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Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. The Model
  5. The Open Economy
  6. Welfare and Policy Analysis
  7. Full Specialization in the Traditional Industry
  8. Conclusion
  9. Appendix
  10. References

This paper explores the role of country asymmetries for trade and industrial policies with heterogeneous firms. The analysis delivers a number of novel results. First, trade policies, infrastructure policies and industrial policies which improve the business conditions in one country have negative productivity and welfare effects on the trading partner. Second, symmetric trade liberalization is immiserizing for a trading partner whose business conditions are inferior. Third, there are gains from trade even for a country whose monopolistically competitive sector with heterogeneous firms is wiped out by switching from autarky to trade.

Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. The Model
  5. The Open Economy
  6. Welfare and Policy Analysis
  7. Full Specialization in the Traditional Industry
  8. Conclusion
  9. Appendix
  10. References

A recent strand of research has started to explore the policy implications of the theories of heterogeneous firms and trade. These theories were developed in response to empirical challenges to old and new trade theory which emerged as micro-data sets allowed to track the production and trade at the firm level (Bernard et al., 2007). The seminal works by Melitz (2003), Bernard et al. (2003) and Yeaple (2005) provided theoretical explanations for the findings that exporting firms are a “rare species” and typically larger and more productive than non-exporting firms.1

Our paper contributes to this nascent policy literature. We consider the role of an extensive list of factors that determine the conditions of doing business and that are affected by trade and industrial policies: the access to technologies, market (country) size, market entry costs, exit rates, fixed costs to serve domestic and foreign markets, the trade infrastructure, and also Ricardian productivity differences which imply that countries exhibit different wage levels. We use a two-sector version of the Melitz (2003) model in the spirit of the new trade theory with a competitive sector (“traditional good”) in addition to the monopolistically competitive sector with heterogeneous firms (“modern/manufacturing sector”). This allows us to integrate these country asymmetries in an analytically tractable and slim way. The analytical tractability of our framework also enables us to compactly synthesize previous policy findings.

Our analysis delivers a number of novel results. First, we show that trade policies, infrastructure policies and industrial policies which improve the business conditions in one country, induce a positive selection effect and bring welfare gains to that country but have a negative welfare effect on the trading partner. The possibility that a trading partner is hurt by a country's technology improvements in the modern sector was identified by Demidova (2008). However, we show that even if technology potentials are identical in both countries, a trading partner experiences negative productivity and welfare effects owing to a variety of differences in business conditions such as entry costs, exit probabilities and/or wages. We also show that these effects are magnified when trade costs are lower.

Second, we show that strong asymmetric productivity and welfare effects derive from symmetric trade liberalization. Such liberalization exerts a positive productivity and welfare effect on the country that has superior business conditions and a negative productivity and welfare effect on the other country. Demidova (2008) has theoretically proven that immiserizing trade liberalization is possible, but her analysis was confined to country differences in terms of technology potentials. We show that such differences are not necessary for immiserization. Rather, a very broad set of business conditions which can be influenced by industrial policies may account for these asymmetric productivity and welfare effects.

Third, while previous analyses have been confined to settings where the countries are diversified in production, we also study the case where the switch from autarky to trade drives one country into full specialization in the traditional good.2 Our model predicts this to happen if countries are strongly asymmetric with respect to business conditions. For that case we show that there are gains from trade even for the country whose monopolistically competitive sector with heterogeneous firms is wiped out by the switch from autarky to trade.

Previous Literature

Our paper is related to an emerging literature that explores policy issues in models with heterogeneous firms à la Melitz (2003). A closely related work is the seminal analysis by Melitz and Ottaviano (2008). They consider country differences in size, import barriers and technologies in the modern sector. Their analysis builds on the linear demand system with horizontal product differentiation developed by Ottaviano et al. (2002). We use the Dixit–Stiglitz (1977) framework, in contrast. This difference brings a benefit but also a cost. The well-known cost is that the mark-ups on marginal costs are constant across firms and invariant to market size in the large-group case that we consider. Hence, the pro-competitive effects that prevail in the Ottaviano–Tabuchi–Thisse framework are absent in our analysis. On the benefit side, we arguably gain tractability, which is important since we focus on country asymmetries along more dimensions than those addressed by Melitz and Ottaviano (2008).3 For example, we are able to provide a meaningful analysis of the effects of fixed costs of serving markets, which are not considered by the authors since they would be inconsequential in their model with bounded marginal utility. Furthermore, neither they nor the other papers that we reference in the following consider the case where one country is driven into specialization on the traditional good by shifting from autarky to trade.4 Another closely related paper is Demidova (2008). She studies differences in the technology potential across countries in a two sector Dixit–Stiglitz (1977) framework.5 We explain in detail how our results relate to hers as we go along. Baldwin (2005) and Baldwin and Forslid (2010) are also related in that they study the welfare effects of trade integration, albeit in a model which lacks the comprehensive set of business conditions that we account for.6 Demidova and Rodriguez-Clare (2009) study trade policy and welfare issues from the point of view of a small open economy. Hence, the international repercussions emerging in a two-country setting that we highlight are absent in their paper.7 Pflüger and Suedekum (2013) analyze the non-cooperative and cooperative choice of entry subsidies.

Our paper is also related to the older literature on (strategic) trade policies, infrastructure policies and industrial policies under monopolistic or oligopolistic competition (e.g. Flam and Helpman, 1987; Venables, 1987; Helpman and Krugman, 1989; Brander, 1995; Martin and Rogers, 1995; Baldwin et al., 2003). The latter branch of this literature highlights strategic firm interaction and government policy incentives in markets with only few firms whereas we are concerned with a monopolistically competitive industry. The former branch of the earlier literature highlights monopolistic competition but ignores firm heterogeneity altogether. There are two key differences between the earlier policy literature and our analysis, which builds on Melitz (2003). First, we highlight firm dynamics featuring ex-ante uncertainty about a firm's productivity, forward-looking entry with sunk entry costs and lethal shocks that force firms out of business. These elements are absent in the older literature. Second, Melitz (2003) established a firm selection effect which is absent in the older literature with homogeneous firms and which plays a central role in our policy analysis. However, all these differences notwithstanding, there are some commonalities between this earlier literature and our analysis which we work out and explain as we proceed.

The paper's structure is as follows. Our basic model is laid out in section 2. Section 3 derives the open economy equilibrium with two countries. Section 4 covers the gains from trade and our welfare and policy analyses under the usual assumption that both countries are diversified in production both before and after trade. Section 5 then turns to the case where one country is forced into full specialization in the traditional industry. Section 6 offers concluding remarks.

The Model

  1. Top of page
  2. Abstract
  3. Introduction
  4. The Model
  5. The Open Economy
  6. Welfare and Policy Analysis
  7. Full Specialization in the Traditional Industry
  8. Conclusion
  9. Appendix
  10. References

General Set-up

Our model is based on a version of the monopolistic competition model with heterogeneous firms (Melitz, 2003) by Demidova (2008). There are two industries. A traditional industry n produces a homogeneous numéraire good under constant returns to scale and perfect competition, and a monopolistic competitive industry c produces a continuum of differentiated manufacturing varieties under increasing returns. Each variety is produced by a single firm and firms' productivities are heterogeneous. Labor is the only factor of production in both industries. There are L workers who supply one unit of labor each without loss of utility. A simple quasilinear utility function characterizes their preferences over the two types of goods as in Pflüger and Suedekum (2013). The twin assumptions of a linear numéraire sector and quasilinear preferences allow us to keep the analysis tractable and still to retain a full-fledged model of trade (Tabuchi and Thisse, 2006) which is well-suited to explore normative issues (Ottaviano and Thisse, 2003).8 We consider an extensive list of factors which affect the conditions of doing business in the modern sector. We allow for country asymmetries concerning effective entry costs, exit rates, the fixed costs to serve domestic and foreign consumers, respectively, market (country) size, trade and transport infrastructure, (Ricardian) productivities in the competitive sector and the access to manufacturing technologies (“technology potential”). We first look at a single country in autarky. Since the Melitz-type model that we use is extensively characterized in the literature (see Melitz, 2003; Baldwin, 2005; Demidova, 2008) the following exposition is deliberately brief.9

Preferences

Household h's preferences are defined over the homogenous good and the set of differentiated varieties, z ∈ Ω, according to a logarithmic quasilinear utility function with a constant elasticity of substitution (CES) subutility10

  • display math(1)

where 0 < ρ < 1 and β > 0 are constant parameters and where qh(z) expresses household h's consumption of variety z. The elasticity of substitution between any two varieties is given by σ ≡ 1/(1−ρ) > 1. It is well known from Dixit and Stiglitz (1977) that ch can be understood as the consumption of the manufacturing aggregate with aggregate price

  • display math(2)

The budget constraint of h is Pch + nh = w, where w denotes a household's (wage) income. Utility maximization implies that per-capita expenditure on the manufacturing aggregate and the numéraire are given by Pch = β and nh = wβ, respectively, and indirect utility is vh = w − β ln P + β(ln β − 1). Since households are identical we drop the index h from now on. We assume β < w in order to ensure that the demand for the homogeneous good is non-negative. Aggregation over all individuals yields that the overall expenditure on manufacturing goods, PcL, equals βL. Aggregate demand for a single variety z is given by q(z) = p(z)σPσ−1βL, and total revenue for that variety is r(z) = p(z) q(z) = [P/p(z)]σ−1βL.

Production and Pricing

In the numéraire sector a units of labor are transformed into one unit of output. This pins down the wage, w = 1/a. Technologies in the modern sector are such that l = f + q/φ units of labor are needed to produce q units of output. The fixed overhead labor f is the same for all firms, the variable labor requirement (1/φ) differs across firms. Firms have zero mass. Each firm thus perceives a demand curve with constant price elasticity −σ. Profit maximization implies that a firm with marginal cost (w/φ) charges the price:

  • display math(3)

Revenue and profits of this firm are then given by r(φ) = βL(ρφP/w)σ−1 and π = r(φ)/σ − wf, respectively. Hence, a firm with higher productivity level φ charges a lower price, sells a larger quantity and has higher revenue and profits. Since all firm-specific variables differ only with respect to φ, the CES price index (2) can be rewritten as

  • display math(4)

where M denotes the mass of manufacturing firms (and varieties) in the market, μ(φ) is the productivity distribution across these active firms with positive support over a subset of (0, ∞) and inline image is an average productivity level as introduced by Melitz (2003).

Entry and Exit

There exists a mass of potential entrepreneurs who can enter the modern sector subject to a sunk entry investment in terms of labor fe. At each point in time a mass of ME entrepreneurs decides to enter. Upon entry these entrepreneurs learn about their productivity φ, drawn from a common and known density function g(φ) with support (0, ∞) and cumulative density function G(φ) (the “productivity lottery”). After the productivity is revealed, an entrant can decide to exit immediately or to remain active in the market, in which case the firm earns constant per-period profits π(φ). It will exit immediately if π(φ) < 0 [LEFT RIGHT ARROW] r(φ) < σ w f. Only those firms remain active whose productivity draw exceeds the cutoff φ* > 0 at which profits are zero, π(φ*) = 0. Once in the market, every firm may be hit with constant probability δ by a lethal shock which forces it to shut down and exit.11 We focus on a stationary equilibrium without time discounting such that in each period the mass of entrants which successfully enter the market equals the mass of firms that are forced to shut down. Analytically, probi ME = δ M, where probi = 1 − G(ϕ*) is the probability to draw a productivity no smaller than the cutoff φ*. The endogenous productivity distribution among surviving firms, μ(φ), is thus the conditional (left-truncated) ex-ante distribution g(φ*) on the domain [φ*, ∞).

Equilibrium and Parameterization

The equilibrium in the modern sector is characterized by a free entry condition (FEC) and a zero cutoff profit condition (ZCPC). Assuming risk neutrality, potential entrepreneurs enter the market (i.e. incur the entry cost wfe to participate in the productivity lottery) until the value of entry inline image is driven to zero (FEC). The FEC can be rewritten as inline image. The ZCPC states that the cutoff firm makes zero profits, π(φ*) = 0 [LEFT RIGHT ARROW] r(φ*) = σ w f which can be rewritten as a function of the average productivity level inline image: inline imageas in Melitz (2003). The equilibrium cutoff productivity φ* simultaneously satisfies the FEC and the ZCPC. In order to conform to the empirical evidence and to obtain closed-form solutions we assume Pareto-distributed productivities, G(φ) = 1 − (φmin/φ)k and inline image where φmin > 0 is the lower bound for productivity draws and k > 1 is the shape parameter.12 The ex post probability of productivities is then conditional on successful market entry, μ(φ) = g(φ)/[1 − G(φ*)] = kφ*kφ−(k+1) if φ > φ* and μ(φ) = 0 otherwise. It follows that inline image, where we strengthen our previous assumption to k > σ − 1. Using these expressions in FEC and ZCPC we obtain the autarky equilibrium cutoff:

  • display math(5)

Throughout the paper we assume the condition ([(σ − 1)f]/[(k − σ + 1)feδ])1/k > 1 to ensure that inline image. The equilibrium cutoff is independent of the number of workers L, positively related to the elasticity of substitution σ, the fixed labor f to serve the market and the lower bound φmin, and negatively related to the fixed investment of labor at the entry stage fe, the death rate δ, as well as the Pareto-shape parameter k, as in Melitz (2003) and Demidova (2008).13 Moreover, inline image is unaffected by the labor coefficient in the competitive sector since a affects the wage and hence the fixed costs both to enter and serve the market equi-proportionately. We show below that countries' labor coefficients affect the cutoffs in the open economy equilibrium. Once the equilibrium cutoff is determined, all other endogenous variables are easily derived (as in Melitz (2003) and Baldwin (2005)). The autarky price level which we need for future reference is given by inline image and the indirect utility of a household is then:

  • display math(6)

The Open Economy

  1. Top of page
  2. Abstract
  3. Introduction
  4. The Model
  5. The Open Economy
  6. Welfare and Policy Analysis
  7. Full Specialization in the Traditional Industry
  8. Conclusion
  9. Appendix
  10. References

Country Asymmetries and Trade Costs

We now turn to an open economy setting with two countries i, j ∈ [H, F], say home H and foreign F. These two countries can potentially differ with respect to a variety of business conditions. There may be differences in country size Li, the labor coefficient in the traditional sector ai and in the technologies in the modern sector. Concerning the latter we assume that entrants in country i draw their productivity from a country-specific Pareto-distribution with common shape parameter k but with potentially different lower bounds, φmin i.14 Exit rates δi and the fixed labor input for entry in the manufacturing sector fe,i as well as the fixed labor input fi to serve domestic markets may also differ across countries. If (after learning its productivity φi) a firm from country i decides to export to region j it faces an additional country-specific fixed cost fxi, on top of the domestic per-period fixed costs fi that accrue irrespectively of export status. We assume that fxi > fi to ensure that only a part of the domestic firms is active in trade. We also assume fxi > fj so that the fixed labor input that has to be incurred to serve the export market exceeds the fixed labor that foreign competitors have to incur in their home market. Moreover, there are variable iceberg costs to serve foreign consumers: for one unit to arrive in j, a firm from country i has to ship τij > 1 units. We shall allow for the possibility that τij ≠ τji, e.g. caused by different trade policies or trade infrastructures. Trade in the traditional sector is costless. As long as both countries produce this good, an assumption that we shall maintain throughout the paper, the law of one price dictates that the foreign wage is tied to the domestic wage, W ≡ wF/wH = aH/aF where W denotes the relative foreign wage. Note that wi = 1/ai by our choice of the numéraire. Hence, we do not impose factor prize equalization.

Domestic Cutoffs and Export Cutoffs

The domestic cutoff productivities inline image and inline image are derived by drawing on the conditions of free entry and zero cutoff profits which become interdependent in the open economy. If a firm from country i exports to country j, its export profits are given by πxi(φ) = rxi (φ)/σ − w · fxi where inline image is the export revenue. There is a critical productivity threshold inline image where such a firm breaks even on the export market, i.e. inline image. We call this the export ZCPC. Furthermore, a firm from country i that serves her home market i derives profits πi(φ) = ri(φ)/σ − wifi where inline image is the associated revenue. The inline image where this firm breaks even is defined by inline image. We call this the domestic ZCPC. As in Demidova (2008) the revenue equations imply a link between export cutoffs and domestic cutoffs, inline image and inline image where ti ≡ τij(fxi/fj)1/(σ−1). The free entry condition (FEC) for country i commands that firms enter the market until the value of entry is zero, inline image. The first term on the left-hand side formalizes the expected profits on the domestic market and the second term expresses expected profits on the export market where inline image denotes the probability for a productivity draw high enough to enter the export market. The right-hand side expresses the entry costs. The resulting equilibrium cutoff productivities can then be derived as in Baldwin (2005) and Demidova (2008):

  • display math(7)
  • display math

where inline image are measures of trade openness which rise as variable trade costs τij and/or the fixed cost ratio fxi/fj fall. Notice that fxi > fj entails 0 ≤ Φi < 1. The parameter inline image captures international differences (ratios) in exit rates D ≡ δF/δH, entry investments Fe ≡ feF/feH, technologies in the manufacturing sector as proxied by the lower productivity bounds of the Pareto-distribution T ≡ φminH/φminF and wage differentials W ≡ wF/wH = aH/aF caused by productivity differences in the competitive sector. inline image rises when home business conditions turn in favor of domestic firms.

Parameter Restrictions

Throughout our analysis in sections 3 and 4 we impose three conditions to ensure meaningful results in the open economy equilibrium. First, we have to ensure that both sectors are active in both countries, Mi > 0 (non-specialization in production). Second, in equilibrium the export cutoffs have to exceed the domestic cutoffs, inline image, so that only domestically active firms can export. Third, it must hold true that inline image. The third condition is implied by the first and the second condition. The Appendix reports the parameter restrictions in terms of exogenous variables which correspond to conditions one and two. Furthermore, we have to ensure that there is a set of parameters which simultaneously fulfils all conditions stated above. We derive and report this necessary condition in the Appendix. Intuitively, the parameter restrictions imply that the overall business conditions for the manufacturing sectors in the two countries must not be too different. Notice that it is clearly conceivable that business conditions are so disparate that one country, call it the “laggard”, is driven into full specialization in the traditional industry and that all manufactures are produced in the “leading” country. We take this case up in section 5. When international differences in business conditions are absent (with inline image and ΦH = ΦF = Φ) the cutoffs are given by inline image both for H and for F as in Melitz (2003).

Trade Balance and Open Economy Equilibrium

To complete the characterization of the open economy equilibrium we impose balanced trade. This allows us to derive the firm masses. The CES price indices inline image are immediately implied by the domestic ZCPC (see the Appendix). The indirect utility then follows as:

  • display math(8)

Welfare and Policy Analysis

  1. Top of page
  2. Abstract
  3. Introduction
  4. The Model
  5. The Open Economy
  6. Welfare and Policy Analysis
  7. Full Specialization in the Traditional Industry
  8. Conclusion
  9. Appendix
  10. References

This section assumes that the two countries are diversified in production before and after trade. The following subsection begins with the gains from trade. The policy analyses that we perform in the further subsections start from an international equilibrium as characterized in section 3.

The Gains from Trade

The welfare effect of opening up an economy from the state of autarky to trade is unambiguously positive as stated in

Proposition 1. (Gains from trade). Both countries have higher welfare under free trade than under autarky.

Proof. Proposition 1 is immediately implied by equations (7) and (8). By (7) the equilibrium cutoffs are higher in the two countries under trade than under autarky. The price level is then lower in both countries and this entails by equation (8) that welfare (indirect utility) is higher, vi − vaut > 0. □

Proposition 1 is a straightforward extension of the gains from trade theorems proven by Melitz (2003) for the case of identical countries and by Demidova (2008) for the case of countries which are asymmetric with respect to technologies in the modern sector. We extend this result to economies which are asymmetric with respect to a comprehensive set of factors that determine the conditions to do business. As in Melitz (2003) the welfare gain associated with the move from autarky to trade derives from the selection effect which drives up the productivity cutoffs.

Unilateral Trade Integration and Infrastructure Policies

We now turn to the analysis of the effects associated with a reduction of trade costs between the two countries. We start with the case of unilateral trade integration where one country (say j) allows firms located in i better access to its consumers. This is captured by an increase in Φi which may stem either from reductions in variable trade costs τij and/or from reductions in the fixed export costs fxi. Our results are summarized in:

Proposition 2. (Welfare gains and losses from unilateral trade integration). (i) A unilateral reduction in trade costs to serve market j (captured by dΦi > 0) leads to welfare gains in country i and welfare losses in country j. (ii) The effect of unilateral trade integration on country i's productivity is the stronger, the more favorable are the business conditions in i relative to j.

Proof. To prove the first part of Proposition 2 first note that, by equation (7), inline image and inline image. Taking this into account in the indirect utility, equation (8), immediately implies our claim. The second part follows from noting that inline image. □

The intuition behind Proposition 2(i) is the following. Granting firms located in country i better access to consumers located in country j raises the profitability to produce manufacturing varieties in country i. This stimulates entry and tightens competition in i. The least productive firms are driven out of the market in i and the cutoff is raised. This benefits domestic consumers and leads to a competitive advantage of firms in i over firms located in j. The latter increases import competition in market j which reduces the incentive for foreign firms to enter the market in j. Competition is thus weakened resulting in a reduction in the foreign productivity cutoff which negatively affects the welfare of foreign consumers. Proposition 2(i) has previously been established by Melitz and Ottaviano (2008) in a setting with heterogeneous firms and linear demand (cf. section 1). It should also be noted that a corresponding finding has been established by Venables (1987) in a setting of monopolistic competition with homogeneous firms. Market exit and entry are also key in his analysis (see also Baldwin et al. (2003) and Ossa (2011)). The firm selection effect that is a hallmark of trade theory with heterogeneous firms, is absent in his and related work in the older literature, however. Proposition 2(i) obtains further significance because it shows that immiserization occurs even if the liberalizing country has business conditions which are much superior to those of its trading partner. The results comprehended by Proposition 2(i) involve trade and infrastructure policies. Reductions in variable trade costs (ij < 0) can both be thought of as being due to lower import tariffs, similar trade costs or infrastructure policies (such as greater and more efficient harbors or airports) in country j. Proposition 2(ii) carries an important message for trade negotiations: it shows that the incentive on part of a country to request better market access to a foreign country rises the more favorable are its own business environment.15

Symmetric Trade Integration

We now turn to the case of a symmetric reduction in trade costs which we formalize in a very broad way as a policy reform which is characterized by dΦH = dΦF > 0. Recalling the definition inline image, our concept of symmetric trade cost reduction may come about through a fall in variable trade costs τij, a fall in the fixed cost ratio fxi/fj or any combination of the two. Moreover, it need not be the case that both countries strictly reduce each of these trade cost components one for one (i.e. we do not require that, for example, ij = ji). However, our concept requires that both countries increase their overall trade freeness Φi and Φj such that dΦH = dΦF > 0. Finally, we do not impose the condition that the overall level of trade freeness or any component of trade costs is identical across countries before the trade policy reform takes place (i.e. we allow that, initially, τij ≠ τji, fxi/fj ≠ fxj/fi and Φi ≠ ΦF). The welfare effects of a symmetric trade liberalization formalized in this way are expressed in:

Proposition 3. (Welfare gains and losses from symmetric trade integration). A symmetric reduction in trade costs (dΦH = dΦF > 0) leads to welfare gains in both countries if business conditions are similar, i.e. if inline image. Otherwise, one country experiences welfare losses whereas the other reaps welfare gains, e.g. if inline image, country H wins and F loses.

Proof. A country's welfare rises (falls) when the productivity cutoff rises (falls). Totally differentiate inline image, use the derivatives of the equilibrium cutoffs inline image and inline image for i, j, impose dΦH = dΦF > 0, and then explore the sign of the derivatives. □

This proposition shows that the possibility of immiserization through trade integration first identified by Demidova (2008, proposition 1) may have many causes. Demidova allows technology potentials in the manufacturing sector to differ across countries and she shows that it is possible that the “laggard” (the country with the inferior technology potential) may lose from falling trade costs. We extend this result in two dimensions. First, we show that asymmetric business conditions in a much more comprehensive sense are accountable for the possibility of immiserization. In fact, there is the possibility of immiserization even without differences in technology potentials in the modern sector. To see this consider the case where country F is the laggard and H is the leading country and remember that inline image. The condition inline image can be fulfilled even if T ≡ φminH/φminF = 1, indicating identical technology potentials.16 Second, in contrast to the previous literature, we allow for a symmetric reduction of trade costs in a very broad manner (see our previous discussion). In particular, the policy reform that we consider may proceed from an initial situation where firms face different conditions to accede consumers in the other country (i.e. where ΦH and ΦF may differ initially).17

Industrial Policies and Business Conditions in the Open Economy

Industrial policies have a direct effect on business conditions. Business conditions, in turn, impact on the productivity of firms and on country welfare under international trade. We have:

Proposition 4. (The effect of industrial policies and business conditions under trade). Lower domestic entry investments fei, lower labor productivity in the traditional sector 1/ai, a lower default risk δi and/or greater technological potential φmini in country i raise the cutoff productivity and welfare in this country and decrease productivity and welfare in country j.

Proof. This proposition follows immediately by considering the effects of changes in fei, 1/ai, δi and φmini on equations (7) and (8). □

Intuitively, any improvement in business conditions in country i, such as a better technology potential, lower entry investments, a lower exit probability and/or lower wages, raises the profitability of the domestic market and gives local firms a competitive edge over their foreign competitors. This stimulates entry in country i and reduces the incentive to enter the manufacturing industry in country j, which sets in a selection effect that leads to higher cutoffs and welfare in i and lower cutoffs and welfare in j (similarly to the case of unilateral improvements in market access that we discussed before). Proposition 4 generalizes the finding that productivity improvements in one country hurt the other country (Demidova 2008, proposition 2). We show that the same result holds with respect to competitive advantages owing to lower wages, a lower exit risk and easier market entry. Note that asymmetric effects on productivities and on welfare are obtained in the two countries even without differences in technology potentials that were envisioned by Demidova (2008).

In contrast to the factors considered in Proposition 4 the effect of changes in the domestic fixed labor input necessary to serve the domestic market has an ambiguous effect on the domestic productivity cutoff, but an unambiguous effect on welfare as stated in:

Proposition 5. (The effect of domestic fixed labor input under trade). An increase in domestic fixed labor inputs (fi) leads to (i) an increase in the domestic productivity cutoff iff the domestic market is sufficiently protected from foreign competition, i.e. iff ΦHΦF < (σ − 1)/(k − σ), (ii) unambiguous welfare losses in country i, and (iii) an unambiguous increase in the cutoff productivity and welfare in country j.

Proof. The method of proof follows the one employed to prove the previous proposition. □

Proposition 5 shows a remarkable difference from our finding for the closed economy. In the closed economy, an increase in f necessarily drives up the productivity cutoff (see equation (5)) owing to a stronger selection effect which drives the least efficient firm out of the market. In the open economy, an increase in fi has a further effect, it facilitates the access of foreign firms to the domestic market, as dΦj/dfi > 0. This implies a competitive disadvantage for domestic firms vis-à-vis their foreign competitors whose effect it is to reduce the productivity cutoff. This leads to the ambiguity. However, the effect on domestic welfare is unambiguously negative, as the increase in the fixed labor input reduces the domestic number of firms Mti and hence the product variety available. Furthermore, the impact on foreign productivity and welfare is positive, as firms from j now enjoy a competitive advantage.

Propositions 4 and 5 are of crucial importance from a policy perspective. Fixed investments that are needed to enter and serve the domestic market and the technology potential can be influenced by industrial policy. For example the necessary fixed investments to start and do business are associated with a country's level of corruption, the costs to enforce contracts, the costs to provide protection against crime, product piracy and product imitation. Technology policies have an influence on a country's technological potential. Crucially, any improvement from the point of view of one economy has a negative welfare effect on the other economy.

Trade Cost Sensitivity of Industrial Policies

Policymakers should be aware of how sensitive the effects of industrial policies (noted in Propositions 4 and 5) are with respect to the level of trade integration. We can show:

Proposition 6. (Trade cost sensitivity of policies). (i) Consider the effect of changes in country i's technology potential, fixed market entry investment, exit rate or wage rate on the domestic productivity cutoff (as captured by inline image). (i-a) Suppose ΦH = ΦF = Φ. The effect of any such change is the greater, the greater is the level of trade freeness (Φ). (i-b) Suppose ΦF ≠ ΦH. The effect of any such change is the greater, the higher is Φi, i.e. the better is the market access of firms from country i to market j. The effect of any such change is insensitive to Φj. (ii) Consider the effect of changes in country i's fixed labor input on the domestic productivity cutoff. (ii-a) If ΦHΦF < (σ − 1)/(k − σ), changes in the domestic productivity get smaller by trade integration. (ii-b) Otherwise, the effect on the domestic productivity cutoff is the greater, the higher is Φi.

Proof. The proposition follows from differentiation of equation (7). □

The findings in part (i-a) of Proposition 6 have previously been obtained in models of the new trade theory and the new economic geography with homogeneous firms (cf. Helpman and Krugman, 1985; Baldwin et al., 2003), the underlying mechanism being similar. A key difference from our analysis that we already highlighted in the introduction and in section 4 is that the firm selection effect is absent in this earlier literature. Our analysis extends this result to a comprehensive set of factors affecting business conditions. Part (i-b) of Proposition 6 is novel. It reveals that domestic policies are more powerful when domestic firms have easy access to foreign markets. Part (ii-a) reveals that if a country is sufficiently protected from international trade (i.e. if ΦHΦF < (σ − 1)/(k − σ) holds true), the (positive) impact of higher fixed labor inputs on the domestic productivity is smaller at higher levels of trade freeness. In case (ii-b), where the country is sufficiently exposed to international trade (i.e. if ΦHΦF > (σ − 1)/(k − σ)), it becomes evident that trade integration even magnifies the (negative) impact of higher domestic fixed labor inputs.

Full Specialization in the Traditional Industry

  1. Top of page
  2. Abstract
  3. Introduction
  4. The Model
  5. The Open Economy
  6. Welfare and Policy Analysis
  7. Full Specialization in the Traditional Industry
  8. Conclusion
  9. Appendix
  10. References

Our analysis has so far rested on the assumption that the two countries are diversified in production both under autarky and under trade. Hence, each country had an active manufacturing sector in addition to a traditional industry. However, we have already noted that it is conceivable that one country (the “laggard”) may be forced into specialization in the traditional industry if asymmetries are very strongly in favor of doing business in the other country (the “leading economy”). This section considers this possibility. We shall assume that the “leading country” is still diversified in production. We discuss the key results here.18

Condition for Specialization

Both countries have a non-negative number of manufacturing firms if (see the Appendix):

  • display math

Outside this range, one country will be fully specialized in the production of the traditional good: country H is fully specialized if inline image and country F is fully specialized if inline image. On inspection of these conditions we see that a country is fully specialized on the homogeneous good if conditions are strongly unfavorable for doing business in that economy.

We now explore the welfare consequences of switching from autarky to trade and the welfare consequences of further trade liberalization under full specialization. We can state:

Proposition 7. (a) Gains from trade under specialization. Both countries have higher welfare under international trade than under autarky even if trade opening forces one of the countries into full specialization in the traditional industry while the other country remains diversified. (b) No immiserization under trade integration. Starting from a situation where trade opening has forced one country into full specialization, no country is made worse off by further trade integration.

Proof. Since we assume that both countries produce the traditional good both under autarky and under trade (such that a consumer has the same wage under autarky and trade), the welfare comparison boils down to a comparison of the price levels. Even if a country is forced into full specialization by opening up to trade, its price level is lower than under autarky where it produces both types of goods). The country which produces both types of goods has a lower price level for the same reason as in Proposition 1. Hence, it holds true that vs,i − vaut,i > 0 for both countries. This proves Proposition 7. Proposition 7 is proven by noting that the welfare of a country increases when the price level falls. Using the price indices under specialization (see the Appendix) it can immediately be seen that they do not rise through trade integration. □

To the best of our knowledge, Proposition 7 is novel. Intuitively, the country which is driven into full specialization in the traditional industry benefits from the productivity increase of the trading partner. Our proposition shows that this beneficial effect is so strong that it compensates for the fact that the “laggard” country has to incur trade costs for all manufacturing goods.

The scope of Proposition 7 can best be seen by contrasting it with Proposition 3. The latter was derived under the assumption that both countries are diversified in production and showed that one country may experience immiserization under trade integration. Because of trade cost savings, this result no longer holds true under specialization: the country that is fully specialized on the production of the homogeneous good unambiguously gains from trade integration because the access to the manufacturing goods that are produced by the other country becomes cheaper. The country that hosts both industries will not be worse off under trade integration.19

Conclusion

  1. Top of page
  2. Abstract
  3. Introduction
  4. The Model
  5. The Open Economy
  6. Welfare and Policy Analysis
  7. Full Specialization in the Traditional Industry
  8. Conclusion
  9. Appendix
  10. References

This paper explores the role of country asymmetries for trade and industrial policies in a two-sector general equilibrium model with heterogeneous firms. We consider an extensive list of factors that determine the conditions of doing business: technology access, market (country) size, market entry costs, exit rates, fixed costs to serve markets, the trade infrastructure, and Ricardian productivity differences. Our analysis delivers a number of novel results. First, trade policies, infrastructure policies and industrial policies which improve the business conditions in one country have negative productivity and welfare effects on the trading partner. Second, symmetric trade liberalization is immiserizing for a trading partner whose business conditions are inferior. Third, there are gains from trade even for a country whose monopolistically competitive sector with heterogeneous firms is wiped out by the switch from autarky to trade.

The tractability of our model allows us to work out these effects in a very slim way and it also allows us to synthesize previous policy findings very compactly. The ease with which the model can be employed to address country asymmetries should make it an attractive tool to study the endogenous choice of policies and to address political economy applications in future work.

Appendix

  1. Top of page
  2. Abstract
  3. Introduction
  4. The Model
  5. The Open Economy
  6. Welfare and Policy Analysis
  7. Full Specialization in the Traditional Industry
  8. Conclusion
  9. Appendix
  10. References

Firm Masses, Price Level and Indirect Utility under Trade

To derive the firm masses in the open economy equilibrium we have to impose balanced trade. From the perspective of the domestic economy, this condition is given by:

  • display math

where inline image is the conditional probability to become an exporter in country i and where γH denotes the share of labor employed in the modern sector in country H. The left-hand side of the trade balance conditions gives the value of country H's manufacturing exports and the first term on the right-hand side gives the value of manufacturing imports. The second and third terms on the right-hand side are the values of domestic consumption and production of the traditional good, respectively. Any imbalance in trade in manufacturing must be matched by a trade surplus or deficit in the numéraire good. Now use balanced trade and substitute inline image where inline image, wH = 1/aH and β(LH + LF) = γHLHwH + γFLFwF. Solving for the γi then gives:

  • display math

where inline image is an increasing measure of relative conditions favoring business in H (against F). Using γi, the masses of firms are immediately implied by inline image where inline image follows from the domestic ZCPC and is given by inline image. Hence, we have

  • display math(A1)
  • display math

The number of exporting firms is implied by Mxi = cprobxiMi and the mass of entrants follows according to inline image. The consumption variety available in country i is Mti = Mi + Mxj. The domestic ZCPC implies inline image, which can immediately be solved for the price level: inline image.

Parameter Restrictions

Non-specialization

Using equations (A1) and imposing Mi ≥ 0, both countries have manufacturing producers if inline image. By substituting inline image, where λ ≡ LH/LF is the ratio of labor endowment in H relative to F, and solving for inline image, the condition for non-specialization in both countries can be rewritten as

  • display math
Meaningful export-cutoffs

We assume that only firms that serve the domestic market can export, i.e. inline image. Using the domestic and the export ZCPC we obtain the revenue equations inline image and inline image for domestic sales and for exports, respectively. These equations imply, inline image. The condition inline image thus holds true whenever τij(fxi/fi)1/(σ−1)(Pi/Pj)(Li/Lj)1/(σ−1) > 1. Substituting inline image and rearranging yields inline image. Using the equilibrium cutoffs reported in eq. (7) and solving the inequality for inline image, we have meaningful export cutoffs, whenever

  • display math

Note that in Demidova (2008) the condition inline image implies inline image (i.e. that a domestic firm finds it easier to break even in its domestic market than a foreign exporter does) since her model assumes W = 1. However, in the presence of a possibly large wage differential it is quite conceivable that an exporting firm might find it easier to break even than a local firm does. Hence, the implication will not carry over to our model, in general.

Linking the restrictions

To ensure that there is a range of parameters which simultaneously fulfils both inequalities we have to make sure that the lower bound of each parameter restriction is smaller than the upper bound of the other. This boils down to a third restriction given by inline image.

Numerical examples

For the reader's convenience we provide two numerical examples to illustrate that there is a broad parameter space despite the parameter restrictions made above.

  • display math

(A) If ΦH = 0.5 and ΦF = 0.35, the non-specialization condition reads inline image, the condition for meaningful export cutoff is inline image and the linking condition 0.14 < λ < 8.16 which is fulfilled by λ = 0.9. The interval for mutual gains from symmetric trade liberalization is given by inline image. For inline image country H loses, whereas country F wins.

(B) If ΦH = 0.4 and ΦF = 0.65, the non-specialization condition is inline image, the condition for meaningful export cutoff is inline image and the linking condition is 0.21 < λ < 5.49. If inline image both countries win by symmetric trade integration. For inline image country F loses, whereas country H gains.

References

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  2. Abstract
  3. Introduction
  4. The Model
  5. The Open Economy
  6. Welfare and Policy Analysis
  7. Full Specialization in the Traditional Industry
  8. Conclusion
  9. Appendix
  10. References
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Notes
  1. 1

    Helpman (2006) and Redding (2011) survey the literature.

  2. 2

    The full specialization case has obtained much attention in neoclassical modeling of international trade. See e.g. Davis and Weinstein (2001) and Schott (2003).

  3. 3

    The Melitz–Ottaviano (2008) model is much more tractable than the Melitz (2003) model. An extension and calibration of the Melitz–Ottaviano model is provided in Del Gatto et al. (2006).

  4. 4

    Behrens et al. (2007) use the Melitz–Ottaviano model to numerically (graphically) show that trade liberalization may force the modern sector to disappear in a technologically backward economy. See section 5 for more on this.

  5. 5

    See also Falvey et al. (2011).

  6. 6

    The empirical analysis of the Melitz model by Feenstra and Kee (2008) addresses welfare as well.

  7. 7

    There are a number of further works, e.g. Chor (2009) uses a two-country model but focuses exclusively on FDI subsidies and Jorgensen and Schröder (2008) explore tariffs.

  8. 8

    Our assumptions on the traditional sector and the quasilinear utility fix the real wage (and the terms of trade) and remove income effects from the modern sector, respectively. This gives the framework a partial equilibrium flavor, but does not remove the interaction between product and labor markets (Tabuchi and Thisse, 2006). Quasilinear preferences “behave reasonably well in general equilibrium settings” (Dinopoulos et al., 2011) and they have extensively been used to study normative issues because the utilitarian concept of welfare is the reasonable as the marginal utility is then constant and income redistributions do not affect aggregate welfare (Ottaviano and Thisse, 2002). These considerations may help to explain why these twin assumptions are very often used in the trade and geography literature (e.g. Antràs and Helpman, 2004; Borck et al., 2012, Melitz and Ottaviano, 2008).

  9. 9

    We provide a supplement containing a more extended exposition of the model and our results on request.

  10. 10

    Demidova (2008) assumes Cobb–Douglas preferences.

  11. 11

    We follow Melitz (2003) and assume that once a firm is hit by a lethal shock it leaves the market instantaneously. See e.g. Hopenhayn (1992) for a dynamic analysis of firm exit.

  12. 12

    For empirical support see e.g. Del Gatto et al. (2006) and Ikeda and Suoma (2009). The Pareto parameterization has been used extensively in the theories of heterogeneous firms and trade, examples include Bernard et al. (2003), Helpman et al. (2004), Baldwin (2005), Helpman et al. (2008) and Melitz and Ottaviano (2008).

  13. 13

    The statements concerning φmin and k refer to versions of the Melitz model with Pareto-distributed productivities (cf. the references in note 12). The independence of country size is a particular feature of the CES framework. In Melitz and Ottaviano (2008) the cutoff productivity is positively related to country size.

  14. 14

    Demidova's (2008) treatment of productivity differences in the manufacturing sector is more general than ours. She allows for general country-specific productivity distributions Gi(φ), which may dominate the productivity distribution Gj(φ) of the other country in terms of the hazard rate order. Since we consider further asymmetries and since we want to keep the model as tractable as possible, we have chosen to sacrifice some generality here.

  15. 15

    We know from Krugman (1980) that the wage, which is fixed in our two-sector model (cf. note 7), adjusts in a one-sector version of the model. Dropping the second sector overturns the results stated in Proposition 2 as we show in section 5. See also Demidova and Rodriguez-Clare (2011) and Felbermayr and Jung (2012).

  16. 16

    Note that Demidova (2008) allows technology potentials to differ in a general sense. Our specification which only involves the support of the technology distribution suffices to make the point, however. Also note that size differences as proxied by the number of workers in the two countries are inconsequential. This result was already obtained in Baldwin (2005) and in Baldwin and Forslid (2010). However, these authors concluded that symmetric trade integration must raise welfare in both countries. This difference to our findings can be explained by noting that they did neither account for differing technology potentials nor the set of business conditions that we highlight.

  17. 17

    Proposition 3 also holds true in a qualitative sense, when we consider a proportionate increase in trade freeness as expressed by dΦHH = dΦFF > 0. It is readily derived that the thresholds where both countries benefit are now given by inline image. Country H wins and F loses if inline image.

  18. 18

    The supplement, which is available on request to the authors, contains an extended technical exposition of this case.

  19. 19

    This effect is also found in the numerical analyses of the Melitz–Ottaviano model by Behrens et al. (2007).