmentation, such that each firm is able to “price-tomarket” by setting a price specific to each destination market. Accordingly, maximizing profit with respect to prices pdt and p∗dt given the demand functions (2) and (4), leads to the optimal pricing decisions for the Home and export (Foreign) markets respectively: pdt = µdt τtw Wt ,

and

p∗dt = τ

µ∗dt pdt , µdt

(13)

where µdt and µ∗dt represent the markups extracted by the domestic firm on the Home and Foreign markets respectively. As standard, the markup rates are a decreasing function of the price elasticity of demand on each market εdt and ε∗dt , according to: µdt =

εdt , εdt − 1

and

µ∗dt =

ε∗dt . ε∗dt − 1

(14)

Notice that, if the price-elasticity of demand is identical across countries εdt = ε∗dt , then it is optimal for firms to transfer the iceberg trade costs to the foreign consumers, i.e. we obtain the standard “mill-pricing strategy” as p∗dt = τ pdt , implying a higher export price relative to local everything else equal. However, this strategy is no longer optimal as long as price-elasticities differ across markets. Whenever εdt 6= ε∗dt , it is optimal for firms to break the law of one price by also setting different prices (and markups) across markets. We come back to this point with more details in Section 2.2.2. Firm Entry Decision Consider now the first step of entry decision. Firm’s entry is subject to a sunk entry cost – measured in labor units, made up of administrative regulation costs (fR ) and the R&D expenditures (fT ), as in Cacciatore et al. (2016c) (among others). We assume that the regulation cost can be changed by public authorities at the gross rate τ e ≷ 1. Product market deregulation will henceforth be modeled through a decrease in τ e . The setting up of ne,t startups requires Het units of labor, such that the labor demand for new firms creation is Het = [fR τte + fT ] net . Entry occurs until firm value vt is equalized with the entry cost, leading to the free-entry condition: Pt vt = [fR τte + fT ] Wt . 10

(15)

Entrants at time t only start to produce at time t + 1. Both new firms and incumbents may be hit by an exogenous exit shock, that occurs at the very end of the period (after production and entry) with probability δ. Accordingly, the law of motion for the number of firms in the domestic country is given by: nt+1 = (1 − δ) [nt + net ] . (16) 2.2.2

Markups and PTM

Within a given sector, due to the limited number of firms, each firm takes into account the effects of its pricing decision on the sectorial price index, which ultimately affects the price-elasticity of demand for its variety. Precisely, this setup establishes a link between the price-elasticity of demand for a variety and the firm’s market share. Consider the case of the demand for a domestic variety emanating from the Home and Foreign households respectively. Defining the firm’s market share on pdt cdt ∗ the local market mdt ≡ nt pdt cdt +n∗t pf t cf t (its market share on its export market mdt being similarly defined), we indeed obtain the following link between the price-elasticities of domestic and foreign demand εdt and ε∗dt , and the Home firm’s market share on each market: εdt = σ − (σ − θ) mdt ,

(17)

ε∗dt = σ − (σ − θ) m∗dt ,

(18)

where, making use of the optimal demand functions (2) and (4), the market shares can be rewritten as: " "  1−σ #−1  ∗ 1−σ #−1 pf t p f t mdt = nt + n∗t , m∗dt = nt + n∗t . (19) pdt p∗dt Price-elasticity, market share and PTM As noted by Atkeson & Burstein (2008), one advantage of this modeling structure is that it uncovers the standard Dixit-Stiglitz case in a very straightforward way. When goods are as substitutable within sectors than across sectors (σ = θ), the competition structure indeed implies a constant price-elasticity of demand (εd = σ in Equation (17)), hence a constant markup µ = σ/(σ − 1), identical across destination markets. In this case, the mill-pricing rule applies as result of optimal pricing decisions, such that: p∗dt = τ pdt . As long as σ 6= θ, price-elasticities of demand, as well as markups, are no longer constant and endogenously vary with the economic environment. Precisely, we will focus on the case where σ > θ, based on the empirical evidence of Broda & Weinstein (2006) that varieties are more substitutable within than across sectors. As in Atkeson & Burstein (2008), this setup implies that the price-elasticity of demand addressed to one firm, rather than constant, is negatively related to the market share of a firm, as displayed in Equations (17) and (18). In a open-economy setting, this market structure also implies PTM as optimizing result of the firms’ pricing behavior. Under σ 6= θ, the price-elasticities of the local demand and the foreign demand for the same good are no longer necessary equal (Equations (2) and (4) for a domestic variety). Accordingly, it is optimal for firms to set a specific markup for each destination market

11

(see Equation (13)). This bridges a supplementary price gap (on top of the iceberg trade cost) for the same variety across markets (i.e., p∗d 6= τ pd under σ 6= θ, as shown with more details in Appendix A). In this respect, having σ > θ implies both endogenous markups and PTM, driving us to use both terms interchangeably. Markups determinants Linking Equation (14) with Equations (17), (18) and (19) allows us to get some insights about the driving forces behind markup decisions. We focus here on the decisions made by a Home firm. From Equation (19), the firm’s market share on a given market (hence its markup) depends on two dimensions: the so-called “competition effect” (i.e. the number of competitors, both domestic and foreign) and the price of its good relative to that of their foreign competitors on the market (pf /pd ), which we refer to as the “relative-price effect”. Combining the above set of equations and reasoning in deviation from the symmetric steady state, the (change in) the markups made by a Home firm on its local and export market can be written as:6 Rel. price effect

1 ∆1 1 = − ∆2

µ bd = − µ b∗d

Competition effect }| }| { σ − 1 i{ hz z w ∗ 1−σ ∗ 1−σ c c c −(W − W + ∆τ ) + µ bf , n b + φ¯ κ n b + φ¯ κ ∆1 i  h   ∗  σ−1 c−W c ∗ + ∆τ cw +µ b∗f n b + φ¯ κ1−σ n b + − W ∆2

(20) (21)

Using a similar reasoning, the markups set by a Foreign firm on both its local and export market are: i  σ − 1 1−σ h w 1  ∗ ∗ ∗ ∗ 1−σ c c c µ bf = − (22) W − W + ∆τ + µ bd , n b + φ¯ κ n b + φ¯ κ ∆1 ∆1 i h  σ−1 1  c−W c ∗ + ∆τ cw +µ µ bf = − (23) W bd n b + φ¯ κ1−σ n b∗ + ∆2 ∆2 with ∆τ w ≡ τ w /τ w∗ and ∆1 , ∆2 positive constant terms defined as: ∆1 ≡ ∆2 ≡

  1  ε¯(¯ ε − 1) + φ¯ κ1−σ σ(¯ ε − 1) + (σ − ε¯)2 > 0, σ − ε¯   1 ε¯X (¯ εX − 1)(1 + φ¯ κ1−σ ) + (σ − 1)(σ − ε¯X ) > 0, σ − ε¯X

In the above expressions, ε¯ is equal to the price-elasticity of Home demand for the good locally produced and ε¯X is the price-elasticity on the export market in the initial symmetric steady state.7 Let us now comment on the two determinants of markups that show up in Equations (20) to (23). The so-called “competition effect” has a straightforward interpretation: Given the oligopolistic-type of competition within each sector, a marginal firm entry (whatever the country it locates in) raises the price-elasticity of demand addressed to each producer in place, thereby exerting a downward pressure on its markup on both destination markets (Equations (20), (21) from the domestic firm 6

In what follows, x bt denotes the log-deviation of variable xt from the steady-state in a model with symmetric countries. Variables without time-index are at the symmetric steady-state. We drop the time dimension subscript t for sake of notational simplicity. 7 Precisely, ε¯ = εd = ε∗f and ε¯X = ε∗d = εf in the initial steady state.

12

viewpoint). However, due to trade costs, the weight of foreign competitors is dampened relative to that of local incumbents. Put it differently, ceteris paribus the Home firms reduce their markup set on the Home market µd when a marginal firm enters, but with a lower magnitude when the new competitor is a foreigner (Equation (20)). For the same reason (but working in the opposite direction), the markup extracted by Home firms abroad (µ∗d ) is more sensitive to the number of foreign competitors than to the number of other domestic firms that compete with her on its export market (Equation (21)). Accordingly, both µ∗d and µd reduce with a marginal domestic firm entry, but not to the same extent (the markup reduction being more pronounced for the Home market). This is a first source of markups divergence across market destinations. The “relative-price effect” depends on both the relative unit labor cost and the markup charged by the foreign competitors on the local market. As reported in Equations (20) and (22), an increase in the Home unit labor cost relative to Foreign (either through an increase in the relative tax burden ∆τ w or in the relative wage W/W ∗ ) reduces the price-competitiveness of the domestic goods. This, in turn, pushes the domestic firms to reduce their markups on both destination markets (Equations (20) and (21)); conversely, it enables foreign firms to raise theirs (Equations (22) and (23)). The relative-price effect also depends on the markup set by the foreign competitors on this market. On the Home market for instance, the lower the markup set by the Foreign competitors (µf ), the lower the price of imports everything else equal. In order to preserve their market share, Home firms have to reduce their own markup as well (µd ). Further, due to market segmentation, what matters for setting the markup on each destination market is the markup set by the foreign firms exporting to this market (µf for µd , but µ∗f for µ∗d ). In case of an asymmetric shock across countries, this constitutes a second source that amplifies the divergence between countries by disconnecting markups set by the same firm across destination markets.

2.3

Closing the Model

Government We assume that in each country, the government runs a balanced budget. Absent public spending, collected distortive taxes are rebated to the households as lump-sum transfers, according to the following budget constraint:   ψB Bt+1 2 ¯ w c ¯ ¯ = LTt . (24) (τt − 1)nt Wt yt + (τt − 1)LPt Ct + LPt 2 Pt Recall that product market deregulation is modeled by a reduction of the shadow cost of entering the market (reducing τ e < 1, vs τ e = 1 in the initial steady state). Accordingly, it does not appear in the government budget constraint (24). By contrast, the fiscal reform consists in a reduction of the payroll tax rate τ w , that is financed by a reduction in lump-sum transfers (for a given value of the VAT rate τ c ), so as to ensure the government’s balanced budget (24). Market Clearing Conditions At each period, the market for international financial assets ¯ t+1 + L ¯ ∗ B ∗ = 0. In each country, labor market is perfectly competitive. clears, such that LB t+1 Accordingly, labor supply is fully used either in the production of manufactured goods or for 13

paying entry costs. Given the technological constraint (11), the labor market equilibrium thus writes: ¯ t = nt yt + net [fT + τ e fR ] . LH t From the domestic household budget constraint, incorporating the firms’ pricing decisions, the fact that, in the symmetric equilibrium, each household holds an equal share of the mutual funds (i.e., ¯ ∀t), the free-entry condition as well as the government budget constraint and the various xt = 1/L market equilibrium conditions, we can derive the balance of payments equilibrium condition (for the Home country): ¯ ∗ p∗ c∗ − n∗t Lp ¯ f t cf t , ¯ t+1 − (1 + it )LB ¯ t = nt L (25) LB dt dt ¯ ∗ p∗ c∗ equal to domestic exports and Mt ≡ n∗ Lp ¯ f t cf t to domestic imports (in value). with Xt ≡ nt L t dt dt Equation (25) states that a current account deficit (the RHS being negative) has to be financed by foreign indebtedness (the LHS should be negative). Notice that we can also express the balance of payments equilibrium condition as: ¯ t+1 − (1 + it )LB ¯ t = Pt (Yt − LC ¯ t − It ), LB where It represents aggregate investment (in new firms, expressed in terms of the composite good, e 8 t with It = net W Pt [fT + τt fR ]) and Yt GDP, defined according to the expenditure approach as: ¯ t + It ) + Xt − Mt . pdt Yt = Pt (LC

3

Real Exchange Rate in a Partial-Equilibrium Analysis

Real exchange rate determinants In this section, we devote a particular attention to understanding the sources of exchange rate movements. We define the real exchange rate qt as the relative price of the Foreign basket of goods in terms the Home one, such that qt ≡ Pt∗ /Pt . Before going further, let us mention an important point. As explained in Ghironi & M´elitz (2005), endogenous firm entry induces changes in the composition of the consumption baskets across countries which are not captured in the data. The primary reason is that the empirical CPI measures do not reflect changes in the availability of new varieties which, in turn, induces a potential difference between the “welfare-based” and the “data-consistent” real exchange rate. Importantly, this is not the case in our model, where we can show that the welfare-based real exchange rate, qt , and its data-consistent counterpart coincide exactly.9 8

Notice that GDP can alternatively be defined according to the revenue approach (in terms of the locally produced ¯ t + nt Pt π good) as the sum of labor income and raw operational profits (before taxation): pdt Yt = Wt LH et , with raw ∗ ∗ operational profits (before taxation) equal to nt Pt π et = pdt cdt + pdt cdt − Wt yt . We also check the equivalence with the value-added approach of GDP, amended here to take into account sunk entry costs and PTM, according to:  ∗  Wt µdt ¯ ∗ c∗t Yt = nt yt + net (fT + τte ff ) + nt τ −1 L pdt µdt Let P˜t and P˜t∗ denote the data-consistent average prices indices for all varieties sold in the two countries. In our 1 set-up, they are uncovered from the welfare-based CPIs through the relations: P˜t = (n + n∗ ) 1−σ Pt , and similarly 9

14

This point clarified, let us now deepen the analysis of the determinants of the real exchange rate. Since Ghironi & M´elitz (2005), it is well understood that the real exchange rate not only relies on the relative price of home goods, but also on the relative number of exporting firms (i.e., the extensive margin of trade). Consistently with this view, both dimensions show up here. One originality of our work is to point out the role of a third determinant that channels through endogenous markups adjustment. This can be analytically shown through the real exchange rate equation given the CPIs expressions (3) and (5), expressed in deviation from the symmetric steady state as:   h  i  ∗ 1 1 1 − φ¯ κ1−σ  ∗ w w∗ ∗ b b c c  , (26)  − W − W + (b τ − τ b ) + + [ µ e − µ e ] qbt = [b n − n b ] t t t t t t t t 1 + φ¯ κ1−σ  | κ1−σ | {z } {z } σ − 1 | {z } 1 − φ¯ (b)

(a)

(c)

where κ ¯≡µ ¯∗d /¯ µd is the export markup ratio in the initial steady state and φ ≡ τ 1−σ is the freeness of trade (between 0 and 1, decreasing in τ ). b Equation (26) decomposes the real exchange rate in three terms. Term µ et ≡ µ bdt + φ¯ κ1−σ µ bf t is the weighted value of the markups set on the Home market by both local and foreign firms ∗ b κ1−σ µ b∗dt is the weighted value of the markups in the Foreign market. Term and µ et ≡ µ b∗f t + φ¯ (a) represents the unit labor cost in the Home country relative to Foreign, Term (b) corresponds to the relative number of firms at Home and Term (c) is the overall weighted markup extracted in the Foreign country relative to its counterpart extracted at Home. In this section, we adopt a partial-equilibrium approach to study the role of these three forces behind real exchange rate movements. Interpretation First, it is worth noticing that interpretation of Equation (26) depends on the sign of φ¯ κ1−σ ≷ 1. Throughout the paper, we will assume φ¯ κ1−σ < 1 (or equivalently τ κ ¯ > 1). This condition has an economic interpretation that relies on the optimal pricing decision (13). Under constant markups (σ = θ), markups are identical among destination (¯ κ = 1) such that local firms ∗ fully reports the trade cost on foreign households (pd = τ pd ). When firms can differentiate markups among destinations (σ > θ), they have an incentive to not fully report trade cost on the foreign household. Rather, they will optimally absorb part of it by reducing the export markup relative to the local one (pushing κ ¯ < 1 everything else equal, as shown in Appendix A with more details). abroad. As a result, the associated data-consistent real exchange rate q˜t writes according to: q˜t ≡

1 (n + n∗ ) 1−σ Pt∗ P˜t∗ = = qt . 1 Pt∗ (n + n∗ ) 1−σ Pt

Notice that the equality between q˜t and qt would not hold under i) firm-specific productivity (in which case the number of firms that sell on the Foreign market would not necessarily be the same as those selling on the Home market, as in Ghironi & M´elitz (2005), among others); ii) translog preferences (in which case the functional forms of the CPIs would imply some additive component, which would prevent the simplification in the above equation to occur; see Cacciatore et al., 2016); iii) the presence of home bias in preference (which would intervene in the link between P˜t and Pt , again bridging a gap between qt and q˜t , as emphasized in Cacciatore et al., 2015b (online appendix)).

15

The condition τ κ ¯ > 1 states that the endogenous reduction of the export-to-local markup gap (¯ κ lower than 1) is not sufficiently strong to overcome the trade costs (τ > 1), such that the steady state export price remains higher than the local one (p∗d > pd in Equation (13)). That said, Equation (26) decomposes the real exchange rate into three determinants. Term (a) is the relative unit labor cost of producing at Home relative to Foreign. A reduction in the relative unit cost of producing the Home goods pushes both the local and export prices of Home varieties downward (b pd < 0 and pb∗d < 0). All goods being consumed locally and exported, this tends to reduces the CPIs in both countries. With positive trade costs though, the downward pressure is stronger for the Home CPI than abroad, thereby inducing a real exchange rate depreciation. The real exchange rate also positively depends on the relative number of Home varieties as shown in Term (b). The mechanism channels through the “love-for-variety effect” that links the number of firms and the CPI. In a two-country world in presence of trade costs, an increase in the number of Home firms reduces the Home CPI more than the same increase in the number of Foreign firms. Put it differently, the same increase in n has a stronger dampening effect on the Home CPI than on the Foreign CPI. The differentiated impact of the variety effect on CPIs therefore induces a real exchange rate depreciation. Equation (26) points out a third determinant of the real exchange rate. In the case of endogenous markups (σ 6= θ), the extent of markups differentiation across countries does indeed matter, through Term (c). Everything else equal, an increase in the Foreign-market markup relative to Home ∗ b b (µ et − µ et > 0) pushes individual prices in the Foreign country upwards in relative terms. This induces an increase in the Foreign CPI (relative to Home), i.e. a real exchange rate depreciation. At this stage, we have analyzed the forces behind the PTM behavior (Section 2.2.2) and international relative prices in a partial-equilibrium setting. If this delivers a clear understanding of the mechanisms at work, it remains limited insofar as all the variables are deeply intertwined. Next step is to study the general-equilibrium effects of the two policies under focus, product market deregulation and labor tax reduction.

4

Reforms, Real Exchange Rate and Endogenous Markups

A key objective of the paper is to assess the potential of the reforms to depreciate the country’s real exchange rate in a long-run perspective. This drives us to carefully study the long-run effects on the real exchange rate of a product market deregulation and a payroll tax reduction implemented in the Home country, these reforms being permanent (i.e., modeled as a once-and-for-all change in the administrative cost of entry or in the payroll tax). This will be made in Section 4.2. We will also take advantage of the dynamic structure of our model to study the transition dynamics to the new long-run equilibrium, in Sections 4.3 and 5. We start with presenting the calibration of the model.

16

4.1

Parametrization

¯=L ¯∗ We assume that at the pre-reform steady-state, the two countries are identical in all aspects, L and τ x = τ x∗ for x = {w, e, c}. The number of firms in both countries are identical (n = n∗ ) and all goods are sold abroad at an identical price, such that q = 1. As standard in the literature, we assume an initial zero-trade balance. We calibrate the model (on a quarterly basis) based on either values commonly retained in the literature or by making the steady-state model replicate some empirical targets, that we base on evidence reported for European periphery countries over the recent period. The elasticities of substitution across goods and across sectors are set to σ = 5 and θ = 2 respectively, in line with empirical estimates.10 We assume a typical CES preference function by setting ν = (σ − 1)−1 . We set ψ = 1, implying a log specification on consumption, as standard in the related literature (see Corsetti et al. (2007), Floetotto & Jaimovich (2008), among others). The Frisch labor supply elasticity is set to η −1 = 0.5, in line with the empirical estimates of MaCurdy (1981). As usual in the literature, we calibrate the aggregate hours worked as one third of the total amount of time, normalized to one, H = 0.3. The trade costs are set to τ = 1.3, as suggested by di Mauro & Pappad` a (2014) for countries of the Euro Area. The firm exit rate is set to δ = 0.029, as standard in the literature (see Cacciatore & Fiori (2016), among others). The bond adjustment costs parameter ψb is arbitrary set to ensure the model’s stationarity. We set the regulation cost instrument τ e to 1 in the initial steady state. Home labor is considered as num´eraire, implying W = 1. We also endogenously derive the values of some structural parameters so as the pre-reform steady state matches some empirical targets, the reference country being a periphery European country in the recent period. We thus calibrate µd = 1.36, based on the figures reported by Eggertsson et al. (2014) for Italy and Spain.11 It follows that the export market is lower than on the local market, such that µ∗d = 0.97µd (symmetrically, µf = 0.97µ∗f ), in accordance with the empirical estimates of Moreno & Rodriguez (2004). Given our calibration for τ , this ensures the condition τ κ ¯ > 1. w c The (gross) payroll tax rate is calibrated to τ = 1.34, while the VAT rate is set to τ = 1.2, in line with values observed in continental European countries over the period 1995-2005 based on data provided by Nickell (2006). Administrative entry costs, in terms of GDP per capita, are set equal to 18.7%, in line with the values reported for Italy and Spain by Ebell & Haefke (2009). The aggregate R&D expenditures to GDP is set to 1.94%, as observed in the Euro Zone (Cacciatore ¯ which are invariant during the et al., 2016a). These targets allows us to set values for fR , fT , L 10

There is no clear consensus on these values though. Broda & Weinstein (2006) estimate the elasticity of substitution among goods at the sectoral level for the US. Their median estimate of the substitution elasticity between 3-digit level goods (corresponding roughly to our θ) is 2.50 over the sample 1972-1988. At a most disaggregated level (our σ), they estimate a median substitution elasticity equal to 3.7. Benkovskis & W¨ orz (2014) estimate σ to a value close to 2 for the US between 2 and 2.17 for several countries of the Euro Area. Soderbery (2017) suggests estimates of a same range for these countries. However, Anderson & van Wincoop (2004) suggest a range between 5 and 10 for σ. Atkeson & Burstein (2008) calibrate σ = 10 and θ close to 1, meaning that they allow for a strong pricing-to-market behavior. 11 Notice that a markup calibration of 36% also corresponds to the value adopted by Ghironi & M´elitz (2005).

17

experiments. We conduct our analysis by contrasting our benchmark model featuring endogenous markups (σ > θ), with constant-markups setup (imposing θ = σ = 5). Both reforms are set such that they imply a 1% increase in the long-run value of Home welfare in the endogenous markup case.12 The corresponding reduction of τ e implies a decrease in administrative entry costs from 18.7% of GDP per capita to 17.6%. As for the fiscal policy reform, this amounts reducing the payroll tax rate from 34% to 23.2%. Table 1 reports the set of structural parameters (either calibrated ex-ante or revealed). Table 1: Parametrization Deep parameters

Value

Reference

σ θ τ δ 1/η ψ ψb

5 2 1.3 0.25 0.5 1 0.001

Anderson & van Wincoop (2004) Broda & Weinstein (2006) di Mauro & Pappad` a (2014) Cacciatore & Fiori (2016) MaCurdy (1981) Floetotto & Jaimovich (2008)

R&D entry costs, in % of GDP Regulation entry costs, in % of GDP per capita

1.94 18.7

Cacciatore & Fiori (2016) Ebell & Haefke (2009)

Markup on local market Hours worked Gross payroll tax rate Gross VAT rate Regulation cost instrument

1.36 0.3 1.34 1.2 1

Eggertsson et al. (2014)

Elast. of substitution btw goods Elast.of substitution btw sectors Trade costs Firm destruction rate Frisch labor supply elasticity Curvature of utility function Bond adjustment cost

Pre-reform empirical targets ne fT W/(pd Y W fR pd Y /L

µd H τw τc τe

Own calculations, Eurostat data Own calculations, Eurostat data Normalization

Implied parameters fR fT L σL

Regulatory entry cost R&D entry cost Home country size Scale parameter

0.089 0.0125 0.69 23.19

Note: In the pre-reform steady-state, Home and Foreign countries are symmetric. Deep parameters and implied parameters are fixed during the experiment, implied parameters being calibrated to fit the empirical targets values (set at the pre-reform steady-state).

12

Precisely, we calculate the values of τ w and τ e such that utility raises by 1% in the long run (under σ > θ), i.e. such that ∆U/U0 = 1%, with ∆U = U ref orm − U0 and U0 the initial utility level (before the reform).

18

4.2

Reforms and the Real Exchange Rate: Long-run impact

The first line of Figure 1 reports the long-run effects of a product market deregulation (panel (1)) and a payroll tax cut (panel (2)) on the real exchange rate under constant and variable markups. To get better insights on the transmission channels, we also report, for each reform, the change in the three determinants of the real exchange rate identified in Equation (26), namely the relative unit labor cost in the Home country (Term (a)), the relative number of Home firms (Term (b)) ∗ b b and the overall markup by country (i.e, Term (c) decomposed in its two components, µ e and µ e) (In Appendix B, we also report the responses of the different markups). Variables are expressed in percentage deviation from their pre-reform steady state. Two main comments emerge from Figure 1. First, both a product market deregulation and a payroll tax cut induce a permanent real exchange depreciation. Second, the magnitude of this effect is substantially altered by endogenous markups. The real exchange rate depreciation induced by deregulating the goods market is magnified under endogenous markups while it is dampened after a payroll tax cut. This result thereby suggests an important role for the endogenous PTM behavior. We go deeper in the analysis by considering each reform successively. Product Market Deregulation The first column of Figure 1 disentangles the long-run effects of a product market deregulation at Home on the real exchange rate’s components. We study the underlying mechanisms by first focusing on the model with constant markups (σ = θ). The primary effect of product market deregulation is to play on the number of active firms. By reducing the cost of entry, the reform induces more firms to enter the domestic market, until the free-entry condition (15) is restored. In presence of trade costs, the induced variety effect pushes to a real exchange rate depreciation everything else equal. Yet, this effect is counteracted by the increase in the relative cost of labor in the Home country (panel (1-a)), which conversely tend to induce a real exchange rate appreciation. As more entry exerts an upward pressure on marginal costs for each incumbent firm, this drives the relative price of the Home goods upwards, hence the terms of trade (p∗d /pf ).13 How do variable markups affect this result? Remember that markups’ variations are driven by the “competition effect” as explained in Section 2.2.2: The reduction in the entry cost intensifies competitive pressures between oligopolistic producers and reduces the market share of incumbents on this market. It implies that markup rents extracted on the Home market by both domestic and foreign firms decrease substantially (b µd < 0, µ bf < 0, see Appendix B, Figure 4). On the one hand, the markup reduction at Home moderates the increase in the operational profit and therefore, less Home firms are needed to restore the free-entry condition. Consequently, the increase in the relative number of Home firms (b nt − n b∗t ) is of lower magnitude when markups endogenously adjust (panel (1-b)), which limits the ability of the reform to depreciate the real exchange rate, everything else equal.14 On the other hand, as illustrated by Term (c) in Equation (26), the direct effect of 13

This result is also found in Corsetti et al. (2007), Cacciatore et al. (2016b) or Cacciatore et al. (2016c). Our results show that taking into account the endogenous PTM moderates this effect, as detailed below under σ > θ. 14 The spillover effect of the reduction of τ e on the Foreign number of firms is mainly sensitive in the case of endogenous markups. Through the increase in n, Home product market deregulation reduces the rent that Foreign

19

Figure 1: Reforms and International Competitiveness: Long-Run Effects (1) qbt

0.15

0.2

0.1

0.1 0.05

0

0 <=3

<=3

$ Ud LC t

1

0.5

$ Ud LC t

-0.5

0

-1 <=3

<>3

(1-b) n bt !

6

<=3

n b$t

4

2

0

<>3

(2-b) n bt !

0

FP, % dev.

PMD, % dev.

<>3

(2-a) Ud LC t !

0

FP, % dev.

PMD, % dev.

<>3

(1-a) Ud LC t !

1.5

n b$t

-2

-4

-6 <=3

<>3

<=3

(1-c) Weighted Markups 0.6

-0.2

0.4

-0.4

-0.6

<>3

(2-c) Weighted Markups

0

FP, % dev.

PMD, % dev.

(2) qbt

0.2

FP, % dev.

PMD, % dev.

0.3

0.2

0 Foreign market

Home market

Foreign market

Home market

Long-run responses to a permanent product market deregulation (PMD) and payroll tax cut (FP, for “fiscal policy”) under constant (σ = θ) and variable (σ > θ) markups. Column 1 (2, resp.) displays the long-run effects of a permanent reduction in τ e (τ w , resp.). Both shocks are normalized in order to increase the long-run Home welfare by 1 percent in the endogenous markups model. All deviations are expressed in percentage deviation from the pre-reform steady-state. ct + τbtw The first line shows the real exchange rate, qbt . The second line shows the relative unit labor cost, with U[ LC t = W ∗ ct∗ + τbtw∗ . The third line shows the relative number of firms, n and U[ LC t = W bt − n b∗t . The last line shows the total markups ∗ 1−σ b b et = µ bdt + φ¯ κ µ bf t ) and in the Foreign market (µ et = µ b∗f t + φ¯ κ1−σ µ b∗dt ). extracted in the Home market (µ

20

b lower markups at Home is to drive the weighted markup at Home downwards (µ e < 0) which should magnifies the real exchange rate depreciation. This is all the more at work, as the markup reduction is much weaker on the Foreign market. Indeed, in presence of trade costs, the price-elasticity of Foreign demand is less sensitive to a marginal entry from the Home country than Home demand. This enables the domestic firms to reduce their export markups less than domestically (µ∗d reduces but less than µd ).15 As a result, product market deregulation reduces markups in the Home country more than in the Foreign one (Figure 1, panel (1-c)). This markup contraction at Home, in turn, implies a marked reduction in the domestic CPI that translates into a larger real exchange rate depreciation. Labor tax policy The long-run effects of a payroll tax cut on the real exchange rate are reported in the second column of Figure 1. Consider first the case of constant markups (σ = θ). The primary effect of the labor tax cut implemented in the Home country is to reduce the relative Home unit labor cost (Figure 1, panel (2-a)). This reduces the relative price of Home goods domestic prices, inducing an improvement in price-competitiveness that pushes to the real exchange depreciation. Yet, this effect is compensated by a reduction in the number of domestic firms (in relative terms, panel (2-b)). As discussed by Corsetti et al. (2007), this notably depends on the strength of the substitution effect between consumption and leisure. Indeed, the reduction in the Home good prices pushes the Home CPI downward (see Equation (13)) hence the domestic real wage upward. When the substitution effect is small enough relative to the wealth effect in consumption choices, as in our calibration, the raise in real wages makes households favor leisure to consumption (which only moderately increases). The reduction in the value of total sales leads to a contraction in operational profit, which requires some firms to exit the market in order to restore the zero-profit condition.16 Accordingly, the equilibrium number of firms is lower after the payroll tax cut. From Equation (26), the negative effect on the trade extensive margin counteracts the unit labor cost effect in limiting the magnitude of the real exchange rate depreciation.17 How are these mechanisms affected when markups endogenously adjust? As reported in Figure 1, the magnitude of the real exchange rate depreciation induced by the Home fiscal policy is firms can extract on both their local and export markets, inducing a reduction in the number of Foreign firms under endogenous markups. However, due to trade costs, the magnitude of the effect is much lower than for Home firms. 15 Further, the markup set by Foreign firms for their local market is moderately reduced, in particular as they benefit from the relative-price effect. Indeed, the increase in the Home relative labor cost (Figure 1, panel (1-a)) enables Foreign firms to limit the magnitude of their markup contraction on both destination markets, in particular on their local market. 16 Under the case of constant markups (σ = θ) and a log-utility function on consumption (ψ = 1), assuming linear disutility on labor (η = 0) implies that the two effects cancel each other, such that the payroll tax cut has no impact on the number of firms, as shown in Corsetti et al. (2007). 17 Notice that this negative effect is likely to be amplified if the payroll tax cut was offset by an increase in the indirect tax rate τ c (the so-called “fiscal devaluation” reform) rather than a reduction of lump-sum transfers. Indeed, the increase in the tax burden supported by households tends to reduce the domestic aggregate demand. This, in turn, further reduces incentive to entry, hence ultimately the number of domestic active firms provided the payroll tax rate does not affect the firm entry cost (as in our setting). Accordingly, one might expect a lower magnitude of real exchange rate depreciation with the labor tax policy under this financing scheme.

21

substantially lowered in this case. The lessening of the depreciation can be attributed to the “relative-price effect” on markups, that increases the overall markup at Home relative to Foreign. As discussed in Section 2.2.2, the reduction in the relative unit labor cost for Home firms enables them to extract part of these productivity gains through higher markups on both destination markets. Conversely, this drives Foreign firms to cut their markups to restore their price-competitiveness (see Appendix B, Figure 4). In the presence of trade costs, the strong increase in the markup extracted by the Home firms on the Home market drives the weighted average markup at Home upward, in absolute and in relative terms (panel (2-c)). This raises the relative CPI at Home, thereby limiting the magnitude of the real exchange rate depreciation induced by the gains in unit labor cost (see Term (c) in Equation (26)). Interestingly, this overcomes the fact that the negative extensive margin of trade effect is of lower magnitude under σ > θ. As the Home firms make use of the fiscal reduction to raise their margins, this limits the reduction of operational profits that drives the equilibrium number of Home firms downward. Summary Two main results emerge. First, the two reforms succeed in depreciating the real exchange rate in the long run. This is channeled through distinct channels. The real exchange rate depreciation is driven by a price effect for the payroll tax policy (reduction in the relative price of Home goods), versus the extensive margin of trade in the case of a product market deregulation. Second, these transmission channels are substantially affected by markups endogenous adjustments. With a product market deregulation, the “competition effect” (through the relative number of firms) reduces the weighted average markup at Home. This, in turn, amplifies the effectiveness of the reform to depreciate the real exchange rate. The “relative-price effect” has an opposite effect on markups under the fiscal policy. As domestic firms partly compensate the reduction in relative unit labor cost by an increase in markups, this limits the ability of the labor tax policy to enhance a real exchange rate depreciation.

4.3

Reforms and real Exchange Rate: Transitional effects

Up to now, we have studied the long-run effects of the reforms. However, it is clear that the transitional effects of implementing these reforms does also matter. We now investigate this point, keeping focus on the real exchange rate in this section. Figure 2 thus reports the transition paths of the real exchange rate and its determinants (identified in Equation (26)) to both reforms under the two cases of constant and varying markups. Consistently with Section 4.2, the two reforms succeed in depreciating the real exchange rate in the long run. However, the transition dynamics offers contrasted results. If it depreciates in the long run, the real exchange rate appreciates in the short run after a product market deregulation. By contrast, fiscal policy induces an overshooting dynamics of the real exchange rate, as the magnitude of the instantaneous depreciation is larger than the permanent one. These effects can be explained by the difference of adjustment speeds between the extensive margin of trade channel and the relative price effect.

22

Figure 2: Reforms and International Competitiveness: Transition Dynamics

(a) qbt

1 0.8

$ (b) Ud LC t ! Ud LC t

1.45

-0.8 -0.85

1.4

0.6

-0.9

0.4

% dev

-1 0 1.3

-1.05

-0.2 -1.1

-0.4

PMD, < > 3 PMD, < = 3 FP, < > 3 FP, < = 3

-0.6

1.25 -1.15 1.2

-0.8 5

10

15

6

20

25

30

35

-1.2 5

40

10

15

20

25

periods

periods

(c) n bt ! n b $t

$ b b (d) 7 et ! 7 et

0.5 0.4

4

30

35

40

PMD, < > 3 FP, < > 3

0.3 0.2

2

% dev

% dev

0.1 0

0 -0.1

-2

-0.2 -0.3

-4

-0.4 -6

-0.5 5

10

15

20

25

30

35

40

periods

5

10

15

20

25

30

periods

Transitional responses to a permanent product market deregulation (PMD) and payroll tax cut (FP) under constant (σ = θ) and variable (σ > θ) markups. The variables are similarly defined as in Figure 1. All variables are expressed in percentage deviation from their pre-reform levels. In Panel (b), the response of the difference in unit labor costs reads on the left axis (in blue) for the product market deregulation, and on the right axis (in red) for the labor tax policy.

23

35

40

% dev

-0.95

1.35 0.2

Product market deregulation The increase in the relative number of domestic firms (which pushes toward a real exchange rate depreciation), is only progressive (Panel (c), consistently with Equation (16)). In the period of the reform implementation, given the fixed number of active firms, the deterioration of the price-competitiveness of Home goods causes a real exchange rate appreciation, all the more as the increase in the relative unit labor cost at Home is maximal on impact (Panel (b)). From the free-entry condition (15), the reduction in administrative entry costs τ e reduces the value of the firm, thereby enticing the households to invest in firm creation, see Equation (10). Everything else equal, labor demand increases as required to pay the fixed cost, leading to an increase in the relative Home wage. As long as new firms are created, this effect progressively vanishes, such that the relative unit labor cost decreases to come back to its new longrun value (which remains higher than initially, see also Figure 1). Accordingly, the maximum of the real exchange rate appreciation is reached on impact, to decrease progressively until reaching the new (depreciated) long-run value. Markups endogeneity moderates the magnitude of the temporary appreciation though, as shown in Figure 2, panel (a). As explained above, the overall Foreign ∗ b b markup increases (µ e > 0) while it reduces in the Home country on impact (µ e < 0). This markup differentiation is strengthened along the transition path as the progressive entry of new domestic firms drives further reduction in markups at Home. Endogenous PTM therefore both accelerates and amplifies the real exchange rate depreciation induced by the goods market reform. Payroll tax policy On impact, with sluggishness in the number of firms, the real exchange rate is only driven by the reduction of the relative labor cost (2, panel (b)), leading to a large depreciation. The progressive downward adjustment in the (relative) number of domestic firms then reduces the extent of the immediate depreciation through the variety effect (Panel (c)). The delay between the immediateness of labor cost’s reaction and the inertia in firm entry thus appears at the root of the overshooting dynamics of the real exchange rate. In this respect, it is reminiscent of the seminal Dornbusch’s (1976) result, but in a setup without nominal price rigidity.18 As for the product market deregulation, the endogeneity of markups alters the magnitude of the overshooting dynamics induced by the labor tax policy (Figure 2, panel (d)). Yet, it plays in the other direction. In the immediate of the payroll tax cut, for a given number of firms, the reduction in the relative unit labor cost induces Home firms to raise their markups. Conversely, it drives Foreign firms to reduce theirs. The higher average markup on the domestic market, in turn, moderates the magnitude of the real depreciation along the transition path of the payroll tax policy. Summary These results emphasize the importance of taking into account the transition dynamics if willing to correctly evaluate the effects of the reforms on the real exchange rate. In particular, we share in common with Cacciatore et al. (2016c) and Cacciatore et al. (2016b) the finding that

18

In Dornbusch’s (1976) original setting, the delay of adjustment speeds lies between the financial markets adjusting instantaneously and the goods market, whose price is fixed.

24

the favorable effect of the product market deregulation on the long run takes time to materialize.19 However, our results differentiate from them in two dimensions. First, we shed light on the transitional effects of the product market reform on international relative prices, while this dimension is left behind by these authors. Second, we extend the scope of reform analysis to study the effects of fiscal reform. Importantly, we stress that the real exchange rate dynamics can be understood by a difference in the adjustments speed of the firm entry – which takes time to materialize – and the reaction of the relative prices which is immediate.20 This turns out to be key in shaping the dynamics of the real exchange rate to the reforms.

5

Enlarging the Scope of the Reforms

One may argue that looking only at the real exchange rate provides a truncated view to assess the effectiveness of the reforms. This drives us to enlarge the analysis in two dimensions. On the positive side, we investigate the effects of the reforms on a broader set of macroeconomic variables. On the normative side, we conduct a welfare analysis of the two reforms.

5.1

Assessing the Overall Effects of the Reforms

We start by studying the effects of the reforms conducted in Section 4.2 on a broader set of macroeconomic aggregates. Figure 3 reports the effects of the two reforms on a selected set of variables, focusing on the case σ > θ.21 Two general comments emerge from Figure 3. First, both reforms lead to an increase in GDP and consumption in the Home country in the long run, relative to their pre-reform levels. Second, the transition dynamics of the macroeconomic variables displays quite opposite patterns between the two reforms. At Home, consumption and GDP positively respond to the labor tax cut, the maximum effect being on impact; by contrast, consumption and GDP only progressively increase in response to the product market deregulation. This reform even induces a negative GDP answer the first periods after the policy implementation. This generalizes the conclusion drawn for the real exchange rate: The two reforms apply through distinct - and opposite - channels, which notably 19

The transitional costs of product market deregulation have also been pointed out by Cacciatore & Fiori (2016) in a closed-economy setting. 20 One may investigate the relevance of this intuition by running an experiment that alters the degree of adjustment of one of the two channels. This can easily be made in our framework through varying the firm destruction rate δ, that controls for the degree of inertia of the extensive margin channel. As δ is lower (less firms destroyed each period), the lower the need for firm creation, which turns to be more sluggish. Accordingly, we can expect a larger and more lasting appreciation period with the product market deregulation under a low δ; conversely, a more pronounced exchange rate overshooting dynamics with the labor tax reform. A sensitivity analysis to the value of δ confirms this view. The results are not reported here for sake of space saving. They are available upon request to the authors. 21 Appendix B, Figure complements the IRFs reported here. Notice that we report the dynamic effects of the reforms under the variable-markup case only. If the macroeconomic effects of the reforms are quantitatively different under the case of constant markups, they remain qualitatively unchanged. The whole set of transitional responses under σ = θ is available upon request.

25

Figure 3: Assessing the Macroeconomic Effects of the Reforms (under σ > θ)

(a) Cbt

5 4

bt (b) H

2.5

4

2

3

2

1.5

% dev

% dev

3 % dev

(c) Ybt

5

1

1

2 1

0.5

0 -1

0

0 10

20

30

40

-1 10

periods

1

30

40

10

periods

(d) Cbt$

1.5

20

b$ (e) H t

0.4

20

30

40

30

40

periods

(f) Ybt$

1

0.2

0

% dev

0.5 % dev

% dev

0.5 0

-0.5

0 -0.2

-1 -1.5

-0.4 10

20

30

40

-0.5 10

periods

1

30

40

periods

(g) pb$d;t ! pbf;t

1.5

20

10

20 periods

(h) Net exports

2

1 % of GDP

% dev

0.5 0

0

-0.5 -1

Product Market Deregulation Fiscal Policy

-1 -1.5

-2 10

20 periods

30

40

10

20

30

40

periods

Transitional responses to a permanent product market deregulation (PMD) and payroll tax cut (FP) in the bt (C bt∗ ) is Home (Foreign) consumption, H b t (H b t∗ ) is Home (Foreign) benchmark model with variable markups (σ > θ). C ∗ ∗ b b total worked hours, Yt (Yt ) is Home (Foreign) output, pbd,t − pbf,t is the terms of trade (defined as the relative price of Home exports) and net exports are defined as the difference between exports and imports in the Home country. All variables are expressed in deviation from the pre-reform steady-state, except for the current account expressed in percentage of GDP.

26

differ by their time implementation delay. Going in deeper details of each policy helps clarifying the mechanisms at work. Product market deregulation We find results that are most in accordance Cacciatore et al.’s (2016a, 2016b) findings, even though in a much simpler framework (that abstract from labor market real rigidities and nominal rigidities). The answer of consumption results of two opposite forces: On the one hand, the rise in the number of varieties requires to reduce consumption in order to invest in startups. On the other hand, households can borrow abroad in order to convert the (lasting) rise in real wages into a higher level of consumption. These two forces offset each other’s and consumption hardly change on the very short run (Figure 3, panel (a)). As for the open-economy performances, domestic exports suffer from the deterioration of the price-competitiveness of domestic goods (panel (g)).22 Combined with the rise in imports to sustain aggregate consumption and investment (see Appendix B, Figure 6), this implies a marked trade balance deficit throughout the transition path (panel (h)). The deterioration of net exports, combined with the (even if moderate) negative response of consumption, explains the slightly recessionary effect of the reform on GDP.23 As time goes by, the progressive increase in the number of active firms leads to an increase in GDP, hence consumption which both go beyond their pre-reform levels. However, the magnitude of the GDP increase is quite modest even in the long term, in particular in comparison with the payroll tax policy. Let us now study the spillover effects of the Home goods market reform in the Foreign country. If domestic firms lose, the Foreign firms benefit from the reduction in their relative export price, which boosts their exports. Everything else equal, the improvement in the foreign trade balance thus drives GDP upward, the maximal effect being on impact. Yet, as Foreign households invest at Home through financial assets, private consumption as well as investment in firm creation contract, inducing a reduction of the number of active firms in the foreign country. This, in turn, counteracts the initial upsurge in foreign GDP, which gradually reduces to its pre-reform level (panel (f)). In this respect, if product market deregulation succeeds in depreciating the real exchange rate in the long run, the transition dynamics delivers a more contrasted picture. The Home country faces a trade balance deficit in the short run along with a deterioration of the price-competitiveness of its exported goods (which is permanent). Further, the reform has transitional painful effects on consumption in both countries as well (at best) very modest effects on outputs in both countries. 22

This result stands in line with the related literature, see Corsetti et al. (2007) or Cacciatore et al. (2016b). As detailed in Section 4, this is attributable to the increase in the relative labor cost which drives the relative price of Home goods upward (even though it is partially compensated by the contraction of relative markup). As shown by Cacciatore et al. (2016a), this can be overcome if the production structure assumes an intermediate layer of nontradable goods, which is the sector where product market deregulation occurs. Modeling this production structure in our setting is hence likely to overturn the effects of the reform. Yet, this would not jeopardize the main mechanisms at the root of the real exchange rate dynamics we have identified so far, even if the direction of the effects would change. We thus leave the modeling of this issue for further research. 23 Introducing physical capital may amplify the recession in the short-run since household would reduce both private consumption and investment in physical capital in order to invest into new varieties (see Cacciatore & Fiori, 2016).

27

Payroll tax policy The responses of consumption and hours worked can be explained relying on the consumption-leisure arbitrage condition (Equation (8)). The payroll tax policy induces an increase in the real wage, which drives consumption and hours worked upward through the substitution effect of the consumption-leisure arbitrage (Figure 3, panels (a) and (b)). The maximal effect on consumption is on impact as the contraction in the number of firms (hence, in labor demand) progressively reduces the magnitude of the real wage increase. Yet, consumption persistently remains above its pre-reform level. Home exports benefit from the improvement in their price-competitiveness induced by the payroll tax cut (Panel (g)), explaining a positive response of the Home trade balance (panel (h)). The increase in private consumption and net exports then drive Home GDP upward, despite the reduction in aggregate investment due to lower firm creation.24 Sluggishness of the firm creation (here, destruction) process also explains why the maximal impact on GDP is on impact. As such, the effects of the labor tax reform stand in sharp contrast with the product market deregulation. The difference is also well pronounced regarding the spillover effects of the fiscal reform. The labor tax cut at Home drives Foreign consumption upwards throughout the transition dynamics. Home households investing abroad through financial assets induces a positive wealth effect in the Foreign country, that sustains an increase in Foreign consumption (panel (d)) all along the transition path. By contrast, the domestic payroll tax cut has transitionary negative effects on Foreign GDP. In the very short run, this is mainly attributable to the negative effect on Foreign exports, which drive the trade balance downward. As time goes by, the expansion of world consumption raises positive profit opportunities that induces (slight) positive firm entry in the Foreign country (Appendix B, Figure 6). Combined with the sustained increase in consumption, the induced rise in investment counteracts the initial contraction in foreign GDP, which accordingly gradually comes back to its initial pre-reform level.

5.2

Welfare Analysis

We complete our analysis by investigating the welfare effects of the two reforms. In accordance with the strategy implemented in Section 4, we notably study how these are altered by endogenous PTM behavior. Following Lucas (1987), we express welfare in terms of consumption equivalent units, i.e. we define the compensation Θ that should be given to the households each period for them to accept to stay in the unreformed economy (Θ is positive if the reform is welfare-improving, negative otherwise). This amounts comparing two economies, the first economy which stays ad vitam on the initial steady state, and the second economy experiencing a reform on either τ e or τ w that triggers a transitory dynamics. Let {Ctref orm , Htref orm }∞ and t=0 denote the h dynamic paths of consumption i ref orm ref orm ∞ ref orm worked hours in the second economy and W ≡ W {Ct , Ht }t=0 the associated 24

Notice that the reduction in the number of Home firms is of lower magnitude under endogenous markups, as the increase in the markups of incumbent firms moderates the reduction of operational profit. Domestic GDP thus converges toward a higher level under σ > θ.

28

welfare level. Let also {C0 , H0 } be the levels of consumption and hours in the initial steady state (i.e. in the absence of reform). The welfare gain (loss) is then the Θ solution to:25 ref orm W [{(1 + Θ) C0 , H0 }∞ t=0 ] = W

Table 2 provides the results, with compensation Θ expressed in percentage points of the initial steady-state consumption, for the same policy changes as before (i.e., such that the utility gain amounts to 1% in the long run under variable markups). Table 2: Welfare Gains from the Reforms

Reform

Home Country σ=θ σ>θ

Foreign Country σ=θ σ>θ

Product market deregulation (τ e )

1.36

1.51

0.05

0.01

Payroll tax cut (τ w )

1.19

1.51

0.10

0.18

Note: The reform consists in a reduction in τ e and τ w that increases the long-run utility level at Home by one percent in the endogenous-markups model. Welfare gains are expressed in terms of consumption equivalent units, i.e. Θ, in % of the pre-reform consumption.

Two main comments can be made. First, the positive permanent effect on private consumption dominates the possibly short-term pain effects (Figure 3, panels (a) and (c)) such that both reforms have positive welfare effects, even once the transition dynamics is taken into account, in both countries. Second, and more originally, a given reform (either structural or fiscal) yields higher welfare gains under varying markups (with the exception of the foreign country under the product market deregulation, in which case welfare spillover effects are virtually null). This is a quite intuitive result for the product market deregulation. As the reform leads to a markup contraction (e.g. Figure 4), the monopoly distortive rent reduces, at the benefit of the consumer. This might be viewed as more surprising in the labor tax reform, where conversely markups increase with the payroll tax cut. This is not the sole effect at work though. By affecting firm entry, the reforms also affect consumption in the intertemporal consumption/saving arbitrage (Equation (10)). As discussed in Section 5.1, the reforms have permanent wealth effects on consumption that notably channel through GDP expansion. Taking into account the general equilibrium effects of the reforms is important to understand their impact on welfare. Product market deregulation As reported in Table 2, the reform is welfare-improving in the Home country. From Figure 3, one might infer that welfare gains mostly come from consumption (which permanently increases with the reform), while hours worked hardly move in the long run. 25


Under the assumption ψ = 1, we obtain from Equation (6) that Θ = exp((1 − β) W ref orm − W0 ) − 1, with W0 ≡ W [{C0 , H0 }∞ t=0 ] the discounted flow of utility for the unreformed economy that remains in the initial steady state forever.

29

Further, as noticed, welfare gains are higher under varying markups. This can be rationalized as follows. As discussed in Section 5, a rise in the number of firms penalizes Home consumption since it requires investment in startups (even though international borrowing partly counteract this effect). Since firm entry is less stimulated under endogenous PTM, less saving effort is needed along the transition path, at the benefit of consumption.26 As a result, the welfare gain of the PMD reform, which amounts to 1.36% of permanent consumption under constant markups, raises to a gain of 1.51% of permanent consumption under endogenous PTM.27 Fiscal policy The difference in the welfare gains is even stronger for a payroll tax cut: While it amounts to 1.19% of permanent consumption under constant markups, it raises to 1.51% under endogenous markups. By reducing the labor tax wedge, the fiscal policy raises the real wage which stimulates consumption and hours worked through the substitution effect. On top of that, the rise in the wage bill depresses Home operational profits which in turn reduces the number of firm. Under variable markups though, the relative-price effect leads to a rise in Home markup. This makes the reduction in the operational profit less pronounced than under constant markups. Consequently, households at Home expect a higher stream of future dividends, which magnifies the rise in consumption (See Figure 7, panel (i) in Appendix B) and explains that the welfare gains are larger under variable markups. Spillover effects Let now turn to the spillover effects of the reforms. Unsurprisingly, the welfare effects in the Foreign country are much less substantial than in the reforming one. The product market deregulation has even virtually no impact on Foreign welfare, whatever if markups are variable or not. This stands in line with Figure 3, as neither Foreign consumption nor hours worked are affected by the domestic reform in the longer run (Panels (d) and (e)). By contrast, the fiscal policy exerts a positive welfare spillover abroad, even if modest in magnitude, equal to a 0.1% gain under constant markups and 0.2% under variable markups. From Figure 3, it is clear that this comes from consumption, as the domestic reform has no permanent effect on hours worked aboard. The larger welfare gain under endogenous PTM can be explained by the negative long-term effect of the reform on the number of Foreign active firms under variable markups (see Figure 7, panel (i) in Appendix B), which tends to boost Foreign consumption since less investment in startups are required. Summary Altogether, these results show that both reforms improve welfare in the reforming country. Additionally, the rise in Home consumption is magnified by the presence of variable markups leading to larger welfare gains. Interestingly, the underlying factors depend on the type of 26

See Figure 7, panels (a) and (c) in Appendix B, which reports the responses of a selected set of variables to both reforms, in the two cases of constant and varying markups. 27 To gauge these results more concretely, let note that real final consumption expenditures in the Euro Area were by about 21 104 euros per person in 2015. Therefore, welfare would rise permanently by 287 euros and 329 euros per person and per year under constant markups and variable markups, respectively.

30

reform which is implemented. Variable markups dampen firm entry after a product market deregulation and the associated saving effort, while it lessens the reduction in future dividends after the payroll tax. In both cases, this induces consumption to rise by more than under constant markups which leads to a better welfare improvement. Through a different angle, this result confirms our previous findings, pointing out the importance of taking into account the endogenous PTM behavior if willing to correctly evaluate the overall effects of the reforms.

6

Conclusion

This paper shows how PTM behavior affects the channels through which fiscal and structural reforms affect the real exchange rate. We address this question in a theoretical way, by a developing a two-country dynamic model with endogenous firm entry under international trade costs. Our modeling of the production structure implies that firms can endogenously adjust their PTM behavior on each destination market. In this setup, we study the effects of a payroll labor tax reduction on one side, and a product market deregulation implemented through a reduction in administrative barrier to firm entry on the other side. With this quite simple framework, we provide a careful understanding of the way both reforms operate on the real exchange rate. Two main results emerge. First, if both reforms succeed in depreciating the real exchange rate in the long run, this works through very distinct channels, that also affect the transitional dynamics of the reforms. Further, the divergent effects of the two reforms on the real exchange rate generalizes to broader set of macroeconomic variables. If it succeeds depreciating the real exchange rate in the long run, deregulating the goods market induces a temporary appreciation along with a trade balance deficit at Home and a recession abroad. By contrast, the exchange rate overshooting dynamics induced by the fiscal policy contributes to a trade balance surplus in the reforming country, as well as a temporary expansion in both economies. Second, we show the important role of the endogenous PTM behavior of firms as a propagation channel of both reforms on international relative prices. If it strengthens the ability of the product market deregulation to depreciate the real exchange rate in the long run, endogenous markup adjustment conversely reduces that of the fiscal policy. Endogenous PTM also has implications in a normative perspective. While both reforms are welfare-improving, the welfare gains are larger when markups endogenously adjust. Through a different angle, this result thus confirms our previous findings about the role of endogenous markups adjustment. In this respect, our paper points out the importance of taking into account the firms’ PTM behavior if willing to correctly evaluate the overall effects of the reforms, both from a positive and a normative perspectives. We purposely kept our model simple, to shed light on the deep transmission channels at work in a very transparent way. This opens the route in a number of directions. One fruitful extension could be to incorporate the role of firm heterogeneity. By introducing a new channel of firm competition within the country, firm heterogeneity modifies the adjustments along the extensive margin of trade as well as through relative prices, hence ultimately on endogenous markups decisions. Taking this dimension into account may accordingly enrich the effects of the two reforms. Second, one might 31

want to address the issue of the effects of the reforms in a vertically-linked world, with spillover effects between the upstream and the downstream sectors. This might be particularly relevant in view of the policy debates that call for deregulating the services up-stream markets, that are not exposed to international competition. Addressing these issues is left for further research.

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A A.1

Real exchange rate, markups: More details Markups and PTM

In this section, we come back to the point relating endogenous markups and PTM made in Section 3. To this aim, we start considering the expressions of the price-elasticities of demand for the Home variety from the Home and Foreign markets (Equations (17) and (18)) in the initial symmetric steady state, denoted ε¯ and ε¯X for notational simplicity:28 m ¯

}| { 1 ε¯ = σ − (σ − θ) n ¯ (1 + φ¯ κ1−σ ) 1−σ φ¯ κ ε¯X = σ − (σ − θ) n ¯ (1 + φ¯ κ1−σ ) {z } | z

(A-27) (A-28)

m ¯X

with φ ≡ τ 1−σ the freeness of trade (between 0 and 1), κ ¯≡µ ¯X /¯ µ the export-to-local markup ratio ¯ and m ¯ X the market ¯ = µd = µ∗f in the symmetric steady state) and m (with µ ¯X = µ∗d = µf and µ shares of the firm on the local and the export markets respectively. Consider first the standard CES case (σ = θ). As noted above, in this case price-elasticities of demand and markups are constant and equal across destination markets. Trade costs yet induce an asymmetry between the market shares a firm can obtain depending on the destination market, as in this case: m ¯ =

1 , n ¯ (1 + φ)

m ¯X =

φ n ¯ (1 + φ)

As long as φ < 1 (ie, in presence of trade costs), the market share of the firm is higher when it sells on the local market relative to abroad. The mill-pricing strategy of firms on their export market (ie, firms passing on the iceberg trade costs to foreign consumers) indeed raises the relative price of imports. This drives consumers to favor locally produced goods, hence an asymmetric market share in favor of local firms (m ¯ >m ¯ X ). Note that this holds in the absence of home bias in preferences. As long as σ > θ, positive trade costs (φ < 1) also affect the price-elasticities of demand, hence the markups set by firms. As can be inferred from Equations (A-27 and (A-28), everything else equal an increase in trade costs raises the price-elasticity of the demand for imports, while it decreases ε¯X < 0, the price-elasticity of the demand for the local good ( ∂∂φ

∂ ε¯ ∂φ

> 0). From Equation (14), this,

in turn, affects markups differently depending on the destination market. Precisely, trade costs tend to induce lower markup on the export market, due to a higher price-elasticity of demand than on the local market (ie pushing κ ¯ < 1 everything else equal). If in the initial steady state the magnitude of the PTM behavior is not strong enough to more than compensate the effects of trade costs, then firms face a more elastic demand on the export 28

In the initial symmetric steady state, payroll tax rates are identical (τ w = τ w∗ ) and the wage ratio implying a ratio of unit labor cost equal to 1.

35

W W∗

= 1,

market, leading to a lower export markup. From Equations (A-27) and (A-28), this is the case when φ¯ κ1−σ < 1, or equivalently τ κ ¯ > 1. In this case further, the export price (pX ) remains higher than the local one (p), as:

µ ¯X pX =τ >1 p µ ¯

Note that this is reminiscent of the condition

1 τ

<

pX p

< τ for PTM to be sustainable in equilibrium

pointed out by Atkeson & Burstein (2008). Transposed in terms of markups, this condition becomes: κ1−σ < 1, we ensure the first part of the inequality condition holds 1 < τ µ¯µ¯X < τ 2 . By imposing φ¯ analytically. In our simulations, our calibration τ µ ¯X /¯ µ = 1.3 × 0.97 = 1.26 ensures the inequality holds.

B B.1

Complements on the effects of the reform A detailed view of markup changes

Figure 4 displays the long-run effects of the product market deregulation (first line, PMD) and the fiscal policy (second line, FP) on the markups by both domestic and foreign firms on the two destination markets. Figure 4: More on the long-run effects of the reforms 0

(a) Home market (PMD)

0

(b) Foreign market (PMD)

-0.05 -0.1 -0.15

-0.05

% dev.

% dev.

-0.2 -0.25 -0.3 -0.1

-0.35 -0.4 -0.45 -0.5

-0.15 7d

7f

(c) Home market (FP)

0.45

7$ d

7$ f

(d) Foreign market (FP)

0.2

0.4 0.15

0.35 0.3

0.1

% dev.

% dev.

0.25 0.2

0.05

0.15 0

0.1 0.05

-0.05

0 -0.05

-0.1 7d

7f

7$ d

7$ f

Similarly, Figure 5 reports the transitional responses of the four types of markups following the two reforms (Panels (a) to (d)). We also report the IRFs of the average markup by destination market, µ e and µ e∗ .

36

Figure 5: More on the short-term effects of the reforms (1)

B.2

Reforms and macroeconomic aggregates: Complements

Transitional dynamics effects In complement to Figure 3, we report the transitional responses of the number of firms, the individual output by each active firm and the aggregate investment in each country in Figure 6. Understanding welfare effects

In view of analyzing the welfare effects of the reforms (Section

5), Figure 7 reports the long-run responses of the number of firms and aggregate consumption at Home and abroad as well as Home GDP to both reforms, in the two cases of constant and varying markups.

37

Figure 6: More on the short-term effects of the reforms (2)

38

Figure 7: More on the long-run effects of the reforms

39