Product Mix, Trade, and the Environment: Theory and Evidence from Indian Manufacturing

Transcription

1 Product Mix, Trade, and the Environment: Theory and Evidence from Indian Manufacturing Geoffrey Barrows and Hélène Ollivier January 29, 2014 Abstract We develop a multiproduct multi-factor model with heterogeneous firms, variable markups, and monopolistic competition in which each product has a specific environmental emission intensity. Trade affects firm-level emission intensity through the endogenous response of product mix. First, we find that when varieties that are away from the core competency of the firm are greener, then tougher competition increases firm-level emission intensity, whereas when they are dirtier, then tougher competition improves the environmental performance of the firm. Second, we find that even though trade may cause some firms to become dirtier through product mix changes, selection effects dominates at the industry level so that trade still generates both economic and environmental efficiency gains. Third, we investigate the correlation between unit cost and emission intensity in a unique panel dataset of Indian Manufacturing firms which reports both physical output and energy input by product. We find that the sign of the correlation varies by industry, but that in aggregate, core varieties tend to be dirtier. Fourth, we find that exporting increases firm-level emission intensity, as well as the output share of core products within a firm. Keywords: heterogeneous firms; trade and the environment; monopolistic competition; environmental performance JEL codes: F14; F18; Q56 Department of Agricultural and Resource Economics, UC Berkeley. Paris School of Economics - CNRS and ETH Zurich. Address: Centre d Economie de la Sorbonne, Boulevard de l Hopital, Paris Cedex helene.ollivier@ps .eu. 1

2 1 Introduction Trade has the potential to generate substantial economic benefits, but its impact on pollution remains ambiguous. Early studies of trade s effect on pollution focused on endogenous environmental regulation and industry location, positing that trade might exacerbate environmental externalities through the pollution haven effect (Copeland & Taylor, 1994, 1995); however, empirical investigations at the industry level failed to uncover robust relationships. 1 More recently, empirical and theoretic investigations focus instead on firm-level effects. Grounded in new trade theory models (i.e., heterogeneous firms within monopolistically competitive industries), researchers hypothesize that trade improves emission efficiency independent of environmental regulation and comparative advantage. 2 New and better firm-level datasets yield some support for this view, but restrictive assumptions employed in the literature ensure that economic and environmental benefits move in the same direction. In this paper, we investigate a new channel within the heterogeneous firm framework through which trade could theoretically either increase or decrease emission intensity at the firm level, thus linking the new framework to the old second best" thinking associated with pollution havens. The literature so far has assumed some complementarity between total factor productivity (TFP) and emission intensity. Given that emissions result from energy consumption, and that energy is just one factor among others, one finds that the impacts of trade on TFP are symmetric to its impacts on emission intensity. The literature has identified two channels that illustrate this symmetry. In the first channel, dubbed by Kreickemeier & Richter (2012) the reallocation effect, falling trade costs increase domestic competition, driving down (or out) the sales of low-efficiency firms, while larger, more-efficient firms expand to serve the export market. This result follows immediately from the Melitz (2003) model. Assuming that pollution is proportional to either input or output, the shift in market share to moreefficient firms lowers emission intensity at the industry level. Empirically, researchers find that exporters have lower emission intensity than non-exporters, which they take as evidence in support of the reallocation mechanism. 3 In a second channel, trade causes firms to alter their production technology, which changes their emission intensity. Several mechanisms could explain trade-induced technological change, 1 See Copeland and Taylor 2004, Karp 2011 for suverys 2 See Kreickemeier & Richter (2012); Holladay (2010) for environmental extensions of Melitz (2003) 3 Holladay (2010), using a panel of 13,000 US firms from NETS between , finds that exporters emit roughly 5% less emissions (as measured in the TRI) than nonexporters, controlling for sales. Forslid et al. (2011) uses a panel of 5000 firms from the Swedish census of manufacturers between and finds that emission intensity of production is 13% lower for exporters, controlling for estimated TFP. Cui et al. (2012), with data on 40,000 US plants in the years 2002, 2005, and 2008 from the NEI and NETS, finds that exporters have 25% lower emissions intensity then nonexporters, controlling for estimated TFP and environmental regulation. Jing Cao & Zhou (2013) regresses energy intensity on a quadratic in TFP for a panel of 800 Chinese plants from and finds that energy intensity is decreasing in TFP, but that abatement expenditures are inverted-u shaped. Finally, with a panel of 73 Spanish food processing firms from , Galdeano-Gómez (2010) finds that an index of environmental performance is increasing in export orientation. 2

3 including bankruptcy costs (Durceylan, 2009), trapped factors (Bloom et al., 2011), and searching (Perla et al., 2012), but the mechanism mostly cited is the fixed cost model of Bustos (2011) in the context of increased export markets. In this model, firms can pay fixed costs to invest in a variable cost saving technology, which lowers emission intensity (and marginal cost) if, again, pollution is proportional to input or output. Cui et al. (2012) augments the Bustos model with an environmental component to study the effect of trade on firm-level emission intensity, and find that just as in Bustos (2011), trade should lower emission efficiency for firms in a particular TFP-range. Empirically, some papers have found that trade liberalization lowers emission intensity at the firm level and explained their results with a Bustos-type argument. 4 A third channel, which has been the focus of little work until now, is that trade could induce firms to change the relative shares of products within their output portfolio (i.e., their product mix). 5 This would change firm-level emission intensity if products generate different levels of environmental emissions per unit of output. Thus firm-level emission intensity could vary even absent any technological investment. If the two channels are present, they can either magnify or counterbalance each other. The reason is that it is not a priori obvious that the product mix effect will be good for the environment. When firms skew their mix towards their more profitable products (i.e., core competency) as a result of trade, the impacts on their emission intensity depends on whether these more profitable products are cleaner or dirtier. We make two primary contributions in this paper. First, we formalize a model in which trade induces changes in firm-level product mix, which in turn alters firm-level emission intensity. Theoretically, our first objective is to determine what structural restrictions on production are sufficient to ensure an ambiguous correlation between economic benefits and environmental benefits, to match our intuition that trade could be either good or bad for the environment via product mix. We find that a CES production structure using effective inputs can generate the desired ambiguity. Next, we compare the strength of the product mix channel with the reallocation channel at the industry level. We find that within our Melitz framework, the reallocation effect is so strong that even if trade causes firms to become dirtier through product-mix changes, the emission intensity at the industry level always falls. It is surprising that theoretically one channel always dominates the other. It could be that the distributional assumption for firm- 4 Gutiérrez & Teshima (2011) find that increased import competition resulting from NAFTA caused Mexican firms to reduce their emissions intensity. Similarly, Martin (2012) exploits changes in import tariffs into India across industries and finds that trade improves energy efficiency at the firm level, though these results are driven mostly by firms having access to cheaper intermediate products rather than by increased import competition. Finally, Cherniwchan (2013) finds that trade liberalization caused by NAFTA reduced the emissions of some pollutants (volatile organic compounds and lead) while increasing the emissions of others (particulate matter) by affected U.S. manufacturing plants. 5 A few researchers have remarked that changes to the product mix could explain trade-induced changes in firm-level emission intensity (Cherniwchan, 2013), but could not provide any test for it since datasets usually do not contain input and output information at the product-level. Lipscomb (2008) investigates the product-mix channel with a focus on the impacts of environmental regulation, and not trade. 3

4 level TFP heterogeneity (Pareto) ensures this ordering, in which case the result should be viewed as the artifact of a technical restriction. Or, it could be that reallocation effects in heterogeneous firm trade models are very strong independent of distributional assumptions, so the model tends to favor across-firm effects over within-firm effects. To assess the overall impacts of trade on the environment, we need to compare emission levels before and after trade liberalization. Even though trade causes industry-level emission intensity to fall, it could also increase output so much that the level of emissions at the national level would increase. In a final theoretical section, we identify scenarios under which domestic emissions levels increase or decrease in asymmetric countries depending on their technological parameters, trade costs, and the difference in environmental taxation across countries. Our second contribution is to assess empirically the impact of product-mix on firm-level emission intensity. We use a unique firm-level dataset of Indian Manufacturers the Prowess dataset which reports not only firm-product-specific outputs, but also firm-product-specific energy intensity. 6 From these measures, we compute emission intensity by firm-product directly from the data. To our knowledge, no other dataset allows for these calculations. With these measures, we first assess the correlation between unit cost and emission intensity to both validate the product mix channel and determine the sign of correlation between economic benefits and environmental benefits. If firm-product emission intensity does not vary systematically with unit cost, then there would be no reason to believe that trade systematically alters firm-level emission intensity via product mix. We follow Mayer et al. (2011) and take product sales rank within a firm as a proxy for unit cost.we find that overall, low cost products tend to be more emission intensive, i.e., follow-on varieties tend to be cleaner. Disaggregating the data, we find that for some industries, the correlation is negative, as in the aggregate analysis, but for some industries, the correlation is positive. These findings confirm our prediction that the relationship between unit cost and environmental performance is a priori ambiguous and likely depends on parameters of the production function. Next, we investigate trade s effect on firm-level environmental performance by regressing firm-level emission intensity on export orientation. We find that increased export orientation increases firm-level emission intensity by 8.4%. With our product-specific data, we can disaggregate further and separate export premiums into product-specific effects (technological upgrading) and cross-product within-firm effects (product mix). We find that product-mix explains about one quarter of overall firm-level effects. To bring some caution here, even if we find that exporting increases firm-level emission intensity, it could be that some omitted variable correlates with both emission intensity and export orientation and drives the result. This call for further research that would utilize an exogenous change in export market access to assess the causal link between trade and changes in firm-level emission intensity. 6 De Loecker et al. (2012) pioneered empirical economic research with Prowess data, investigating the link between trade, markups, and productivity changes. They exploit the multiproduct dimension of the data to estimate firm-year specific markups and TFP. 4

5 Beyond the trade and environment literature, this paper contributes to two other literatures. First, we contribute to recent work on multiple product firms in the trade literature (Bernard et al., 2011, 2013; Mayer et al., 2011). Our model can be thought of as a twofactor generalization of the Mayer et al. (2011) multiple product trade model and could be used to study comparative advantage in the heterogeneous firm framework à la Bernard et al. (2007). Second, we contribute to the broader literature on trade and efficiency. Several papers investigate the impact of trade liberalization on an Hicks-neutral firm-specific total factor productivity measure. 7 Relatively little attention has been paid to the possibility of factor-biased changes in response to trade. 8 As our model allows that environment benefits do not necessarily correlate with economic benefits at the firm level, we investigate the factor neutrality of trade-induced efficiency gains. In the rest of the paper, we first present the theoretical model in a closed economy, and prove our result that the correlation between unit cost and environmental performance determines the impact of competition (and hence, trade) at the firm level. We then extend the model to open economies and assess the trade impacts on emissions levels in asymmetric countries. Then, we present descriptive evidence of the trade-induced product-mix effects on emission intensity using the Prowess data. 2 Closed Economy Our model is based on an extension of Melitz & Ottaviano (2008) and Mayer et al. (2011) that allows firms to endogenously determine the level of emissions that are generated while they produce. This decision is channeled through the choice of product mix since one product corresponds to a specific technology that emit more or less emissions. By choosing its product mix, the firm chooses a set of technologies, and thus an average emission intensity. Our objective is to analyze how trade liberalization affects firm-level emission intensity when firms differ in productivity and when they can choose their product mix. We start with a closed economy version of this model where L consumers supply each one unit of labor. 2.1 Preferences and Demand Preferences are defined over a continuum of differentiated varieties indexed by i Λ, and a homogeneous good chosen as numeraire. All consumers share the same utility function given by U = q0 c + α qi c di 1 i Λ 2 γ (qi c ) 2 di 1 ( ) 2 i Λ 2 η qi c βz w, (1) i Λ 7 See the survey in Wagner (2007) 8 See some older literature on factor-biased technological change. 5

6 where q0 c and qc i represent the individual consumption levels of the numeraire good and each variety i. The demand parameters α, γ, and η are all positive. The parameters α and η index the substitution pattern between the differentiated goods and the numeraire: increases in α and decreases in η both shift out the demand for the differentiated varieties relative to the numeraire. The parameter γ indexes the degree of product differentiation between the varieties. In the limit when γ = 0, varieties are perfect substitutes. The varieties other than the numeraire are responsible for emitting pollution. Consumers are negatively affected by the worldwide level of pollution Z w, hence we assume β > 0. World aggregate emissions Z w l Zl, where l is an index for countries, and Z l = i Λ zl idi where corresponds to emissions generated by the production of variety i in country l. z l i The marginal utilities for all varieties are bounded, and a consumer may not have positive demand for any particular variety. We assume that consumers have positive demand for the numeraire good (q0 c > 0), which is also the non polluting good. The inverse demand for each variety i is then given by p i = α γq c i ηq c, (2) whenever qi c > 0, and where Q c i Λ qc i di is the consumption level over all varieties. Let Λ Λ be the subset of varieties that are consumed. (2) can be inverted to yield the linear market demand system for these varieties: q i Lq c i = αl ηm + γ p L i γ + ηl pm γ(ηm + γ) i Λ, (3) where M is the measure of consumed varieties in Λ and p = (1/M) i Λ p i di is their average price. The set Λ is the largest subset of Λ that satisfies p i αγ + η pm ηm + γ pmax, (4) where the right hand side price bound p max represents the price at which demand for a variety is driven to zero. Note that (2) implies that p max α. Here, the price elasticity of demand is not uniquely determined by the level of product differentiation as in the case of CES demand functions. Lower average prices p or a larger number of varieties M induce a decrease in the price bound p max, and an increase in the price elasticity of demand at any given p i. We characterize this as a tougher" competitive environment. 2.2 Production Labour is the only factor of production that is mobile across sectors, and that is inelastically supplied in a competitive market. The numeraire good is produced under constant returns to scale at unit cost and sold in a competitive market. These assumptions imply a unit wage. 6

7 Entry in the differentiated product sector is costly as each firm incurs product development and production startup costs. Those costs are labour costs. Subsequent production of each variety exhibits constant returns to scale, but this production requires another factor, emissions (z), as well as labour (l). 9 Thus the differentiated sector is polluting. We assume that the price of emissions mostly depends on an exogenous environmental tax τ that is fixed by the national government. 10 Each firm decides to produce depending on its total factor productivity ϕ and the level of environmental tax τ. While it may decide to produce several products using different technologies with specific emission intensity, each firm has one core variety with minimal marginal cost given the tax level τ. Research and development yield uncertain outcomes for ϕ, and firms learn about their productivity only after making the irreversible investment f E required for entry. We model this as a draw from a common (and known) distribution G(ϕ) with support on [0, ]. The introduction of an additional variety that uses another technology pulls a firm away from its most efficient technology. The new variety is thus more expensive to produce. Because it uses a different technology, it can also be either less emission intensive or more emission intensive than the core competency. If it is greener, then the emission intensity of the product decreases with its marginal cost. If it is dirtier, however, this new variety entails both a higher marginal cost and a higher emission intensity. The relationship between marginal cost and emission intensity of one product is a matter of empirical evaluation. Therefore we adopt a flexible framework where this relationship can go either way. A firm can introduce any number of new varieties that correspond to different technologies. We index by m the varieties produced by the same firm in increasing order of distance from its core variety m = 0. Consider a firm with total factor productivity ϕ that produces a variety m given the following production function q(ϕ, m) = ϕ[(e σm l) ɛ + (e νm z) ɛ ] 1/ɛ. (5) The production function combines effective" inputs in the standard CES structure where effective input" equals actual input scaled by a distance function from core competency. 11 Production function (5) is quasi-concave if ɛ 1, which is assumed in the rest of the paper. Given that the firm has to pay the tax level τz and given the normalization assumption for the wage rate (w = 1), the cost-minimizing firm with productivity ϕ chooses emission 9 We refer to z as emissions for convenience, but z can be thought of as energy as well. Copeland & Taylor (2003) shows the equivalence between treating emissions as a by-product of production and as an input. 10 Or, alternatively, if z represents energy, then the effective price τ depends mostly on an exogeneously set tax/subsidy from the government. 11 There is no loss in generality in omitting sharing parameters. 7

8 intensity of the variety m to be E(ϕ, m) = z q = 1 ϕ [ e νmɛ + (τe m(ɛν σ)) ] ɛ 1/ɛ 1 ɛ. (6) The unit-cost function for variety m is thus given by Φ(ϕ, m) = wl + τz = 1 ϕ [τ ɛ νmɛ ɛ 1 e ɛ 1 ] ɛ 1 σmɛ ɛ + e ɛ 1, (7) which implies Lemma 1. The unit cost of variety m produced by firm with productivity ϕ, Φ(ϕ, m), is increasing in m if ν > 0, σ > 0. Proof. Φ(ϕ, m) m = 1 ϕ [τ ɛ νmɛ ɛ 1 e ɛ 1 ] 1 σmɛ ɛ + e ɛ 1 [ντ ɛ νmɛ ɛ 1 e ɛ 1 ] σmɛ + σe ɛ 1 which is positive if ν > 0, σ > 0. Lemma 1 ensures that the firm s core competency corresponds to m = 0, for which the unit cost of production is the lowest in the firm with productivity ϕ. Adding a new variety m away from this core competency raises the unit cost of production. The sufficient condition on parameters ν and σ implies that the technology for producing this new variety m uses both factors less efficiently given (5). Though the emission intensity E(ϕ, m) is unambiguously decreasing in the firm s productivity ϕ, we have Lemma 2. The emission intensity of variety m, E(ϕ, m) is increasing (decreasing) in m if and only if ɛ (1 ɛ) (τe m(ν σ)) ɛ ɛ 1 < (>) σ ν. The emission intensity of variety m can be either increasing or decreasing in m only if ɛ > 0 and ν > σ. Proof. de(ϕ, m) dm = 1 ϕ [ e νmɛ + (τe m(ɛν σ)) ] ɛ 1 ɛ [ ɛ 1 ɛ νe νmɛ ɛν σ (τe m(ɛν σ)) ] ɛ 1 ɛ, 1 ɛ which is positive if and only if the LHS of the inequality in Lemma 2 is less than the RHS. This holds if ɛ 0, or if σ > ν. 8

9 Lemma 2 suggests that the emission intensity and the unit cost of new varieties are not necessarily correlated. Whereas the unit cost is increasing in m if parameters ν and σ are positive, E(ϕ, m) can still be either increasing or decreasing in m depending on production parameters. If either ɛ 0 or σ > ν, then the LHS of the inequality in Lemma 2 is for certain less then the RHS, which means higher-m varieties are more emissions intensive. 12 However, if ɛ > 0 and ν > σ, then the equality could be reversed (depending on relative magnitudes), implying that higher-m products are potentially cleaner. We do not want to assume away the possibility that trade could increase emission intensity at the firm level, so we restrict attention to the case ɛ > 0 and ν > σ for the rest of the paper. These conditions imply that labor and emissions exhibit a high-degree of substitutability, and higher-m varieties use even less efficiently emissions than labor. Under these conditions, firms substitute labour for emissions as they add higher-m products, which might reduce emission intensity. 2.3 Profit Maximization Firms that can cover the marginal cost of production survive and produce. All other firms exit the industry. Surviving firms maximize their profits using the residual demand function (3). In so doing, those firms take the average price level p and total number of varieties M as given because of the monopolistic competition framework. The profit maximizing price p(φ) and output level q(φ) of a variety with marginal cost Φ(ϕ, m) must then satisfy q(φ) = L γ [p(φ) Φ(ϕ, m)]. (8) The maximizing price p(φ) may be above the price bound p max from (4), in which case the variety is not supplied. Let Φ D reference the cutoff marginal cost for a variety to be profitably produced. This variety earns zero profit as its price is driven down to its marginal cost, hence Φ D = p max, and its demand level is driven to zero. A firm decides to produce when its core competency m = 0 earns some profit. For each producing firm with Φ(ϕ, 0) < Φ D, more profits can be earned by diversifying its product mix, hence its technology mix. The set of technologies used by a firm is determined by the values of m that satisfy the condition Φ(ϕ, m) Φ D. Let r(φ) = p(φ)q(φ), π(φ) = r(φ) q(φ)φ, λ(φ) = p(φ) Φ denote the revenue, profit, 12 For example, when the elasticity of substitution between emissions and labor is positive and close to 1 (ɛ 0), both unit cost and emission intensity are increasing in m. This corresponds to the standard framework in the trade and environment literature following Copeland & Taylor (1994) where emissions are a by-product of production, and where abatement requires labour in such a way that net output can be represented in a Cobb-Douglas function with emissions and labour as inputs. To illustrate, consider the following Cobb-Douglas function for variety m: q(ϕ, m) = ϕ(e σm l) β (e νm z) 1 β. It implies that both the unit cost function and the emission intensity function can be factorized by e m[βσ+(1 β)ν]. Thus these functions are both increasing in m for σ, ν > 0. 9

10 and (absolute) markup of a variety with production cost Φ. All these performance measures can then be written as functions of Φ D and Φ(ϕ, m): p(φ) = [Φ D + Φ(ϕ, m)]/2, (9) λ(φ) = [Φ D Φ(ϕ, m)]/2, (10) q(φ) = L 2γ [Φ D Φ(ϕ, m)], (11) r(φ) = L 4γ [Φ2 D Φ(ϕ, m) 2 ], (12) π(φ) = L 4γ [Φ D Φ(ϕ, m)] 2. (13) The cutoff marginal cost Φ D thus summarizes the competitive environment for all performance measures of all produced varieties. As expected, lower marginal cost varieties have lower prices and earn higher profits than varieties with higher marginal costs. However, lower marginal cost varieties also have higher markups than varieties with higher costs. Firms with marginal cost for their core competency Φ(ϕ, 0) > Φ D cannot profitably produce their core variety and exit. by Hence, the cutoff productivity for firm survival is given ϕ D = 1 [ ] 1 + τ ɛ ɛ 1 ɛ ɛ 1. (14) Φ D Hence, Φ D measures the toughness of competition in the market. All firms with productivity ϕ > ϕ D earn positive profits (gross of the entry cost) on their core variety m = 0, and remain in the industry. Some firms will also earn profits from the introduction of additional varieties. [τ ɛ νmɛ σmɛ ɛ 1 e ɛ 1 + e ɛ 1 In particular, firms with productivity ϕ such that Φ(ϕ, m) Φ D, i.e., ] ɛ 1 ɛ /Φ D ϕ, earn positive profits on their m-th variety and produce at least m + 1 varieties. The total number of varieties produced by a firm with productivity ϕ is zero if ϕ < ϕ D whereas it is { M(ϕ) = max m [τ ɛ νmɛ ɛ 1 e ɛ 1 ] ɛ 1 } σmɛ ɛ + e ɛ 1 /Φ D ϕ + 1 if ϕ ϕ D, (15) which is (weakly) increasing for all ϕ [0, ]. Accordingly, the number of varieties produced by firm with productivity ϕ is an integer. This number is an increasing step function of the firm s productivity. 10

11 2.4 Free Entry and Equilibrium Prior to entry, the expected firm profit is ϕ D Π(Φ(ϕ, m))dg(ϕ) f E where Π(Φ(ϕ, m)) M(ϕ) 1 π(φ(ϕ, m)) (16) denotes the profit of a firm with productivity ϕ. As long as some firms produce, the expected profit is driven to zero by the unrestricted entry of new firms. The equilibrium free entry condition is such that the fixed cost of entry f E must equal = ϕ D Π(Φ(ϕ, m))dg(ϕ) = [ [τ ɛ ɛ 1 e νmɛ ɛ 1 +e σmɛ ɛ 1 ϕ D {m Φ(ϕ,m) Φ D } ( [ ] ɛ 1 π τ ɛ νmɛ ɛ 1 e ɛ 1 ɛ /Φ D π [τ ɛ νmɛ ɛ 1 e ɛ 1 ] ɛ 1 σmɛ ɛ + e ɛ 1 ϕ ] ɛ 1 ) ] σmɛ ɛ + e ɛ 1 /ϕ dg(ϕ) dg(ϕ) where the order of integration is reversed in the last inequality as in Mayer et al. (2011). This condition pins down the endogenous cost cutoff Φ D, or equivalently ϕ D given (14). This cutoff also determines the aggregate mass of varieties, 13 since Φ D must be equal to the zero demand price threshold p max, hence (17) Φ D = αγ + η pm ηm + γ. (18) 2.5 Parameterization of Technology Following Mayer et al. (2011), we use a specific parametrization for the productivity distribution that simplifies the analysis and provides closed form solutions. In particular, we assume that productivity draws ϕ follow a Pareto distribution with shape parameter k 1. This implies the following distribution G (ϕ) = 1 ϕ k. (19) The shape parameter k indexes the dispersion of productivity draws. When k = 1, the productivity distribution is uniform. As k increases, the relative number of low productivity firms increases, and the productivity distribution is more concentrated at these lower initial productivity levels. Any truncation of the productivity distribution from below will retain the same distribution function and shape parameter k. The productivity distribution of surviving firms will therefore also be Pareto with shape k. We can rewrite (17) using the parameterization 13 See Appendix B for details 11

12 (19) as f E = LΦ k+2 D 2γ(k + 1)(k + 2) [ [ τ ɛ νmɛ ɛ 1 e ɛ 1 + e σmɛ ɛ 1 ] ɛ 1 ] k ɛ. (20) We need the sequence to converge, but it turns out that ν > 0, σ > 0 is sufficient to ensure this, so we denote Ω ] [τ ɛ (1 ɛ)k νmɛ σmɛ ɛ ɛ 1 e ɛ 1 + e ɛ We thus get [ 2γ(k + 1)(k + 2)fE Φ D = LΩ ] 1 k+2. (21) An increase in market size L, as well as an increase in the environmental tax τ, decrease the cost cutoff Φ D, which translates into a tougher competitive environment. 2.6 Competition and Firm-level Productivity and Emissions Intensity We analyze the impact of tougher competition on the aggregation of output, total cost and pollution level at the firm level. For any firm with productivity ϕ, this is simply the sum of output, total cost and pollution level over all varieties produced: Q(ϕ) M(ϕ) 1 q(φ(ϕ, m)), C(ϕ) M(ϕ) 1 Φ(ϕ, m)q(φ(ϕ, m)), Z(ϕ) where, using (6) and (11), we have z(φ(ϕ, m)) = L 2γ E(ϕ, m)[φ D Φ(ϕ, m)]. M(ϕ) 1 z(φ(ϕ, m)), We construct two efficiency measures, one for economic efficiency, the other for environmental efficiency. Our measure of firm productivity is simply the inverse of the average cost per product, i.e., ψ C (ϕ) Q(ϕ)/C(ϕ), and our measure of firm emission intensity is the average emissions level per unit of output, i.e., ψ Z (ϕ) Z(ϕ)/Q(ϕ). Tougher competition affects firms through two margins: the intensive margin of adjustment corresponds to a change in the output of each variety produced by the firm, and the extensive margin corresponds to a change in the set of varieties that the firm produces. As competition increases, a firm can choose to drop some of the most expensive varieties. But the firm can also change the relative output share of each variety. To isolate the product mix response to competition, consider two varieties m and m produced by a firm with productivity ϕ, where m < m. The ratio of the firm s output of the ] 14 We have [τ ɛ 1 ɛ e νmɛ ɛ 1 + e σmɛ (1 ɛ)k ɛ ɛ 1 m 0 if and only if ν, σ > 0 and ɛ 1, which corresponds to the condition in Lemma 1. 12

13 two varieties is given by q(φ(ϕ, m)) q(φ(ϕ, m )) = Φ D Φ(ϕ, m) Φ D Φ(ϕ, m ). (22) We thus have d[q(φ(ϕ, m))/q(φ(ϕ, m ))] dφ D = ϕ2 [Φ(ϕ, m) Φ(ϕ, m )] [Φ D Φ(ϕ, m )] 2, (23) which is negative given the increasing unit-cost function in varieties. As competition increases, the firm skews its production toward its core varieties. Thus trade s impacts on firm-level emission intensity depend crucially on the relationship between emission intensity and the unit cost of production of a variety. If core varieties that have lower production costs also have lower emission intensities, then trade induces firms to become cleaner through this interproduct reallocation effect. Conversely, if core varieties have higher emission intensities, then trade induces firms to become dirtier. More precisely, we have Proposition 1. Tougher competition (a decrease in Φ D ) improves firm-level productivity measure, and it reduces (increases) firm-level emissions intensity if and only if E(ϕ, m) is increasing (decreasing) in m. Proof: see the appendix. Proposition 1 shows that even though increased competition always raises firm-level economic efficiency, it does not necessarily raise firm-level environmental efficiency. The environmental impact depends on the link between the emission intensity of a variety and its distance to the core competency of the firm. This result includes both intensive and extensive margins of adjustment at the firm level. If increased competition results in an increase in firm-level emission intensity, its impact on emission intensity at the the industry level might not be the same. In aggregate, the product-mix channel is combined with the reallocation channel under which less productive firms exit while more productive firms enter the market and increase their market share. We get the industry productivity measure by aggregating over firms: ψ C ϕ D Q(ϕ)dG(ϕ) ϕ D C(ϕ)dG(ϕ) = k (24) k Φ D Similarly, the industry emissions intensity depends on the aggregate emissions level, which is given by ϕ D Z(ϕ)dG(ϕ) ϕ D M(ϕ) 1 z(φ(ϕ, m)) dg(ϕ) = LkΦ k+2 D Γ 2γ(k + 1)(k + 2), 13

14 where Γ ϕe(ϕ, m) [τ ɛ νmɛ ɛ 1 e ɛ 1 ] (1 ɛ)(k+1) σmɛ ɛ + e ɛ 1 (25) We must impose that the sequence Γ is finite. This is guaranteed under the conditions ɛ > 0 and ν > σ, as shown in the Appendix. Because these conditions are precisely the sufficient conditions required in Lemma 2 to preserve the ambiguous relationship between E and m, and because we are only interested in cases that preserve this possibility, we need no further restrictions to ensure that Γ converges. The aggregate emission intensity measure is thus given by and we have ψ Z ϕ D Z(ϕ)dG(ϕ) ϕ D Q(ϕ)dG(ϕ) = kφ DΓ (k + 2)Ω. (26) Proposition 2. Assuming ɛ > 0 and ν > σ, tougher competition (a decrease in Φ D ) implies i/ an increase in aggregate productivity; ii/ a decrease in aggregate emission intensity; iii/ and a decrease in aggregate emissions. Proof: see the appendix. These aggregate responses combines the effects of competition on both firm productivity (including product mix effect) and inter-firm reallocations (including entry and exit). The effect of tougher competition on aggregate productivity is similar to the result obtained by Mayer et al. (2011). Indeed, firms skew production towards their better-performing products, and less competitive firms exit the market as competition increases. This reduces the average cost of production at the sector level. The effects on aggregate emission intensity and on aggregate emissions are novel. Despite the potential ambiguity in the correlation between unit cost and emission intensity at the product level, we find that tougher competition reduces aggregate emission intensity at the industry level. We know that more productive firms have a lower average emission intensity, because they are more efficient at using inputs. Thus, the (across-firm) reallocation channel reduces industry-level emission intensity. Because firms also skew production towards their core competency, the product mix effect can either increase firm-level emission intensity if new varieties are cleaner than the core competency, or reduce it if new varieties are dirtier. In the latter case, the product mix effect thus magnifies the reallocation effect, and aggregate emission intensity decreases a lot. By contrast, in the former case, the two effects counterbalance each other, but the inter-firm reallocation effect outweighs the within-firm product mix effect. 14

15 The reduction in aggregate emissions rests on both the fact that the differentiated sector sees its emission intensity decrease, and on the aggregate output reduction. This negative scale effect results from tougher competition driving some firms and some products out of the market, thereby reducing total output. 3 Open Economy The closed-economy model used in the previous section can be immediately applied to open economies that are perfectly integrated through trade. In fact, the transition from autarky to free trade is equivalent to an increase in market size, which would lower the cost cutoff Φ D in each country. However, this simple extension of the closed-economy model does not apply to goods that are not freely traded. We thus need to consider some trade costs whenever a good is exported or imported. Furthermore, the fact that countries are trading impacts firms productivity, emission intensity, and markups in a way that the analysis of each market in insolation cannot deal with. Consider two countries h and f, with L h and L f identical consumers in each country. Consumers in both countries share the same preferences. The two markets are segmented, but firms in either country can produce in one market and sell in the other (country l) by incurring an iceberg trade cost θ l > 1 where l = h, f. Thus, the delivered cost of a variety with manufacturing cost Φ(ϕ, m) to country l is θ l Φ(ϕ, m). Let p max l indicates the maximum price of a variety that is sold in country l. Then (4) implies p max l = αγ + η p lm l, l = h, f, (27) ηm l + γ where M l is the total number of varieties selling in country l (adding domestic and foreign varieties) and p l is their average price. Because countries are symmetric except for their market size L l and for their barrier to imports θ l, we focus on country h in the following. We denote by hh domestic variables, by hf export variables, and by fh import variables. Let p hh (ϕ, m) and q hh (ϕ, m) represent the domestic levels of the profit maximizing price and quantity of variety m sold by a firm with productivity ϕ producing in country h. Such a firm may also decide to export some of its variety m at a delivered price p hf (ϕ, m). Because the markets are segmented, firms separately optimize for each market, yielding domestic profits π hh (ϕ, m) = [p hh (ϕ, m) Φ(ϕ, m)]q hh (ϕ, m) and export profits π hf (ϕ, m) = [p hf (ϕ, m) θ f Φ(ϕ, m)]q hf (ϕ, m) for a firm with productivity ϕ producing a variety m in country h. Firms must earn positive profits on a variety if they sell it in a given market, 15

16 yielding cost cutoffs Φ hh = sup{φ(ϕ, m) : π hh (ϕ, m) > 0} = p max h (28) Φ hf = sup{φ(ϕ, m) : π hf (ϕ, m) > 0} = pmax f, (29) θ f and thus Φ hf = Φ ff /θ f. Similarly to the closed economy case, the cutoffs Φ hh and Φ hf summarize all the effects of markets conditions in both countries relevant for all firm performance measures. Using (14), we can obtain the respective productivity cutoffs, ϕ hh and ϕ hf, associated to the previous cost cutoffs. Thus ϕ hh corresponds to the cutoff for firm survival in country h whereas ϕ hf corresponds to the export cutoff from country h to f. Assuming that markets are segmented as in Melitz & Ottaviano (2008), the profit functions can then be written as π hh (ϕ, m) = L h 2γ [Φ hh Φ(ϕ, m)] 2 (30) π hf (ϕ, m) = L f θ 2 f 2γ [Φ hf Φ(ϕ, m)] 2 = L f 2γ [Φ ff θ f Φ(ϕ, m)] 2. (31) A firm with productivity ϕ will produce all varieties m such that π hh (ϕ, m) 0, and it will export a subset of varieties m such that π hf (ϕ, m) 0. The total number of varieties produced and exported by a firm with productivity ϕ in country h are thus { M hh (ϕ) =max m [τ ɛ νmɛ ɛ 1 e ɛ 1 { M hf (ϕ) =max m [τ ɛ νmɛ ɛ 1 e ɛ 1 ] ɛ 1 } σmɛ ɛ + e ɛ 1 /Φ hh ϕ + 1 iff ϕ ϕ hh (32) ] ɛ 1 } σmɛ ɛ + e ɛ 1 /Φ hf ϕ + 1 iff ϕ ϕ hf, (33) and zero otherwise. We can then define a firm s total domestic and export profits by aggregating over these varieties: Π hh (ϕ) = M hh (ϕ) 1 π hh (ϕ, m), Π hf (ϕ) = M hf (ϕ) Free Entry Condition and Number of Entrants π hf (ϕ, m). (34) Entry is unrestricted in all countries. Firms decide where to locate prior to entry and paying the sunk entry cost. We assume that the entry cost f E and productivity distribution G(ϕ) are common across countries. We maintain the Pareto parametrization for this distribution. 16

17 A prospective entrant s expected profits are then given by ϕ hh {m Φ(ϕ,m) Φ hh } The free entry condition implies π hh (ϕ, m)dm dg (ϕ) + ϕ hf {m Φ(ϕ,m) Φ hf } π hf (ϕ, m)dm dg (ϕ). Ω h L h Φ k+2 hh + Ω f L f (θ f ) 2 Φ k+2 hf = 2γ(k + 1)(k + 2)f e, (35) where Ω l is defined as in the closed-economy case, i.e., it is determined by the pollution tax and the technology of varieties. If environmental taxes vary across countries, hence τ h τ f, the sequence Ω h would differ from Ω f. Using Φ hf = Φ ff /θ f and the symmetry across countries that gives a system of equations, we obtain ( ) 1 2γ(k + 1)(k + 2)fe (1 ρ f ) k+2 Φ hh =, (36) Ω h L h (1 ρ f ρ h ) where ρ f = θ k f < 1 is a measure of freeness of trade from country h to country f that varies inversely with the trade costs θ f. 3.2 Impacts of Asymmetric Environmental Taxes and Market Sizes We focus on the impacts of environmental tax differences for cross-country characteristics in the open-economy equilibrium. These cross-country differences are revealed by the differences in the cost cut-offs Φ ll defined in (36). By observing (36), we can draw a parallel between the impacts of market size differences and the impacts of environmental tax differences. As in Melitz & Ottaviano (2008), when trade costs are symmetric (ρ h = ρ f ), the larger country will have a lower cost cut-off, and thus higher average productivity and product variety, along with lower markups and prices. Similarly, because Ω l is decreasing in τ l, and thus because Ω h > Ω f is equivalent to τ h < τ f (see the Appendix B.4), and vice versa, the country with the lowest environmental tax will have a lower cost cut-off (everything else being equal). Assuming symmetric market sizes, welfare levels will be higher in the low regulation country. This result rests on the global nature of GHG emissions, because environmental damages are suffered equally across countries whatever the location of emissions. If market sizes differ, however, and if market size differences are proportional to environmental tax differences, the larger country with stringent regulation could be better off than the smaller country with low regulation. As in Melitz & Ottaviano (2008), (36) also indicates that the characteristics of the trading partner do not affect the domestic cost cut-off, beside the trade cost. This highlights important offsetting effects of the trading partner size for instance. For exporters, a larger trading 17

18 partner implies increased export market opportunities. However, this is offset by increased competitiveness that drives markups down. For the domestic market, a larger trading partner implies an increased level of import competition. In the long run, this is offset by a smaller proportion of entrants (see the appendix B.3), and thus less competition in the smaller market. By contrast, the export cost cutoff depends on the characteristics of the trading partner, and not on the domestic market, since Φ hf = Φ ff /θ f. 3.3 Aggregate Emissions Measures Total emissions generated by production in country h, Z p h, can be decomposed into emissions for producing goods that are domestically consumed and goods that are exported: Z p h = ϕ hh Z hh (ϕ)dg(ϕ) + ϕ hf Z hf (ϕ)dg(ϕ), (37) which simplifies to Z p h = kf eγ h 1 ρ h ρ f 1 ρ f Ω h + (1 ρ h)θ Ω f (k+1) f. (38) The environmental tax of the trading partner, as well as the trade cost, affect the domestic level of emissions from production in country h. This impact is channeled through the goods exported to country f, hence through the export cost cutoff. Because Ω l / τ l < 0, a higher tax in country f reduces Ω f, and thus raises country h s domestic emissions from production for export (everything else being equal). Even though we can ensure that Γ h is decreasing in τ h for τ h 1 (see Appendix B.4 for the details), the variation of Z p h with respect to the domestic tax is ambiguous. An increase in the cost of polluting a priori must reduce total emissions. By changing the relative factor price, this increase in τ h induces firms to substitute labor for pollution. However, a change in τ h also modifies the competitive environment in which firms operate. This translates into an increase in the domestic cost cutoff Φ hh, which induces an increase in total emissions through a positive scale effect. By symmetry, the worldwide level of emissions, Z wt Z p h + Zp f, is thus given by Z wt = kf e 1 ρ h ρ f (1 ρ f )(Γ h + Γ f θ (k+1) h ) Ω h + (1 ρ (k+1) h)(γ h θ f + Γ f ). (39) Ω f 4 Trade Liberalization With the open economy model described in Section 3, we can study the impact of bilateral or unilateral liberalizations on economic and environmental performance. Overall welfare is 18

19 the sum of utility from consumption and environmental benefits. When these two quantities move in the same direction, the sign of the welfare impact is unambiguous. However, when economic and environmental benefits move in opposite directions, a complete welfare analysis requires some comparison between the two. Remaining agnostic on the magnitude of β, which determines the marginal cost of emissions, we do not compare economic and environmental benefits. Rather, we analyze the impact on overall emissions, only concluding when emissions fall and economic benefits increase that trade for sure increases welfare. 4.1 Bilateral Liberalization Consider the case of bilateral liberalization where we assume that trade costs are symmetric, θ h = θ f = θ. Thus we analyze the effect of a decrease in θ, which corresponds to an increase in ρ h = ρ f = ρ. In this case, the equilibrium cost cutoff (36) can be written as ( ) 1 2γ(k + 1)(k + 2)fe k+2 Φ ll = for l = h, f. (40) Ω l L l (1 + ρ) Bilateral liberalization thus increases competition in both markets by lowering Φ hh and Φ ff proportionally, which leads to a proportional increase in aggregate productivity in both countries. The economic impacts of such liberalization are qualitatively similar to the ones described for the transition from autarky to free trade in Mayer et al. (2011): product variety increases, whereas mark-ups and prices decrease, all of which are good for consumers. Indeed, the increase in competition drives inefficient domestic firms out of the market, and causes surviving firms to drop their highest-cost products and skew production towards their core competency. When one country s competitive environment becomes tougher for its domestic firms, the opportunities for foreign firms that export to this country improve. Indeed, bilateral liberalization increases the export cost cutoff, Φ hf and Φ fh, in both countries (see Appendix B.5). These export opportunities arise because of the fall in the trade cost. As it becomes less costly to ship goods to the trading partner, more firms start to export and more varieties are shipped. The competitive effect of trade liberalization on the domestic market and on the export market thus goes in opposite directions. Similarly, the effect on the environment depends on the changes in emissions related to both the domestic and the export markets. Given (38), domestic emissions depend on two components: emissions related to the production of goods sold in the domestic market, and emissions related to the production of exported goods. Bilateral trade liberalization decreases emissions related to the domestic market whereas it increases emissions from exports. The effect on the domestic market is similar to the one observed in the closed economy when the competitive environment becomes tougher (see Proposition 2). The effect on the export market goes in the opposite direction because the decrease in trade costs outweighs the effect 19

20 of tougher competition in the trading partner. The presence of these two countervailing forces in each country makes trade s impacts on the environment non-monotonic. We have Proposition 3. Assuming ɛ > 0 and ν > σ, as well as τ l 1 for l = h, f, bilateral trade liberalization implies that i/ the worldwide level of emissions decreases when countries are starting from an autarkic situation; ii/ after trade costs have fallen below a threshold, either one country or both countries increase their emissions as trade costs further decrease; iii/ the worldwide level of emissions is larger under full trade liberalization than under autarky. Proof: See Appendix B.5. Emissions decrease due to the competitive effect of trade on the domestic market whereas they increase due to the expansion of the export market. Proposition 3 thus states that when trade costs are high (i.e., when countries are close to autarky), the domestic effect dominates so that trade is good for the environment. By contrast, when trade costs are low, the export effect tends to dominate so that trade might be bad for the environment when countries are trading almost freely. To assess the total effect of trade on the global environment, we compare the worldwide level of emissions in autarky and in free trade. Full trade liberalization implies that θ = 1. Comparing (39) with its equivalent in autarky (denoted Z wa ) yields Z wt Z wa = kf e 2Ω h Ω f (Ω h Ω f )(Γ h Γ f ), (41) which is positive whatever the environmental regulation difference across countries, given τ l 1. Full bilateral liberalization is thus bad for the environment. This increase in worldwide emissions affect all consumers welfare negatively due to the global nature of pollution. The impacts of trade liberalization on national emissions must depend on the environmental policy difference across countries. Suppose τ h > τ f 1 so that country f is the one with the lowest environmental regulation. If the tax difference is not too large, i.e., if 1 < Ω f /Ω h < (4 + k)/k (see Appendix B.5 for details), then starting from autarky bilateral trade liberalization first reduces emissions in both countries, then at a certain level of trade cost country f s emissions starts to rise, and then for an even lower trade cost, country h s emissions also rises. Thus trade liberalization is good for the environment when countries are almost autarkic, whereas it is bad for the environment when countries trade almost freely. For intermediate trade costs, the impact depends on the relative change in emissions across countries. 20