A Model of Trade with Quality Choice. Robert Feenstra (UC Davis) and John Romalis (University of Chicago GSB) Draft: July 12, 2006

Transcription

1 A Model of Trade wth Qualty Choce. Robert Feenstra (UC Davs) and John Romals (Unversty of Chcago GSB) Draft: July 2, 2006 Very Prelmnary - Do ot Quote Results Rcher countres supply and demand hgher-qualty products. We study ths n an extended Hecscher-Ohln framewor on the supply sde wth a contnuum of ndustres, each wth dfferentated products produced under monopolstc competton. In addton to choosng prce, each frm n each country also smultaneously chooses qualty. The cost of producng goods of a gven qualty depends on factor prces. We employ the AIDS demand system to model consumer demand wth qualty and quantty multplyng each other n the utlty functon. We estmate ths system usng detaled blateral trade data and occupatonal wage data for over 00 countres for Our system dentfes qualty-adusted prces from whch we wll construct prce ndexes for mports and exports for each country. These prce ndexes have mportant applcatons. They drectly enable the calculaton of the terms of trade, and therefore they enable the calculaton of output-sde measures of real GDP (whch measure the producton possbltes of an economy) n addton to exstng expendture-sde measures whch are real expendtures adusted for the trade balance. The dfference between these two measures s essentally the terms of trade and these dfferences can be substantal for small open economes.

2 . Introducton The dea s to develop a model of trade wth qualty choce by frms. From recent emprcal wor by Peter Schott and Juan-Carlos Halla, we expect that rcher countres wll supply hgher-qualty products, and possbly also demand hgher-qualty products. We propose to study ths n an extended HO framewor, much le Romals (2004) on the supply sde. That s, there wll be a contnuum of ndustres wth Cobb-Douglas demand over these. Each ndustry has a number of dfferentated products, produced under monopolstc competton. In addton to choosng prce, each frm n each country wll also choose qualty, denoted by the vector z (we mght change ths to a scalar for convenence). In the notes below we do not dstngush the ndustres at all, but deal wth only a sngle ndustry. On the demand sde, consumers n each ndustry demand the dfferentated products, possbly wth a non-homothetc utlty functon. (We presume that two-stage budgetng s stll vald, n vew of the Cobb-Douglas assumpton across ndustres). In secton 2, we deal wth a general functonal form for utlty (also used n Feenstra, 2004, chapter 5), but whch has the specal condtons that: () qualty and quantty multply each other n the utlty functon; () frms choose qualty and prces smultaneously. Under these two condtons, we show that there s a strong separablty result: frm s choce of product qualty s ndependent of the ceberg transport costs, but wll depend on the margnal cost of provdng characterstcs. We can model ths as dependng on factor prce dfferences across countres, so country factor prces/endowments wll determne qualty. In secton 3 and 4, we begn to explore the specal case of an AIDS demand system. Ths s a specfc way to model non-homothetc demand that mght be useful. The translog functon

3 whch s a specal case of the AIDS when demand s homothetc has been used n monopolstc competton and trade model by Bergn and Feenstra (2000, 200), and extended to varyng numbers of products by Feenstra (2003) (see the Appendx here). That functonal form allows marups to vary, whch can be desrable n theory or for emprcal wor. These notes are openended and ust ndcate some progress to date. 2. Demand Model wth Qualty Suppose that there are =,, varetes of a dfferentated product. We use the ndex for products and also for the country of orgn for each product. Country need not send the same qualty to each country, however: the orgn country wll choose the qualty characterstcs to send to country. We wll suppose that the demand for the products n country arses from an aggregate utlty functon, gven by: U[f (z)c,...,f (z )c ], () z where c denotes the consumpton of each varety, =,,, and the functon f ( ) converts the vector of characterstcs z nto a scalar qualty f (z ), whch then multples consumpton. The functons f and U are common across destnaton countres. We suppose there are a general form of ceberg transportaton costs between the = countres, so that T T(z,d ) > unts of the good must be exported n order for one unt to arrve n country, where d denotes the dstance between the countres. otce that we are allowng the transportaton costs to depend on the qualty choce (you mght thn of nsurance costs as an example). We let p denote the f.o.b. prce receved by the frm n country, and then p nclusve the transportaton costs, the c..f. prce abroad s T.

4 Consumers n country are presented wth a set of =,, varetes, wth characterstcs z and c..f. prces T p, and then choose the optmal quantty of each varety. It wll be convenent to wor wth the qualty-adusted c..f. prces, whch are defned by p~ T p / f (z ). That s, the hgher s overall product qualty f (z ), the lower are the qualtyadusted prces p~. The aggregate consumer maxmzes utlty n (), subect to the budget constrant = T p c Y L = U[f (z. The Lagrangan for country s, )c,...,f (z )c ] + λ(y = T p c ) U(c ~ =,..., c~ ) + λ(y p~ c~ ), (2) = where the second lne of (2) follows by defnng c~ f (z ) c as the effectve qualty-adusted demand, and also usng the qualty-adusted prces p~ T p / f (z ). Ths re-wrtng of the Lagrangan maes t clear that nstead of choosng c gven prces we can nstead thn of the aggregate consumer as choosng p T and characterstcs z, c~ gven qualty-adusted prces =,,. Let us denote the soluton to problem (2) by (p ~ c~, Y ), =,,, where vector of qualty-adusted prces (the demand functons are common across countres). g(z prces Producng one unt of product wth characterstcs z requres margnal costs of p~ s the, w ), where w are factor prces n country. Frms smultaneously choose prces f.o.b. p and characterstcs y n country and exportng to country s z for each destnaton maret. Revenue receved from producng c T p = p y, where output s related to p~, consumpton by y = c T. Then profts from exportng to all destnaton countres are:

5 max p,z = [p g(z, w )]y = = p max,z max p~,z = = [T p~ p T g(z, w )]c T g(z, w ) c~ (q, Y ) f (z ) (3) The frst equalty n (3) converts from f.o.b. to c..f. prces, and the second equalty converts to qualty-adusted prces p~ and demands c~. The latter transformaton reles on our assumpton that prces and characterstcs are chosen smultaneously, as well as our specal functonal form n (), whereby qualty multples quantty. It s mmedate that to maxmze profts n (3), the frms must choose T(z,d )g(z, w ) / f (z z to mnmze ), whch s nterpreted as the c..f. costs per unt of qualty for the good that country send to. Then tang logs and mnmzng over the choce of characterstcs leads to the frst-order condtons, z f z (z f (z ) ) gz (z, w ) Tz (z,d ) = +,, =,,. (4) g(z, w ) T(z, d ) Thus, we obtan equalty between the relatve margnal utlty from each characterstc and ts relatve margnal cost, nclusve of transport costs, smlar to Rosen (974). Defne the soluton to mnmzng T(z,d )g(z, w ) / f (z ) as: mn h(w,d ) T(z, d )g(z, w ) / f (z ). (5) z Ths s the envelope of c..f. costs per unt of qualty, dependng on factor prces w and the dstances between countres. We can substtute ths expresson bac nto (3). Then to determne the optmal qualty-adusted prce p~, dfferentate (3) to obtan:

6 c~ [ p~ h(w, d )] 0 (p ~ c~, Y ) + =. =,,. (6) p~ We let ( p~, Y ) ln ~ c ~ (p ~, Y ) / ln p η denote the elastcty of demand from country varety sold n country. Then (6) can be re-wrtten as the famlar condton: η ( p, Y ) p = h ( w, d ), =,,. (6') η ( p, Y ) Recallng that p~ T p / f (z ), We can therefore solve for the c..f. prces as a log-lnear functon: ln(t p ) = ln f (z ) + ln h(w,d ) η ( p, Y ) + ln. (7) η ( p, Y ) In addton, notce that the transport costs are: = ln(t p ) ln(p ) ln T(z,d ). (8) 3. Emprcal Strategy Run (8) usng the dfference between c..f. mporter prces and f.o.b. exporter prces as the dependent varable. On the RHS we nclude dstances and exporter wages, snce the latter ndrectly affects the choce of characterstcs. From ths frst stage regresson we can get estmated transports cost ln Tˆ. Wrte the qualty-adusted c..f. costs h(w,d ) as a Cobb-Douglas functon over factor prces w, for factors =,,K. We allow the factors n country to each have ther own effcency level π, as n Trefler (993), so that the effectve factors prces are w /π. Usng

7 estmated transports cost costs can be wrtten as: ln Tˆ from ths frst stage regresson, and addng a year subscrpt t, the K θ h(w,d ) [ln w ln π ] + = t ln Tˆ t. (9) We model qualty as dependng on exporter fxed effects, a tme trend, and the dstance to the mporters: lnf( z t 2 3 ) δ + δ t + δ ln d. (0) Substtutng these n the c..f. prcng equaton, we get: ln(t t p t ) = δ + δ2t + δ3 ln d + K = θ [ln w t ln π ] + ln Tˆ t + ln[ η t /( η t )]. () In order to dentfy the factor effcences, we use the assumpton: K θ = πt = ρ0 + ρlnf( zt ) ε t. (2) In other words, the average effcency of factor s correlated wth the qualty of goods: goods of hgher qualty and produced by more productve factors. Substtutng (2) nto (), the prcng equaton becomes: ln p K ~ ~ ~ t = ρ0 + ( δ + δ2t + δ3 ln d ) + θ ln wt + ln Tˆ t + ln[ ηt /( ηt )] = + ε t, (5) where ~ δ ( ρ) δ and lewse for 2 ~ ~ δ, and δ 3. Intally (5) s estmated wthout the marup term on the RHS. To nclude that, we add a demand sde. The demand sde gves us addtonal power n dentfyng qualty from the nonhomothetcty of demand. In the next secton we explore the AIDS system, to see whether the

8 demand sde of ths equaton can help dentfy the qualty-adusted prces, and solve for the elastctes of demand that appear on the rght of (8). 4. Demand System The expendture needed n country to obtan a utlty level of U under the AIDS s: = 2 = = ln E(q, U ) = α + α ln q + γ ln q ln q + uβ (q ), (6) 0 where wthout loss of generalty we set γ =γ. The restrctons α = and = β = 0 ensure that E(q, U ) s homogeneous of degree one n q. Dfferentatng (6) wrt. s = α = ln q we obtan the expendture shares: β + γ q + uβ0β (q ) = = ln, =,,, 0 = = β γ = α + γ ln q + β ln(y / P ), (7) = where the second lne follows from (6) by denotng expendture as Y = E(q, U ), and defnng P as an aggregate of the prces: = 2 = ln P = α + α ln q + γ ln q ln q. (8) 0 otce that good s a luxury (necessty) as β >(<) 0, wth an expendture share rsng (fallng) n = = ncome, so the underlyng utlty functon s non-homothetc. If β = 0 for =,,, then (6) otce that the expendture shares defned n terms of qualty-adusted prces and quanttes, or unadusted prces and quanttes, are dentcal.

9 reduces to the translog functon. In the Appendx we summarze a few propertes of the translog system as the number of goods vares, drawng on Feenstra (2003). Worng wth (7) and (8), the elastcty of demand s: η d lns = d ln q γ = s s + β β ln(y s / P ) 2 γ + β ln(y / P ) = + β. (9) s Thus, once we have an estmate of the share equaton n (7), then the elastcty of demand can be computed as n (9), and substtuted bac nto the prcng equaton (5). 5. Estmatng Equatons wth Demand Re-wrte (7) whle ncludng the tme subscrpts as: t s = α + γ [ln(t p ) ln f (z )] + β ln(y / P ) = t t t ~ = α + γ ln(ttp t ) γ( δt ) + β ln(yt / Pt ), (20) ( ρ ) = = ~ ~ ~ where δ ( δ + δ t + δ d ) s the estmated qualty from (5). Thus, we estmate the share ~ t 2 3 t equaton usng observed prces on the rght, as well as the estmated qualty obtaned from (5). Then we adust the qualty terms by the coeffcent /(-ρ ) obtaned from (20), to obtan the ~ true qualty δ = δ /( ρ ). These are subtracted from the observed prces to obtan the t qualty-adusted prces. t The emprcal strategy for estmatng (5) and (6) wll be to estmate them teratvely. That s, we could begn wth the share equatons run on observed prces; then use those estmates t t

10 to obtan the elastctes of demand and run the prcng equatons; then return to the share equatons usng those estmates of product qualty, etc. Appendx: To smplfy ths system mpose symmetry of the coeffcents as follows, from the α = /, γ = γ( ) /, and γ = γ / for, wth, =,,. (2) Then the share equaton becomes: t γ ~ ~ t t t t t t t t. (22) ( ρ ) s = (/ ) γ[ ln(t p ) ln(t p )] + [ δ δ ] + β ln(y / P ) 6. Data Internatonal Trade Data Blateral trade values and quanttes at the 4-dgt SITC Revson 2 level are from BER-Unted atons Trade Data, Tarffs Blateral tarff data s from Jon Haveman s TRAIS extracts; the raw TRAIS fles obtaned from the World Ban s WITS ste; and tarff schedules scanned from the Internatonal Customs Journal. Tarffs are converted from the tarff-lne level to 4-dgt SITC Revson 2 level usng smple averages. Wages Industry wage data at the 3-dgt ISIC Revson 2 level are from UIDO ndustry wage data and the ILO yearboo, Tables 5A and 5B. World Development Indcators Data on populaton and GDP are from the World Ban World Development Indcators. 7. Results

11 Observed unt values are frst decomposed nto qualty and a qualty-adusted prce components usng the supply Equaton (5). The qualty and observed unt prces are then used n the demand Equaton (22) - n a sense the decomposton has to prove tself n the demand equaton. The frst ey parameter estmated n the demand Equaton (22) s γ - whch gves how mport share responds to observed prce movements, condtonal on qualty. A separate γ s estmated for each combnaton of mportng country and 4-dgt SITC Revson 2 product. The mean estmate for γ s -.04 wth the medan at The dstrbuton of γ estmates s gven n Fgure - over 90% of estmates are negatve. These estmates wll be used to calculate demand elastctes below. Fgure : How Import Shares Respond to Prces: Dstrbuton of Estmates of γ Densty gamma The coeffcents γ can be converted nto elastctes of demand η usng Equaton (9). The mean demand elastcty s estmated as 6.8, whle the medan s.5. The dstrbuton of demand elastcty estmates s gven n Fgure 2.

12 Fgure 2: Dstrbuton of Demand Elastcty Estmates Densty neta The second ey coeffcent estmated n the demand Equaton (22) s on the qualty varable n the demand equaton (the relatonshp between the qualty varable and true qualty s explaned above at Equaton (5)). The mean and medan estmate for how mport share responds to qualty s.0, and the dstrbuton s depcted n Fgure 3. Almost 90% of coeffcent estmates are postve - mport share responds postvely to estmated qualty. Fgure 3: Dstrbuton of Coeffcent Estmates on Qualty

13 Densty qgamma The dfference between the coeffcents on the observed prces and on the qualty varable allows us to estmate the coeffcent /(-ρ ) usng Equaton (20), allowng us to observe true qualty. These qualty estmates can then be subtracted from the observed prces to obtan qualty-adusted prces. The parameter ρ s also of drect nterest - our dentfcaton assumpton (2) says that factor-effcency s correlated wth the qualty of goods. Fgure 4 shows the dstrbuton of the parameter - two-thrds of estmates suggest that factor effcency s postvely correlated wth the qualty of the goods produced. It wll be possble to use the model to bac out factor-effcency estmates usng Equaton (4). Fgure 4: Assocaton Between Qualty and Factor Effcency

14 Densty rho 8. Qualty-Adusted Prces and Terms of Trade [Qualty-adusted prces wll be used to construct mport and export prce ndexes and terms of trade measures. These measures can be used to correct the PWT so that real GDP can also be measured as the growth n real output rather than ust the growth n real expendture - see Feenstra et al. (2006).] 9. Concluson We develop a supply and demand framewor that enables us to decompose observed unt mport and export prces nto a qualty component and a qualty-adusted prce component. We estmate ths system usng detaled blateral trade data and occupatonal wage data for over 00 countres for , and plan to extend ths bac to 962. Our system dentfes qualty-adusted prces from whch we wll construct prce ndexes for mports and exports for each country. These prce ndexes have mportant applcatons. They drectly enable the calculaton of the terms of trade, and therefore they enable the calculaton of output-sde measures of real GDP

15 (whch measure the producton possbltes of an economy) n addton to exstng expendturesde measures whch are real expendtures adusted for the trade balance. The dfference between these two measures s essentally the terms of trade and these dfferences can be substantal for small open economes.

16 Appendx Feenstra (2003) consders the translog functon as the number of goods vares. In prncpal, we should eep trac of reservaton prces for goods not avalable,.e. prces at whch demand s dentcally zero. But t turns out that eepng trac of reservaton prces can be smplfed by usng a symmetrc translog functon, by whch we mean that the parameters α are equal across goods, and the parameters γ, for, are equal across goods. In that symmetrc case, we can solve for the reservaton prces, and substtute them bac nto the expendture functon to obtan (omttng the country superscrpt): lne(q, U) 2 = = = a 0 + α ln q + γ ln q ln q + = where there s a parameters γ > 0 wth: ln U, (A) α = /, γ = γ( ) /, and γ = γ / for, wth, =,,. (A2) In other words, we can use the translog functon shown n (A)-(A2) wthout havng to explctly eep trac of reservaton prces: they are solved for n the bacground. Ths mght be useful f we extend the theory to the free-entry case. We wll later chec that smlar results holds for the AIDS system.

17 References Bergn, Paul R. and Feenstra, Robert C., Staggered Prce Settng and Endogenous Persstence, Journal of Monetary Economcs, 45, June 2000, Bergn, Paul R. and Feenstra, Robert C, Prcng to Maret, Staggered Contracts, and Real Exchange Rate Persstence, Journal of Internatonal Economcs, 54(2), August 200, Feenstra, Robert C., 995, Exact Hedonc Prce Indexes, Revew of Economcs and Statstcs, 78(4), Feenstra, Robert C. A Homothetc Utlty Functon for Monopolstc Competton Models, Wthout Constant Prce Elastcty, Economc Letters, 78, 2003, Feenstra, Robert C., Advanced Internatonal Trade: Theory and Evdence. Prnceton Unversty Press, 2004 Feenstra, Robert C., Alan Heston, Marcel P. Tmmer and Hayan Deng, Estmatng Real Producton and Expendtures Across atons: A Proposal for Improvng the Penn World Tables, mmeo., Unversty of Calforna, Davs, June Trefler, Danel, 993, Internatonal Factor Prce Dfferences: Leontef was Rght! Journal of Poltcal Economy, December, 0(6), Kremer, Mchael, 993, The O-Rng Theory of Economc Development, Quarterly Journal of Economcs, 08(3), August, Romals, John, 2004, Factor Proportons and the Structure of Commodty Trade, Amercan Economc Revew. Rosen, Sherwn, 974, Hedonc Prces and Implct Marets: Product Dfferentaton n Pure Competton, Journal of Poltcal Economy,