Imported Inputs and Sectoral Wage Dispersion

Transcription

1 Imported Inputs and Sectoral Wage Dsperson Zhel He and Feran Zhang September 2017 Abstract Ths paper proposes a new mechansm through whch trade lberalzaton a ects ncome nequalty wthn a country: the use of mported nputs. Intutvely, a frm wth hgher ntal productvty s better at usng hgher qualty foregn nputs. Ths justfes payng the fxed costs for a larger set of mported nputs when nput tar lberalzaton decreases ther relatve prce. The frm becomes more mport ntensve, whch enhances ts productvty advantage. As a result, the frm hres hgher qualty workers, produces hgher qualty products and pays hgher wages to ts workers, ncreasng wthn-sector wage dsperson. We fnd that both the mean and the dsperson of the dstrbuton of frm productvty, markup and sze went up durng a perod when Chna reduced ts tar s on mported nputs. More mportantly, these results stll hold when we consder the subset of frms that survved throughout the sample perod, from 1998 to In addton, we develop a partal-equlbrum, heterogeneous-frm model wth endogenous mported nputs and labor qualty choce that s consstent wth these observatons. Fnally, we provde emprcal evdence that supports the model s predcton that the d erental change n the mport ntensty of frms wth d erent productvty levels explans these patterns. We would lke to thank Donald Davs, Amt Khandelwal, Erc Verhoogen, Jonathan Vogel and Davd Wensten for ther nvaluable advce and support. We also thank Mattheu Bellon, Pablo Fajgelbaum, Reka Juhasz, Ryan Km, Antono Msco, Ildko Magyar, Paul Pveteau, Stephen Reddng, Ln Tan and other semnar partcpants at Columba Unversty for helpful comments and dscussons. All remanng errors are our own. 220 South 40th Street, Sute 250, Phladelpha, PA Emal: zh2178@wharton.upenn.edu (Zhel He). Department of Economcs, Columba Unversty, 1022 Internatonal A ars Buldng, 420 West 118th Street, New York, NY Emal: fz2179@columba.edu (Feran Zhang).

2 1 Introducton The tradtonal Heckscher-Ohln model predcts that countres export goods that use ntensvely the factor they are most abundantly endowed wth. Accordng to the Stolper- Samuelson theorem, trade ncreases the relatve return to unsklled labor n developng countres, decreasng wage nequalty. However, that predcton s at odds wth many emprcal fndngs. Take Chna as an example, the overall wage nequalty, measured as the d erence between the 90th and the 10th percentle of the log wage dstrbuton, has been gong up consstently n the last two decades, as found n Han et al. (2012). Ths perod of rapd wage nequalty ncrease concded wth Chna s mplementaton of dramatc economc reforms and an open door polcy that promoted ts trade wth the rest of the world. So two mportant questons arse: dd trade lberalzaton contrbute to Chna s rsng wage nequalty? If so, through whch channels? New theoretcal developments have been made to provde nsghts nto the e ects of trade on wage nequalty. Most promnently, Verhoogen (2008) proposes the qualty-upgradng mechansm as an explanaton. In hs model wth heterogeneous plants and qualty d erentaton, an exchange-rate devaluaton leads more productve Southern plants to ncrease exports, upgrade qualty, and rase wages relatve to less productve ones, ncreasng wthnsector wage dsperson. In ths chapter, we propose an alternatve mechansm: the use of mported nputs. Intutvely, a frm wth hgher ntal productvty s better at usng hgher qualty foregn nputs. Ths justfes payng the fxed cost for a larger set of mported nputs when nput tar lberalzaton decreases ther relatve prce. The frm becomes more mport ntensve, whch enchances ts productvty advantage. As a result, the frm hres hgher 1

3 qualty workers, produces hgher qualty products and pays hgher wages to ts workers, ncreasng wthn-sector wage dsperson. We am to emprcally dstngush these mechansms n the data, as they each have d erent welfare and polcy mplcatons. Frst, we use ASIF (Annual Survey of Industral Frms) from Chna s Natonal Bureau of Statstcs that report key operatonal data on Chnese manufacturng frms to document some stylzed facts that are both new and nterestng. We fnd that both the mean and the dsperson of the dstrbuton of frm productvty, markup and sze went up durng a perod when Chna reduced ts tar s on mported nputs. More mportantly, these results stll hold when we consder the subset of frms that survved throughout the sample perod, from 1998 to Therefore, openness to trade has fundamental e ects on the underlyng characterstcs of frms. Most of recent models of frm heterogenety assume that these characterstcs are fxed and examne the mpact of trade on aggregate varables, for example, the average productvty of frms n the economy as a result of change n the composton of survvng frms. On the contrary, we study the d erental mpact of trade lberalzaton on heterogeneous frms allowng these characterstcs to be endogenous. We measure frm-level TFP based on OLS, Olley and Pakes, Levnsohn and Petrn, and Ackerberg, Caves and Frazer to ensure that our estmate of frm productvty s as accurate as possble. For frm-level markup calculaton, we adopt De Loecker and Warzynsk (2012), whch s the best avalable method that we can use gven our data lmtatons. We consder both a Cobb-Douglas gross output producton functon, and more generally, a translog gross output producton functon, whch matches the data much better. Fnally, we measure frm sze both n terms of output value and total employment as a robustness check. The emprcal patterns are very smlar when we use d erent approaches to measure these three 2

4 key frm-level varables. Second, we develop a partal equlbrum, heterogeneous frm model wth endogenous mported nputs and labor qualty choce that s consstent wth these observatons. On the demand sde, we adopt the qualty-meltz model n Kugler and Verhoogen (2012), where hgher prce decreases demand but hgher qualty ncreases demand. On the supply sde, frms d er from each other n the usual dmenson of productvty, as n Meltz (2003). In our model, frms combne labor and ntermedate nputs to produce physcal quantty, n the sprt of Amt et al. (2014). Output qualty, on the other hand, s determned by labor and nput qualtes, and the advantage of mported nputs over domestc counterparts s augmented by a frm s own productvty. Snce Amt et al. (2014) focusonexchangerate pass-through, and assume that frms do not foresee fluctuatons n exchange rates, they hold the set of mported nputs of each frm fxed. We, on the other hand, study precsely how frms adjust the set of foregn varetes they mport n response to nput tar lberalzaton and changes n frm-level varables that follow. Consequently, our model devates from thers n obvous ways, whch we explan n more detal n the theory secton. Fnally, we use Chnese Customs Data on mports and exports, whch provde detaled nformaton on the unverse of Chna s frm-level trade transactons for the years 2000 to 2006, to hghlght frms d erent responses to a dramatc decrease n mport tar s. These observatons emphasze the large and growng mportance of trade n ntermedates, and provde some emprcal evdence that supports our hypothess that the d erental change n mport ntensty of frms wth d erent productvty levels n response to nput tar lberalzaton explans the ncrease n both the average and the dsperson of frm-level varables that are observed n the data. 3

5 Although the man focus of ths chapter s to show that nput tar lberalzaton affects frms at d erent levels of productvty n a heterogeneous way, whch drves ther performance further apart, our results have broader mplcatons. Essentally, we provde a framework n whch the d erental mpact of any element of globalzaton that leads to a decrease n the margnal cost of producton on frm-level characterstcs can be analyzed. Our detaled and very dsaggregated transacton-level trade data allow us to quantfy the mpact of such a change durng a perod when the change was very large n magntude. 2 Related Lterature Ths chapter s related to several strands of lterature. Frst, there have been studes on the labor market e ects of nternatonal trade based on recent models of frm heterogenety, and they ask how trade lberalzaton a ects wages and wage nequalty. For example, Amt and Davs (2012) developamodel,whchpredctsthatafallnoutputtar slowerswages at mport-competng frms but boosts wages at exportng frms, and that a fall n nput tar s rases wages at mport-usng frms relatve to those that only source nputs locally. They fnd support for the model s predctons n Indonesan manufacturng census data for the perod Lke us, they take explct account of frm-level heterogenety and mportance of trade n ntermedates. Extendng the heterogeneous frm model of trade and nequalty from Helpman et al. (2010), Helpman et al. (2017) showthatmuchofoverall wage nequalty arses wthn sector-occupatons and for workers wth smlar observable characterstcs, and wage dsperson between frms s related to frm employment sze and trade partcpaton. They agan emphasze the mportance of employng recent models of 4

6 frm heterogenety n analyzng the contrbuton of trade to the cross-secton dsperson of frms. Frías et al. (2012), on the other hand, o er some emprcal evdence that sortng on ndvdual worker ablty s not enough to explan the relatonshp between exportng and wages at the plant level. They use a combnaton of employer-employee and plant-level data from Mexco, and show that approxmately two-thrds of the hgher level of wages n larger, more productve plants s explaned by hgher levels of wage prema, and that nearly all of the d erental wthn-ndustry wage change s explaned by changes n wage prema. They use the late-1994 Mexcan peso devaluaton as a source of exogenous varaton n the ncentve to export, whle we use mport tar reductons due to Chna s accesson to the WTO n December 2001 as our exogenous varaton. On the contrary, Krshna et al. (2012) fnd an nsgnfcant d erental e ect of trade openness on wages at exportng frms relatve to domestc frms, usng detaled nformaton on worker and frm characterstcs to control for compostonal e ects and allowng for the endogenous assgnment of workers to frms. Whle these papers focus on the e ects of trade lberalzaton on the labor market, we look at other frm-level characterstcs, and ask how they are a ected, and the resultng mplcatons on wage nequalty n Chna. Second, our theoretcal model borrows nsghts from a burgeonng research lterature on frm mport behavor, whch has not been extensvely studed before. Most mportantly, evdence has been found n a wde range of countres that frm productvty rses when a frm mports new nput varetes. For example, Kasahara and Rodrgue (2008) conclude that becomng an mporter of foregn ntermedates mproves productvty usng plant-level Chlean manufacturng panel data. At the same tme, Halpern et al. (2015) fndthatm- portng all foregn varetes would ncrease frm productvty by 12 percent, and that durng 5

7 , one-thrd of the productvty growth n Hungary was due to mported nputs by estmatng a model of mporters n Hungaran mcro data and conductng counterfactual polcy analyss. Bas and Strauss-Kahn (2014), on the other hand, use a frm-level database of mports provded by French Customs for the perod, and fnd a sgnfcant mpact of hgher dversfcaton and ncreased number of mported nput varetes on frm-level TFP and export scope. They argue that mportng more varetes of ntermedate nputs ncreases frm productvty and thereby makes a frm more able to overcome the fxed export costs. Our model predcts that a frm wth hgher ntal productvty has a stronger ncentve to expand ts set of mported varetes when t faces lower tar rates, whch then makes t even more productve, explanng the emprcal patterns observed n the data. Thrd, we want to pont out that these fndngs cannot be explaned by any prevous studes on heterogeneous frms. We dscuss brefly a few mportant papers on the subject. To start wth, the workhorse model developed n Meltz (2003) assumes that the preferences of a representatve consumer are gven by a C.E.S. utlty functon over a contnuum of goods, so each frm chooses the same proft maxmzng markup whch s constant. After payng fxed entry costs, frms draw ther ntal productvty parameter, whch does not change over tme. As a result, the mean and the dsperson of the productvty dstrbuton of a balanced panel of frms reman the same, whch s not what we observe n the data. Gans from trade n ths model come from expanson n product varetes, and more mportantly, the self-selecton of more e cent frms nto exportng. Relaxng the C.E.S. assumpton, Arkolaks et al. (2015) study how varable markups a ect the gans from trade lberalzaton under monopolstc competton, and they show that the welfare e ect of a small trade shock s gven = (1 s the share of expendture on domestc goods, 6

8 and s an elastcty of mports wth respect to varable trade costs, and s a structural parameter that depends, among other thngs, on the elastcty of markups wth respect to frm producton. Although they consder varable markups lke us, they assume that frmlevel productvty s the realzaton of a random varable drawn ndependently across frms from a dstrbuton, whch s unbounded Pareto, and t s fxed over tme. Instead of a counterfactual analyss that focuses on the welfare e ect of a partcular shock, Feenstra and Wensten (2010) useatranslogdemandsystemtomeasurethee ectsofnewvaretesand varable markups on the change n the U.S. consumer prce ndex between 1992 and That s, they use observed trade data to nfer changes n partcular components of the U.S. prce ndex. Ther results hghlght the mportance of takng nto account the mplcatons of pro-compettve e ect of trade. However, they gnore the mpact of trade on productvty sncethat snot theman focusofther paper. On theother hand, Feenstra (2014)showsthat self-selecton of more e cent frms nto exportng s the only source of welfare gans when usng a Pareto dstrbuton for productvty wth a support that s unbounded above. He restores a role for product varety and pro-compettve gans from trade, but stll assumes that frms receve a random draw of productvty from a Pareto dstrbuton, whch does not change. Fnally, borrowng nsghts from Meltz (2003) that trade openness ncreases volatlty by makng the economy more granular snce only the largest and most productve frms export, whle smaller frms shrnk or dsapper, D Govann and Levchenko (2013) show that when the dstrbuton of frm szes follows a power law wth an exponent close to -1, the dosyncratc shocks to large frms have an mpact on aggregate output volatlty. In ther model, these frm-level dosyncratc shocks may explan the observed ncrease n dsperson of frm sze dstrbuton, but they do not provde a mcrofoundaton to explan why both the 7

9 mean and the standard devaton of the dstrbuton go up n a systematc way snce they assume..d. transtory shock. Essentally, these theoretcal papers consder the e ect of a change n the exogenous dstrbuton of frm productvty, whle we take frm productvty as an endogenous varable. Therefore, we are able to add somethng new and nterestng to the conversaton about the mpact of trade based on recent models of frm heterogenety. 3 Data The frst dataset, Chnese Customs Data on mports and exports, provdes detaled nformaton on the unverse of Chna s frm-level trade transactons for the years 2000 to In addton to frm dentfers, ths dataset ncludes nformaton on many mportant transacton characterstcs, ncludng customs regme (e.g. processng trade or ordnary trade), 8-dgt HS product code, transacton value, quantty, and source or destnaton country. Usng frm dentfers provded n the dataset, we construct key varables that descrbe frm-level mports and exports. Fgure I llustrates the customs declaraton form that a frm has to fll out f t ntends to mport from or export to foregn countres. The second key dataset s from Chna s Natonal Bureau of Statstcs, whch conducts frm-level surveys on manufacturng enterprses. These data collected from Chnese frms nclude key operatonal nformaton, such as frm employment, ownershp type (e.g. stateowned enterprse, foregn nvested frm, or prvate frm), sales value, R&D expendture and ndustry. Mergng the frm-level data wth the transacton-level data s challengng because frm dentfers used n the two datasets are d erent. Nevertheless, snce both datasets nclude extensvely detaled frm contact nformaton (e.g. company name, telephone number, 8

10 Fgure I: Customs Declaraton Form zp code, contact person), we merge them usng zp codes and the last seven dgts of a frm s phone number, followng Yu (2015). In ths way, we are able to generate frm-level observatons that combne nformaton on the trade wth the operatonal actvtes of Chnese frms. Table I compares some of the man characterstcs of merged and unmerged frms, and they look very smlar on average n terms of employment, sales, value added per worker and TFP, mtgatng our concern about sample selecton bas. Table I: Comparson of Merged wth Unmerged Frms n the Data Merged Frms Unmerged Frms Log Employment [1.13] [1.17] Log Sales [1.30] [1.31] Value Added per Worker [203.32] [147.69] TFP (Olley Pakes) [1.15] [1.12] 9

11 4 Stylzed Facts To motvate our theoretcal model, we frst present some stylzed facts about the change n frm-level productvty, markup and sze durng a perod of large scale trade lberalzaton. We focus on a balanced panel, that s, the set of manufacturng frms that survved the entre sample perod, from 2000 to 2006, snce we are nterested n the wthn-frm change due to open trade. Unlke most prevous lterature that only looks at how these varables change on average, we also consder the change n dsperson, and argue that the sample mean s no longer su cent to explan the mpact of trade lberalzaton on frm performance and the resulted wage nequalty wthn a country. We fnd that both the mean and the standard devaton of these three varables go up durng ths perod. 4.1 Productvty We measure frm-level TFP based on a few d erent approaches. Besdes smple OLS, we frst use Olley and Pakes (OP), a method for robust estmaton of the producton functon allowng for endogenety of the nputs, selecton and unobserved permanent d erences across frms. Essentally, they use nvestment to proxy for frm productvty shock n the frst stage, and then use sem-parametrc selecton correcton to correct for endogenous ext. We extend the tradtonal OP procedure by ncludng an exporter dummy, followng Amt and Konngs (2007). Second, we use Levnsohn and Petrn (LP), whch nstead of nvestment, use materal expendtures as proxy for productvty shock, snce nvestment s zero for many frms. Fnally, we adopt Ackerberg, Caves and Frazer, a GMM procedure usng orthogonalty of lagged labor and productvty shock. They argue that labor and nvestment n OP, or labor and materal 10

12 expendtures n LP are lkely to be collnear. All of these approaches gve us very smlar measures of TFP, so we report only the results based on OP and LP. However, we want to pont out that these TFP measures are stll subject to the usual crtcsm, that s, they are a resdual that lumps together many thngs: techncal e cency, markups, nput and output qualty and measurement error. We do not address these ssues drectly here snce that s not the focus of ths chapter. Wth better data, on the other hand, a more robust measure of frm-level TFP s possble. 1 Note that there s an ncrease n both the mean and the dsperson of frm-level productvty. Table II: Productvty, Pooled Specfcaton Average TFP (Standard Devaton) Medan TFP LP 3.68 (1.09) 3.7 OP 4.61 (1.02) 4.59 Table III: Productvty, 1999 Specfcaton Average TFP (Standard Devaton) Medan TFP LP 3.32 (1.03) 3.37 OP 4.16 (0.92) 4.18 Table IV: Productvty, 2007 Specfcaton Average TFP (Standard Devaton) Medan TFP LP 4.00 (1.18) 4.03 OP 5.08 (1.09) See De Loecker (2013). 11

13 Fgure II: Balanced Panel TFP Estmaton Panel A: Levnsohn-Petrn Panel B: Olley-Pakes 4.2 Markup To estmate frm-level markups, we adopt the method n De Loecker and Warzynsk (2012). Ther approach reles on cost-mnmzng producers and the exstence of at least one varable nput of producton. Ths emprcal framework reles on the estmaton of a producton functon and provdes estmates of plant-level markups wthout specfyng how frms compete n the product market. There are several advantages n usng ther method. Frst, ther markup estmates are obtaned usng standard producton data where output, total expendtures on varable nputs, and revenue at the plant level are observed. Second, and more mportantly, we are able to relax a few key assumptons mantaned n prevous emprcal work. For example, we do not need to mpose constant returns to scale, or to observe and measure the user cost of captal. Below s a bref summary of ther emprcal model. Suppose a frm at tme t produces 12

14 output usng the followng producton technology: Q t = Q t (X 1 t,...,x V t,k t,! t ) (1) Assumng that producers actve n the market are cost mnmzng, we can therefore consder the assocated Lagrangan functon: L(X 1 t,...,x V t,k t, t) = VX v=1 P Xv t X v t + r t K t + t (Q t Q t (.)) (2) where Pt Xv and r t denote a frm s nput prce for a varable nput v and captal, respectvely. The frst-order condton for any varable nput free of any adjustment costs v t = P Xv t (.) V =0 (3) where the margnal cost of producton at a gven level of output s t, t = t. Rearrangng terms and multplyng both sdes by X t Q t generates the followng t (.) Xt v = v Q t t Defne the markup, µ t,asµ t = P t t,wecanrewrteequaton(3.4)as: Pt Xv Xt v (4) Q t X t = µ t P X t X t P t Q t (5) where the output elastcty w.r.t an nput X s denoted by X t. As a result, we obtan an expresson of the markup as follows: µ t = X t ( X t ) 1 (6) 13

15 where t X s the share of expendtures on nput X t n total sales, P t Q t. Emprcally, we consder two varatons of the producton functon, a Cobb-Douglas gross output producton functon and a translog gross output producton functon. In the second case, the producton functon we take to the data, and estmate for each ndustry separately, s gven by: y t = l l t + m m t + k k t + ll l 2 t + mm m 2 t + kk k 2 t + lm l t m t + lk l t k t + mk m t k t + mkl m t k t l t +! t + t (7) where t are unantcpated shocks to producton and..d. shocks ncludng measurement error. We follow Levnsohn and Petrn (2003) andrelyonmateraldemand, m t = m t (k t,! t,z t ) (8) to proxy for productvty by nvertng m t (.), where we collect addtonal varables potentally a ectng optmal nput demand choce n the vector Z t.wencludeafrm sexportstatus, for nstance, n the control functon. In the frst stage, we run: y t = t (l t,k t,m t,z t )+ t (9) where we obtan estmates of expected output ( c t) and t. Expected output s gven by: 14

16 t = l l t + m m t + k k t + ll l 2 t + mm m 2 t + kk k 2 t + lm l t m t + lk l t k t + mk m t k t + mkl m t k t l t + h t (m t,k t,z t ) (10) The second stage provdes estmates for all producton functon coe cents by relyng on the law of moton for productvty:! t = g t (! t 1 )+ t (11) After the frst stage, we can compute productvty for any value of,where = ( l, k, m, ll, kk, mm, lm, lk, mk, mkl) usng! t ( )= ˆt ll t m m t k k t ll l 2 t mmm 2 t kkk 2 t lml t m t lk l t k t mkm t k t mkl m t k t l t. By nonparametrcally regressng! t ( )ontslag,! t 1 ( ), we recover the nnovaton to productvty gven, t ( ). We can now form moments to obtan our estmates of the producton functon parameters: 15

17 0 1 l t 1 m t 1 k t l 2 t 1 m 2! t 1 E t ( ) = 0 (12) kt 2 l t 1 m t 1 l t 1 k t m t 1 k t B A l t 1 m t 1 k t We apply the standard GMM technques and rely on block bootstrappng for the standard errors. Output elastctes are computed usng the estmated coe cents of the producton functon. For nstance, output elastcty for materal s gven by: ˆ M t = m +2 m m t + lm l t + mk k t + mkl k t l t (13) As mentoned above, we do not observe the correct expendture share for materal, m t, drectly snce we only observe Q t,whchsgvenbyq t exp( t ). The frst stage of our procedure does provde us wth an estmate of t.andweusettocomputetheexpendture share as follows: ˆ M t = P M t m t P Qt t exp( ˆ t ) (14) 16

18 We obtan an estmate of markup for each frm at each pont n tme t usng (3.6) as µ t = ˆ M t (ˆ M t ) 1,whleallowngforconsderableflexbltyntheproductonfuncton,consumer demand, and competton. The estmaton procedure s essentally the same when we consder a Cobb-Douglas gross output producton functon. We smply drop hgher-order and nteracton terms. We assume labor to be ether a fully flexble nput, that s, a control varable correlated wth contemporaneous productvty shock, where we use lagged labor as nstrument, or a predetermned varable, that s, a state varable, ndependent of contemporaneous shock, when we take nto account hrng and frng costs, and we use tself as an nstrument. Table V: Markup, Pooled Specfcaton Average Markup (Standard Devaton) Medan Markup CD (L as control varable) 1.19 (0.27) 1.24 CD (L as state varable) 1.25 (0.23) 1.27 TL (L as control varable) 1.21 (0.13) 1.18 Table VI: Markup, 1999 Specfcaton Average Markup (Standard Devaton) Medan Markup CD (L as control varable) 1.16 (0.26) 1.20 CD (L as state varable) 1.22 (0.22) 1.23 TL (L as control varable) 1.13 (0.09) 1.11 Table VII: Markup, 2007 Specfcaton Average Markup (Standard Devaton) Medan Markup CD (L as control varable) 1.25 (0.30) 1.29 CD (L as state varable) 1.31 (0.26) 1.32 TL (L as control varable) 1.30 (0.16) 1.28 We get qute smlar estmates of markups across d erent specfcatons. When we compare markups across the years, especally at the begnnng and at the end of our sample perod, t becomes clear that there s a substantal ncrease n both the mean and the ds- 17

19 person of the dstrbuton of markups, most evdent n the case of a translog gross value producton functon. Fgure III: Balanced Panel Markup Estmaton I vs Fgure IV: Balanced Panel Markup Estmaton II 1999 vs vs

20 4.3 Frm Sze We measure frm sze n terms of log output value, both n nomnal terms and deflated by 4-dgt ndustry output deflator, and n terms of log employment. Its change follows the same pattern as frm productvty and markups, that s, both the mean and the dsperson of ts dstrbuton go up. Table VIII: Frm Sze, Pooled Specfcaton Mean (Standard Devaton) Medan Log (nomnal output value) (1.35) Log (deflated output value) (1.34) Log (employment) 5.41 (1.12) 5.32 Table IX: Frm Sze, 1999 Specfcaton Mean (Standard Devaton) Medan Log (nomnal output value) (1.22) 10 Log (deflated output value) (1.22) Log (employment) 5.36 (1.13) 5.26 Table X: Frm Sze, 2007 Specfcaton Mean (Standard Devaton) Medan Log (nomnal output value) (1.49) Log (deflated output value) 11 (1.48) Log (employment) 5.4 (1.15)

21 Fgure V: Balanced Panel Frm Sze Estmaton Log nomnal output value Log deflated output value 5 Tar Reductons and Imported Inputs Snce Chna joned the WTO n December 2001, t lowered ts average tar sgnfcantly, from 16% to a lttle above 12% wthn one year from 2001 to 2002, and the average tar kept declnng steadly over the entre sample perod. The last year n our sample, 2006, saw an average tar rate of only about 10%. It s ndeed one of the most dramatc trade lberalzaton epsodes n Chna s hstory. As a commtment to ts WTO accesson, Chna also agreed to elmnate all quotas, lcenses, tenderng requrements and other non-tar barrers to mports of manufactured goods by

22 Fgure VI: Average Tar at HS-8 Level Source: Trade Analyss and Informaton System (TRAINS) and WTO tar database To motvate our theoretcal model, we look at how heterogeneous frms at d erent productvty levels adjust ther set of mported varetes durng ths perod of dramatc nput tar lberalzaton. We fnd n the data that frms that belong to a hgher quartle of the productvty dstrbuton expanded the number of foregn varetes that they mported by more. Ths observaton leads to an mportant feature of our model, whch we explan n the theory secton. We also see n the data that frms on average ncreased the number of ther mported products and source countres sgnfcantly between 2001 and 2002, when they experenced the bggest tar reductons. They kept expandng ther mported varetes (product-country pars) untl 2004, whch then tapered o. Frms typcally mport a large number of products from a number of countres, and therefore, we assume that frms can mport a contnuum of foregn varetes f they fnd t benefcal. 21

23 Table XI: Frm Productvty and Newly Imported Varetes Productvty Quartle Mean of Newly Imported Varetes Productvty Quartle Q Q Q Q Q Q Q Q Productvty Quartle Mean of Newly Imported Varetes Mean of Newly Imported Varetes Productvty Quartle Q Q Q Q Q Q Q4 13 Q Productvty Quartle Mean of Newly Imported Varetes Mean of Newly Imported Varetes Productvty Quartle Q Q Q Q Q Q Q Q Mean of Newly Imported Varetes Table XII: Number of Imported Products, Source Countres and Varetes Products Source Varetes Products Source Varetes Countres Countres Mean Mean Medan Medan Products Source Varetes Products Source Varetes Countres Countres Mean Mean Medan Medan Products Source Varetes Products Source Varetes Countres Countres Mean Mean Medan Medan

24 6 Model In ths secton, we present a partal equlbrum, heterogeneous frm model wth endogenous mported nput and labor qualty choce to account for the aforementoned emprcal fndngs. On the demand sde, we adopt the qualty-meltz model n Kugler and Verhoogen (2012), where hgher prce decreases demand but hgher qualty ncreases demand. On the supply sde, frms d er from each other n the usual dmenson of productvty, as n Meltz (2003). In our model, frms combne labor and ntermedate nputs to produce physcal quantty, n the sprt of Amt et al. (2014). Output qualty, on the other hand, s determned by labor and nput qualty, and the advantage of mported nputs over domestc counterparts s augmented by a frm s own productvty. 6.1 Demand Smlar to Kugler and Verhoogen (2012), a representatve consumer has the followng constantelastcty-of-substtuton (CES) utlty functon: applez U = (q y ) 2I 1 d 1 (15) where I denotes the set of all d erentated varetes avalable; 2 I ndexes a partcular varety; >1stheconstantelastctyofsubsttutonbetweend erentvaretes;y s the quantty of varety consumed; q s the output qualty of varety, chosenbythefrm producng varety and assumed to be observable to all. 23

25 Consumer optmzaton yelds the followng demand functon for varety : 1 y = YP q p (16) h R where p s the prce of varety charged by the frm; Y = U = (q 1 1 2I y ) d s apple 1 R 1 1 p the qualty-adjusted aggregate consumpton n the economy; P = 2I q d s the qualty-adjusted deal prce ndex. Ths demand functon s ncreasng n the qualty and decreasng n the prce. 6.2 Producton There s a contnuum of frms of measure I, eachproducngoned erentatedvarety. Wthout any ambguty, we also use to ndex the frm producng varety. Frms d er from each other n ther productvty, ',drawnfromaknowndstrbutonuponenterng the market and are thereafter fxed, as n Meltz (2003). 2 Let us consder a partcular frm. Its producton can be summarzed by two producton functons - one characterzng the producton of physcal quantty, y,andtheother characterzng the producton of output qualty, q. The producton of physcal quantty s summarzed by a Cobb-Douglas producton functon: y = ' L 1 X (17) 2 Here we assume the support of the dstrbuton s bounded below by 1. Ths assumpton s made manly to elmnate scenaros n whch low productvty frms make hgh qualty foregn nputs less e cent than low qualty domestc nputs. 24

26 Z 1 X =exp 0 j log (X j ) dj (18) X j = Z j + ' b a j M j (19) L s the amount of labor used. 0 < 1 <1sthelaborshareofvarablecosts. X s the ntermedate nput aggregated from a contnuum of nputs of measure 1, ndexed by j. j > 0sthemportanceofnputj among all ntermedate nputs, wth R 1 0 jdj =1. X j s the amount of nput j used. For each nput j, therearebothdomestcandforegn varetes denoted by Z j and M j respectvely, whch are perfect substtutes. The foregn varety has a natural advantage, a j > 1, over ts domestc counterpart. However, the actual advantage, ' b a j, s the natural advantage augmented by a frm s productvty, mplyng that more productve frms are able to use the same foregn nput more e cently than less productve ones. b>0, s a parameter that governs the d erental e cency of foregn nput use between frms at d erent levels of productvty - the larger b s, the greater the d erental e cency. The producton of output qualty s summarzed by a constant-returns-to-scale supermodular functon n labor qualty and ntermedate nput qualty: q = apple (1 ) c + 8 Z 1 0 jb jdj 1 (20) >< 1 j 2 J Z b j = >: ' b a j j 2 J M (21) 25

27 c s the labor qualty chosen by the frm; 3 b j s the qualty of ntermedate nput j; J Z represents the set of nputs for whch domestc varetes are used, and J M = [0, 1] \J Z represents the set of nputs for whch foregn varetes are mported; <0capturesthe constant degree of complementarty between labor qualty and ntermedate nput qualty. A more negatve represents a stronger complementarty. Wth ths specfcaton, frms usng hgher qualty foregn nputs also have a greater ncentve to use hgher qualty labor to complement them. We assume there s only domestc labor market, gven the low nternatonal moblty of labor relatve to captal and ntermedate nputs. Workers, l, areex-antehomogeneous wth wages normalzed to 1. There exsts a sector that transforms homogeneous labor nto d erent qualty, wth the producton functon: F (l, c) = l.thsmplesthatthemargnal c cost of producng one unt of labor wth qualty c s c 1=c. Labor market s assumed to be perfectly compettve, hence the prce of labor of qualty c s p L (c) =c. For ntermedate nput j, there are domestc market and foregn market. Frms are prce takers n both. The equlbrum prces of domestc varety and foregn varety are p Z j and p M j respectvely. 4 However, on top of the prce, p M j,therearevarabletradecosts, j 1, n the form of ceberg costs. In other words, for a frm to acqure one unt of foregn varety of nput j, thastopayfor j unts at the costs of j p M j. We assume that there are no fxed costs of mportng at each nput level. 5 However, each 3 Labor qualty, c, s a contnuous varable wth postve support. It s perfectly observable to frms, so we abstract from any asymmetrc nformaton problems. 4 Both are expressed n terms of a home currency. Exchange rates are not the focus of ths chapter. 5 Ths s manly to avod the problem of multple equlbra. Amt et al. (2014) have fxed costs of mportng at each nput level. But they fx the set of mported nputs before the choce of output n equlbrum, because the exchange rate shocks n ther paper are assumed to be unforeseen. In ths chapter, however, we wsh to allow both output and the set of mported nputs to respond to a change n the varable trade costs. The addton of fxed costs of mportng at each nput level wll thus ntroduce multple equlbra. 26

28 frm has to pay fxed mport costs, f M,ftswtchesfromnotmportngatalltomportng some nputs. There are also fxed costs of producton, f, eachperod. 6.3 Equlbrum In order to solve the frm s proft maxmzaton problem, we follow the strategy n Amt et al. (2014). We break down the problem nto two stages. In the frst stage, we hold the set of mported nputs, J M,fxedandsolvetheoptmzatonproblemcondtonalonJ M.In the second stage, we allow J M to vary so that we can pn down the optmal set of mported nputs, J M Stage 1: Proft Maxmzaton Condtonal on a Fxed Set of Imported Inputs In ths stage, we fx the set of mported nputs, J M 6= ;. 6 Then the frm s profts can be wrtten as: Z = p y p L (c) L = Y 1 Pq 1 y 1 c L J Z Z p Z j Z j dj Z J Z p Z j Z j dj J M j p M j M j dj f M f Z j p M j M j dj f M f (22) J M The second equalty comes from substtutng the prce, p = Y 1 Pq functon and p L (c) =c, ntothefrstequalty. 1 y 1,usngthedemand 6 We restrct attenton to frms that mport. The determnaton of the cuto, ' nm,belowwhchfrms never mport s dscussed n the next secton, by comparng the frm s profts gven ts optmal set of mported nputs wth those when t does not mport any nputs. 27

29 The condtonal proft maxmzaton problem s thus: max = Y 1 Pq y,q,c,l,x,{z j },{M j } 1 y 1 c L Z J Z p Z j Z j dj Z J M j p M j M j dj f M f (23) s.t : y = ' L 1 X (24) ( Z Z ) X =exp j log (Z j ) dj + j log ' b a j M j dj (25) q = " J Z (1 ) c + Z J Z J M Z jdj + J M j' b a jdj!# 1 (26) Let the Lagrange multplers assocated wth (3.24), (3.25) and (3.26) be,, respectvely. Frm optmzaton yelds the followng frst-order condtons: 1 1 Y Pq 1 y 1 = (27) 1 1 Y Pq 1 1 y = (28) L = (1 ) q 1 c 1 (29) c = (1 ) y (30) L y = (31) X p Z j = X j Z j, 8j 2 J Z (32) j p M j = X j M j, 8j 2 J M (33) We can solve for the optmal labor qualty, output qualty, output quantty and profts, 28

30 condtonal on J M,asfollows: c = q = y = " Z J Z Z jdj + J M j' b a jdj # 1 (34) 1 (1 ) (1 ) 1 YP ' q B (35) = (1 ) (1 )( 1) ( 1) YP ' 1 (q B ) ( 1) f M f (36) n R 1 where B =exp 0 j log j dj + R p Z J j M j log 'b a jp Z j j p M j o dj. The frst equaton postulates that, condtonal on the same set of mported nputs, frms wth hgher productvty can make more out of foregn nputs and thus hre hgher qualty labor to complement them, ultmately producng hgher qualty outputs. Condtonal on the same productvty, frms that mport a larger set of nputs also hre hgher qualty labor due to the ncrease n the qualty of ntermedate nputs, and also produce hgher qualty outputs. As a result, these frms pay hgher wages to ts workers Stage 2: Determnaton of the Optmal Set of Imported Inputs In ths stage, we formulate a recursve algorthm that pns down the optmal set of mported nputs. Before that, let us consder a frm wth ts current set of mported nputs, J M, contemplatng on whether to mport foregn varety for nput j. In other words, nput j s moved from the set J Z to J M. After the endogenous adjustment of labor qualty, output 29

31 qualty and quantty, the resultng change n profts s gven by: d = A' 1 d h(q B ) ( 1) = A' 1 ( 1) (q B ) ( 1) j " 1 q ' b a j 1 +log 'b a j p Z j j p M j # (37) where A = (1 ) (1 )( 1) ( 1) YP contans only constants and macroeconomc varables that the frm takes as exogeneously gven. Under the assumptons on the parameters, the sgn of d s gven by:! sgn (d ) = sgn 1 q ' b a j 1 +log 'b a j p Z j j p M j (38) Note that snce we do not have fxed costs of mportng at each nput level, the sgn of d s ndependent of the scale of producton, thus avodng the problem of multple equlbra. The frst term, 1 q ' b a j 1, s always postve, representng the benefts of mportng an extra nput j on output qualty, and hence, total revenue. These benefts are ncreasng n output qualty, q,duetocomplementartybetweenqualtyofnewlymportednputj and qualty of exstng mported nputs n J M. Ths mples that there s no crowdng out e ect - mportng more nputs does not make mportng other nputs less desrable. In fact, there s crowdng n - mportng more nputs ncreases the benefts of mportng an extra nput, thus ncreasng the lkelhood of mportng that nput. These benefts are also ncreasng n frm productvty, ',becausemoreproductvefrmscanmakemoreoutofthesamemported nput j. 7 The second term, log 'b a jp Z j j p M j,canbeetherpostveornegatve,dependngon 7 Here, we condton on fxed output qualty, q. Ths result holds more strongly f q s an ncreasng functon n '. 30

32 the advantage-and-trade-cost-adjusted relatve prce. If foregn varety s relatvely cheaper than domestc varety, jp M j ' b a j apple p Z j,thenlog 'b a jp Z j j p M j 0. As a result, condtonal on already mportng some nputs, that s, the frm has already pad the fxed costs of mportng at the frst unt, f M, t s always wllng to mport such nput j because mportng s both qualty-enhancng and cost-savng. Next, we characterze the optmal set of mported nputs. Unlke the framework n Amt et al. (2014), whch has a cuto mplctly defned because the margnal cost of mportng s fxed and the margnal beneft of mportng s monotoncally decreasng, our model does not have a sortng of the nputs nor an mplctly defned cuto. Instead, we defne the optmal set recursvely and sequentally usng an algorthm. We prove the optmalty of the defned set and some of ts other desrable propertes n the next subsecton. For expostory smplcty, let us defne: applez Z q (S) = jdj + S c S j' b a jdj 1 (39) as the condtonal optmal output qualty for frm that mports the set of nputs, S [0, 1], and uses domestc varetes for the complementary set, S c =[0, 1] \S. An mmedate lemma s: Lemma 1 For any two sets, S 1 S 2 [0, 1], and some frm wth productvty ', q (S 1 ) < q (S 2 ). For any two frms and 0 wth productvty ' <' 0 and any set S [0, 1], q (S) <q 0 (S). Combnng the two results, we also have q (S 1 ) <q 0 (S 1 ) <q 0 (S 2 ). The proof s trval once t s noted that ' b a j > 1. 31

33 Recursve algorthm of computng the optmal set of mported nputs, J M, condtonal on havng pad f M For frm wth productvty ',tsoptmalsetofmportednputs,j M,canbecomputed as the followng: Step 1: Defne J 0 = n j 2 [0, 1] jp M j ' b a j apple p Z j o. Based on the argument above, mportng these foregn nputs s both qualty-enhancng and cost-savng. Therefore, t s always benefcal to mport them once f M s pad. Hence, J 0 J M Step 2: Defne J 1 = n j 2 [0, 1] \ J c 0 1 [q (J 0 )] ' b a j 1 +log 'b a jp Z j j p M j o 0. Snce there s only crowdng n e ect of mportng more nputs and mportng nputs n J 1 ncreases profts, t s optmal for the frm to mport them. J 1 J M Step 3: Defne J 2 = n j 2 [0, 1] \ J c 0 \ J c 1 1 [q (J 0 [ J 1 )] ' b a j 1 +log 'b a jp Z j j p M j o 0. By the same logc, J 2 J M Repeat these steps untl for some N 2 N such that, 8 < N 1 J N = : j 2 [0, 1] \ \ n=0 J c n! 1 " [ q N 1 n=0 J n!# ' b a j 1 +log 'b a j p Z j j p M j 9 = 0 ; = ; 32

34 mplyng that there s no nput, whch the frm has not yet mported, that can ncrease profts. Then we clam the optmal set of mported nputs s: N[ 1 J M = n=0 J n Determnaton of No-mport Cuto Due to the exstence of the fxed costs of mportng, f M,atthefrstunt,noteveryfrm engages n mportng. Frms below a productvty threshold, ' nm,donotmportanynput whle frms above that threshold do. Ths threshold s determned by comparng the profts f the frm mports wth those f t does not. The margnal frm wth productvty ' nm s nd erent between mportng and not. The profts of frm f t mports are gven by: (mportng) =A' 1 q J M B J M ( 1) f M f (40) where J M s the optmal set of mported nputs gven productvty '. The profts of frm f t does not mport are gven by: (not mportng) = A' 1 (q (;) B (;)) ( 1) f Z 1 = A' 1 exp ( 1) j log 0 j p Z j dj f (41) Note that q J M B J M n ( 1) > (q (;) B (;)) ( 1) =exp ( 1) R o 1 0 j log j dj p Z j because of the optmalty of J M.Eventhoughboth (mportng) and (not mportng) 33

35 are ncreasng n ',theformerncreasesmuchfasterthanthelatter,buttheformerstarts at a lower value due to the exstence of f M. Hence, as llustrated by the fgure below, the two proft lnes have one ntersecton, ' nm, after whch mportng nputs generates hgher profts than not mportng. Ths pns down the no-mport cuto.! Proft! Fgure VII: No-mport Cuto Importng! Not!mportng! ϕ nm! ϕ! 6.4 Model Implcatons In ths secton, we outlne some of the propertes mpled by the model that gude our emprcal nvestgatons. Some of these propertes come naturally out of the model whle others requre addtonal assumptons on the parameters of the model. 34

36 6.4.1 No-mport Cuto We frst examne how the set of frms that engage n mportng respond to trade lberalzaton n the form of mport tar reductons. Clearly the proft schedule of not mportng, (not mportng), does not change wth mport tar reductons. The proft schedule of mportng, (mportng), does, but ths change may or may not a ect the no-mport cuto, dependng on the nature of mport tar reductons. We summarze our fndngs n the followng proposton. Proposton 1: Suppose there s trade lberalzaton n the form of mport tar reductons summarzed by {d j apple 0,j 2 [0, 1]}. The no-mport cuto wll ether decrease, ' nm 0 < ' nm, or reman unchanged, ' nm 0 = ' nm. The former s true f and only f the orgnal margnal frm wth productvty ' nm has a strctly larger optmal set of mported nputs, Jnm M { j + d j } 1 j=0 Jnm M { j } 1 j=0,orthesameoptmalset, Jnm M { j + d j } 1 j=0 = Jnm M { j } 1 j=0,butthereexstssomej 2 Jnm M { j } 1 j=0 such that d j < 0. The latter s true f and only f the optmal set does not change, Jnm M { j + d j } 1 j=0 = Jnm M { j } 1 j=0,andforallj 2 Jnm M { j } 1 j=0, d j =0. An mmedate result s that f there s a unform decrease n mport tar s, the no-mport cuto decreases. More generally, f there s a decrease n tar on some nput n the optmal set of mported nputs of the orgnal margnal frm, the cuto decreases. Ths result s consstent wth emprcal fndngs that followng trade lberalzaton, prevously non-mportng frms n the balanced panel start to mport hgher qualty foregn nputs. 35

37 6.4.2 Optmal Set of Imported Inputs Snce the optmal set of mported nputs s at the center of our model, determnng equlbrum labor qualty, output qualty and quantty, we nvestgate the propertes of ths set. Proposton 2: All other thngs beng equal, a more productve frm mports a weakly larger set of foregn nputs. Specfcally, f ' <' 0,thenJ M J M 0. Proof. Let us consder the recursve algorthms for the two frms. Let N 1 and N 2 be defned as n the algorthm for frm and 0 respectvely. There are three possble cases: N 1 = N 2, N 1 <N 2 and N 1 >N 2.Weprovethepropostonnthethreecasesseparately. Frst, suppose N 1 = N 2 = N. To prove J M J M, we just need to prove n each 0 step, S n m=0 J m S n m=0 J 0 m for all n 2 {0, 1,...,N 1}. Clearly when n = 0, J 0 = n o n o j 2 [0, 1] jp M j apple p Z ' b a j j j 2 [0, 1] jp M j apple ' b 0 a pz j j = J 0 0 because ' <' 0. Now suppose S n m=0 J m S n m=0 J 0 m holds for some n 2{0, 1,...,N 2}. Consder n step n +1,some arbtrary nput j 2 J n+1. If j 2 S n m=0 J 0 m, then t becomes trval that j 2 S n+1 m=0 J 0 m. So suppose j /2 S n m=0 J 0 m,butweknowthat 1 q ( S n m=0 J m) ' b a j 1 +log 'b a jp Z j j p M j 0 by defnton of J n+1 ;and S n m=0 J m S n m=0 J 0 m wth ' <' 0 mples q ( S n m=0 J m) < q 0 ( S n m=0 J 0 m)bylemma1.therefore 1 q 0 n[ m=0 J 0 m! ' b 0 a j 1 +log 'b 0a jp Z j j p M j > 1 q n[ m=0 J m! ' b a j 1 +log 'b a j p Z j j p M j 0 Hence j 2 J 0 n+1 S n+1 m=0 J 0 m. Ths proves J n+1 S n+1 m=0 J 0 m, but by assumpton, S n m=0 J m S n m=0 J 0 m S n+1 m=0 J 0 m,sowehave S n+1 m=0 J m = J n+1 [( S n m=0 J m) S n+1 m=0 J 0 m. By mathematcal nducton, we have shown that S n m=0 J m S n m=0 J 0 m for all n 2{0, 1,...,N 1}. 36

38 Evaluatng ths expresson at N 1, we have proven J M J M 0. The case N 1 < N 2 s trval because we have shown already that J M = S N 1 1 S N1 1 n=0 J 0 n SN1 1 n=0 J 0 n [ SN2 1 n=n 1 J 0 n = J M. 0 Now, we consder N 1 >N 2.Wehaveshownnthefrstcasethat S N 2 1 n=0 J n S N 2 1 J M. Now consder any arbtrary j 2 J 0 N 2. j satsfes 1q log 'b a jp Z j j p M j 0, and we know q SN2 1 n=0 J n <q 0 SN2 1 n=0 J 0 n SN2 1 n=0 J n by Lemma 1. So n=0 J n n=0 J 0 n = ' b a j q 0 N[ 2 1 n=0 J 0 n! ' b 0 a j 1 +log 'b 0a jp Z j j p M j > 1 q N[ 2 1 n=0 J n! ' b a j 1 +log 'b a j p Z j j p M j 0 Hence by defnton j 2 J 0 N 2 or j 2 S N 2 1 n=0 J 0 n.theformersmpossblebecausej 0 N 2 = ;, so j 2 S N 2 1 n=0 J 0 n. Ths proves J N2 S N 2 1 n=0 J 0 n. Wth S N 2 1 n=0 J n S N 2 1 n=0 J 0 n,weshow S N2 n=0 J SN2 1 n = n=0 J n [ J N2 S N 2 1 n=0 J 0 n = J M. Repeat ths argument for n = N ,...,N 1 1, we can show that J M = S N 1 1 n=0 J n J M 0. Proposton 3: All other thngs beng equal, a reducton n varable trade costs, j,for nput j ncreases the lkelhood of mportng that nput for a frm that prevously does not mport t. Furthermore, t also ncreases the lkelhood of mportng other nputs that are not mported before by the frm, f nput j s now mported. Proposton 3 s qute ntutve because a reducton n varable trade costs j decreases the costs of mportng j whle keepng benefts unchanged. Hence the frm s more lkely to mport j. Condtonal on j beng mported after the reducton n j,thesetofmported nputs expands and the output qualty ncreases, further ncreasng the benefts of mportng other nputs due to the crowdng n e ect. Hence, the lkelhood of the frm mportng other 37

39 nputs ncreases. Proposton 3 can be generalzed to reductons n multple/all varable trade costs. The ncrease n the lkelhood s much bgger f the varable trade costs of many nputs that are prevously not mported by the frm decrease at the same tme Labor Qualty, Output Qualty, and Wages Recall that for frms above the no-mport threshold, ' nm,theoptmallaborqualtyand output qualty are gven by: c = q = " Z J Z Z jdj + J M j' b a jdj # 1 where J Z =[0, 1] \J M s the equlbrum set of domestc nputs. By proposton 2, we know that a more productve frm mports a weakly larger set of foregn nputs. Hence, t s obvous from the above expresson that ths more productve frm uses strctly hgher qualty labor and produces strctly hgher qualty output. Snce equlbrum labor qualty s hgher for a more productve frm, t also pays hgher wages because p L (c) =c. Trade lberalzaton n the form of tar reductons ncreases the set of mported nputs for some, f not all, frms, by proposton 3. These frms swtch to hgher qualty foregn nputs, and hre hgher qualty labor to complement them. As a result, they produce hgher qualty output and pay hgher wages. Suppose the tar reductons nduce a decrease n the no-mport cuto as n the frst case n proposton 1. Then for those frms wth productvtes ' between ' nm 0 and ' nm,they 38

40 swtch from not mportng at all to mportng some foregn nputs. Ther labor qualty and output qualty ncrease from c = q = h R 1 0 jdj 1 =1to h R J Z jdj + R J M j' b a jdj 1 > 1. Ths ncrease s larger, the more productve the frm s, because ' and J M are both larger by proposton 2. As a result, they also pay hgher wages after trade lberalzaton. For those frms that never mport - frms wth ' <' nm 0 apple ' nm,theresnochange n the labor qualty, output qualty and wages before and after trade lberalzaton. They are consstently usng the low skll labor, c =1,producnglowqualtyoutput,q =1,and payng low wages, p L (1) = Frm Profts In terms of frm profts, we have a set of smlar predctons. Condtonal on the same set of mported nputs, a more productve frm has hgher profts because of ts hgher ' and hgher q.byproposton2,talsomportsaweaklylargerset of nputs. It chooses to do so because by mportng more, ts profts ncrease. Therefore, we have shown that a more productve frm enjoys hgher profts. Trade lberalzaton n the form of nput tar reductons generates hgher profts for any frms, provded that they are mportng nputs after trade lberalzaton. Ths ncrease n profts comes from two potental sources. After trade lberalzaton but condtonal on the same set of mported nputs, frm profts are as least as large as before. It makes strctly larger profts f there s a reducton n tar on at least one of ts mported nputs. Furthermore, the frm chooses to mport a weakly larger set of mported nputs by proposton 3. It chooses to do so only f ts profts ncrease, evdent from the recursve algorthm. However, who enjoys a bgger ncrease n profts n the face of the same tar reductons 39