ABSTRACT. Antoine Gervais, Ph.D., This thesis is concerned with the role of product quality in explaining observed price

Transcription

1 ABSTRACT Title f Dcument: PRODUCT DIFFERENTIATION IN INTERNATIONAL TRADE Antine Gervais, Ph.D., Directed By: Prfessr Nun Limã Department f Ecnmics This thesis is cncerned with the rle f prduct quality in eplaining bserved price and trade patterns. The first chapter intrduces the tpic, summarizes the main findings f the dissertatin and cntrasts them t ther results in the literature. The secnd chapter develps a tractable general equilibrium mdel that includes quality differentiatin amng hetergeneus firms. The thery eplicitly demnstrates hw hetergeneity in a single egenus parameter, prductivity, can prduce dispersin in prduct quality and price. The framewrk predicts that relatively prductive firms will chse t prduce high quality varieties. This finding accrds well with the bservatin that the unit value f eprted varieties increases with eprter s incme, capital- and skill- abundance. The mdel is used t analyze hw internatinal trade plicy and quality differentiatin interact t shape patterns f prductin and trade flws. In particular, the mdel predicts a psitive relatinship between prduct quality and eprt status at the firm level and that trade liberalizatin decreases the average quality f a cuntry s eprts.

2 The third chapter evaluates the imprtance f vertical prduct differentiatin in eplaining price and eprt status patterns bserved in micrdata n U.S. manufacturing plants. The main difficulty in eplring the impact f vertical prduct differentiatin is that prduct quality is nt directly bservable. The analysis tackles the prblem frm tw angles. First, the chapter develps a nvel empirical strategy t btain a pry fr quality, which is then used t evaluate imprtant cnditinal crrelatins. The results shw that bth quality and prductivity are imprtant determinants f price and eprt status pattern. Secnd, the simulated methd f mments is used t btain structural estimates f the parameters f the mdel and t assess the imprtance f quality differentiatin. The estimates suggest that quality differentiatin plays an imprtant rle in eplaining the variatin in price, size and eprt status acrss U.S. manufacturing plants. The furth chapter briefly cncludes by summarizing the main findings and suggesting avenues fr future research. Overall the analysis presented in this dissertatin implies that vertical prduct differentiatin, r quality, plays an imprtant rle in eplaining dispersin in prducer utput price and eprt status.

3 PRODUCT DIFFERENTIATION IN INTERNATIONAL TRADE By Antine Gervais. Dissertatin submitted t the Faculty f the Graduate Schl f the University f Maryland, Cllege Park, in partial fulfillment f the requirements fr the degree f Dctr f Philsphy 2009 Advisry Cmmittee: Prfessr Nun Limã, Chair Prfessr Jhn Haltiwanger Prfessr Jhn Shea Prfessr Jhn Bradfrd Jensen Prfessr Curt Grimm

4 Cpyright by Antine Gervais 2009

5 Frewrd Ring the bells that still can ring. Frget yur perfect ffering. There is a crack in everything. That's hw the light gets in. Lenard Chen ii

6 Dedicatin A mes parents, Jeannine et Maurice Gervais. iii

7 Acknwledgements I am indebted t Nun Limã, Jhn Haltiwanger, and Jhn Shea fr their invaluable guidance thrughut the cmpletin f this prject. Fr chapter 2, I wish t thanks Lurenc Paz and participants at the spring 2008 Midwest Ecnmic Thery and Internatinal Ecnmics Meetings in Urbana- Champaign and at the University f Maryland brwnbag macrecnmic seminar fr their cmments. Fr chapter 3, I am grateful t J. Bradfrd Jensen and Pabl D Erasm fr many useful discussins. I wuld als like t thank participants at the 2009 Nrth American Summer Meeting f the Ecnmetric Sciety in Bstn, at the 2009 Midwest Ecnmics Assciatin Annual Meeting in Cleveland, at the U.S Census Center fr Ecnmic Studies CES seminar in Washingtn, and at the University f Maryland brwnbag macrecnmic seminar fr their cmments. Je remercie mes parents, Jeannine et Maurice Gervais, sans qui cette dissertatin n aurait jamais vu le jur. La liberté dnt j ai juie durant tant d années grâce à leur dur travail m a permis de devenir l hmme que je suis aujurd hui. Un merci grs cmme le ciel à ma très chère Esther. Cmme autant d asis au milieu du désert, ses surires et encuragements m nt sutenu au curs du lng et hardu parcurs qui a mené a ce mémire. À vus tris, je suhaite sincèrement que les innmbrable sacrifices que vus avez fait pur que mes rêves se réalisent vus sient repayé au centuple. iv

8 Table f Cntents Frewrd... ii Dedicatin...iii Acknwledgements... iv Table f Cntents... v List f Tables... vii List f Figures...viii Chapter : Intrductin... Chapter 2: Theretical Results Intrductin Clsed Ecnmy Mdel Preferences and Demand Technlgy and Firm Behavir Quality Industry Equilibrium Analysis f Equilibrium Srting and Optimal Output Industry Price Schedule Welfare The Open Ecnmy Mdel Cstless Trade Cstly Trade The Impact f Trade The Impact f Trade Liberalizatin Cnclusin Chapter 3: Empirical Results Intrductin Thery Preferences Prductin Internatinal Trade Prfit Maimizatin Equilibrium Analysis f Equilibrium Data Empirics Estimating Prduct Quality Quality, Prductivity, and Price Prduct Quality and Eprt Status Rbustness Structural Estimatin Calibratin v

9 3.5.2 Mments Estimatin Cunterfactuals Cnclusin... 8 Chapter 4: Cnclusin Appendices A. Appendi t Chapter A. The Clsed Ecnmy A.2 A Discussin f Assumptin A.3 The Crrelatin between Price and Prductivity A.4. The Open Ecnmy A.5 Prfs f Prpsitins A.6 The impact f Trade Liberalizatin B. Appendi t Chapter B. Equilibrium B.2 Measurement Errr B.3 Slutin Algrithm B.4 Weighting Matri fr SMM Estimatin... 4 Bibligraphy vi

10 List f Tables Table I: Prduct Categries in SIC Table II: Sample Characteristics Table III: Prduct Characteristics Table IV: High vs. Lw Demand Residuals Plants Table V: Investment in Quality I Table VI: Investment in Quality II Table VII: Demand Residuals, Prductivity, and Unit Cst Table VIII: Quality, Prductivity, and Price Table IX: Eprting vs. Nn Eprting Plants Table X: Quality, Prductivity, and Eprt Status Table XI: Rbustness I Reginal Variatin in Demand... 0 Table XII: Rbustness II Learning and Reputatin Table XIII: Rbustness III Remving Hrizntal Differentiatin Table XIV: Fied Parameters fr Simulatin Table XV: Actual and Simulated Mments... Table XVI: Parameter Estimates... 4 Table XVII: Cunterfactual... 6 Table XVIII: Variance-Cvariance Matri f Mments... 4 vii

11 List f Figures Figure : Prfit Functins and Prductivity Cutffs... 8 Figure 2: The Equilibrium Prductivity Threshld Figure 3: Equilibrium Firm-level Output Schedule... 3 Figure 4: Industry Price Schedule Figure 5: Eprters and Nn-eprters Figure 6: The Impact f Trade Liberalizatin viii

12 Chapter : Intrductin The rigrus analysis f U.S. imprt data by Schtt 2004 reveals a striking pattern: within sme narrwly defined prduct categries, firms lcated in high incme, capital-rich and skill-abundant cuntries eprt relatively high priced units t the U.S. This bservatin has at least tw imprtant implicatins: First, assuming that firms in wealthy cuntries are n average mre prductive, it must be the case that relatively prductive firms prduce varieties fr which the cnsumer s willingness t pay is higher. Secnd, fr differentiated prducts, the unit value reflects nt nly the efficiency f the prductin prcess but als the prduct s quality. These cnsideratins suggest that studying the relatinship between firm prductivity and prduct quality wuld lead t an imprved understanding f internatinal trade flws. The ptential fr quality differentiatin frces us t rethink the impact f trade liberalizatin n bth industrialized and develping cuntries. Quality upgrading is an imprtant margin prducers in develped cuntries can eplit t resist lw-wage imprt cmpetitin. Fr instance, the entry f lw cst prducers, such as Chinese and Indian firms, culd lead t a reallcatin f resurces twards high quality varieties in technlgically advanced cuntries. Mrever, since wrker relcatin is likely t be easier within than acrss industries, within-industry specializatin reduces the predicted welfare lss assciated with the shrt-run adjustment that usually fllws a trade liberalizatin episde. Other recent papers lk at price in aggregate trade data. See fr instance, Hummels and Klenw 2005, Faruq 2006, Helble and Obuk 2007, and Jhnsn 2008.

13 The mtives fr quality upgrading are imprtant fr issues beynd internatinal trade. The analysis f vertical differentiatin brings t the fre an imprtant weakness f a widely used prductivity estimatin prcedure. Typically, in the absence f prducer-level price infrmatin, utput revenues and input ependitures are deflated by sectr-level price indices and prductivity estimates are defined as the residual in a regressin f lg deflated utput revenues n lg deflated input ependitures at the prducer-level. If variatin in prduct quality leads t price dispersin, hwever, such a prcedure will lead t systematic biases in the prductivity estimates. Mrever, Fster, Haltiwanger and Syversn 2008 pint t the difficulty f btaining accurate prductivity estimates in the presence f vertical prduct differentiatin even when micrdata infrmatin n utput quantity is available. 2 In general, high input price plants have lw quantity ttal factr prductivity values because their input ependitures per units f utput are larger than thse f their industry cunterparts. 3 Shuld we therefre cnclude that these plants are less prductive if their utput is f superir quality and can fetch a higher unit value n the market? Nt necessarily. If prducing a high quality prduct requires relatively cstly high quality inputs then the quantity prductivity estimates understate the true prductivity f the firm. The same is true if the quantity f inputs required t prduce ne unit f utput is increasing in quality. In general bth inputs and utputs shuld be cmputed n a quality adjusted basis in rder t make accurate inferences n plant prductivity. Understanding the 2 Their wrk eplres the separate cntributins f idisyncratic technlgy and demand t plant survival and prductivity grwth. The analysis uses a subset f hmgenus prducts t minimize differences in quality acrss plants. 3 Quantity TFP reflects prducer s average cst per unit i.e. dispersin in physical efficiency and factr input prices. In Fster et al and the current study it is btained by cmputing the difference between the lg quantity prduced and the lg f a cnstant returns t scale Cbb-Duglas input inde. 2

14 impact f prduct quality n prductin cst, utput price and revenue culd lead t the develpment f imprved measures f prductivity. The imprtance f quality in eplaining trade flws was first emphasized by Linder 96, wh argued that cnsumers in rich cuntries spend relatively mre n high quality gds than cnsumers in pr cuntries. In that case, clseness t demand prvides richer cuntries with a cmparative advantage in the prductin f high-quality gds. In the late 980s several ecnmists frmalized the demand side relatinship between trade and quality in general equilibrium mdels. 4 The main predictin that bilateral trade shuld be decreasing in the cuntries dissimilarity, generally measured by incme per capita difference, received sme empirical supprt. 5 Hwever, it is nt clear that cnsumers in rich cuntries purchase higher quality gds eclusively because they have different preferences. Hlding preferences fied, the distributin f prduct quality may nt be independent f the distributin f firm prductivity. Unfrtunately, despite the wealth f evidence abut the imprtance f vertical differentiatin, the literature still lacks a general framewrk t think abut the supply-side factrs affecting differences in prduct quality acrss cuntries. The main bjective f chapter 2 is t fill this gap by intrducing vertical differentiatin in a hetergeneus firms framewrk. The mdel fcuses n the supply side implicatins linking firms prductivity t quality chice and can be used t 4 The majr cntributins are Falvey and Kierzkwski 987, Flam and Helpman 987, Grssman and Helpman 99 and Murphy and Shleifer Hallak 2006 estimates destinatin-cuntry incme effects and find evidence supprting the hypthesis that richer cuntries have relatively high demand fr high quality. Chi et al reprt that the pairs f imprters whse incme distributins lk mre similar have mre eprt partners in cmmn and mre similar imprt price distributins. 3

15 answer many imprtant questins that have, s far, escaped the scrutiny f ecnmists. Fr instance, hw d vertical differentiatin and trade plicies interact t shape patterns f prductin and internatinal trade within an industry? Hw des trade liberalizatin affect the average quality f utput in a cuntry? Is there a systematic relatinship between firm level prductivity and prduct quality? The basic set-up f the mdel is brrwed frm Melitz 2003 and is etended t allw fr multiple market segments each characterized by a specific level f quality. In the mdel quality is defined as variatin in demand due t vluntary actins by the firm and uneplained by changes in price. 6 The cre f the mdel is relatively simple. After learning their prductivity, firms simultaneusly chse the price and quality f the gds they prduce. If the firm invests in an advanced technlgy and incurs relatively high fied and variable prductin csts, cnsumers classify the utput as high quality. As a result, the firm btains a favrable demand shift and can charge a relatively high unit price fr its utput. The mdel leads t endgenus srting f firms acrss market segments and predicts that, in equilibrium, the mst prductive firms chse t prduce high quality varieties. Intuitively, since within each market segment the increase in firm-level prfit is limited by the decreasing marginal utility f cnsumers, the gain frm a price reductin as firm prductivity increases eventually becmes less imprtant than the gain frm switching t a higher quality variety. As a result, highly prductive firms chse t acquire an epensive technlgy and prduce high quality prducts. 6 Fr eample, the increase in demand caused by an increase advertising ependiture is interpreted as quality. 4

16 Intrducing endgenus prduct quality decisins prvides a number f new results and helps recncile the thery with the bserved facts. Fr instance, in the etended mdel an increase in average firm level prductivity increases the average quality f utput such that, assuming firms in rich cuntries are generally mre prductive than firms in develping cuntries, the average quality f utput will be psitively crrelated with the cuntry s incme. Mrever, the etended mdel predicts a psitive relatinship between trade cst and average eprt quality a result akin t the shipping the gd apples ut paradigm described by Alchian and Allen 964. Bth predictins are ppsite t a benchmark mdel withut endgenus quality and are cnsistent with empirical bservatins. The ability f the mdel t replicate aggregate trade flw patterns hinges n assumptins abut the structure f cst in the industry. Essentially, the framewrk assumes that quality is cstly t prduce, which leads t a psitive relatinship between quality and prductivity. The bvius net step is t evaluate the empirical relevance f this assumptin. This is ne f the main bjectives f chapter 3. Since the mdel is built t replicate aggregate patterns, the analysis must g beynd cuntry level data and fcus n data at the prductin unit level t btain meaningful tests f the thery. Frtunately, the framewrk prvides many imprtant testable predictins. Fr instance, the mdel predicts psitive relatinships between unit price and prductin cst, between prductivity and quality and between eprt status and quality at the prducer level. The main difficulty in eplring the impact f vertical prduct differentiatin is that quality is nt directly bservable in general. Recent papers in the trade literature 5

17 use the average unit value, an estimate f price, t make inferences abut the rle f prduct quality in determining eprt patterns. 7 Hwever, this strategy ptentially leads t biased results. First, many factrs besides variatin in quality can lead t price dispersin. Fr instance, Syversn 2004 shws that variatin in reginal demand and cmpetitin are imprtant surces f price hetergeneity. 8 Secnd, price dispersin des nt necessarily capture the full etent f quality variatin. The mdel in chapter 2 clearly demnstrates that in the presence f vertical prduct differentiatin, prductivity affects price thrugh tw distinct channels. On the ne hand, prductivity leads t a decrease in marginal prductin cst, thereby decreasing the equilibrium price. On the ther hand, prductivity increases the quality f utput, which raises the marginal prductin cst and the equilibrium price. The verall impact f prductivity n price and, as a result, the relatinship between price and quality, depend n the underlying parameters f the mdel. Fr instance, in thse industries where price and quality are nly weakly psitively related, an increase in prduct quality will nt be reflected in price but rather in the quantity demanded. It thus seems imprtant t mve away frm unit value and t take int accunt the separate rles f prductivity and ther factrs affecting price dispersin when studying prduct quality. In the mdel quality is defined as nn randm variatin in demand uneplained by changes in price. These demand residuals are estimated fr U.S. manufacturing plants prducing in 25 five-digit standard industrial classificatin SIC industries 7 In particular, the recent studies f Hallak and Sivadasan 2008 and Kugler and Verhgen 2008 shw that the crrelatin between average unit value and eprt status is psitive. Manva and Zhang 2009 use unit value t study the impact f trade cst n eprt price. 8 Since this variatin demand des nt arise because f the firm s actin it is des nt enter the definitin f quality used in this study. 6

18 ver the perid using the residuals frm prducer level regressins f quantity n price cntrlling fr reginal demand and plant age. The estimated demand residuals are psitively crrelated with advertising and new technlgy ependitures and marginal prductin cst at the prducer level. These results suggest that demand residuals are nt randm but rather arise frm deliberate activities n the part f the plant aimed at increasing the cnsumer s valuatin f its utput. Using the demand residuals as a measure f quality, the study btains the fllwing prducer-level results: i Quality is psitively crrelated with unit cst and price n average; ii Prductivity is negatively crrelated with unit cst and price n average; iii Prductivity and quality are psitively crrelated n average; iv Quality is an imprtant determinant f the plant s eprt status. All f these findings are cnsistent with the mdel and suggests that vertical prduct differentiatin plays an imprtant rle in eplaining plant-level price and eprt status patterns. The secnd part f the empirical analysis uses the simulated methd f mment SMM t btain estimates fr the structural parameters and evaluate the ability f the mdel t reprduced bserved facts. The basic questin is the fllwing. Suppse that the best pssible values in a sense t be made precise fr the structural parameters are selected, hw well can the mdel reprduce patterns bserved in the data, such as the distributin f revenue acrss prducers r the share f eprters in the industry? If the mdel captures the essential behaviral characteristics f prducers, the simulated mments shuld be similar t the actual mments. Overall the mdel is able t replicate imprtant features f the data such as the standard deviatin in price and revenue and the distributin f industry revenue acrss plant. Further, the 7

19 estimated parameter values prvide evidence f the imprtance f vertical prduct differentiatin. T summarize, the dissertatin uses theretical, empirical and cmputatinal methds t study the rle f prduct differentiatin in shaping price dispersin and trade patterns. Overall the thesis demnstrates that the scpe fr quality differentiatin has an imprtant effect n the behavir f prducer and the characteristics f the industry and shuld nt be ignred. 8

20 Chapter 2: Theretical Results 2. Intrductin This chapter develps a theretical mdel that incrprates quality differentiatin int a hetergeneus firm framewrk. The mdel is used t analyze the impact f the quality margin n the relatinship between firm level prductivity, price and eprt status. The basic set-up is brrwed frm Melitz 2003 and is etended t allw fr multiple market segments each characterized by a specific level f quality. The etended mdel is based n tw reasnable assumptins: i hlding quality fied, an increase in prductivity decreases unit prductin cst, and ii hlding prductivity fied, an increase in prduct quality increases prductin cst. The quality f the utput is chsen endgenusly by the firms and depends n the technlgy emplyed in its prductin. Epensive technlgies are assciated with superir prduct quality and, as a result, higher demand cnditinal n price. The mdel leads t endgenus srting acrss prduct quality and predicts that, in equilibrium, high prductivity firms chse t prduce high quality gds. The intuitin fr this result is simple. On the ne hand, the marginal gain frm increasing sales by lwering price is limited by the decreasing marginal utility f cnsumers. On the ther hand, the marginal cst f prductin is decreasing in prductivity, thereby increasing the gains frm quality upgrading. Intrducing endgenus prduct quality decisins prvides a number f new results and helps recncile the thery with the bserved facts. In the benchmark 9

21 mdel withut quality, high prices are charged by firms with lw prductivity. Since a fied cst has t be paid in rder t sell in freign markets, these firms are unlikely t eprt. This implies that cuntries ppulated by relatively prductive firms will eprt lw unit value varieties, a predictin which runs against the bserved trade patterns. In particular, Schtt 2004 presents strng empirical evidence that unit value f U.S. imprts is increasing in the eprter s incme, and capital and skill abundance. In the etended mdel, varieties can be vertically differentiated at sme cst such that higher prices reflect, at least in part, higher quality. When firms are allwed t climb this quality ladder, the relatinship between prductivity and price is n lnger mntnic: the unit price is decreasing in prductivity within a given market segment but it is increasing in quality acrss segments. Since prducing high quality varieties is relatively cstly, nly the mst prductive firms are able t supply them prfitably t the market. As a result, in the etended mdel, an increase in average firm level prductivity increases the average quality f utput such that, assuming firms in rich cuntries are generally mre prductive than firms in develping cuntries, the average quality f utput will be psitively crrelated with the cuntry s incme. Imprtantly, this result is nt driven by cnsumer preferences but by changes in the firms prductivity distributin. The mdel is therefre a supply-side eplanatin fr the pattern f unit-value in trade flws described by Schtt Mrever, the benchmark mdel withut quality predicts that an increase in trade csts frces the marginally prfitable eprters ut f the freign market, thereby decreasing the average unit value f eprted varieties. Again, this predictin is 0

22 incnsistent with bserved characteristics f trade flws. Baldwin and Harrigan 2007, in their study f prduct-level data n bilateral U.S. eprts, reprt that distance has a very large psitive effect n unit values. In the etended mdel, trade liberalizatin decreases the average quality f a cuntry s eprts. This happens because trade liberalizatin leads t tugher cmpetitin by raising the prductivity threshld abve which firms decide t upgrade the quality f their prduct and increases the share f eprting firms. Tgether these results imply that a larger fractin f eprting firms prduce lw quality varieties in equilibrium. Therefre, the etended mdel predicts a psitive relatinship between trade cst and quality a result akin t the shipping the gd apples ut paradigm described by Alchian and Allen An imprtant crllary f this result is that trade liberalizatin, by increasing imprts f high quality gds, leads t an increase in the average quality f cnsumptin. This happens because the average quality f eprted gds is relatively high cmpared t the average quality f verall prductin. The rest f the chapter prceeds as fllws. The net sectin intrduces quality differentiatin amng hetergeneus firms in a clsed ecnmy setting. The equilibrium is then analyzed in detail in sectin 2.3. In sectin 2.4, the mdel is etended t a multi-cuntry trading wrld. Sectins 2.5 and 2.6 analyze the impact f trade and trade liberalizatin respectively while sectin 2.7 cncludes. Derivatin f majr results and prfs f prpsitins are presented in appendi A at the end f the dissertatin. 9 See Hummels and Skiba 2004 fr a recent empirical evaluatin f this cnjecture.

23 2.2 Clsed Ecnmy Mdel Cnsider an ecnmy cmpsed f a measure L f identical infinitely lived cnsumers each endwed with ne unit f labr per perid. Cnsumers have n taste fr leisure and inelastically supply their labr t the market at the prevailing wage rate. Therefre, in each perid, the labr supply is equal t L Preferences and Demand Cnsumers derive their utility frm the cnsumptin f varieties prduced in a single industry. The industry is interpreted as cnsisting f a narrwly defined prduct class that addresses specific needs and admits a fair amunt f differentiatin e.g. the autmbile industry. It is cmpsed f multiple vertically differentiated market segments characterized by a unique level f quality the precise meaning f which will be discussed at length belw within which prducers can develp hrizntally differentiated varieties. 0 In equilibrium, a measure X {X ω i,p} i N f cmmdities, defined n the set f quality r market segments, N and price p is available fr cnsumptin. The number f segments as well as the segment-specific quality levels ω are assumed t be cnstant ver time and egenusly i determined. Fr simplicity, the analysis cnsiders the case f tw market segments; which are called high quality ω and lw quality ω. H 0 The terms hrizntal and vertical have a different meaning here than in the multinatinal firms literature. In the current cntet, the firm s utput within a specific prduct categry is differentiated alng tw dimensins: hrizntal and vertical. Fr instance, cnsider the aut industry. Auts ehibit vertical differentiatin the Hnda Civic and Bentley Cntinental are nt directed at the same cnsumer base and hrizntal differentiatin within segment the Tyta Tercel cmpetes fr the same cnsumers as the Hnda Civic. 2

24 Preferences ver the differentiated varieties are additively separable with weights defined by the quality f the cmmdity. This implies that all varieties f the same quality and trading at the same price are cnsumed at the same rate. The cmpsite gd Q is a versin f the Diit and Stiglitz 977 aggregatr etended t allw fr substitutin between quantity and quality: Q = ω X ρ ρ q d /ρ, where q and ω represent the cnsumptin and the quality f variety. Since all cnsumers are identical and there is n asset accumulatin, there is n brrwing and lending. The ptimal level f cnsumptin f each cmmdity is chsen t minimize the cst f acquiring the aggregate Q, which implies that: q = RP ωp, 2 where R = PQ dentes aggregate ependiture, ρ > is the price elasticity f substitutin between varieties and P is the ideal aggregate quality-adjusted price inde, which is defined as: P Ψ i i {,H} = with i ωi Ψ p d. 3 X i Nte that Ψ i is negatively related t a weighted sum f varieties prices and psitively related t the segment s quality. It will be interpreted as the segment s price-adjusted quality inde. The representatin f preferences given in lends itself t the interpretatin f multiple segments within a single industry. Indeed, cnsumers see varieties f different quality as substitutes and, althugh they have a taste fr diversity, wuld be 3

25 fine with cnsuming, say, nly high quality varieties. The share f ttal ependiture n each f the segments is endgenus and the revenue in each segment can be epressed as fllws: R i = pqd = Xi Ψ Ψ i + Ψ H R, where X {X ω, p} is the mass f varieties f quality i available fr cnsumptin. i i Since the distributin f demand fr varieties acrss segments depends n the relative cmpetitiveness f each segment this characterizatin f preferences intrduces an additinal adjustment margin that allws cnsumers t influence the types f gds prduced in equilibrium. When the segment s price-adjusted quality inde Ψ is relatively high, the share f ependiture that ges t that particular segment will als be relatively high. Finally, all else equal, the preferences defined in imply that it takes a smaller mass f high quality varieties X than lw quality varieties X t attain a given level f utility. Hence, intuitively, cnsumers are willing t sacrifice diversity t btain quality. The ptimal demand schedule, defined in 2, reveals that the quantity demanded f each variety is decreasing in the price f the variety p and increasing in industry size R and aggregate price P all standard results in the Diit and Stiglitz 977 taste fr variety mdel. One difference, hwever, is the presence f the quality inde ω, which acts as a demand shifter. Cnditinal n price and industry characteristics P, Q and, the quantity demanded is increasing in the quality f the cmmdity if H i and nly if ω < ω H. This assumptin will be maintained fr the rest f the chapter. In limiting cases, when Ψ i Ψj ges t zer, nly varieties f quality j will be available in equilibrium. 4

26 2.2.2 Technlgy and Firm Behavir The quality f the utput depends n the technlgy used in its prductin. 2 Fr cnvenience, assume that nly tw technlgies are available: a basic r lw technlgy that can be acquired at lw fied cst f t prduce varieties f lw quality ω, and an advanced r high technlgy that can be acquired at high fied cst f H > f t prduce varieties f high quality ω H > ω. 3 In rder t btain tractable results, mild assumptins are impsed n these technlgies: First, the characteristics f bth technlgies are cmmn knwledge t all ptential entrants in the industry. Secnd, bth technlgies are available fr purchase t all firms. Thus, e-ante, each firm can ptentially enter either market segment. Third, cnditinal n technlgy chice, the quality f prductin is independent f ther firm-level characteristics. Hence, it is pssible t define a ne-t-ne mapping between the set f technlgies and the set f prduct qualities. Furth, the general frm f the ttal cst functin is the same fr bth technlgies and is given by: 2 A number f technlgy adptin mdels have recently been develped in an internatinal trade cntet. Fr instance, in a recent empirical study, Busts 2007 etends Melitz s mdel t allw firms t chse between a high fied cst, lw marginal cst technlgy and a lw fied cst, high marginal cst technlgy, and uses the framewrk t evaluate the impact f trade n technlgy upgrading and demand fr skilled labr. Yeaple 2005 cmbines technlgy adptin and labr frce hetergeneity t generate an endgenus distributin f firm prductivity. These mdels differ frm the current study n tw imprtant dimensins. First, in these studies the chice f technlgy has an impact n the prductin cst, but has n direct influence n the quality f the utput and the cnsumer s willingness t pay. Secnd, in the current study a high fied cst des nt lead t a lw marginal cst. Bth csts are increasing in quality. This assumptin fllws the industrial rganizatin literature starting with Spence When multiple technlgies can be used t prduce the same quality sme cmplicatins arise. Fr instance, cnsider the case when tw different technlgies can be used t prduce varieties f the same quality. T be relevant, the technlgy with the higher fied cst must be assciated with a lwer marginal cst. If this is the case, each technlgy will be perceived as the mst prfitable by a certain range f firms. Thse with lw prductivity will chse the lw fied cst, high marginal cst technlgy, while thse with high prductivity will chse the high fied cst, lw marginal cst technlgy. 5

27 ci Γ i f i q w = +, with f < fh and c < ch, 4 where the subscript i indees the technlgy, r equivalently the quality f prductin, is a measure f firm-level prductivity, and w is the cmmn wage rate hereafter nrmalized t ne. This frmulatin implies that, within each segment i, all firms share the same labr verhead cst f i, but the variable cst c i is decreasing in firm-level prductivity φ. This captures the idea that the acquisitin cst f each technlgy is the same fr all firms but that, as a result f efficient management, firms perated by high ability entrepreneurs will be better able t eplit the technlgy and achieve lwer marginal csts relative t firms managed by entrepreneurs f lesser ability. Finally, bth the fied and cnstant marginal cst f prductin are assumed t increase in quality such that prducing quality is cstly. Firms are assumed t be single-plant, single-prduct prfit maimizers. As a result, they will set marginal cst equal t marginal revenue. This leads t the fllwing cnditinal pricing rule: ci pi =. 5 ρ Thus, mill-pricing with a cnstant mark-up ver marginal cst is ptimal fr all firms. In standard Melitz type mdels firms have hetergeneus prductivity but quality is hmgeneus acrss firms and marginal csts are nrmalized t ne i.e. c i =. 4 As a result prices are given by p = ρ and mre prductive firms always charge lwer prices. In cntrast t the benchmark frmulatin, the etended mdel allws the 4 In the Melitz mdel higher prductivity can als be interpreted as prducing a higher quality variety at equal cst. The current framewrk eplicitly accunts fr bth dimensins. 6

28 schedule f unit prices t be increasing acrss market segments. Therefre, as lng as mre prductive firms prduce higher quality varieties and the effect f quality upgrading dminates the direct influence f prductivity n price, mre prductive firms will charge higher prices per unit. Using the pricing rule 5 and the ptimal demand schedule defined in 2, the firm s revenue as a functin f prductivity and quality can be epressed as: r i = RρP Ωi, where Ω i ici ω. 6 Hence, fr any given level f prductivity φ, revenue is increasing in the aggregate ependiture R and the aggregate price inde P. By definitin, the firm s segment specific prfit is the difference between its revenue and prductin csts, and can be epressed as: π r i i = ri Γ i = f i, 7 where the last equality uses equatins 4-6. Firms will prduce if and nly if prfits are nn-negative. Since prfits are increasing in prductivity there eists a prductivity threshld, i, abve which firms find it prfitable t prduce a variety f quality i. Specifically, let satisfy 0, s that frm 6 and 7: i πi i = f i i = ρp R Ω. 8 i This equatin indicates, in particular, that the prfitability cutff i is increasing in fied csts f i and decreasing in the segment specific cmpnent f revenue Ω i. Eamples f the prfit functins defined in 7 are depicted in Figure in, π space. S far, nthing precludes the pssibility that the prductivity cutff 7

29 fr the high segment is lwer than that f the lw segment as illustrated by H the curves { π, π H}. Similarly, it culd be the case that all firms prefer t prduce a lw quality variety as illustrated by the { π, π H} case. In bth cases every incumbent prefers the same market segment such that all varieties prduced and cnsumed in equilibrium are f the same quality. π π H π H π π H 0 H H f f H Figure : Prfit Functins and Prductivity Cutffs T make the mdel interesting, cnditins that rule ut such specializatin in ne market segment are required. The first step is t find the prductivity level H at which a firm is indifferent between prducing a lw r a high quality variety. Frmally, let the transitin prductivity cutff satisfy π = π s that H H H H frm 7 and 8: H =, with f H f Ω. 9 f Ω H Ω 8

30 This equatin clearly shws that the prductivity f the marginal firm in the high segment H is prprtinal t the prductivity f the marginal firm in the lw segment. Furthermre, the prprtinality factr,, is egenusly fied by the mdel s parameters and, as ne wuld epect, is increasing in the percentage change in fied cst frm upgrading frm the lw t the high quality segment, and decreasing in the assciated percentage change in revenue. By definitin bth qualities are prduced in equilibrium if and nly if >. This requires that tw cnditins are met: i the percentage difference in fied cst between high and lw quality is greater than the percentage difference in revenue, r equivalently Ω H Ω < f H f ; ii cnditinal n prductivity, the revenue earned in the high segment is greater than that earned in the lw segment, s that < Ω Ω. H If cnditin i is nt satisfied, < and every firm finds it ptimal t prduce in the high segment since the etra revenue earned frm upgrading mre than cvers the etra fied cst assciated with the higher technlgy. If cnditin ii is nt satisfied, the transitin prductivity cutff H is negative. In that case, the revenue earned in the lw segment is higher fr every firm and it is never ptimal t upgrade t the high technlgy. Revenue is increasing in quality nly if marginal csts are sufficiently insensitive t quality upgrading; frmally this requires that ch c < ω H ω. Hencefrth, cnditins i and ii are assumed t be satisfied such that: Assumptin. < Ω Ω < f f. H H 9

31 The presence f fied csts implies that firms will chse t prduce a unique variety, different frm the varieties prduced by all ther firms in the same segment. Mrever, since firms are prfit maimizers, they will prduce in segment j nly if segment j prvides them with the highest cnditinal prfit, frmally if { j i j: π π, fr i, j {, H}}, and if their revenue at least cvers the cst assciated with prductin in that segment, π 0. When varieties f bth qualities are prduced in equilibrium, firm behavir can be described as fllws: eit j if <, prduce a lw quality variety if [, H, and prduce a high quality variety if. This crrespnds t the π, π } case illustrate in Figure. H { H This sectin eplained hw vertical differentiatin intrduces a new adjustment margin available t the firm. Since within each segment the increase in firm-level prfit is limited by the decreasing marginal utility f cnsumers, as the firm becmes mre prductive the gain frm increasing sales by decreasing price becmes less imprtant than the gain frm switching t a higher quality market segment. As a result, highly prductive firms will chse t acquire an epensive technlgy and prduce high quality prducts Quality The cre assumptin f the abve framewrk is that firms can chse the psitin f their demand curve in the quantity-price space. By investing in an epensive technlgy and paying mre per unit prduced, firms effectively purchase a psitive demand shift which, fr simplicity, is called quality. In the current cntet, quality shuld therefre be interpreted as a cmprehensive vectr f variables, ther than 20

32 price, that have a direct influence n demand and that can be cntrlled r at least influenced by the firm. 5 These factrs can be classified in tw brad categries. The first includes intangible characteristics, such as the cnsumer s perceptin f the prduct, brand recgnitin, after sale service, warranty, reliability, r availability. The secnd includes tangible characteristics, such as better design r materials which increase the perfrmance and durability f the prduct. Bth types f characteristics increase the service flw btained frm the prduct, thereby raising the cnsumer s willingness t pay Industry Equilibrium This subsectin characterizes the ecnmy s equilibrium. Entry is assumed t be cstly as prduct develpment and prductin start up csts must be disbursed. The entry cst is the same fr all ptential entrants and is dented f e. Prir t entering the industry the firm des nt knw its prductivity. Thus, the value f the investment pprtunity is learned nly nce the fied entry cst is sunk and the firm learns its prductivity, φ, which is assumed t be a randm draw frm the distributin G n supprt Φ [,. Once the firm learns its prductivity, it can decide t eit the industry immediately r develp and prduce a variety in its preferred market segment. Since prfits are increasing in prductivity and firms stay in the industry nly if prfits are nn-negative, free entry determines a prductivity threshld belw which firms will decide t eit the industry. Given the assumptin n technlgy, less 5 Firms may be able t perfectly cntrl their ependitures n advertising but they cannt perfectly cntrl their impact n the cnsumers willingness t pay. 2

33 prfitable firms will chse t prduce lw quality varieties. The equilibrium prfitability threshld is therefre equal t the cutff fr the lw segment. The zer-prfit cnditin that determines this threshld is given by: π 0 r = f. 0 = Firms that draw an ability belw the prfitability threshld will eit the industry. Thse drawing ability abve will engage in prfitable prductin. Each perid prducing firms face a prbability δ f being hit by an egenus shck that will frce them t eit the industry. Hence, the value f the firm is zer if it draws a prductivity belw the prfitability threshld and eits, and equal t the stream f future prfits discunted by the prbability f eit if it draws an ability abve the cutff value and prduces. Since prfit is the same in every perid, the value f the firm, cnditinal n its prductivity, can be epressed as: π = t πh V ma 0, δ π = ma 0,, t = 0 δ δ where t is the time inde. The e-pst prbability density functin fr prductivity, µ, is cnditinal n successful entry and is truncated at the prfitability cutff. T btain clsed frm slutins sme structure needs t be put n the prductivity distributin. It is therefre assumed that prductivity is distributed Paret. 6 Therefre, the e-ante cumulative distributin functin is given by > ma{2, is G = where } 6 The Paret distributin is tractable and prvides a reasnable apprimatin t the actual prductivity distributin; see Cabral and Mata 2003 fr evidence. It is therefre widely used in the literature; see fr instance Helpman, Melitz, and Yeaple 2004 and Helpman, Melitz, and Rubinstein By definitin f the Paret distributin, an increase in the shape parameter decreases bth the mean and the variance f the prductivity and > 2 is required t ensure a finite variance. The assumptin that > is required t ensure a well behaved equilibrium. 22

34 a parameter that affects the shape f the distributin. Under these assumptins, the cnditinal e-pst distributin is given by: µ = 0 + if > therwise, while the prbability f successful entry in the industry is given by ζ e G =. There eists an unbunded set f ptential entrants in the industry. Firms will attempt entry in the industry as lng as the epected value frm entry is greater then the sunk entry cst f e. Since the characteristics f the e-ante distributin f prductivity G are assumed t be cmmn knwledge, the epected value f E entry V is identical fr all ptential entrants and is given by the prduct f the average incumbent s value π δ and the prbability f successful entry ζ e. As a result, the free entry cnditin can be written: ζ, with π π µ d. δ E e V π = fe = The specific prperties f the Paret distributin imply that the relative utput f high quality varieties prduced in equilibrium is unaffected by the value the prductivity cutff. 7 As a result, the average revenue f prducing firms is nt affected by the cutff either and can be epressed as a functin f preferences, technlgy and distributin parameters alne; see the appendi fr details: 7 Any cntinuus slice f the Paret is itself a Paret with the same shape parameter. It is this uncmmn prperty that makes the Paret s attractive. 23

35 r = Λf +, where Λ + ΩH Ω +. 2 Ω This equatin shws that the average revenue is increasing in the threshld revenue f and the percentage increase in revenue assciated with quality upgrading. Further, average revenue is decreasing in, the rati f threshld prductivities fr high and lw quality prductin, since a higher reduces the fractin f firms prducing high quality varieties. Using 7, the average prfit is given by: π = r π µ d = f, 3 where f = f + f H represent the average fied prductin cst and is defined as in 9. Taking 3 int accunt, the free entry cnditin can be epressed as a functin f nly ne endgenus variable, the prfitability threshld : π f 4 E V E π G, δ, = = δ e As illustrated in Figure 2, the epected value f entry is mntnically decreasing in the prfitability threshld. Thus, the free entry cnditin alne pins dwn the equilibrium value f the threshld as a functin f the parameters f the mdel. Frm 4, this threshld can be epressed as: = = Λ f + fh δfe δf e + π, 5 where and Λ are defined in 9 and 2 respectively. It can be shwn that: 24

36 Prpsitin. There eists a unique clsed ecnmy equilibrium. Prf: See appendi. The equilibrium prfitability threshld,, is increasing in average prfit and decreasing in the prbability f eit δ and the fied entry cst f e. A decrease in the prbability f eit increases the epected value f entry which, all else equal, increases the mass f entrants in the industry. Frm 3 this increase leads t a reductin in the price inde and, as a result, a decrease in firm-level revenue. This decrease in prfitability frces the less prductive firms t eit the industry, thereby increasing the equilibrium threshld prductivity and decreasing the epected value f entry, which returns t its equilibrium value f f e. E V f e E V 0 Figure 2: The Equilibrium Prductivity Threshld The equilibrium mass f prducing firms in the industry M can be btained by dividing the ttal revenue R by the average revenue r defined in 2 and can be 25

37 epressed as: + R M =, 6 Λf where Λ is defined in 2. It fllws that the equilibrium mass f incumbents is fied and prprtinal t the size f the industry R. The equilibrium threshld and mass f incumbents can be used t btain an epressin fr the equilibrium price inde defined in 3; see the appendi fr details: P f Λ = 7 ρ R θ where θ + + Ω + ΩH, and, Λ, and are defined in 9, 2 and 5 respectively. This epressin makes clear that the price inde is increasing in the markup /ρ but decreasing in the prductivity threshld and industry size R. Intuitively, when the markup is high all varieties are mre epensive whereas an increase in prductivity will decrease the quality adjusted price f varieties. An increase in industry size R will increase the number f varieties available fr cnsumptin which, because f cnsumers taste fr variety, decreases the price inde. By definitin, in a statinary equilibrium, every aggregate variable must remain cnstant ver time. This requires a mass f new entrants in each perid, such that the mass f successful entrants eactly replaces the mass f incumbents hit by the egenus shck and frced t eit. Frmally, this aggregate stability cnditin requires ζ e M e = δm. Nte that the equilibrium prductivity distributin will nt be 26

38 affected by this dynamic entry/eit prcess, since the successful entrants and failing incumbents have the same prductivity distributin. Finally, the labr used fr investment purpses by entrants must be reflected in the accunting fr aggregate labr and affects the aggregate labr available fr prductin. In equilibrium it must be the case that L + = L e Lp, where p L is the aggregate labr used by incumbents fr prductin purpses and L e dentes aggregate labr used fr investment purpses by prspective entrants. Aggregate payments t prductin wrkers must match the difference between aggregate revenue and prfit in every segment. Nrmalizing the wage rate t ne withut lss f generality, this implies that L p = R Π, where R and Π dente aggregate revenue and prfit, respectively. Mrever, aggregate payments t investment wrkers must satisfy L = M f. Using the aggregate stability cnditin ζ = δm, and the free e e e e M e entry cnditin π = δf e this implies that Le = Mefe = Mπ = Π. Then revenue must equal ttal payments t labr since R = L + L = L + Π L, s that revenue is p e p = egenusly fied by the size f the cuntry. The characterizatin f the unique statinary equilibrium in the clsed ecnmy is nw cmplete. The net sectin analyzes this equilibrium, cntrasts its implicatins with eisting mdels and highlights the mdel s nvel predictins related t prduct quality and endgenus technlgical chice. 27

39 2.3. Analysis f Equilibrium In this sectin, a number f imprtant prperties f the clsed ecnmy equilibrium are eplred. T emphasis the nvel implicatins f the additinal adjustment margin quality, assumptin is maintained thrughut the sectin. Mrever, sme f the results depend n the relatinship between the elasticity f substitutin and the shape parameter f the prductivity distributin. T btain well behaved results the fllwing additinal assumptin is required: Assumptin 2. >. Appendi A cntains an etensive discussin f this assumptin. When it fails t hld the mdel generates unintuitive results. Fr instance, the relative utput f the high t the lw quality segment utput is increasing in the transitin threshld prductivity Srting and Optimal Output As shwn in Figure, in equilibrium lwer prductivity firms chse t prduce lw quality varieties, while higher prductivity firms prduce high quality varieties. Intuitively, since higher prductivity firms face lwer marginal csts they can charge lwer prices and sell a larger number f units. This allws them t vercme bth barriers t quality: the increase in the fied cst f technlgy f and the increase in marginal prductin cst c. Prpsitin 2. There is endgenus srting f firms acrss quality such that higher prductivity firms chse t prduce high quality varieties. Prf: Direct frm assumptin. 28