CEP Discussion Paper No 975 May 2010

Transcription

1 ISSN CEP Discussion Pper No 975 My 200 Trde Liberliztion nd Heterogeneous Firm Models: An Evlution Using the Cnd - US Free Trde Agreement Holger Breinlich nd Alejndro Cuñt

2 Abstrct We exmine the qulittive nd quntittive predictions of heterogeneous firm model à l Melitz (2003) in the context of the Cnd - US Free Trde Agreement (CUSFTA) of 989. We clibrte our model to the pre-trde liberliztion stge, simulte the trde liberliztion, nd compute the resulting growth rtes of Cndin industry productivity, exports nd imports. We compre them with Trefler s (2004) estimtes of the effects of CUSFTA. Our results show tht our model performs well in replicting the qulittive spects of Trefler s results. In prticulr, we correctly predict tht US triff cuts hve smller productivity enhncing effects thn Cndin triff reductions due to the entry of less efficient exporters. Quntittively, the model tends to underpredict the impct of CUSFTA on growth rtes of productivity, but overpredicts the increse in Cndin exports nd imports. We discuss how liberliztion-induced chnges in the firm-level productivity distribution cn reconcile the model with the evidence. Keywords: Heterogeneous firm models, trde liberliztion, CUSFTA, empiricl evlution JEL Clssifictions: F2, F3, F5 This pper ws produced s prt of the Centre s Globlistion Progrmme. The Centre for Economic Performnce is finnced by the Economic nd Socil Reserch Council. Acknowledgements We re grteful to Mrc Melitz, Alex Michelides nd Ntli Rmondo for helpful discussions. We would lso like to thnk seminr prticipnts t CEU, CORE, LSE, nd Vienn for comments nd suggestions. All errors remin ours. Cuñt grtefully cknowledges finncil support from Spin s CICYT (SEJ nd ECO ). Holger Breinlich is Reserch Associte with the Centre for Economic Performnce, London School of Economics nd Lecturer in the Deprtment of Economics, University of Essex. Alejndro Cuñt is Lecturer in the Deprtment of Economics, University of Essex. Published by Centre for Economic Performnce London School of Economics nd Politicl Science Houghton Street London WC2A 2AE All rights reserved. No prt of this publiction my be reproduced, stored in retrievl system or trnsmitted in ny form or by ny mens without the prior permission in writing of the publisher nor be issued to the public or circulted in ny form other thn tht in which it is published. Requests for permission to reproduce ny rticle or prt of the Working Pper should be sent to the editor t the bove ddress. H. Breinlich nd A. Cuñt, submitted 200

3 Introduction Since the seminl contribution by Melitz (2003), heterogeneous rm models hve become widely used instrument in the toolkit of interntionl economists. These models were motivted by number of stylized fcts: (i) the existence of lrge productivity di erences mong rms within the sme industry; (ii) the higher productivity of exporting rms s compred to non-exporting rms; (iii) the lrge levels of resource relloctions cross rms within exporting industries following trde liberliztion reforms; nd (iv) the resulting gins in ggregte industry productivity. In generliztion of the Krugmn (979, 980) model, the introduction of within-industry productivity heterogeneity nd bechhed costs enbles this clss of models to produce equilibri nd comprtive sttics long the lines of these fcts. While these models re thus brodly consistent with vilble empiricl evidence, thorough evlution of their qulittive nd quntittive predictions with regrds to trde liberliztion is still outstnding. This is despite the fct tht the models predictions on the link between trde liberliztion nd chnges in ggregte productivity or trde ows re of rst-order importnce for economic policy nd welfre nlysis. In this pper, we ttempt for the rst time to provide such n evlution. We go beyond the stylized fcts listed bove nd sk to wht extent heterogeneous rm models in the trdition of Melitz (2003) re ble to replicte both qulittive nd quntittive ndings from speci c trde liberliztion. We do so in the context of the Cnd - US Free Trde Agreement of 989 (henceforth, CUSFTA). As hs been rgued elsewhere, CUSFTA is n idel setting for the evlution of trde liberliztion episodes (see Tre er, (2004)). It ws pure trde liberliztion in the sense tht it ws not ccompnied by ny other importnt economic reform, nor ws it response to mcroeconomic shock. It ws lso lrgely unnticipted since its rti ction by the Cndin prliment ws considered highly unlikely s lte s November 988. Finlly, the min instrument of liberliztion were tri cuts which re esily qunti ble nd s such idelly suited for n econometric nlysis. Not surprisingly then, CUSFTA hs been extensively studied over the pst decde (e.g. Tre er (2004); Hed nd Ries (999) nd (200)). We tke the results of these studies s our strting point, in prticulr Tre er (2004). Consistent with the stylized fcts outlined bove, Tre er nds tht CUSFTA led to strong productivity increses in Cndin mnufcturing which to lrge extent were due to relloction of mrket shres towrds high-productivity rms. He lso uncovers some more subtle e ects. For exmple, Cndin tri cuts hd much stronger e ect on Cndin productivity gins thn US tri reductions. The mgnitudes of some of the e ects documented by Tre er See Breinlich (2008) for discussion of this point. Frizzell et l. (989) provide detiled ccount of the politicl context in which the greement ws signed.

4 re lso stonishing - the third of Cndin mnufcturing industries subject to the highest domestic tri cuts sw lbor productivity increse by 5% over the eight yers following the implementtion of CUSFTA. The gol of our nlysis is to evlute the extent to which version of Melitz s heterogeneous rm model cn ccount for these fcts, both qulittively nd quntitvely. We begin by constructing Melitz-style model which cptures the min fetures of the Cndin-US liberliztion experience. In prticulr, we llow for symmetries cross countries in terms of size, bilterl tri s nd prmeter vlues such s xed costs. We then clibrte the model s prmeters to the pre-liberliztion period, simulte the liberliztion using the ctul tri cuts, nd confront the model s predictions with regrds to industry productivity growth nd trde ows with the empiricl evidence provided by Tre er. Our results indicte tht the model performs well in replicting the qulittive fetures of Tre er s results. Consistent with his empiricl estimtes, our model predicts n symmetric e ect of Cndin nd US tri reductions on ggregte Cndin productivity, with Cndin tri cuts hving the lrger impct. Our model lso cptures the brod qulittive ptterns of the e ects of tri reductions on Cnd-US trde ows. The results of comprison of the quntittive predictions of our model with Tre er s estimtes re more mixed. In our bseline speci ction, we only predict round qurter of the estimted impct of liberliztion on ggregte lbor productivity. On the other hnd, we overestimte the increse in Cndin exports nd imports by fctor of t lest two, nd up to fctor of 30 in some simultions! In nl step, we look t wys to reconcile the theoreticl predictions with the dt. We show tht llowing for empiriclly plusible chnges in within- rm productivity signi cntly improves the model s performnce. In conclusion, it thus seems tht the stndrd pproch of bstrcting from rm-level productivity gins is useful for modeling qulittive ptterns of trde liberliztions. However, to mtch quntittive ptterns s well, future work on heterogeneous rm models will hve to tke within- rm productivity chnges more seriously. We re not the rst to clibrte models with heterogeneous rms. Eton nd Kortum (2002) use interntionl trde ows to clibrte Ricrdin model with perfect competition nd perform vrious counterfctul policy experiments. Bernrd et l. (2003) use modi ed version of Eton nd Kortum (2002) to explin di erences between US exporting nd non-exporting mnufcturing rms nd to nlyse the e ects of severl trde-relted policy chnges. Irrrzábl nd Opromoll (2005) lso use the Eton-Kortum model to study Chile s liberliztion experience of the 970s nd 980s. Del Gtto et l. (2006) clibrte the model by Melitz nd Ottvino (2008) on Europen dt to evlute the bene ts of trde liberliztion in the EU. None of these contributions uses Melitz s originl contribution s their modeling 2

5 frmework. In contrst to these ppers, we re lso not primrily interested in counterfctul experiments. Rther, we see our clibrtion exercise s wy to test the fundmentl predictions of models of the clss of Melitz (2003). 2 The Cnd-US Free Trde Agreement together with Tre er s seminl study provide n optiml setting for this endevour. In prticulr, we re not obliged to compre our model s predictions to the rw moments of the dt. Using Tre er s empiricl techniques, we cn insted isolte the e ect of tri cuts from the lrge number of confounding fctors which lso in uenced productivity nd trde over the period under study nd which will never be fully cptured by stylized model such s ours. We lso contribute to the literture by providing trctble extension of Melitz (2003) to n symmetric multi-country setting. In this, our pper is relted to recent contributions by Melitz nd Ottvino (2008) nd Chney (2008). Finlly, our pper lso reltes to number of ppers which hve used CUSFTA for testing trde theories. For exmple, Hed nd Ries (999) nlyze the impct of tri cuts on the number nd scle of Cndin rms in order to test competing models of imperfect competition. Hed nd Ries (200) use CUSFTA to evlute Krugmn nd Armington style models of interntionl trde. Kehoe (2005), too, dvoctes the use of trde liberliztion episodes (in his cse, NAFTA) s wy to ssess the empiricl vlidity of pplied generl equilibrium models. The rest of the pper is structured s follows. In section 2, we revisit Tre er s results nd extend his methodology to dditionl vribles of interest. Section 3 discusses our extension of the Melitz model. Sections 4 nd 5 evlute the model s qulittive nd quntittive predictions in the light of Tre er s results. In section 6 we discuss to wht extent liberliztion-induced chnges in the rm-level productivity distribution cn reconcile the model with the evidence. Section 7 concludes. 2 Revisiting Tre er s Results for Trde nd Productivity Tre er (2004) tries to estimte the cusl impct of CUSFTA-mndted reductions of Cndin nd US tri s on set of Cndin vribles such s lbor productivity nd trde. His identi ction strtegy thus needs to isolte these e ects from lrge number of confounding fctors. He strts from di erence-in-di erences speci ction in which he regresses chnges in the dependent vrible (e.g. lbor productivity growth) on chnges in US nd Cndin tri s pre- nd post-cusfta: (y i y i0 ) = 0 + CA t CA i t CA i0 + US t US i t US i0 +X (X i X i0 )+" i ; 2 Two recent ppers, Eton et l. (2008) nd Armenter nd Koren (2009) lso explore the quntittive performnce of Melitz (2003), but focus their ttention on the model s export fetures outside of the context of trde liberliztion. 3

6 where y i y i0 is the nnulized double log-di erence in the dependent vrible of interest in industry i. Likewise, t CA i t CA i0 nd t US i t US i0 represent the double di erence in Cndin nd US tri s, nd X i X i0 is the double log-di erence in dditionl control vribles. 3 For our purposes, it is importnt to note tht Tre er controls for lrge number of fctors which lso in uence the dependent vrible of interest nd might bis the estimted impct of tri reductions. His pproch is thus close in spirit to the comprtive sttic exercises which we will perform below. Tht is, Tre er estimtes the impct of CUSFTA-mndted tri chnges on chnges in lbor productivity nd trde, holding ll other fctors constnt. In our view, compring our model s results to Tre er s conditionl moments is better suited for n evlution of our model thn comprison with the rw moments of the dt in the sense tht it does not plce n unfirly hevy burden on reltively stylized theory. In tble, we rst replicte Tre er s key results on lbor productivity nd Cndin imports. We estimte the speci ction bove with dt provided on Dniel Tre er s website nd compre the results to his bseline speci ctions (row in his tbles 2 nd 3). As seen in columns nd 2, we re ble to replicte Tre er s results lmost exctly. For exmple, Cndin tri cuts hve strongly signi cnt impct on domestic lbor productivity in Cnd. A one-percentge point chnge in led, on t CA i t CA i0 verge, to.4% increse in the rte of nnul lbor productivity growth in US tri cuts lso rised lbor productivity, lthough the estimted e ect is smller nd sttisticilly insigni cnt. Tre er re nes his results by clculting weighted totl e ect on the third of Cndin industries fcing the highest domestic tri cuts ( import-competing industries ) nd on the third of industries which enjoyed the lrgest US tri concessions ( export-oriented industries ). He lso computes the totl weighted impct of CUSFTA through both US nd Cndin tri cuts. 4 Lines 5-7 of tble report the corresponding results. Cndin tri reductions in the most impcted, import-competing industries cused totl lbor productivity increse of 0.5 log points or pproximtely 5% over the period The e ect of US tri concession on productivity in the most impcted, export-oriented industries ws much smller t just 5%, nd the totl e ect of CUSFTA ws productivity increse of 6%. 3 See Tre er (2004) for detils on these dditionl controls nd further robustness checks. Most importntly, Tre er tries to control for industry-time vrying trends nd generl business cycle e ects. He ddresses the rst issue by including chnges in the dependent vrible for the US economy s n dditionl regressor. He lso constructs business cycle control which is in essence n industry-speci c prediction of the e ect of business cycle conditions on the dependent vrible. He lso uses instrumentl vrible methods but does not nd evidence for signi cnt endogeneity problems. 4 In ll three cses, Tre er weighs industry-speci c tri cuts using 988 sectorl dt on the numertor of the dependent vrible (i.e., vlue dded for lbor productivity nd import nd exports for the trde regressions). He lso converts nnul chnges into totl e ect for the period See ppendix B of Tre er (2004) for detils. 4

7 Column 2 shows the results from estimting the bove eqution using Cndin imports from the US s the dependent vrible. Agin, Cndin tri concessions hd lrge positive impct, with imports rising by 45% in the most impcted, import-competing industries nd 4% overll. Surprisingly, US tri concessions lso hd positive impct on Cndin imports, lthough the e ect is smller nd less sttisticlly signi cnt. In columns 3-4, we reproduce Tre er s ndings for the subset of industries which we will use in our clibrtion. As discussed below, dt vilbility nd theoreticl considertions prevent us from using Tre er s full smple. However, columns 3-4 show tht Tre er s qulittive results re not ected by the reduction in smple size. The results for Cndin tri cuts re lmost exctly identicl. The impct of US tri cuts is somewht smller thn before, but the qulittive pttern is very similr to the one rising from the full smple. Finlly, in column 5 we extend Tre er s methodology to Cndin exports to the US. US tri concessions hd the expected positive e ect on Cndin exports lthough the e ect is sttisticlly insigni cnt. In contrst, Cndin tri cuts reduced Cndin exports but gin the e ect is not signi cnt. We estimte tht lower US tri s cused n increse in Cndin exports by 6% in the most impcted, export-oriented industries. Cndin tri cuts reduced exports by 8%, however, so tht the overll e ect is essentilly zero. To summrize, Cndin nd US tri concessions hd strongly symmetric e ects on Cndin lbor productivity. Lbor productivity ws strongly positively impcted by Cndin tri cuts, nd to lesser extent by US tri reductions. Lower Cndin import tri s led to higher Cndin imports while lower US tri s incresed Cndin exports. These ndings set the stge for the rest of this pper. We will investigte to wht extent our version of Melitz (2003) cn replicte these ndings, both in terms of the signs of the estimted e ects s well s their quntittive mgnitude. 3 The Model Our model is n extension of Melitz (2003) tht is close to Helpmn et l. (2004). We llow for mny industries nd symmetries cross countries. Initilly we simplify the model by bstrcting from its free-entry stge. 5 However, further below we lso model the free-entry stge s in the originl Melitz model. 5 In this sense, our model is close to Chney (2008). 5

8 Demnd Consumers mximize the following two-tier utility function: U = X i2i i ln Q i + A; () Q i = Z q i () i i i i d ; (2) 2 i where i represents the (endogenous) set of vilble vrieties in the mnufcturing sector i. i > is the elsticity of substitution between ny two goods in industry i. Choosing good A s the numérire, utility mximiztion on the upper level yields demnd functions A = Y P i i nd Q i = i =P i, where Y is totl expenditure per consumer. In the mnufcturing goods sector, utility mximiztion yields demnd function q i () = p i () P i i. Technology nd Environment There re mny countries, denoted by j. All countries produce positive mounts of the numérire good, which is freely trded; its industry opertes under perfect competition nd with liner production function A = l A everywhere, where l A is lbor employed in the numérire industry. This implies w j = for ll j. Mnufcturing goods re produced using lbor s the only production fctor. rms s output q nd productivity determine its vrible lbor requirements q () =. 6 In order to supply goods to its own domestic mrket, rm must lso py xed cost F jj in terms of the numérire good. In order to export to country j 0, country-j rms must incur n dditionl xed cost F jj 0, lso in terms of the numérire good. 7 trde is lso subject to the stndrd iceberg trnsport cost jj 0 domestic sles re subject to no trnsport costs: jj = for ll j. A Interntionl. We ssume tht In ech country, there is given lrge mss M j of potentil entrnts to n industry. The productivity prmeter is reveled to rms before they py the xed costs nd strt production. In equilibrium, only those rms tht cn ern non-negtive pro ts will enter mrket. Firm-level Outcomes Ech mnufcturing rm hs monopoly power over the vriety it produces. The pricing rule of country-j rms is p jj 0() = jj 0 : (3) 6 In wht follows, industry nd country nottion is suppressed for simplicity wherever unnecessry. 7 This ensures tht only rms tht lso produce domesticlly will export, which is the empiriclly relevnt cse. 6

9 The rms ssocited demnd levels (net of trnsport costs in the cse of exports) re q jj 0() = jj 0 P j 0 j 0: (4) The rm s resulting revenues (once gin, in the cse of export revenues they re expressed net of trnsport costs) re r jj 0() = jj 0 P j 0 j 0: (5) Pro ts re Entry Thresholds jj 0() = r jj 0() F jj 0: (6) A rm with productivity will enter the domestic mrket if jj () 0. Hence, jj ( jj) = 0 de nes the domestic entry cuto jj: 8 Similrly, rm will enter export mrket j 0 " # =( ) F jj jj = j P : (7) j ( ) in ddition to producing domesticlly if jj 0() 0. Hence, the export cuto jj is implicitly de ned by 0 jj 0( jj0) = 0. Using country-j rms export cuto condition nd country-j 0 rms domestic mrket entry condition, j 0 j 0( j 0 j0) = 0, we cn express country-j s export cuto s function of country-j 0 s entry cuto : The consumer price index is =( jj = Fjj 0 0 F j 0 j 0 ) jj0 j 0 j0: (8) P j = " X j 0 Z j 0 j p j 0 j() M j 0v j 0()d!# : (9) 8 As in Melitz (2003), we ssume prmeter vlues such tht the mrginlly pro tble rm will not export: jj jj = 0 () rjj jj = Fjj : For jj 0 jj = P j 0 j 0 jj 0 P r jj j j jj F jj 0 < 0; we need to impose jj F 0 jj 0 > P j 0 j 0 F P j jj. The price index P j cn be expressed s function of the j model s prmeters. 7

10 A common ssumption in the heterogeneous rm literture is tht is Preto distributed (Chney (2008); Melitz nd Ottvino (2008)). 9 Tht is, v() = k (+), with ; k > 0 nd k. Assuming the shpe prmeter is equl for ll countries, (7)-(9) yield expressions for productivity cuto s jj nd jj0 in terms of the model s prmeters, which we cn summrize s jj 0 = Fj 0 j 0 j 0 2 = Fjj 0 jj0 4 X + F j 0 j 0 j 00 M j 00k j 00 j 00 j 0 Fj 00 j 0 F j 0 j = : (0) In the following, we ssume tht >. 0 The xed cost F jj hs positive e ect on the domestic entry threshold jj, s higher F jj mkes it hrder for domestic low-productivity rms to brek even. F j 0 j nd j 0 j ect jj negtively: the higher the cost to export into the home mrket, the esier it is for country-j s low-productivity rms to survive. F j 0 j 0 hs negtive e ect on jj0: the higher this xed cost, the esier it is for country-j s rms to brek even in country-j 0 s mrket. Higher costs to export into the foreign mrket (F jj 0 nd jj 0) rise the productivity threshold jj0 for country-j s rms to brek even when exporting to country j 0. Industry Aggregtes Once we hve expressed the entry cuto s s functions of the model s prmeters, it is esy to do the sme for ll industry ggregtes. We will pro t from this informtion in two wys. First, we will clibrte the model s prmeters by mtching its moments to the vilble dt. Secondly, once we hve clibrted the model, we will simulte the tri cuts implemented under CUSFTA nd compre the resulting model predictions to the empiricl evidence discussed in section 2. Mss of Firms The mss of country-j rms ctive in mrket j 0 is given by N jj 0 = V j jj 0 Mj = M j k j jj 0 ; () where V () denotes the distribution function of. Our nottionl convention nd our ssumption tht ll ctive rms operte in the domestic mrket implies N jj is the totl mss of country-j rms. 9 See the evidence discussed in Luttmer (2002). 0 For the n th -moment of Preto distribution to exist, we need > n. We impose > to ensure existence of the moments which re of interest for our purposes. 8

11 Trde Flows The f.o.b. vlue of exports from country j 0 to country j is X j 0 j = + M j 0k j 0F jj Fj 0 j F jj j 0 j jj : (2) Sles Aggregte sles by industry re Employment R j = M j k j Industry employment is Productivity L j = M j k j " X # Fjj 0 jj F + 0 j F 0 j 0 j 0 j : (3) 0 j 0 j 0 j 0 " ( ) X # Fjj 0 jj F + 0 j F 0 j 0 j 0 j : (4) 0 j 0 j 0 j 0 Following Melitz (2003), we de ne n industry s ggregte productivity s ~ j = " X j 0 N jj0 P j 0 N jj 0 # ~ jj 0 ; (5) where " ~ jj 0 jj = 0 V j jj 0 Z jj 0 () v j () d # = + jj 0: (6) As further explined below, our clibrtion will not enble us to identify the level of ~ j, but only its growth rte - which is ll we need to compre the model s predictions to Tre er s results. 2 Alterntively, we will work with two more de nitions of productivity. First, we simply In comprison with Melitz (2003), we do not djust the productivity of exporters by the trde cost jj 0. This spres us some mbiguities in the derivtion of the theoreticl results in the next section. Regrding our numericl results, discussed further below in the pper, this djustment hs negligible relevnce from both quntittive nd qulittive point of view. The corresponding results re vilble from the uthors upon request. 2 ~ j is hrmonic verge. Notice tht our ssumptions on prmeters imply jj > 0 jj (see footnote 8), which in turn yields ~ jj 0 > ~ jj. 9

12 ggregte rms outputs linerly: ~Q j L j 2 = 6 X 4 L j j 0 Z jj jj0q jj0m j v j ()d5 = M " jkj ( ) X Fjj 0 jj L j 0 F j 0 j 0 j 0 Agin, we will work with the growth rte rther thn the level of ~ Q j =L j. # Fj 0 j 0 j 0 j 0 Finlly, we lso use mesure which is most closely relted to the wy Tre er mesures lbor productivity in his pper. He uses the industry-level growth rte in de ted vlue dded per hour worked to clculte lbor productivity growth. We proxy for this with the growth rte of (R j =L j ) =p ~ j. (7) We think of p ~j s the verge price chrged by country j s producers (or, put di erently, the price chrged by the producer with productivity level equl to the ggregte verge, ~ j ). Notice tht this verge price neglects the product vriety component of idel price indices bsed on CES functionl forms. This is similr to the clcultion of the de tors underlying Tre er s growth rtes, which do not ccount for chnges in product vriety. 3 As we will see when presenting our simultion results below, the growth rte of (R j =L j ) =p ~ j is very similr to tht of ~j. This suggests tht de ted sles per worker is not bd proxy fter ll for Melitz s ggregte productivity. The intuition for this slightly surprising result is s follows. First, the rtio R j =L j does not move much with chnges in tri s. This is due to the CES ssumptions of the model: rm-speci c f.o.b. sles r () re proportionl to rm-speci c employment l () which explins the lmost identicl expressions we obtin for R j nd L j (see equtions (3) nd (4)). This leves most of the ction in our third productivity mesure to =p ~ j which in turn is closely relted to ~ j (see the pricing eqution (3)): n increse in verge productivity reduces the verge producer price, thus rising the vlue of de ted sles. : 4 Model Evlution - Qulittive Predictions We now turn to n evlution of the bility of our version of Melitz (2003) to replicte the qulittive nd quntittive fetures of Tre er s results from section 2. In this section, we strt by performing comprtive sttics exercises to check whether our model correctly predicts the signs of the e ects of trde liberliztion on ggregte productivity nd trde ows. In line with our nottion, we denote Cndin vribles by subscript j nd US vribles by subscript j 0 in the following propositions. In our model, we interpret trde liberliztion s reduction in the iceberg trnsport cost. Since the min instrument 3 We re grteful to Mrc Melitz for pointing this out. See lso Ghironi nd Melitz (2005) for relted discussion. Detils on the construction of Sttistics Cnd s price de tors cn be found on t 0

13 of liberliztion under CUSFTA were bilterl reductions in d-vlorem tri s, this theoreticl interprettion ts well with the ctul liberliztion experience. Proposition Reductions of country-j import tri s (i.e. lower j 0 j) rise country-j ggregte productivity ~ j. Proof. First, from (0) nd () it is esy to see j =@ j 0 j > 0, jj=@ j 0 j < 0. Intuitively, more domestic protection mkes it esier for domestic low-productivity rms to survive. Secondly, from (5), ~ j is weighted verge of ~ jj nd ~ jj 0, with ~ jj < ~ jj 0. More domestic protection reduces jj nd thus ~ jj ; besides, N j rises, rising the weight of ~ jj. ( jj 0, ~ jj 0 nd N jj 0 remin constnt.) Hence the verge ~ j flls with more domestic j =@ j 0 j < 0. Proposition 2 Reductions of country-j 0 import tri s (i.e. lower jj 0) hve n mbiguous e ect on country-j ggregte productivity ~ j. Proof. More foreign protection reduces the mss of domestic exporters N jj 0: from (0) nd jj 0=@ jj 0 < 0 jj 0=@ jj0 > 0. This e ect hs negtive impct on ~ j, s the weight on the lrger component (~ jj 0) of verge productivity flls. On the other hnd, verge exporter productivity ~ jj 0 rises through the increse in jj 0. ( jj, ~ jj nd N j remin constnt.) Whether the overll e ect is positive or negtive depends on prmeter vlues. Appendix A illustrtes this issue by working out n exmple in which, depending on the vlues of trnsport jj 0 cn tke positive or negtive vlues. Our model thus correctly predicts tht reductions in Cndin import tri s rise ggregte productivity in Cnd. It lso predicts tht the sme need not hold true for reductions in US import tri s. Intuitively, lower foreign brriers men tht existing exporters (which re the most productive rms) gin mrket shre. However, there is lso export mrket entry by less productive rms which lso expnd output. overll e ect on ggregte productivity is thus mbiguous. This is gin consistent with Tre er s result of positive but reltively smll (compred to Cndin tri concession) nd sttisticlly insigni cnt impct of US tri reductions. The Interestingly, one of the explntions dvnced by Tre er for this nding is tht US tri cuts encourged export mrket entry by less productive Cndin rms which prtly o set the gins rising from mrket shre expnsions of existing exporters. This is exctly wht is underlying our mbiguity result. Proposition 3 Reductions of country-j import tri s rise country-j imports from country j 0, but hve no e ect on country-j exports to country j 0. Proof. From (2), we obtin j 0 j=@ j 0 j < 0 j 0 j=@ jj 0 = 0.

14 Thus, our model replictes Tre er s nding tht reductions in Cndin tri s rise imports from the US, nd tht US tri concessions cuse Cndin exports to the US to increse. Recll from section 2 tht Tre er lso nds tht the impct of US tri reductions on Cndin imports is smller nd less sttisticlly signi cnt thn the e ect of Cndin tri reductions. 4 Similrly, the e ect of US tri concessions on Cndin exports is lrger thn tht of Cndin reductions the ltter is ctully negtive lbeit sttisticlly insigni cnt. This is gin consistent with our model s prediction on the reltive importnce of domestic nd foreign tri concessions on trde ows. 5 5 Model Evlution - Quntittive Predictions The lst section demonstrted tht our version of Melitz (2003) is cpble of replicting the qulittive results of Tre er (2004). We now rise the br further by evluting whether our model cn lso replicte Tre er s ndings quntittively. To this end, we clibrte the model s prmeters on pre-liberliztion dt. We then simulte the fll in tri brriers implied by CUSFTA, holding ll other prmeters equl. For this, it is useful to think of trde costs jj 0 s hving nturl component, jj 0, nd policyinduced component, t jj 0: jj 0 = + jj 0 + t jj 0. We simply let t jj 0 fll s observed in CUSFTA, nd compute the resulting chnges in productivity nd trde ows. To simplify this exercise, nd for resons of dt vilbility, we strt with twocountry version of our model, including Cnd nd the US only. Initilly, we lso set jj 0 = 0. 6 In robustness checks reported below, we llow for positive nturl component of trde costs nd introduce third country, the Rest of the World (RoW), consisting of Germny, Jpn nd the United Kingdom. We reduce the number of prmeters to be clibrted in severl wys. First, the prmeters M j nd k j (mss of potentil entrnts nd the Preto distribution prmeters, respectively) cnnot be identi ed seprtely but only s their product, K j M j k j. Moreover, K j itself cncels out frequently from the expressions bove. Still, we cn identify the rtios K j =K j, with which we cn compute the growth rtes of productivity nd bilterl trde ows. 7 4 This is prticulrly true for our smller smple, see column 4 of tble. 5 The fct tht we predict no e ect of domestic tri concessions on domestic export is of course n rtifct of our bstrction from the relevnt generl equilibrium e ects. We thus regrd the comprison of reltive e ects of domestic nd foreign tri concessions s more informtive. However, in section 3 we show tht running Tre er s regressions on dtset generted by our model ctully does yield positive e ects of US tri cuts on Cndin imports. (This is becuse Tre er imposes prticulr functionl form in his regressions.) 6 In recent pper, Brod nd Weinstein (2008) compre Cndin nd US brcode dt for the period , nd nd tht the lw of one price holds eqully well for city pirs of the sme country nd for city pirs with cities on di erent sides of the Cnd-US border. Since we implicitly normlize intrntionl trde costs to one, this result suggests tht ssuming no interntionl trde costs in the post-liberliztion phse is not implusible priori. 7 This discussion obviously ssumes tht we cn tret the mss of potentil entrnts s constnt 2

15 Finlly, we hve direct proxies from the dt for prmeters t jj (d-vlorem tri s) nd j (industry-level expenditures). In the two-country model, we re thus left with 7 prmeters which need to be estimted for ech industry: the shpe prmeter of the Preto distribution ; the elsticity of substitution ; xed costs F dd, F ff, F df, nd F fd ; nd rtio K f =K d. (For the ske of clrity, when discussing prmeter clibrtion issues, we deprt from our stndrd nottion of countries j, nd denote Cnd, the US nd RoW with d, f, nd w, respectively.) Clibrtion Strtegy We proceed in two stges. First, we obtin estimtes for nd from rm- nd industrylevel dt. We then need to crete system of ve prmeters nd ve moments to clibrte the remining prmeters. For this purpose, we use the following moments: totl number of rms (2), bilterl trde ows (2), nd one Cndin concentrtion rtio. We show in ppendix B tht the implied system of non-liner equtions cn be solved for unique set of positive prmeter vlues. Thus, our model is ble to mtch the pre-liberliztion empiricl moments exctly. 8 Prmeters nd Totl sles by exporting rms cn be expressed s r () = P j r 0 jj 0() =, which is proportionl to (the term is constnt cross rms). Since is distributed Preto with shpe prmeter, sles re distributed Preto with shpe prmeter r = = ( ) nd cuto k r = k. Thus, we cn estimte r nd, nd then recover. Obtining r from Sles Dt Aggregte sles for rms with sles equl or lrger sles thn r x re (ssuming r > ): R rx = Z r x rv(r)dr = rkr r r (r x) r : (8) Tke the sles vlue r x tht corresponds to the x-th lrgest rm. The frction n rx of rms tht re bigger thn or equl to this rm is n rx = V (r x ). Hence, r x = k r n (=r) nry ry = r x. r =r. Tking the rtio to the y th lrgest rm s sles elimintes k r : x n rx We do not hve dt on r x, but we know the sles volume R rx de ned bove (totl shipments prmeter, which might be ne in the short run, but more controversil for the long run. We ddress this issue below by modeling free-entry s in Melitz (2003): once gin, we cnnot identify K j in the post-trde liberliztion stedy stte, but we cn compute its stedy-stte chnge, which is ll we need to compute the long-run growth rtes of our vribles of interest. 8 We focus on n exctly identi ed system in the initil clibrtion stge, since we re primrily interested in evluting the out-of-smple predictions of our model rther thn the consistency of the model with the pre-liberliztion dt. Using other moments for which we hve dt (such s dditionl concentrtion rtios) does not lter the qulittive nture of the ndings below. 3

16 times the concentrtion rtio): =( Rrx R ry r) = nry n rx =r : (9) Solving for r, r = ln n ry ln n rx : (20) ln R rx ln R ry + ln nry ln n rx If rm x is lrger thn rm y, we hve n ry > n rx nd R ry > R rx. Thus, r > from bove s long s ln R rx ln R ry + ln nry ln n rx > 0, which holds by construction. Obtining of from Firm-level Dt costs) re Operting pro ts (tht is, pro ts net of xed o () = r() : (2) Since we hve dt on operting pro ts nd revenue for US nd Cndin rms, we cn obtin estimtes of from the bove expression seprtely for ech rm. Our industryspeci c estimte of is simply the medin cross ll rms within in n industry. Dt Description For our clibrtion we require sector-level dt on output, trde ows, tri s, the number of rms nd concentrtion rtios. We lso need rm-level informtion on operting pro ts nd sles for the clibrtion of. Most of our dt on output, tri s nd trde ows come from Tre er (2004). 9 the three-country version of our model, we complement these dt with informtion on sectorl-level output for Germny, Jpn nd the UK from UNIDO s Industril Sttistics Dtbse, nd with informtion on US exports nd imports from the NBER. We use gross output in Cndin, US nd RoW mnufcturing industries s proxies for R d, R f, nd R w (where w denotes RoW). As proxies for X df, X fd, X dw, X wd, X fw, nd X wf, we use sector-level trde ows between the three countries. We lso use these dt to clculte d, f nd w s industry-level bsorption, e.g. d = R d + (X fd + X wd X df X dw ). 20 Tre er lso provides dt on Cndin nd US import tri s which we use s proxies for t fd nd t df. We convert ll dt to the 4-digit level of the Cndin Stndrd Industril Clssi ction of 980. Vlue dt re expressed in 992 Cndin dollrs using the US-Cndin Dollr exchnge rte nd 4-digit industry price nd vlue dded de tors. To ensure 9 These dt re vilble on Dniel Tre er s website t er/. Tre er s originl sources re specil tbultions by Sttistics Cnd nd the NBER Mnufcturing Productivity Dtbse. See Tre er (2004) for detiled description. 20 For the two-country version, this simpli es to d = R d + (X fd X df ) nd f = R f + (X df X fd ). For 4

17 comptibility with our choice of numérire, we further normlize ll vlue dt by Cndin industry-level wges, proxied by totl nnul ernings per worker. Dt on exchnge rtes, de tors nd wges re lso from Tre er (2004). Secondly, we use informtion from Sttistics Cnd, the US Census Bureu nd UNIDO on the number of enterprises s proxies for N dd, N ff nd N ww. Sttistics Cnd lso provides the output shre ccounted for by the top 4, 8, 2, 6, 20, nd 50 enterprises in ech 4-digit Cndin industry. Multiplying these shres with totl industry output (R d ) we obtin the totl output of the top 4, 8, etc. enterprises which we use s proxies for R rx. Finlly, the computtion of requires dt on operting pro ts ( o ) nd sles (r) t the rm-level. We obtin these from Compustt North Americ nd Compustt Globl. We proxy o s operting income before deprecition nd r s net sles. 2 Prmeter Estimtes Tble 2 presents descriptive sttistics on the prmeter estimtes. We estimte di erent set of prmeter vlues for ech mnufcturing industry in our smple. Avilbility of concentrtion rtios nd trde dt reduces the number of industries from 23 in Tre er to 96 in our nlysis. We furthermore drop 8 dditionl sectors which violte prmeter restrictions of our model, leving us with 78 sectors in totl. 22 Our estimtes of the elsticity of substitution re of the sme order of mgnitude s estimtes t similr ggregtion levels by Brod nd Weinstein (2006), (2006b). The estimtes of the shpe prmeter of the sectorl-level sles distribution r re lso comprble to other estimtes in the literture: Chney (2008), who mesures r s the regression coe cient of the log of the rnk on the log of sles (cross US listed rms), reports estimtes for r of round 2. Eton et l. (2008), with n lterntive method using the propensity of French rms to export to multiple mrkets, report estimtes for r of round.5. This compres to medin vlue of.9 in our estimtes. For the rest of the prmeters there re no esily comprble estimtes from other sources, but their medin vlues seem mostly plusible. For exmple, reclling tht we normlized ll vlue terms by Cndin sectorl wges, the estimtes for F dd nd F ff indicte tht the medin cost for Cndin nd US mnufcturing rms of entering their domestic mrket ws 339,000 nd 509,000 Cndin dollrs in 988, respectively. While our model thus produces brodly resonble prmeter estimtes, the minimum 2 Informtion on these vribles is contined in Compustt North Americ dt items 2 (net sles) nd 3 (operting income before deprecition). For Compustt Globl, net sles re contined in dt item nd operting pro ts re clculted s operting income plus deprecition (dt items 4 plus ). 22 We drop sectors for which our clibrtion yields < or jj > jj0. We lso experimented with minimizing squred devitions between theoreticl nd empiricl moments, subject to the second constrint. Results were lmost identicl to the ones presented below. 5

18 nd mximum vlues reported in tble 2 indicte tht there re lso number of outliers. In the robustness checks reported below, we experiment with excluding such sectors insofr s they produce extreme growth rtes for productivity or exports which could drive our results. Bseline Results In this section we simulte the tri cuts of CUSFTA (tht is, reduction in trde cost prmeters df nd fd, holding ll other prmeters constnt), nd compre the productivity gins nd increses in trde ows predicted by the model with the estimtes reported in tble, columns 3-5. Recll tht we de ned trde costs s jj 0 = + jj 0 + t jj 0, where jj 0 re nturl trde costs nd t jj 0 re policy-induced brriers (tri s). For exmple, in 988 the poultry products industry (SIC 02) hd Cndin nd US import tri s of 6.6% nd 3.7%, respectively. For our bseline results, we lso ssume tht fd = df = 0. We thus set fd;t = :066 nd df;t = :037. Since CUSFTA ws free-trde greement, we simulte the trde liberliztion by setting df;t nd fd;t to one. We compute the growth rtes of productivity nd trde ows discussed bove for ech industry seprtely by using our clibrted prmeter vlues, nd fd;t, df;t, df;t nd fd;t. We rst do so seprtely for ech of the tri s nd then for both of them together. These simultions correspond to the three comprtive sttics results implicit in Tre er s regressions - the e ect of Cndin tri s (corresponding to CA ), the e ect of US tri s (corresponding to US ), nd their joint impct. Thus, we obtin set of three simultion results for ech of our mesures of productivity growth nd for import nd export growth. Tble 3 presents the results of these bseline simultions. For comprison with Tre er s results, we report weighted verges of our sector-speci c simultion results. Speci clly, we clculte weighted verge for the most impcted, import-competing third of industries when performing the simultion corresponding to unilterl Cndin liberliztion (reducing t fd to zero). When simulting the reduction in t df (unilterl US liberliztion), we similrly use weighted verge of results for the most impcted, export-oriented third of industries. for the bilterl liberliztion simultion (both t df weighted verge cross ll sectors. 23 Finlly, nd t fd set to zero), we compute The rst line in tble 3 is thus comprble to line 5 in tble ( Impct on most impcted, import competing industries ). Depending on the productivity mesure we use, we predict round qurter (3.2%-4.0%) of the 4% overll increse estimted erlier. 23 Following Tre er (2004), we use vlue dded nd trde ows by industry in 988 to weigh our sectorspeci c simultion results for trde nd productivity increses.(compre footnote 4). Tht is, we clculte P ii ~y i$ i, where ~y i is the simultion forecst for sector i nd $ i the shre of i in totl exports, imports or vlue dded in the group of industries I (import- competing industries, export-oriented industries or ll industries). 6

19 We do better on the predicted e ects of US tri reductions (line 2). In column 3 of tble, we estimted n increse of 2%, very close to the prediction for our second productivity mesure (Q=L). The other two productivity mesures do essentilly predict no e ects, however, so tht on verge we underpredict the productivity impct of US tri cuts s well. More importntly, however, our simultion results cpture the key stylized fct bout the symmetric e ect of tri reductions on productivity. Cndin tri reductions led to much bigger increse in ggregte productivity thn US tri s. Agin, the reson why this hppens in our simultion is tht lower US import tri s encourge entry by less e cient exporting rms. 24 As mentioned before, our model mtches the brod qulittive pttern of predicted chnges in Cndin imports nd exports from nd to the US. The results in tble (column 4) show tht Cndin imports in the most impcted, import-competing third of industries incresed by 46% in response to Cndin tri cuts, nd by 7% in response to US tri cuts in the most impcted, export-oriented industries. We predict positive impct of Cndin tri reductions nd no e ect of US tri reductions, so the ordering of mgnitudes is similr. With regrds to quntittive ccurcy our model does less well. We predict n increse of 380% for the response of Cndin imports with respect to domestic tri s which is roughly eight times lrger thn the 46% estimted erlier. As sid, our model predicts no increse in response to US tri reductions so we re gin some wy o the 7% increse estimted in section 2. In terms of the CUSFTA s totl e ect our model gin overpredicts lthough not s bdly s for the unilterl Cndin liberliztion (we predict 50% increse versus 2% increse in our repliction of Tre er s results for our smller smple). Our model lso overpredicts the increse in Cndin exports to the US in response to trde liberliztion (tble 3, column 5). We predict weighted verge increse of 400% in response to US tri cuts nd no increse in response to Cndin tri cuts. The corresponding estimtion results from section 2 re 6% nd -8%. We lso overpredict the overll e ect by n order of mgnitude (+35% vs. no overll e ect). To summrize, our simultion results gin con rm tht our version of Melitz (2003) mtches the qulittive ndings of Tre er s nlysis quite well. Our model does somewht less well on the quntittive spects. It systemticlly underestimtes productivity gins nd overestimtes increses in trde ows. In the following sections, we investigte how robust these ptterns re to vritions in our simultion design. 24 An dditionl reson is tht US tri cuts re on verge only hlf s lrge s Cndin tri cuts. However, this does not explin the negtive growth rtes we obtin for substntil frction of industries when we simulte US unilterl trde liberliztion (note tht the weighted verge impct for our de ted-sles mesures is negtive, too). 7

20 Robustness Checks Outliers For some sectors, our model cn only mtch the pre-liberliztion moments with extreme vlues for prmeters (see tble 2). This is source of concern insofr s it might generte outliers in predicted trde ow nd productivity chnges. Tble 4 thus presents results for the sme simultions s in tble 3, but excludes sectors with either very low or very high growth rtes for ech of our ve vribles of interest. Vrible by vrible, we rst exclude the top nd bottom % of sectors nd then the top nd bottom 5%. Removing outliers does indeed reduce the predicted increse in trde ows by up to hlf, but this still leves us considerbly bove Tre er s estimtes. At the sme time, the predicted productivity increses drop s well, tking us even further wy from the results in tble. Regression-bsed Approch Tre er estimtes the reported e ects of CUSFTA on trde nd productivity ssuming speci c functionl form for the impct of tri s reductions (his estimtes re semielsticities). In this section, we sk how his results would look like if we estimted speci ction motivted by Tre er s regression eqution on our simulted dt. Of course, our model bstrcts from both pre-cusfta trends in the dt nd other fctors which Tre er tries to control for through di erencing nd the inclusion of control vribles. We thus estimte reduced version of Tre er s speci ction: y i = ln y i ln y i0 = 0 + CA lt t CA i + US lt t US i ; (22) where y i is the prediction of our model for growth rtes of productivity nd trde ows, respectively, nd t CA i = t CA i t CA i0 nd t US i tri cuts which we used in our simultions. = t US i t US i0 re the CUSFTA-mndted Since Tre er s dt were of course generted by bilterl trde liberliztion, we lso generte the dt for the estimtion of (22) by setting both US nd Cndin tri s to zero in our simultions. Once we hve obtined estimtes of CA lt nd US lt, we clculte the sme mgnitudes reported in tble, using the sme pproch s Tre er (i.e., the impct on the most-impcted, import-competing industries, the impct on the most-impcted, export-oriented industries, nd the totl impct of CUSFTA). As shown in tble 5, using this lterntive pproch brings our results closer to Tre- er s estimtes long some dimensions but not long others. The e ect of Cndin reductions on ggregte productivity is qulittively comprble to our bseline, lbeit slighly weker. On the other hnd, we now do better on the predictions on trde ows. 8

21 We predict 06% increse in Cndin exports in response to US tri reductions nd 37% increse in Cndin imports in response to Cndin tri cuts (compred to 6% nd 46% in our estimtions reported in tble, respectively). We lso do quite well in replicting US tri cut-induced productivity gins, in prticulr for our productivity mesure Q d =L d. Long-run Results So fr we hve bstrcted from rm entry by holding xed the mss of potentil entrnts, M d nd M f, during our simultion of CUSFTA. Our results up to now re thus best thought of s short-run response to trde liberliztion. We think tht this corresponds best to Tre er s study, which covers period of eight yers fter CUSFTA. However, since ny de nition of short vs. long run is somewht rbitrry, we lso nlyse the long-run responses predicted by our model. To do so, we rst extend our theoreticl frmework to include free entry nd then repet the sme simultions s bove. Consider thus the following free-entry condition for country j: V jj j N jj = j F j ; (23) where j denotes country-j industry s ggregte pro ts; j is country j s discount rte; nd F j is the xed cost (in terms of the numérire) tht rm hs to py to pick drw from the productivity distribution. 25 Appendix C demonstrtes how (23) cn be used to solve for long-run chnges in the prmeters K j nd clcultes the corresponding long-run growth rtes of trde nd productivity. Tble 6 presents the corresponding results. The key chnge in the long run is tht the mss of potentil entrnts, M j, djusts. 26 Speci clly, unilterl Cndin liberliztion reduces M d s operting pro ts re reduced through the e ect of stronger import competition on the price level. At the sme time, lower Cndin tri s increse M f s US exporters cn now mke dditionl pro ts on the Cndin mrket. These chnges led to similr djustments in the number of exporters in ech country, nd explin why we now observe stronger increse in US exports thn in the short-run, nd decrese in Cndin exports in response to lower Cndin tri s. Exit by Cndin rms in the long-run lso implies lower cuto on the domestic mrket, nd thus lower productivity gins. 27 A unilterl US liberliztion hs the opposite e ects on M d nd M f more Cndin nd less US entrnts. Accordingly, the e ect on trde ows mirrors the one of Cndin 25 This free-entry condition cn be generted s in Melitz (2003), nd is consistent with the rest of our model s setup. We omit detiled discussion of the corresponding ssumptions for the ske of brevity. 26 More precisely, we only identify chnges in K j = M j kj. Assuming tht k j stys constnt, chnges in K j cpture chnges in the mss of entrnts. 27 Note tht the verge long-run e ect of unilterl liberliztion on the liberlizing country s productivity cuto is positive in our simultions. This stnds in contrst with the results in Melitz nd Ottvino (2008), where the short-run increse in the cuto is wiped out completely in the long run. 9