New Trade Models, New Welfare Implications

Transcription

1 New Trae Moels, New Welfare Implications Marc J. Melitz Harvar University, NBER an CEPR Stephen J. Reing Princeton University, NBER an CEPR August 13, 2014 Abstract We show that enogenous firm selection provies a new welfare margin for heterogeneous firm moels of trae relative to homogeneous firm moels. Uner some parameter restrictions, the trae elasticity is constant an is a sufficient statistic for welfare, along with the omestic trae share. However, even small eviations from these restrictions imply that trae elasticities are variable an iffer across markets an levels of trae costs. In this more general setting, the omestic trae share an enogenous trae elasticity are no longer sufficient statistics for welfare. Aitional empirically observable moments of the micro structure also matter for welfare. KEYWORDS: firm heterogeneity, welfare gains from trae, trae policy evaluation J.E.L. CLASSIFICATION: F12, F15 We are grateful to Harvar an Princeton Universities for research support. This paper is a revise version of Firm Heterogeneity an Aggregate Welfare, NBER Working Paper, We woul like to thank the eitor, four referees, conference an seminar participants at AEA, Harvar, Hong Kong, LSE, Minneapolis, NBER, NYU, Paris, Princeton, UBC, Vancouver an Wharton, an Pol Antras, Costas Arkolakis, Ariel Burstein, Arnau Costinot, Rob Feenstra, Gene Grossman, Goron Hanson, Keith Hea, Elhanan Helpman, Thierry Mayer, Gianmarco Ottaviano, Anres Roriguez- Clare, Esteban Rossi-Hansberg, Jon Vogel an Davi Weinstein for helpful comments. We are also grateful to Davi Krisztian Nagy for research assistance. Responsibility for any results, opinions an errors is the authors alone. Littauer Center 215, Cambrige, MA Tel: mmelitz@harvar.eu. Fisher Hall, Princeton, NJ Tel: reings@princeton.eu. 1

2 1 Introuction Over the last ecae, new theories of trae with heterogeneous firms in ifferentiate prouct markets have been evelope. These theories were esigne to account for features of isaggregate trae ata: only some firms eport, eporters are more prouctive than non-eporters an trae liberalization inuces intra-inustry reallocations of resources between those ifferent types of firms. These reallocations represent a new potential channel for the gains from trae. However, the implications of these moels for aggregate welfare combining together all welfare channels were left unanswere. In a recent paper, Arkolakis, Costinot an Roriguez-Clare 2012, henceforth ACR show that there eists a class of heterogeneous an homogeneous firm moels in which a country s omestic trae share an the elasticity of trae with respect to variable trae costs are sufficient statistics for the aggregate welfare gains from trae. Therefore, if the ifferent moels within this class are calibrate to the same omestic trae share an the same trae elasticity, they imply the same welfare gains from trae. Base on this result, ACR summarizes the contribution of new theories of heterogeneous firms to the aggregate welfare implications of trae as So far, not much. In this paper, we compare a heterogeneous firm moel to a homogeneous firm moel that is a special case with a egenerate prouctivity istribution. We use a theoretical comparative static to show that the heterogeneous firm moel has an etra ajustment margin that is absent in the homogeneous firm moel: the enogenous ecisions of heterogeneous firms to enter an eit the omestic an eport markets. Furthermore, ajustment along this margin is efficient, in the sense that the market equilibrium correspons to the constraine efficient allocation chosen by a social planner. As a result, if the egenerate prouctivity istribution in the homogeneous firm moel is chosen so that the two moels have the same welfare for an initial value of trae costs, this etra ajustment margin implies that the heterogeneous firm moel has higher welfare for all other values of trae costs. It follows that the two moels have ifferent aggregate welfare implications: there are larger welfare gains from reuctions in trae costs an smaller welfare losses from increases in trae costs in the heterogeneous firm moel than in the homogeneous firm moel. Quantitatively, we fin that this etra ajustment margin is substantial for a calibration of our heterogeneous firm moel to U.S. firm-level an aggregate ata. Uner aitional restrictions on the parameter space, our heterogeneous an homogeneous firm moels belong to the class analyze by ACR. 1 In this class of moels, the elasticity of trae with respect to variable trae costs is constant an then also serves as a sufficient statistic for welfare along with the omestic trae share. We show that this eistence of a single constant trae elasticity an its sufficiency property for welfare are highly sensitive to small epartures from those ACR parameter restrictions. In the heterogeneous firm moel, the restrictions inclue an untruncate Pareto istribution for prouctivity. Even a slight generalization of this istribution to a truncate 1 We focus on monopolistic competition moels featuring imperfect competition, enogenous prouct variety, an increasing returns to scale. ACR also consier perfect competition moels without those features, such as Armington 1969 an Eaton an Kortum

3 Pareto with a finite upper boun for prouctivity implies a variable trae elasticity that iffers across markets an levels of trae costs. As a result, a trae elasticity estimate from one contet nee not apply for the evaluation of trae policy in another contet. In this more general setting, evaluating a trae policy base on an estimate trae elasticity is subject to the Lucas Critique: This elasticity is not invariant with respect to trae policy. 2 Furthermore, once we move beyon those ACR restrictions on the parameter space, the trae share an enogenous trae elasticity are no longer sufficient statistics for welfare. Even conitional on these variables, micro structure matters for the welfare gains from trae. In this more general setting, the impact on welfare of the etra ajustment margin in the heterogeneous firm moel is not capture by the trae elasticity. We evelop several eamples of trae liberalization scenarios in which this aitional impact of the micro structure on welfare can be substantial, even for small, empirically relevant, epartures from the ACR parameter restrictions. We eten the ACR approach of epressing the welfare gains from trae as a function of observable empirical moments incluing the trae share an elasticity to the more general cases of our homogeneous an heterogeneous firm moels. We provie a framework for assessing whether the ACR formula provies a goo approimation to the true welfare gains from trae liberalization. We quantitatively measure the iscrepancies between the ACR formula an the true welfare gains using our more general moel calibrate to U.S. aggregate an firm-level ata. We fin substantial iscrepancies ranging up to a factor of four. Using an elasticity estimate e post for the observe local changes in trae costs will reuce but not eliminate the iscrepancy between the preicte an true welfare gains from trae. In aition to the two aggregate moments of the omestic trae share an trae elasticity, our more general welfare epression highlights ifferences in the hazar rate of the istribution of log firm size between the omestic an eport markets an the response of firm entry to changes in trae costs, both of which can be eamine empirically using firm-level ata. Our paper is relate to other recent research on the welfare gains from trae when the ACR parameter restrictions are not satisfie. ACR an Costinot an Roriguez-Clare 2014 eplore multiple sectors, traable intermeiate inputs an multiple factors of prouction; Arkolakis, Costinot, Donalson an Roriguez-Clare 2012 an Emon, Mirigan an Xu 2012 eamine variable markups; Hea, Mayer an Thoenig 2014 analyze a log normal prouctivity istribution; Feenstra 2014 introuces variable markups using Quaratic Mean of Orer r preferences an consiers a truncate Pareto prouctivity istribution; an Fajgelbaum an Khanelwal 2013 investigate non-homothetic preferences. In contrast to these stuies, we show theoretically that enogenous firm selection provies an etra margin of ajustment in the heterogeneous firm moel. We emonstrate the fragility of a constant trae elasticity to small epartures from the ACR restrictions even in the benchmark case of a single sector with no intermeiate inputs, constant elasticity of substitution CES preferences an monopolistic competition, as consiere by Krugman 1980 an Melitz When there is a single constant trae elasticity as in the class of moels consiere by ACR this elasticity must be invariant so the Lucas Critique oes not apply. 3

4 The remainer of the paper is organize as follows. In Section 2, we introuce the heterogeneous an homogeneous firm moels. In Section 3, we use our theoretical comparative static to show that the heterogeneous firm moel has an etra margin of ajustment that is absent in the homogeneous firm moel. In Section 4, we eten the ACR approach of epressing welfare gains from trae as a function of observable empirical moments incluing the trae share an elasticity to the more general cases of the homogeneous an heterogeneous firm moels. In Section 5, we provie several eamples of trae liberalization scenarios where the aitional impact of the moel s micro structure on welfare can be substantial. In Section 6, we eamine the quantitative relevance of our theoretical results. Section 7 conclues. 2 Heterogeneous an Homogeneous Firm Moels We compare the canonical heterogeneous firm moel of Melitz 2003 to a homogeneous firm moel that is a special case with a egenerate prouctivity istribution as in Krugman We hol all other parameters incluing the traing technology constant across the two moels. 2.1 Close Economy Heterogeneous Firm Moel The specification of preferences, prouction an entry is the same as in Melitz There is a continuum of firms that are heterogeneous in terms of their prouctivity ϕ 0, ϕ ma, which is rawn from a common cumulative istribution G ϕ after incurring a sunk entry cost of f e units of labor. We allow the upper boun of the support of the prouctivity istribution to be either finite ϕ ma < or infinite ϕ ma =. Labor is the sole factor of prouction. Prouction involves a fie prouction cost an a constant marginal cost that epens on firm prouctivity, so that l ϕ = f + q ϕ /ϕ units of labor are require to supply q ϕ units of output. Consumers have constant elasticity of substitution CES preferences with elasticity σ > 1 efine over the ifferentiate varieties supplie by firms. Profit maimization implies that variety prices are a constant mark-up over marginal cost that is etermine by the elasticity σ. The revenue of a firm with prouctivity ϕ is then given by: σ 1 σ 1 r ϕ = ϕ σ 1 RP σ 1 w 1 σ, 1 σ where R is aggregate revenue, P is the CES price ine, an w is the wage. We use the subscript to reference the omestic market. We begin by consiering the close economy equilibrium, which can be summarize by the following three relationships, where we use the superscript A to enote the autarky equilibrium. First, fie prouction costs imply a prouctivity cutoff ϕ A below which firms eit. This cutoff is efine by a zero-profit conition equating operating profit to the fie cost: r ϕ A = R σ 1 P ϕ A = wf. 2 σ σ σ w 3 A web-base technical appeni contains the erivations of all epressions in the paper. 4 Following most of the subsequent international trae literature, incluing ACR, we consier a static version of Melitz 2003 in which there is zero probability of firm eath. 4

5 Secon, free entry requires that the probability of successful entry 1 Gϕ A times average profits conitional on successful entry π equals the sunk entry cost: [ 1 G ϕ A ] π = wfe. Using the relationship linking relative firm revenue to relative firm prouctivity an the zero-profit cutoff conition above, this free entry conition can be epresse as: f J ϕ A = fe, 3 where J [ ϕ A ϕma ϕ σ 1 = ϕ A ϕ A 1] Gϕ, 4 where J ϕ A is a monotonically ecreasing function of the prouctivity cutoff. We can then write J ϕ A in terms of the ratio of average prouctivity to cutoff prouctivity: J ϕ A [ = 1 Gϕ A ] [ A ϕ A 1]. 5 Following Melitz 2003, we efine A as a weighte average of firm prouctivity corresponing to a harmonic mean weighte by output shares: A = [ ϕma ϕ A ϕ σ 1 ] 1 σ 1 G ϕ 1 G ϕ A. 6 Thir, the mass of proucing firms M equals the mass of entrants M e times the probability of successful entry 1 Gϕ A. This mass of proucing firms also equals aggregate revenue R ivie by average firm revenue r. Using the relationship linking relative firm revenue to relative firm prouctivity an the free entry conition, the mass of proucing firms can be written in terms of the economy s labor supply L relative to average fie costs per firm: M = [ 1 Gϕ T ] M e = R r = L σf A. 7 In this erivation, we choose labor as the numeraire so that aggregate revenue R equals labor payments L, an we efine F A to represent the average fie cost pai per surviving firm: F A = f e 1 Gϕ A + f. 8 Using the CES price ine an the mass of firms 7, close economy welfare can be then written in terms of the mass of firms L/σF A an the weighte average prouctivity of these firms A : W A Het = w P = σ 1 σ 2.2 Open Economy Heterogeneous Firm Moel { } 1 L A σ 1 σ 1 σf A. 9 We consier the case of trae between two symmetric countries. We use the subscript to reference the eport market an the superscript T to reference the open economy equilibrium. We assume that 5

6 there is a fie eporting cost of f units of labor in the source country an an iceberg variable trae cost, whereby τ > 1 units of a variety must be shippe from one country in orer for one unit to arrive in the other country. The open economy equilibrium is characterize by prouctivity cutoffs for serving the omestic market ϕ T an eport market ϕt that are efine by zero-profit conitions equating the operating profit in each market to the relevant fie costs: r ϕ T σ = R σ σ 1 σ P ϕ T w = wf, 10 r ϕ T σ = R σ σ 1 σ P ϕ T τw = wf. 11 The revenue functions r ϕ an r ϕ separate firm sales by estination market omestic an eport. Together these two zero-profit conitions imply that the eport cutoff is a constant multiple of the omestic cutoff, where this multiple epens on the fie an variable costs of trae: ϕ T = τ f For sufficiently high fie an variable trae costs τ f /f 1 σ 1 f 1 σ 1 ϕ T. 12 > 1, only the most prouctive firms eport, consistent with an etensive empirical literature see for eample the review in Bernar, Jensen, Reing an Schott The free entry conition again equates the epecte value of entry to the sunk entry cost, [ 1 G ϕ T ] π = wfe, an can be written as: f J ϕ T + f J ϕ T = fe, 13 where J is efine in 4. Using the relationship between the prouctivity cutoffs 12, an noting that J is a ecreasing function, the free entry conition 13 etermines a unique equilibrium value of the omestic cutoff ϕ T, which in turn etermines the eport cutoff ϕt. Furthermore, the omestic cutoff in the open economy is strictly greater than the omestic cutoff in the close economy ϕ T > ϕa for positive values of fie eporting costs. As in the close economy, the mass of proucing firms M equals the mass of entrants M e times the probability of successful entry 1 Gϕ T, an is etermine by the economy s labor supply L relative to average fie costs: M = [ 1 Gϕ T ] M e = R r = L σf T, 14 where F T summarizes average fie costs per surviving firm in the open economy: F T = f e 1 Gϕ T + f + χf, 15 an χ = [ 1 Gϕ T ] / [ 1 Gϕ T ] is the proportion of eporting firms. In this erivation, we choose labor in one country as the numeraire an use country symmetry, which implies that aggregate revenue R still equals labor payments L in each country. 6

7 Using the CES price ine an mass of firms 14, open economy welfare can be written in terms of the mass of varieties available for consumption L1+χ/σF T an the weighte average prouctivity of these varieties T t : W T Het = w P = σ 1 σ { L1 + χ σf T } 1 T σ 1 σ 1 t. 16 This weighte average prouctivity T t in the open economy is constructe using the same weighting scheme 6 as we use for the close economy. However the prouctivity of eporters is reuce by τ to account for the units lost in transit. Letting T enote the average prouctivity of eporters, efine as in 6, the overall prouctivity average for the open economy can be written: T σ 1 1 [ t = T σ χ + χ τ 1 T ]. 17 Aggregate trae between the two countries is inversely relate to the omestic trae share the proportion of omestic sales in total sales: λ Het = ϕma ϕ T r ϕgϕ R = τ 1 σ Λ, 18 where Λ = δϕ T /δϕ T 1 is the market share of eporters in the omestic market an δϕ j = ϕma ϕ j ϕ σ 1 Gϕ is a function that epens only on G an σ. The sensitivity of aggregate trae to changes in variable trae costs is capture by the full trae elasticity: ln 1 λhet { λ Het σ 1 ln Λ θ Het = = ln τ > 0 for τ f /f 1/σ 1 > 1 ln τ σ 1 > 0 for τ f /f 1/σ 1 < 1, 19 where ln Λ/ ln τ < 0. When trae costs are sufficiently low, all firms eport an there is no etensive margin of trae. Given CES preferences, the elasticity of the intensive margin of trae is constant at σ 1. When there is selection into the eport market, the elasticity of trae θ Het is the sum of the intensive margin elasticity σ 1 an the etensive margin elasticity ln Λ/ ln τ. 2.3 Close Economy Homogeneous Firm Moel We construct a homogeneous firm moel that is a special case of the heterogeneous firm moel with a egenerate prouctivity istribution. Firms pay the same sunk entry cost of f e units of labor an raw a prouctivity of either zero or ϕ with eogenous probabilities Ḡ an [ 1 Ḡ] respectively. Fie prouction costs imply that only firms rawing a prouctivity of ϕ fin it profitable to prouce. Therefore proucing firms are homogeneous an there is a egenerate prouctivity istribution conitional on prouction at ϕ. The close economy equilibrium of this homogeneous firm moel is isomorphic to that in Krugman 1980, in which the representative firm s prouctivity is set equal to ϕ an the fie prouction cost is scale to incorporate the epecte value of entry costs F f + f e / [ 1 Ḡ]. These values for the representative firm s prouctivity an the fie prouction cost are eogenous an hel constant. 7

8 To simplify the eposition, we aopt this Krugman 1980 interpretation. The representative firm s prouction technology is: l = q ϕ + F. 20 Consumers have the same CES preferences that we efine previously. Profit maimization implies that equilibrium prices are a constant markup over marginal cost. Profit maimization an free entry imply that equilibrium output an employment for the representative variety are proportional to the fie prouction cost: q = ϕ F σ 1, l = σ F. Using equilibrium employment for the representative variety, the mass of firms can be etermine from the labor market clearing conition: M = L σ F. 21 Using the CES price ine an the mass of firms 21, close economy welfare can be written in terms of the mass of firms L/σ F an prouctivity ϕ : W A Hom = w P = σ 1 σ where we again choose labor as the numeraire. 2.4 Open Economy Homogeneous Firm Moel { } 1 L σ F ϕ σ 1, 22 We again consier trae between two symmetric countries an assume the same traing technology as in the heterogeneous firm moel, so that there is a fie eporting cost of f units of labor an an iceberg variable trae cost of τ > 1 units of each variety. In the homogeneous firm moel, the probability of successful entry an prouctivity conitional on successful entry are eogenous an remain unchange an equal to [ 1 Ḡ] an ϕ respectively. For sufficiently high fie an variable trae costs τ σ 1 f / F > 1, the representative firm oes not fin it profitable to eport. In contrast, for sufficiently low fie an variable trae costs τ σ 1 f / F < 1, the representative firm fins it profitable to eport, an there is trae in both moels. The open economy equilibrium of this homogeneous firm moel is isomorphic to a version of Krugman 1980 with the same traing technology as in Melitz Profit maimization again implies that equilibrium prices are a constant mark-up over marginal costs, with eport prices a constant multiple of omestic prices ue to the variable costs of trae. Profit maimization an free entry imply that equilibrium output an employment for the representative variety are proportional to fie costs: q = ϕ F + f σ 1, l = σ F + f. 8

9 Therefore both output an employment rise for the representative firm following the opening of trae to cover the aitional fie costs of eporting. Using equilibrium employment for the representative variety, the mass of firms can be etermine from the labor market clearing conition: M = L σ F + f. 23 Using the CES price ine an the mass of firms 23, open economy welfare can be written in terms of the mass of varieties available for consumption 2L/σ F + f an average prouctivity ϕ t : W T Hom = w P = σ 1 σ { 2L σ F + f ϕ t } 1 σ where average prouctivity ϕ t is constructe in the same way as in 17 for heterogeneous firms: 5 ϕ t = 1 2 [ ϕ + τ 1 ϕ ]. 25 We again choose the wage in one of the symmetric countries as the numeraire. In the case of homogeneous firms, the omestic trae share simplifies to: λ Hom = τ 1 σ There is no etensive margin of trae, so the trae elasticity is given by the constant elasticity for the intensive margin of trae so long as there is some trae: θ Hom = { σ 1 for τ σ 1 f / F < 1 0 otherwise Theoretical Comparative Static We now show that enogenous firm selection provies a new margin of ajustment through which the economy can respon to trae liberalization that leas to ifferent aggregate welfare implications in the heterogeneous an homogeneous firm moels. Holing all other structural parameters constant across the two moels same f, f e, f, τ, L, σ, we first pick the parameters Ḡ an ϕ for the egenerate prouctivity istribution with homogeneous firms such that welfare in an initial equilibrium is the same in the two moels. We net eamine the effects of changes in trae costs from this initial equilibrium. We unertake this analysis both for the opening of the close economy to trae an for changes in trae costs in the open economy equilibrium. 3.1 Opening the Close Economy to Trae We begin by picking the parameters Ḡ an ϕ of the egenerate prouctivity istribution with homogeneous firms such that the autarky equilibrium is isomorphic to that with heterogeneous firms, an eamine the effect of opening the close economy to trae. 5 With a representative firm, average prouctivity across omestic firms an eporters is ϕ t, an the proportion of eporting firms is one. 9

10 Proposition 1 Consier a homogeneous firm moel that is a special case of the heterogeneous firm moel with an eogenous probability of successful entry [ 1 Ḡ] = [ 1 Gϕ A ] an an eogenous egenerate istribution of prouctivity conitional on successful entry ϕ = A. Given the same value for all remaining parameters {f, f e, L, σ}, all aggregate variables welfare, wage, price ine, mass of firms, an aggregate revenue are the same in the close economy equilibria of the two moels. Proof. Comparing 9 an 22, equal welfare follows immeiately from ϕ = A an [ 1 Ḡ] = [ 1 Gϕ A ], which implies F = F A. This also implies equal price inices. Equal masses of firms follow immeiately from equal price inices an ϕ = A. R = L in both moels. Equal aggregate revenue follows from This first proposition reflects the aggregation properties of the heterogeneous firm moel. All aggregate variables in this moel take the same value as if there were a representative firm with prouctivity ϕ an fie costs F. The key ifference between the heterogeneous firm moel an such a representative firm moel is that aggregate prouctivity in the heterogeneous firm moel is enogenous an respons to changes in trae costs. Proposition 2 Choosing the egenerate prouctivity istribution in the homogeneous firm moel so that the two moels have the same close economy welfare an the same structural parameters f, f e, f, τ, L, σ, the proportional welfare gains from opening the close economy to trae are strictly larger in the heterogeneous firm moel than in the homogeneous firm moel W T Het /WA Het > WT Hom /WA Hom, ecept in the special case with no fie eporting cost. In this special case, the proportional welfare gains from opening the close economy to trae are the same in the two moels. Proof. See the Appeni. The intuition for this result involves reveale preference arguments of the kin commonly use in international trae. 6 Our starting point is to note that, with CES preferences an monopolistic competition, the open economy equilibrium in the heterogeneous firm moel is efficient. As shown in the web appeni, a welfare-maimizing social planner face with the same prouction an entry technology woul choose the same allocation as the market equilibrium. When the economy is opene to trae, the planner coul choose not to ajust the set of firms selecte for prouction an eports. Average prouctivity woul then remain constant, an this outcome woul replicate the opening to trae in the homogeneous firm case. The latter is thus a feasible allocation for the planner with the heterogeneous firm prouction an entry technology. However, efficiency implies that this planner chooses to replicate the market equilibrium of the heterogeneous firm moel, which involves ajustments in the set of firms selecte for prouction an eports an an associate increase in average prouctivity. This inuce allocation therefore yiels higher welfare than any other feasible allocation 6 For the sake of parsimony, we focus on symmetric countries; however, this reveale preference argument applies more generally for asymmetric countries. 10

11 incluing the homogeneous firm outcome. Aitionally, the planner s objective function is strictly concave. Thus, welfare in the heterogeneous firm open economy must be strictly higher than in the homogeneous firm case whenever the cutoffs ajust to the opening to trae. 7 The ifference in aggregate welfare implications between the two moels arises because of the aitional efficient ajustment margin of firm entry an eit ecisions in the heterogeneous firm moel for both the omestic an eport markets. In the special case with no fie eporting cost, the omestic prouctivity cutoff is unaffecte by the opening of the close economy to trae. As a result, the aitional ajustment margin of firm entry an eit ecisions is inoperative in the heterogeneous firm moel, an the welfare effects of trae liberalization are the same in the two moels. We consier this special case uninteresting, since firm prouctivity ispersion then plays no role in the heterogeneous firm moel the eit threshol an average prouctivity are the same in the close an open economies. Furthermore, this special case stans at os with an etensive boy of empirical evience that only some firms eport, eporters are larger an more prouctive than non-eporters, an there are substantial fie eporting costs Changes in Trae Costs in the Open Economy Equilibrium The role of the etra ajustment margin of firm entry an eit ecisions for generating ifferent aggregate welfare implications is not limite to the opening of the close economy to trae an also hols for reuctions in trae costs in the open economy equilibrium. To show this, we recast our heterogeneous an homogeneous firm moels so that they have the same welfare in an initial open economy equilibrium. In orer to ensure that the two moels have the same initial welfare an only iffer in their prouctivity istribution keeping the same structural parameters f, f e, f, τ, L, σ, we eten the homogeneous firm moel to allow for two types of firms: eporters an noneporters. In this etension, firms again pay a sunk entry cost of f e units of labor before observing their prouctivity. With probability [ 1 Ḡ] a firm raws a prouctivity of ϕ an can eport; with probability Ḡ the firm raws a prouctivity of ϕ an cannot eport; with probability [ ] Ḡ Ḡ the firm raws a prouctivity of zero an oes not fin it profitable to prouce. We pick the parameters of this etene homogeneous firm moel ϕ, ϕ, Ḡ, Ḡ such that the open economy equilibrium features the same aggregate variables as the initial open economy equilibrium with heterogeneous firms same welfare, price ine, mass of firms, aggregate revenue, an omestic trae share. Nevertheless these two moels respon ifferently to changes in trae costs from this common initial equilibrium along a key imension. In the heterogeneous firm moel, the enogenous selection responses to trae costs lea to changes in the average prouctivity of eporting an non-eporting 7 In contrast, if the elasticity of substitution between varieties is variable, the market equilibrium is not in general efficient see Diit an Stiglitz 1977 for the case of homogeneous firm moels an Dhingra an Morrow 2012 for the case of heterogeneous firm moels. Enogenous firm selection still provies an etra margin of ajustment in the heterogeneous firm moel relative to the homogeneous firm moel. This again generates ifferent aggregate welfare implications in the two moels, as consiere in the web appeni. 8 For reviews of the etensive empirical literatures on firm eport market participation, see Bernar, Jensen, Reing an Schott 2007 an Melitz an Reing For evience of substantial fie eporting costs, see Roberts an Tybout 1997 an Das, Roberts an Tybout

12 firms an in the proportion of eporting firms. In contrast, in the etene homogeneous firm moel, the average prouctivity levels of eporters an non-eporters an the proportion of eporting firms remain constant. 9 The presence of this etra ajustment margin in the heterogeneous firm moel implies that welfare following the change in trae costs must be strictly higher than in the etene homogeneous from moel. This argument hols irrespective of whether trae costs ecrease or increase. Therefore, welfare gains are larger in the heterogeneous firm moel whenever trae costs fall, an welfare losses are smaller in the heterogeneous firm moel whenever trae costs increase. Proposition 3 Starting from an initial open economy equilibrium with the same welfare an the same structural parameters in the two moels f, f e, f, τ, L, σ, a common ecrease increase in variable or fie trae costs generates larger welfare gains smaller welfare losses in the heterogeneous firm moel than in the etene homogeneous firm moel. Proof. See the Appeni. Note that the etene homogeneous firm moel is equivalent to a version of the heterogeneous firm moel in which the omestic an eport prouctivity cutoffs are hel constant at their values in an initial open economy equilibrium. Put another way, consier a planner who is constraine to keep the same set of firms operating in both the omestic an eport markets i.e. the enogenous selection margin is inoperative. Uner this constraint, the welfare-maimizing allocation coincies with the market equilibrium of the etene homogeneous firm moel. In contrast, in the absence of this constraint, the welfare-maimizing allocation coincies with the market equilibrium of the heterogeneous firm moel. Therefore, the welfare ifferential between the two moels provies a irect measure of the impact of selection on aggregate welfare. In other wors, it isolates the aitional contribution to aggregate welfare of the new enogenous selection/prouctivity channel highlighte by the heterogeneous firm moel of trae this represents the new welfare implications that we refer to in the title of this paper. Later in Section 6, we show that this aitional welfare channel is quantitatively substantial for a moel calibrate to U.S. aggregate an firm statistics. Atkeson an Burstein 2010 consiers this welfare ifferential from enogenous firm selection in a moel with prouct an process innovation. They fin that this welfare ifferential is of seconorer. Proposition 3 is consistent with this result. As iscusse above an shown formally in the web appeni, the initial equilibrium of the heterogeneous firm moel is efficient. Therefore the envelope theorem implies that the changes in the prouctivity cutoffs in the heterogeneous firm moel have only secon-orer effects on welfare. But, as we show later, these secon-orer welfare effects can be quite substantial for larger changes in trae costs. 9 Unless trae costs become sufficiently high that firms with prouctivity ϕ no longer fin it profitable to eport or firms with prouctivity ϕ no longer fin it profitable to prouce. In both cases, the average prouctivity of the two types of firms remains constant at ϕ an ϕ 12

13 3.3 Untruncate Pareto Distribution Since the homogeneous firm moel is a special case of the heterogeneous firm moel, our comparison of the two moels above is equivalent to a iscrete comparative static of moving from a non-egenerate to a egenerate prouctivity istribution within the heterogeneous firm moel. In the special case of an untruncate Pareto prouctivity istribution, the egree of firm heterogeneity is summarize by a single parameter: the shape parameter k. Lower values of k correspon to greater firm heterogeneity an the homogeneous firm moel correspons to the limiting case in which k. Therefore, we can complement the above iscrete comparative static with a continuous comparative static in the egree of firm heterogeneity k, holing all other structural parameters constant. Proposition 4 Assuming that prouctivity in the heterogeneous firm moel has an untruncate Pareto istribution gϕ = kϕ k min ϕ k+1, where ϕ ϕ min > 0 an k > σ 1 an fie eporting costs are positive, greater ispersion of firm prouctivity smaller k implies: a larger welfare gains from opening the close economy to trae larger W T Het /WA Het, b larger smaller welfare gains losses from a ecrease increase in variable trae costs in the open economy equilibrium. Proof. See the appeni. Intuitively, a larger ispersion of firm prouctivity smaller k implies greater scope for ajustment along the margin of enogenous firm entry an eit ecisions, which implies ifferent aggregate welfare effects from a change in trae costs. 4 Welfare an Trae Policy Evaluation To isolate the etra ajustment margin from enogenous firm selection, our theoretical comparative static changes the istribution of prouctivity holing all other eogenous variables fie across moels. This eercise oes not restrict the equilibrium values of the enogenous variables in particular the omestic trae share λ an the trae elasticity θ to be the same in the two moels. Instea the equilibrium values for these enogenous variables iffer systematically across the two moels. In the appeni, we show that the heterogeneous firm moel generates a higher trae elasticity than either the homogeneous firm moel or its etension given the same value of the eogenous variables. On the one han, moving from the close economy to the open economy, there is less trae higher λ in the heterogeneous firm moel than in the homogeneous firm moel. On the other han, starting from an open economy equilibrium, trae liberalization generates more trae lower λ in the heterogeneous firm moel than in the etene homogeneous case For sufficiently high trae costs, the omestic trae share is higher in the homogeneous firm moel than in the heterogeneous firm moel, because the representative firm oes not fin it profitable to eport. As trae costs fall below the threshol at which the representative firm eports, the omestic trae share in the homogeneous firm moel falls from one to a value below that in the heterogeneous firm case, an the trae elasticity jumps from zero to σ 1 less than the trae elasticity in the heterogeneous firm case. 13

14 ACR show that there eists a restricte subset of our heterogeneous an homogeneous firm moels in terms of parameter space restrictions in which the trae elasticity is constant. Uner these parameter restrictions, this constant trae elasticity an the omestic trae share become sufficient statistics for welfare. Even then, the micro structure of the unerlying moel still matters for the welfare gains from trae, but only through its effect on the trae share an trae elasticity. Therefore, if aggregate ata can be use to measure the trae elasticity inepenently of a moel the trae share, by efinition, is irectly observe from aggregate ata then these aggregate ata can be use to accurately measure the welfare gains from trae; an this welfare computation will be inepenent of the micro structure of the unerlying moel. Furthermore, since the trae elasticity is constant uner the ACR parameter restrictions, it has a structural interpretation, an hence its use in trae policy evaluations is not subject to the Lucas Critique. The key feature of those parameter restrictions is to inuce a single constant trae elasticity that can be applie across moels. However, when using the ACR sufficient statistics for an e ante trae policy evaluation, one nees to assume more than a ata generation process conforming to one of those moels within the ACR class. One also nees to assume that these moels are universal an eternal, in the sense that their structural parameters are always the same, inepenent of the time or country to which they are applie. If this assumption is not satisfie, an one wants to estimate the welfare gains from trae in a new contet where the trae elasticity is unknown an cannot plausibly be taken from an eisting contet, one nees to start with a specific structural moel an assumptions about its behavioral parameters. As shown in our theoretical comparative static, this structural moel will generate ifferent e ante preictions for the aggregate welfare implications of changes in trae costs, epening on whether or not it features firm heterogeneity. In particular, we show how the eistence of a single constant elasticity breaks own uner very small epartures from the ACR parameter restrictions. In such a setting, a trae elasticity estimate from one contet nee not apply for the evaluation of trae policy in another contet, even when the moel parameters remain unchange. Therefore trae policy evaluations using an estimate trae elasticity become subject to the Lucas Critique, because this elasticity is not invariant to trae policy. More funamentally, we show that even the enogenous trae elasticity is no longer a sufficient statistic for welfare along with the omestic trae share: even conitioning on those two aggregate moments, the micro structure influences the welfare gains from trae. The reason is that welfare epens on the entire istribution of firms proucing an selling in a market which is summarize by the omestic prouctivity cutoff. Therefore, changes in welfare epen on the change in the omestic prouctivity cutoff which can be measure using a omestic trae elasticity. Only in the case of an untruncate Pareto istribution is the omestic trae elasticity equal to the eport trae elasticity. Departing from this parametrization, these two elasticities iverge an epen on the micro structure an the level of the trae costs. In the remainer of this section, we eten the ACR approach of epressing the welfare gains from trae as a function of observable empirical moments to the more general cases of the homogeneous an 14

15 heterogeneous firm moels from Section 2 without imposing the ACR parameter restrictions. These empirical moments inclue the trae share an trae elasticity, but also aitional ones that capture micro structure an iffer between the two moels. In Section 5, we provie several eamples of trae liberalization scenarios in which the aitional impact of the micro structure on welfare can be substantial, even for small empirically relevant epartures from the ACR restrictions. In Section 6, we quantitatively assess these ifferences in welfare preictions. 4.1 ACR Welfare Derivation ACR show how the omestic trae share λ an trae elasticity θ are sufficient statistics for the welfare gains from trae in a large class of trae moels incluing special cases of our homogeneous an heterogeneous firm moels, so long as three macro-level restrictions are satisfie: R1 balance trae; R2 aggregate profits are a constant share of aggregate revenues; an R3 a CES import eman system with a constant elasticity of trae with respect to variable trae costs. Uner these restrictions, the welfare gains from trae regime T 0 to T 1 can be written: W T 1 W T 0 = λ T 0 1 θ. 28 Thus, 28 will characterize the welfare gains from trae for both our homogeneous an heterogeneous firm moels so long as R1-R3 are satisfie. Trae is balance in both of these moels, so R1 is always satisfie. However, the general versions of both moels imply epartures from a constant aggregate share of profits emboie in R2. Given CES preferences, the constant aggregate trae elasticity restriction R3 will be satisfie in all versions of our homogeneous firm moel, whereas it will be violate along with R2 in our general heterogeneous firm moel. 4.2 Gains from Trae in the Homogeneous Firm Moel We consier a lowering of trae costs from τ 0 an f 0 trae regime T 0 to τ 1 an f 1 trae regime T 1. λ T 1 To simplify notation, we assume that τ 0 an f 0 may be high enough such that no trae is generate in T 0. Let χ T 0 enote an inicator variable for positive trae. Then, using the epressions for welfare in the close economy 22 an open economy 24 an the omestic trae share 26, we can write the welfare gains from trae in the heterogeneous firm moel as: W T 1 W T 0 = [ λ T 0 F + χ T 0 f 0 λ T 1 F + f 1 where θ = σ 1 is the elasticity of trae with respect to variable trae costs. ] 1 σ 1, 29 In this more general setting, the welfare gains epen on the same two aggregate moments the omestic trae share an trae elasticity as in ACR 28, but also on the change in firm size capture in 29 by the total fie costs pai by the representative firm. This change in firm size is an observable empirical moment, but one that characterizes a change in micro structure. Even after controlling for the two aggregate moments, these changes in micro structure will affect the welfare gains from trae. 15

16 Such changes in micro structure will occur whenever the fie eporting cost changes in an open economy with trae χ T 0 = 1 or even in the presence of any positive fie eporting costs in an economy that opens up to trae from χ T 0 = 0. These changes represent a violation of R2 as the share of profits in revenue changes with firm size in the homogeneous firm moel. 4.3 Gains from Trae in the Heterogeneous Firm Moel We now seek to epress the welfare gains from trae liberalization in terms of observable empirical moments for the general case of our heterogeneous firm moel. Since trae continuously rops to zero when trae costs increase, we can start from an open economy trae regime T without loss of generality. To simplify notation, we rop the T superscript. For now, we also assume that there is eport market selection in this trae regime so that ϕ > ϕ. From 19, the full trae elasticity with eport market selection is θ Het = σ 1 ln Λ/ ln τ, where Λ = δϕ /δϕ represents the omestic market share of eporters an hence changes in Λ capture changes in the etensive margin of trae. This full trae elasticity θ Het incorporates the irect effect of τ on the etensive margin of trae via its impact on the eport cutoff ϕ = τf /f 1/σ 1 ϕ see 11, as well as inirect effects through the price ine via its impact on the omestic cutoff ϕ. As argue by ACR, only the partial trae elasticity capturing the irect effect of τ is observe empirically, since it is estimate from a gravity equation with eporter an importer fie effects. In the contet of our symmetric country moel, this partial elasticity can be erive from 18, which relates the omestic trae share to variable trae costs an the two prouctivity cutoffs λ = λτ, ϕ, ϕ, an from 12, which relates the two prouctivity cutoffs to one another ϕ = ϕ τ, ϕ. 11 the partial erivative of the omestic trae share with respect to τ holing ϕ constant, we have: ϑ = ln 1 λ λ = σ 1 ln Λ ln ϕ ln τ ln ϕ ln τ, ϕ ϕ Taking where the relationship between the prouctivity cutoffs 12 implies ln ϕ / ln τ ϕ = 1. Therefore the partial elasticity can be further written as: ϑ = σ 1 ln Λ ln ϕ, ϕ = σ 1 + γϕ, 30 where γϕ j = ln δϕ j / ln ϕ j is the elasticity of δϕ j for market j {, }. Note that δϕ j is proportional to the cumulative market share in any given market of firms above any cutoff ϕ j. Therefore γϕ j represents the hazar function for the istribution of log firm size within a market. If the istribution of prouctivity ϕ is an untruncate Paretok, then the istribution of firm size in any given market also will be an untruncate Paretok σ + 1 an the hazar function γ will be constant at k σ 1. In this case, the partial an full trae elasticity 11 In the web appeni, we show how a multi-country version of our moel yiels an epression for log bilateral trae that is linear in eporter an importer fie effects an ϑ ln τ. 16

17 are equal to one another an constant at k. Even a slight eparture from an untruncate Pareto to a truncate Pareto implies that the partial an full trae elasticity are istinct from one another an variable. In this case, the hazar function γϕ j becomes: γϕ j = k σ 1 ϕmin ϕ j k σ 1 ϕmin ϕ j k σ 1 ϕmin ϕ ma k σ 1, 31 where ϕ ma is the upper boun to the support of the prouctivity istribution. As ϕ ma, the hazar function γϕ j converges to its constant value for an untruncate Pareto istribution: lim ϕma γϕ j = k σ 1. More generally, for ϕ ma <, γϕ j takes a strictly higher value than for an untruncate Pareto prouctivity istribution an iffers between the omestic an eport market. The hazar function for each market is increasing in the prouctivity cutoff, attaining its minimum value as ϕ j ϕ min, an converging towars infinity as ϕ j ϕ ma. Since higher variable trae costs reuce the omestic prouctivity cutoff an increase the eport prouctivity cutoff, they imply a lower γϕ an a higher γϕ. Using welfare 16 an the trae share 18, welfare in the heterogeneous firm moel can be written: W Het = σ 1 1 σ M e σ 1 δϕ λ 1 σ 1, 32 Since welfare 16 also implies that changes in welfare are proportional to changes in the omestic prouctivity cutoff ln W = ln ϕ an ln δϕ = γϕ ln ϕ, we can then write the welfare change using the observable partial trae elasticity from 30: ln W = 1 ϑ + [γϕ γϕ ] ln M e ln λ. 33 As highlighte by ACR, restricting the istribution of prouctivity raws Gϕ to be untruncate Pareto an assuming that there is eport market selection ϕ T > ϕ T, ensures that the macro restrictions R1-R3 are satisfie. In this case, the hazar function is constant so that the ifference γϕ γϕ is zero, an entry oes not respon to changes in trae costs ln M e = 0. In this case, we recover the welfare gain erivation 28 from ACR. Since the partial trae elasticity ϑ is constant in this case, the welfare ifferential can be integrate to capture proportional welfare changes between any two trae regimes, so long as there is eport market selection in both. However, the welfare ifferential 33 highlights how, in the general case, the welfare gains from trae liberalization will change with the micro structure. Even after controlling for the trae share an trae elasticity, this micro structure matters for welfare through the hazar ifferential γϕ γϕ. In Section 6, we show quantitatively how small changes in the shape of the istribution of firm prouctivity Gϕ away from an untruncate Pareto istribution can lea to large changes in the hazar ifferential γϕ γϕ. This issue is istinct from the challenge of measuring the appropriate trae elasticity ϑ in a worl where this elasticity is variable both across countries an within each country for ifferent values of trae costs. The preicte welfare effects of trae 17

18 liberalization base on the ACR formula will also iverge from the true welfare effects because of the variable nature of the partial trae elasticity ϑ. Finally, the welfare ifferential 33 also shows that, in cases where trae liberalization leas to responses in firm entry ln M e 0, then this change in micro structure will also affect the welfare gains from trae, even conitional on the omestic trae share an trae elasticity. Our analysis also highlights the irection of the bias in the ACR formula. With a truncate Pareto prouctivity istribution, the hazar function γϕ j is monotonically increasing in the prouctivity cutoff ϕ j. Furthermore, in an equilibrium with eport market selection, the omestic prouctivity cutoff ϕ is less than the eport prouctivity cutoff ϕ, which implies a negative hazar ifferential γϕ γϕ. Therefore, even with a correct estimate of the variable partial trae elasticity ϑ, an evaluation of welfare changes 33 that oes not control for the hazar ifferential will ten to unerstate the absolute magnitue of changes in welfare in response to changes in trae costs, since ϑ > ϑ + γϕ γϕ. To make our argument as clearly as possible, we have evelope these results for two symmetric countries. But the epression for welfare in the heterogeneous firm moel with a general prouctivity istribution 32 hols more generally in a setting with many asymmetric countries, as shown in the web appeni. In such a setting, there is a separate partial trae elasticity for each eporterimporter pair. Empirical estimates of the coefficient on variable trae costs from a gravity equation incluing eporter an importer fie effects capture the average value of this elasticity across all eporter-importer pairs in the regression sample. This average elasticity nee not provie a goo approimation to the partial trae elasticity for any one iniviual eporter-importer pair either insie or outsie the regression sample. The appropriate elasticity for welfare in 33 is the partial trae elasticity for any one iniviual eporter-importer pair ajuste for the hazar ifferential between that eporter-importer pair an the omestic market. A somewhat separate implication of an untruncate Pareto istribution is that the increase in prouct variety from imports following trae liberalization is eactly offset by a ecrease in omestic prouct variety associate with tougher selection. Hsieh an Ossa 2011 establish this result for a multi-sector setting with asymmetric countries an CES preferences see also Feenstra Feenstra 2014 shows that this implication of the untruncate Pareto prouctivity istribution etens to a general class of non-ces preferences, but that it is similarly broken by small epartures away from an untruncate Pareto istribution to a truncate Pareto istribution. In our setting with a general prouctivity istribution, the response of firm entry to trae liberalization implies changes in prouct variety available for consumption. Lastly, we briefly characterize the gains from trae in terms of observable moments when trae costs are sufficiently low that all surviving firms eport. In other wors, there is no eport market selection an ϕ T = ϕt. As we previously iscusse, the equilibrium in this case will have ientical aggregate properties to an equilibrium with homogeneous firms, in which all firms have a common prouctivity level T an face a fie cost F T = f e / [ 1 Gϕ T ] + f + f. Thus, the welfare gains 18

19 associate with a transition from trae regime T 0 to T 1 can be measure using: W T 1 W T 0 = λ T 0 F T 0 λ T 1 F T 1 1 σ 1, 34 where in this case the full an partial trae elasticities are equal to one another: θ = ϑ = σ 1. As in the homogeneous firm case, we see that the welfare gains from trae epen on changes in average firm size capture by F T as well as the omestic trae share an trae elasticity which is now constant at σ 1. Average firm size is now enogenous an varies with the omestic prouctivity cutoff ϕ T affects F T. Any change in the fie eporting costs between T 0 an T 1 will inuce changes in average firm size - even when prouctivity has an untruncate Pareto istribution as was the case in the homogeneous firm moel, this situation represents a violation of ACR s macro restriction R2. Taking the results of this subsection together, our generalization of the ACR welfare representation provies a way of quantitatively assessing whether preictions for the welfare gains from trae liberalization base on the omestic trae share an the assumption of a constant trae elasticity provie a goo approimation to the true welfare gains. The success of this approimation epens on the etent to which the partial trae elasticity is constant, the size of the hazar rate ifferential between the omestic an eport markets an the egree to which firm entry respons to changes in trae costs. If firm-level ata are available, these ifferences in hazar rates an the response of firm entry can be eamine empirically. Amittely, measuring the response of firm entry to changes in trae costs raises challenges. But these challenges are similar to those face in estimating a partial trae elasticity an recovering the change in trae inuce by a change in variable trae costs alone. Hea, Mayer an Thoenig 2014 propose a gooness of fit test of firm size istribution to the Pareto istribution that is similar to checking for changes in the hazar rate which is constant uner Pareto. Even in cases where only aggregate trae ata is available, one can in principle estimate ifferences in trae elasticities across country-partner pairs. Helpman, Melitz an Rubinstein 2008 an Novy 2013 both implement gravity estimation proceures that allow for variation in the elasticity of trae with respect to observable trae frictions such as istance. Both papers fin substantial variation in these elasticities. Unless this variation is eactly offset by an equal an opposite variation in the elasticity of trae costs with respect to the observable trae frictions, these results imply a variable elasticity of trae with respect to trae costs. In the setting with many asymmetric countries iscusse above, our generalize welfare erivations highlight that the iscrepancy between the preicte an true welfare effects of trae liberalization will be minimize by choosing a trae elasticity for country-partners that most closely approimates the elasticity for a country s trae with itself. If the hazar rate function γϕ j is monotonic in the cutoff ϕ j, then the hazar ifferential γϕ ii γϕ ik will be minimize when ϕ ik is closest to ϕ ii, which occurs for the traing partner with the highest share of eporting firms. 19

20 5 Trae Policy Evaluation In the previous section, we introuce small eviations from the ACR parameter restrictions an showe how the micro structure then affects the measurement of the welfare gains from trae even when conitioning on a given trae elasticity an a given omestic trae share. This le to iscrepancies between the true welfare effects of trae liberalization an those preicte by the ACR formula. We now illustrate more concretely how such iscrepancies may arise when evaluating the welfare gains generate from a few specific trae liberalization scenarios. Our starting point is the heterogeneous firm moel with two symmetric countries evelope in Section 2. We consier the welfare gains from liberalizing trae first from trae regime T 0 τ 0, f 0 to T 1 τ 1, f 1, an then to T 2 τ 2, f 2. We contrast the true welfare gains from 16 with those measure by a policy analyst who applies the ACR formula 28. We also contrast the cases of e post an e ante policy evaluation using a similar approach to ACR an Costinot an Roriguez-Clare Specifically, we assume that trae liberalization from T 0 T 1 is evaluate e post so that the omestic trae shares λ T 0 an λ T 1 are observe, an the arc trae elasticity therefore can be irectly measure as: 12 ln ˆθ 01 = 1 λ T 1 λ T 1 ln 1 λ T 0 λ T 0 ln τ 1 ln τ The ACR preicte welfare gains from trae are then Ŵ01 = λ T 0 /λ T 1 1/ˆθ01. On the other han, we assume that trae liberalization from T 1 T 2 is evaluate e ante, so the omestic trae share λ T 2 is unobserve an is recovere from the moel using the elasticity ˆθ 01. That is, ˆλ T2 solves: ln 1 ˆλT 2 ln 1 λ T 1 ˆλ ˆθ 01 = T 2 λ T ln τ 2 ln τ 1 E ante, the ACR welfare erivation yiels preicte welfare gains from trae given by Ŵ12 = λ T 1 /ˆλ T 2 1/ˆθ01. We assume that the trae costs in the trae regimes T0 an T 1 are high enough to generate eport market selection. However, we o not impose this restriction on the hypothetical trae regime T 2 : A policy analyst may be intereste in evaluating the welfare gains from trae for scenarios that go most or all of the way to free trae. 5.1 Scenario 1: Untruncate Pareto Prouctivity Distribution We assume that Gϕ is istribute untruncate Paretok an initially assume no change in the fie eport costs: f 0 = f 1 = f 2. Then, the measure elasticity ˆθ 01 will recover the constant elasticity k, an Ŵ01 will eactly measure the true welfare gains from the e post liberalization T 0 T 1. Also, if the hypothetical trae regime T 2 features eport market selection the trae costs τ 2 an f 2 are high enough, then ˆθ 01 = k will also capture the trae elasticity between T 1 an T 2, an the analyst woul 12 When the istribution of prouctivity raws Gϕ is an untruncate Pareto a necessary conition for the ACR macro restrictions to hol there is no ifference between the full an partial trae elasticities θ an ϑ. 20