Estimating Cross-Country Differences in Product Quality

Transcription

1 Etimating Cro-Country Difference in Product Quality Juan Carlo Hallak Univerity of Michigan & NBER Peter K. Schott Yale School of Management & NBER PRELIMINARY September 20, 2005 Abtract We develop a methodology for decompoing countrie oberved export product price into quality veru quality-adjuted-price component. In contrat to the tandard approach of equating export price with quality, our methodology account for cro-country variation in product price induced by factor other than quality, e.g. comparative advantage or currency mialignment. Even though variation in quality-adjuted price i unoberved, it can be inferred from countrie trade balance with the ret of the world. Holding oberved export price contant, for example, countrie exhibiting trade urplue mut be offering higher quality (i.e., lower quality-adjuted price) than countrie running trade deficit. We implement the methodology by etimating the evolution of manufacturing product quality among the United State top 45 trading partner. Preliminary reult reveal ubtantial cro-ectional variation in product quality growth between 1980 and 1997 that i not apparent in export price alone. China and Ireland, in particular, experience relatively rapid gain in manufacturing quality. Keyword: Export Unit Value; Export Quality; Revealed Preference JEL claification: F1; F2; F4 Special thank to Alan Deardorff for many fruitful dicuion. We alo thank Keith Chen, Rob Feentra, Jame Harrigan, Jutin McCrary, Peter Neary, Serena Ng, Ben Polak, Marhall Reindorff and eminar participant at the LSE, Maryland, Michigan, NBER, Penn State, San André and NBER Summer Intitute for their comment and inight. 611 Tappan Street, Ann Arbor, MI 48109, tel: (734) , fax: (734) , hallak@umich.edu 135 Propect Street, New Haven, CT 06520, tel: (203) , fax: (203) , peter.chott@yale.edu

2 Etimating Cro-Country Difference in Product Quality 2 1. Introduction Theoretical and empirical reearch increaingly point to the importance of product quality in international trade and economic development. Cro-ectional variation in product quality i emphaied a an influential determinant of global trade pattern and international pecialiation 1, while quality upgrading i highlighted a a crucial dimenion of the development proce. 2 Unfortunately, relatively little i known about how countrie increae their product quality or which policie are more likely to foter it. A major impediment to reearch in thi area i the fact that reliable etimate of product quality do not exit for a wide range of countrie, indutrie and year. The purpoe of thi paper i to develop a methodology to obtain uch etimate. Reearcher typically confront the abence of quality meaure by contructing ad hoc proxie of quality. The mot common of thee meaure i a comparion of countrie oberved export price (unit value). 3 If good are differentiated horiontally a well a vertically, however, export price may vary for reaon other than their quality. Chinee hirt might be cheaper than Italian hirt becaue their feature are le deirable, but they may alo ell for le becaue China ha lower production cot or an undervalued exchange rate. The methodology developed here decompoe countrie oberved export unit value into quality veru quality-adjuted-price component. We define quality to be any tangible or intangible attribute that increae conumer valuation of a product. We extract etimate of countrie relative product quality by combining data on their oberved export price with information about conumer demand contained in their trade balance. The intuition behind our identification i traightforward: becaue conumer care about price relative to quality in chooing among product, two countrie with the ame export price but different trade balance mut have product with different level of quality. Among countrie with identical export price, the country with the higher trade balance i revealed to poe higher product quality. 4 We generalie thi intuition to a etting where countrie alo differ in term of the number of unoberved horiontal varietie they export in each product category. Accounting for unoberved horiontal differentiation i difficult becaue it introduce an additional factor 1 Flam and Helpman (1987) i repreentative of a theoretical line of reearch tudying how product quality affect trade pattern. The role of quality a a determinant of global trade pattern i addreed empirically by Schott (2004) and Hallak (2005). Cro-country and time-erie variation in product quality ha alo been linked to firm export ucce (Brook 2003, Verhoogen 2004), countrie kill premia (Verhoogen 2004), and quantitative import retriction (Aw and Robert 1986, Feentra 1988). 2 The contribution of quality growth to macroecomic growth i invetigated theoretically by Groman and Helpman (1991) and empirically by Hummel and Klenow (2005). 3 Unit value difference figure prominently in urvey of countrie quality competitivene (e.g., Aiginger 1998, Verma 2002 and Ianchovichina et al. 2003) and alo are often ued to ditinguih horiontal from vertical intra-indutry trade flow (e.g., Abed-el-Rahman 1991 and Aiginger 1997). More broadly, equating price with quality i often done in the computation of the U.S. Conumer Price Index (Bokin et al. 1998). 4 The ue of market hare to infer unoberved conumer valuation i well-etablihed in the indutrial organiation and index number literature (e.g. Berry 1994 and Bil 2004, repectively). Here, countrie net trade with the ret of the world (conditional on trade cot) i a natural expreion of their market hare.

3 Etimating Cro-Country Difference in Product Quality 3 beide quality that can increae conumer demand for a country product. Indeed, in the abence of horiontal differentiation, price variation i equivalent to quality variation becaue any difference in quality-adjuted price would be arbitraged away. All ele equal, conumer love of variety implie that countrie producing a larger number of varietie in a product category export larger quantitie and therefore exhibit higher trade urplue. Unle the number of horiontal varietie that countrie export i accounted for, thi increae in net trade will be interpreted, erroneouly, a higher product quality. 5 We pin down quality by auming a negative relationhip between quality-adjuted price and the number of varietie a country export. Thi aumption i jutified by recent theoretical finding in Romali (2004) and Bernard et al. (2005), who how that comparative advantage ector exhibit both relatively low price due to relatively low factor cot and a relatively high number of varietie due to diproportionate ue of factor input. The ue of countrie trade balance with the ret of the world to identify conumer demand impoe a practical contraint on the implementation of our methodology. Currently, the mot reliable time-erie information on countrie global net trade i recorded at the ector level. 6 A a reult, trade balance are tracked at a coarer level of aggregation than countrie export price, which can be oberved at a finer level of aggregation (i.e., at the product level) in U.S. import tatitic. 7 To deal with thi mimatch, we develop a theoretically appropriate price index of a country export product unit value within a ector. Thi index, which we denote the impure price index becaue it i contaminated by quality, can be decompoed into quality veru quality-adjuted-price component. We derive etimate of countrie quality relative to a numeraire country by ector and year under the aumption that each country product quality i contant acro all product in a ector. Thi aumption made neceary by the different level of aggregation at which export price and global trade balance are oberved create an aggregation trade-off in our methodology: while product quality i more likely to be contant acro product the more diaggregate i the ector, data on countrie global net trade become more carce, and meaurement error likely increae, with diaggregation. Our methodology ha three tep. Firt, we how that the bilateral impure price indexe, although unobervable, are bounded by obervable Paache and Lapeyre indexe defined over the countrie common export to a third country. Baed on thoe bound, we etimate an impure-price-index number for each country. Second, we demontrate that the quality-adjuted- (or pure- ) price component of countrie ectoral impure price indexe can be inferred from their ectoral trade balance with the world. In the finaltep,wetrip away the pure price component of the impure price index to etimate change in countrie 5 Feentra (1994) outline a methodology for computing import price indexe that account for the introduction of new product varietie. (See alo Broda and Weintein 2004). Given it focu on change in price over time, that methodology require no knowledge of cro-ectional variation in the number of varietie countrie export within product categorie o long a that number i contant over time for a ubet of countrie. 6 The mot diaggregate ector for which net trade information i available for a large et of countrie i a four-digit SITC indutry. In our preliminary reult below, we report reult for the more aggregate all manufacturing ector. 7 U.S. import are tracked according to roughly 20,000 ten-digit Harmonied Sytem product. By comparion, there are approximately 1000 four-digit SITC ector.

4 Etimating Cro-Country Difference in Product Quality 4 relative product quality over time. We report preliminary etimate of relative manufacturing product quality growth for the United State top 45 trading partner relative to numeraire country Switerland for the period 1980 to Thee reult reveal ubtantial variation in product quality growth acro countrie that i not apparent in export price alone. China and Ireland, in particular, experience relatively rapid gain in manufacturing quality. Thi paper focu on cro-ectional variation in product quality differentiate it from a very large index number literature devoted to contructing quality-adjuted cot-of-living indexe. Here, rather than meaure quality change in bundle of product purchaed over time, we eek to identify quality variation over imultaneouly purchaed bundle from different ource of upply. In addition, we aume no knowledge of product underlying attribute. A a reult, we are unable to make ue of tandard trategie uch a hedonic pricing that explicitly incorporate information on product characteritic that might be linked to pecific dimenion of quality. 8 Our methodology complement uch effort, however, becaue it ue of publicly available trade data permit etimation of product quality acro a broad range of countrie, indutrie and year for which urvey of product characteritic may be unavailable or prohibitively expenive to collect. 9 Ouranalyiimot cloely related to Hummel and Klenow (2005), who ue import price and quantitie to make inference about the cro-ectional elaticity of quality with repect to per-capita income and country ie. The methodology we develop here permit explicit etimation of product quality (relative to a numeraire country) by country, ector and year. An ability to decompoe export unit value into quality and quality-adjuted-price component i obviouly ueful for teting model of international pecialiation and development. It alo contribute to reearch in other field. In the productivity, growth and macroeconomic literature, quality adjutment i crucial for computing the import and export price deflator ued to contruct real national account aggregate. Current etimate of real GDP in the Penn World Table, for example, deflate nominal GDP uing a purchaing-power-parity deflator baed on final expenditure data, which may not be optimal for capturing change in countrie production over time becaue the latter require a term-of-trade adjutment (Feentra et al. 2004). An ability to net quality out of countrie import and export price indexe before performing the term-of-trade correction would enhance their accuracy. Development of country-ector pecific quality-adjuted price indexe may alo prove ueful in analying iue of public policy. The ditributional conequence of international trade implied by the Stolper-Samuelon theorem, for example, cannot be properly identified if the import and export price change ued to compute real wage do not properly account for change in countrie product quality. The remainder of the paper i tructured a follow. Section 2 outline our aumption about conumer demand and introduce the Impure and Pure Price indexe that will be the 8 Feentra (1995), for example, demontrate how information on product attribute can be ued to etablih bound on the exact hedonic price index. 9 The International Price Program of the U.S. Bureau of Labor Statitic contruct import and export price indexe by combining urvey data on firm price with firm aement about change in the quality of their product over time (Alterman et al. 1999).

5 Etimating Cro-Country Difference in Product Quality 5 focu of our analyi. Section 3 how that the unobervable Impure Price Index i bounded by obervable Paache and Lapeyre indexe. Section 4 derive the relationhip between the Pure Price Index and countrie ectoral net trade. Section 5 decribe how information on export unit value and countrie net trade can be combined to etimate country-ector quality indexe and preent preliminary empirical etimate. Section 6 conclude. 2. Preference and Price Indexe 2.1. Preference Thi ection decribe the preference tructure underlying our analyi and formally introduce the price and quality indexe that are the focu of the methodology. Good are claified into product categorie, which are in turn claified into ector. Sector are indexed by =1,...,S, while product categorie (within ector) are indexed by =1,...,Z. 10 There are C countrie, indexed by c =1,...,C. Preference are common acro countrie, and are repreented by a two-tier utility function that incorporate conumer love of variety. The upper tier i Cobb-Dougla, with expenditure hare b for each ector. The lower tier ha the following CES form 11 " 1/ϕ X X u = n c (ξ λ # c x c ) ϕ ϕ (0, 1). (1) c In the ubutility function (1), n c i the number of horiontally differentiated varietie of product produced by country c, andx c i the quantity conumed per variety. 12 Thi function include two utility hifter, ξ and λ c.thefirt hifter, ξ, varie acro product categorie but i contant acro countrie for a particular product category. It capture conumer common valuation of the eential characteritic that define heterogeneou varietie in a particular category (e.g. table veru chair). The econd hifter, λ c,varie acro countrie and ector, but i contant acro product within a particular country and ector. It repreent product quality and capture the combined effect of all product characteritic, other than price and thoe already captured by ξ, on conumer valuation of a good. Product quality encompae both phyical attribute (e.g. durability) and intangible attribute (e.g. product image due to advertiing). Thee aumption are formalied a follow: Aumption 1: ξ c = ξ, c =1,...,C. 10 In our empirical invetigation below, product categorie correpond to even-digit Tariff Sytem of the United State (TSUSA) and ten-digit Harmonied Sytem (HS) categorie, the finet poible level of aggregation. 11 To implify notation, ubindexe on ummation refer to all member of a et unle otherwie noted, e.g. P c and P c 0 both um over all countrie c =1,..., C while P c 0 6=c um over all countrie except c. For product categorie, P denote the um acro all product categorie in ector, =1,..., Z. 12 Note that by indexing product categorie intead of varietie, we implicitly aume ymmetry acro varietie in the ame product category.

6 Etimating Cro-Country Difference in Product Quality 6 Aumption 2: λ c = λ c, =1,...,Z. With the preference tructure defined by (1), product demand depend on qualityadjuted or pure price. Letting p c be the export price of a typical variety of product produced in country c, wedefine the pure price of that variety by ep c = p c /(ξ λ c ). The pure price i a quality-adjuted price. It i alo divided here by ξ for notational compactne, but none of the reult or their interpretation i affected by thi choice The Pure and Impure Price Indexe Before defining price indexe of quality-adjuted and quality-unadjuted price, we develop notation to keep track of countie unoberved number of varietie. Define n c to be the average number of varietie acro product categorie produced by country c (in ector ), n c = 1 X n c c =1,...C, (2) Z and define n to be the (country o normalied) world average number of varietie of product, n = 1 C X c n c n o n c =1,...Z. (3) The normaliation in (3) re-cale the number of varietie of each country into common, country-o unit, according to the ratio of the average number of varietie between o and c. Define alo en c to be country c exce variety in product relative to the world average, en c = n c n o n c n. (4) Note that exce variety ha the convenient property that P enc =0, c =1,...,C. Define an aggregator 13 of product price produced in country c and ector a P c = " X # 1 n ξ σ 1 (p c ) 1 σ 1 σ. (5) We define the Impure Price Index between countrie c and d a P cd = P c /P d. (6) The Impure Price Index i a ummary meaure of price variation between good produced by countrie c and d in ector. The index i impure in the ene that it i defined over price that are contaminated by quality. The index i tranitive, o that P cd P do = P co. 13 Thi type of price aggregator i often called a price index in the trade literature (e.g. Anderon and van Wincoop, 2004). We reerve the term index here for price comparion between countrie, in accordance with terminology employed in the index number literature.

7 Etimating Cro-Country Difference in Product Quality 7 Chooing country o a the numeraire country, we can aociate an index number, P co, with each country c, notingthatp cd can alway be recovered from the ratio P co /P do. In particular, the value of thi ratio i independent of which country i choen a the numeraire. The Impure Price Index can be decompoed into an index of quality and an index of pure price: P cd = P e cd λ cd, λ cd = λc λ d, P ecd P = e c ep d = X n (ep c ) 1 σ X n (ep d ) 1 σ The Quality Index, λ cd, between countrie c and d in ector i imply defined a the ratio of the two countrie quality level. The Impure Price Index and the Quality Index. The Pure Price Index i a ummary meaure of pure price variation between countrie, and it i alo tranitive. Combining etimate of countrie Impure Price Indexe with inference about their Pure Price Indexe derived from their global net trade, we ue the decompoition in (7) to identify countrie relative product quality. implicitly define the Pure Price Index, e P cd 3. Bounding the "Impure" Price Index The bilateral Impure Price Index defined in the previou ection cannot be oberved becaue it depend upon unobervable uch a the number of varietie exported by the country pair and the elaticity of ubtitution. In thi ection we outline a et of aumption which allow the Impure Price Index to be bounded by obervable Paache and Lapeyre indexe defined over the two countrie common export to a third country. In Section 5, we demontrate how overlapping bilateral bound acro country pair can be ued to identify Impure Price Indexe for all countrie (relative to a numeraire country) Contrained Expenditure Function In thi ection, we focu on countrie export to a ingle common importer, which we refer to a the United State given the focu of our empirical examination below. The analyi would be identical were it to be applied to any other common importer. We define a country a active in product if it report poitive export to the United State in that category. Let I be the et of all product categorie in ector, andleti c be the ubet of active categorie in country c. Define vector p to include the U.S. import price of all active categorie in ector from all countrie. Define analogouly vector q, n, λ, and ξ. A vector of per-variety conumption x i implicitly defined by q and n. Finally, tack thee vector acro ector to form vector p, q, n, λ, ξ, andx. Since our methodology i baed on comparing import price (a meaured by unit value) acro pair of U.S. trading partner, we need to ue notation pecific tocountrypair. 1 1 σ Index countrie in a pair of U.S. trading partner by c and d. Denote by I cd active categorie common to c and d in ector. Z cd Denote alo by I c, d (7) the et of i the number of uch categorie. the et of the et of product in which c i active but not d, byi d, c

8 Etimating Cro-Country Difference in Product Quality 8 product in which d i active but not c, andbyu cd the union of thee two et. Finally, cd i the et of product in which neither of the two countrie i active. The et I can be partitioned into I cd, U cd,and cd. We can ue I cd tobreakeachofvectorp and q into two component. Firt, alternatively for each i = c, d, p i (cd) and qi (cd) include price and quantitie, repectively, of export by i of product in categorie I cd. The remaining part of p and q are denoted by p i (cd) and q i (cd). Thee vector include categorie Icd exported by all countrie other than i, and alo categorie / I cd exported by all countrie (including i). 14 For a pair of exporting countrie c and d, wenowdefine the contrained expenditure (or import) function m c (cd) (pi (cd), q c (cd), n, λ, ξ,u). Thi function repreent the minimum expenditure that the repreentative conumer in the U.S. would be required to pend on varietie exported by country c in categorie I cd in order to attain utility level U when import price of thoe varietie are p i (cd), if thi conumer i contrained to conume quantitie q c (cd) of all other product, and the number of varietie, quality, and product hifter are, repectively, n, λ, ξ. The contrained expenditure function olve the problem min q c (cd) p i (cd) qc (cd).t. U(q c (cd), q c (cd), n, λ, ξ) =U, i = c, d (8) where U(.) i the repreentative conumer utility function. 15 By revealed preference, the minimum import expenditure on product produced by country c in categorie I cd, when import price of thoe product are p c (cd) while q c (cd), n, λ, ξ, and U take their uncontrained equilibrium value, i the oberved amount of import: m c (cd) (pc (cd), q c (cd), n, λ, ξ,u) =pc (cd) qc (cd). (9) However, when price are p d (cd) intead of pc (cd), the minimum import expenditure i equal to or lower than p d (cd) qc (cd), becaue the amount pd (cd) qc (cd) i ufficient to attain utility U but q c (cd) i not necearily optimal given pd (cd).hence m c (cd) (pd (cd), q c (cd), n, λ, ξ,u) pd (cd) qc (cd). (10) Taking the ratio of (9) over (10), we obtain M(cd) c = mc (cd) (pc (cd), q c (cd), n, λ, ξ,u) m c (cd) (pd (cd), q c (cd), n, λ, ξ,u) p c (cd) qc (cd) p d (cd) qc (cd) = H cd. (11) Equation (11) diplay a tandard reult in index number theory tating that the cot-ofutility price index M(cd) c i larger than a Paache price index, Hcd,definedhereinacroectional rather than a time-erie context. The left hand ide of (11), M(cd) c,capturethe 14 The term in parenthei in the ubindex denote the ubet of product within ector in which countrie c and d export in common to the U.S., i.e. ª : I cd. 15 Neary and Robert (1980) and Anderon and Neary (1992) ue the contrained expenditure function to analye conumption choice under rationing.

9 Etimating Cro-Country Difference in Product Quality 9 change in minimum expenditure on country c varietie (in categorie I cd )thatwould be neceary to maintain utility U, if import price of thoe varietie changed from p d (cd) to p c (cd), holding contant their number and characteritic (including quality), and the number, characteritic and quantity conumed of all other good. The right hand ide of (11), H cd, i a Paache price index defined over the oberved price of the country pair common export to the U.S. in ector. Similarly, we can focu on import from country d to obtain M(cd) d = md (cd) (pc (cd), q d (cd), n, λ, ξ,u) m d (cd) (pd (cd), q d (cd), n, λ, ξ,u) where L cd p c (cd) qd (cd) p d (cd) qd (cd) = L cd, (12) i a Lapeyre price index defined over the country pair common export to the U.S. in ector. Thi i another tandard reult, which tate that the cot-of-utility index M(cd) d i bounded from above by a Lapeyre price index.16 Given that the Cobb-Dougla form aumed for the upper tier of the utility function i eparable into ectoral CES ubutility indexe u, the contraint in problem (8) can be rewritten a U(q c, q c, n, λ, ξ) = Y 0 u b 0 0 = U. (13) The value of all ubutility indexe for ector other than are contant, a their argument are held contant in problem (8). Therefore, contraint (13) determine the minimum value of u that i required to attain utility U, conditional on the (fixed) value of the ubutility indexe for the other ector: U u = Y 0 6= u b0 0 Since we focu on expenditure (import) only on varietie produced by country c in categorie I cd, it i convenient to rewrite the ubutility function for ector a u = X 1/ϕ n c (ξ λ c x c ) ϕ + bu, bu = X n c (ξ λ c x c ) ϕ + X X n k k6=c I I cd / I cd (14) ³ ξ λ k x k ϕ.(15) The firt term on the right-hand ide of thi expreion repreent the utility from categorie imported from country c in ector that are not alo imported from country d. The econd term capture the utility from good imported from all other countrie (including d) inany category in ector. Subtituting (15) into (14), and after ome algebra, we obtain ϕ 1/ϕ X U I cd n c (ξ λ c x c ) ϕ 1/ϕ = Y 0 6= u b0 0 bu u. 16 Paache and Lapeyre indexe are typically defined in a time erie context, where there i a natural ordering of time period. Since there i no natural ordering of countrie in a multilateral context, calling one of thee indexe Paache and the other one Lapeyre rather than vice vera i arbitrary.

10 Etimating Cro-Country Difference in Product Quality 10 Then, we can rewrite the problem in equation (8) that define the contrained expenditure function a X min n c x p i x c c.t X n c (ξ λ c x c ) ϕ 1/ϕ = u, i = c, d. I cd I cd The olution to thi problem i the product between a CES aggregator meauring the unit cot of utility and the target level of utility, u 17 m c (cd) (pi, q c, λ, ξ,u) = X I cd n c µ ep i λ i λ c 1 σ 1 1 σ u. (16) We can now obtain an explicit expreion for M(cd) c in equation (11): P M(cd) c = P I cd I cd n c n c (ep c ) 1 σ ³ ep d λ d λ c 1 σ 1 1 σ = e P cd λ cd P P I cd I cd n c ³ ep c e P c n c ³ ep d ep d 1 σ 1 σ 1 1 σ (17) Taking logarithm on both ide of (17) and uing the fact that P cd combine thi equation with (11) to obtain ln H cd ln M c (cd) =lnp cd +lnφ c, φ c = P P I cd I cd n c ³ ep c e P c n c ³ ep d ep d 1 σ 1 σ = P e cd λ cd,wecan 1 1 σ. (18) Similarly, an expreion analogou to (17) can be obtained for M(cd) d, which combined with (12) yield 18 ln L cd ln M d (cd) =lnp cd +lnφ d, φ d = P P I cd I cd n d ³ ep c e P c n d ³ ep d ep d 1 σ 1 σ 1 1 σ. (19) 17 It i here where Aumption 1 and 2 are critical. In equation (16) we ue thee aumption to derive p i = pi λ c λ i ξc λ i ξi ξi λ c ξc λ i = ep i, i = c, d. λ c 18 Note that all price (oberved and pure) conidered up to now in thi ection are import price. Since trade cot are aumed contant acro product categorie within a ector, the indexe can be alternatively defined in term of export price, if they are appropriately M c (cd),m d (cd),h cd,l cd caled by the factor τ cus. A a reult, the inequalitie in equation (18) and (19) alo hold if the indexe τ dus are definedoverexportprice.weuethelatterdefinition for the indexe in the remainder of the paper.

11 Etimating Cro-Country Difference in Product Quality 11 Equation (18) and (19) relate the implication of conumer cot minimiation to croectional Paache and Lapeyre price indexe, where each of the cot-of utility indexe ha obervable bound on jut one ide. Our conideration of two cot-of-ultility indexe, a well a the one-idedne of their bound, differ from the tandard bounding of cot-ofutility indexe from both above and below found in the index number literature. Here, inceweallowforhoriontaldifferentiation, we mut deal with two cot-of-utility indexe becaue M(cd) c and M (cd) d are defined over different number of varietie, i.e., nc and n d, repectively. 19 A a reult, φ c and φ d are alo different. Under plauible aumption decribed below, however, we can how that ln φ c < 0 and ln φ d > 0, which implie that the Paache and Lapeyre indexe bound the Impure Price Index, i.e., ln H cd ln M(cd) c ln P cd ln M(cd) d ln Lcd Paache and Lapeyre Bound on the Impure Price Index Before decribing the main reult of thi ection, we develop additional notation pecific to country pair. For each pair of countrie c and d, define the pair (o normalied) average number of varietie in product category : bn cd = 1 2 µ n o n c n c + no n d n d, (20) and the country pair (o normalied) multilateral exce variety in product relative to the world average: = bn cd n. (21) Multilateral exce variety meaure the extent to which the average number of varietie in countrie c and d i above or below the world average. Alo, for each country i = c, d in the country pair, define i (o-normalied) bilateral exce variety in product relative to the country-pair average, en cd en i,cd = no n i n i bn cd. (22) Bilateral exce variety meaure the extent to which the number of varietie in a country i above or below the bilateral average. Thee meaure of exce variety poe three convenient propertie: X X en i,cd =0, en cd =0, en c,cd = en d,cd (23) The firt and econd propertie indicate that, acro product categorie within country i, both bilateral and multilateral exce variety um to ero. The third property reveal that two countrie cannot both have poitive bilateral exce variety in the ame category. 19 M c (cd) and M d (cd) would be equal, for example, if the number of varietie in countrie c and d were proportional to one another for every product category.

12 Etimating Cro-Country Difference in Product Quality 12 Define the bilateral difference in two countrie pure price in product category relative to their countrie pure price aggregator a Ã! ep cd ep c 1 σ Ã! ep d 1 σ =. (24) ep c ep d A poitive ep cd indicate that country c ha a lower pure price of (relative to the price aggregator) than country d. A lower pure price may arie, for example, due to comparative advantage, i.e., variation in exporter relative production efficiency or factor cot. Finally, for et of product A, define the ample covariance over that et of product a cov A (x, y) =(1/Z A ) P A (x x)(y y), wherez A i the number of element in A. We now lay out a et of ufficient condition for the Impure Price Index to be bounded by obervable Paache and Lapeyre price indexe. Aumption 3 tate that country c relative to country d will tend to have poitive bilateral exce variety in thoe product in which it ha a lower relative pure price. Aumption 3: cov I cd ³ en c,cd, ep cd = cov I cd ³ en d,cd, ep dc 0 Thi aumption i baed on the reult of theoretical model of international trade with product differentiation that do not aume factor price equaliation (e.g., Romali 2004, Bernard et al. 2005). Thee model find that, acro good, the relative number of varietie between two countrie i a negative function of the countrie relative price. Thi finding upport the intuitive notion that countrie hould have a relatively higher (lower) number of firm in ector or product categorie in which they are relatively more (le) competitive, i.e. thoe ector with relatively lower (higher) price. It i poible to reformulate thee model in term of quality-adjuted variable. Thu reinterpreted, thee model predict that the relative number of varietie in a ector or product category i a negative function of relative pure (or quality-adjuted) price. Aumption 4 impoe the retriction that there i no correlation between the countrypair multilateral exce variety and bilateral difference in pure relative price. Aumption 4: cov I ³en cd, ep cd =0 Thi aumption i not very trong, a there i no obviou relationhip between the country pair exce variety relative to the world average and relative comparative advantage among countrie within the pair. Aumption 5 require that countrie c and d be imilarly active in exporting good to the United State. Aumption 5: δ cd = δ dc δ cd = =0,where P U cd en c,cd 1 Z cd P I cd P I cd n c µ ep cd + ep d ep d P U cd bn cd epcd 1 σ, and

13 Etimating Cro-Country Difference in Product Quality 13 δ dc i defined analogouly. The magnitude of the term δ cd and δ dc depend on the extent to which countrie c and d are imilarly active. Aumption 5 require that thee term are ero. A ufficient condition that implie aumption 6 i that the two countrie are active in the ame categorie. In that cae, the numerator in the expreion for δ cd iero,aitumoverelementofan empty et, U cd.sincetheuminthenumeratorinvolvepoitiveandnegativeterm,iti till poible that the numerator i ero even if U cd i non-empty. More generally, δ cd and δ dc will tend to be maller (in abolute magnitude) the maller i the number of mimatched active categorie (in the numerator) relative to the number of matched active categorie (in the denominator). Alo, ince ep cd > 0 and en c,cd > 0 for I c, d,and ep cd < 0 and en c,cd < 0 for I d, c, thee term will tend to be maller the more imilar i the number of product in I c, d to the number of product in I d, c. With aumption 3, 4 and 5 a well a our earlier aumption about conumer utility, Propoition 1 demontrate that a country pair unobervable Impure Price Index i bounded by the obervable Paache and Lapeyre indexe defined over their common export to a third country. Propoition 1 Under Aumption 1 through 5, for any two countrie c and d, the(unobervable) Impure Price Index i bounded by the(obervable) Paache and Lapeyre indexe: ln H cd ln P cd ln L cd Proof. See Appendix. Thi finding provide the bai for our etimation of the Impure Price Index in the firt-tage of our empirical trategy. 4. Net Trade a Indicator of Pure Price Variation Thi ection derive the theoretical relationhip between countrie net trade and their Pure Price Indexe Net trade a a function of pure price Exporting good from country c to country c 0 require paying iceberg trade cot of τ cc0 Therefore, p c τ cc0 i the import price of product in country c 0. Given the CES preference tructure aumed in (1), it i eay to derive country c bilateral export and import flow (in ector ) with every other country c 0. Summing export flow over c 0 6= c, we can obtain the value of country c export, Export c = X X c 0 6=c n c ³ ep c τ cc0 1 σ (G c0 ) 1 σ. b Y c0 (25)

14 Etimating Cro-Country Difference in Product Quality 14 where Y c0 i the income of country c 0, σ =1/(1 ϕ ) > 1 i the elaticity of ubtitution, and " # X X ³ 1/(1 σ) G c0 = n c00 ep c00 τ c00 c 0 1 σ (26) c 00 i a conumption-baed price aggregator capturing the impact of trade barrier on conumer in country c 0. Note that the export of country c are decreaing in τ cc0 and increaing (via increae in G c0 ) in the cot of hipping good to country c 0 from all other countrie c 00. The expreion in bracket in equation (25) i country c hare in country c 0 ectoral expenditure, b Y c. Thi hare doe not depend on price and quality level independently of one another, but only on the ratio of the two, ep c. 20 In a imilar manner, we can obtain the value of country c import, ³ 1 σ Import c = X X n c0 ep c0 τ c0 c " c 0 6=c (G c ) 1 σ b Y c = 1 X # n c (ep c ) 1 σ (G c ) 1 σ b Y c. (27) Subtracting equation (27) from equation (25), we obtain country c global net trade in ector, T c, a a proportion of it expenditure in the ector, ³ 1 σ 1 T c b Y c = 1+X X n c ep c τ cc0 Y c0 c 0 (G c0 ) 1 σ Y c, (28) Equation (28) how that countrie trade balance in ector i a function of all the productlevel pure price in that ector. Our objective i to implify thi expreion by relating net trade of country c in ector to the Pure Price Index Net trade a a function of the Pure Price Index To expre equation (28) a a function of the Pure Price Index, we mut impoe tructure on the relationhip between pure price and number of varietie countrie produce. Note, however, that our methodology doe not require that we identify the economic force that determine pure price in equilibrium. Variation in pure price can be driven by traditional ource of comparative advantage, or it can be the reult of macroeconomic condition, uch a over- or under-valued currencie. Baed on the ame theoretical reult that motivate Aumption 3, we potulate a imilar negative relationhip between number of varietie and pure price, defined here acro ector rather than acro categorie within ector. Aumption 6: n c /Y c n o /Y o = ³ η ep co, c =1,...,C, η > We can aociate and infinite price ep c with a product that i not produced in country c. Since pure price are elevated to a negative exponent, thi product will have no effect on the volume of trade or the price aggregator.

15 Etimating Cro-Country Difference in Product Quality 15 A particular cae of thi aumption i when η =0, in which cae the average number of varietie in a ector i a contant proportion of income. More generally, the number of varietie here i allowed to decreae a pure price increae. We alo characterie the relationhip between pure price and number of varietie acro product categorie within ector a the um of a common component acro countrie (V ), and a mean-ero, countrypecific idioyncratic component ³ 1 σ cov en c, ep c / P e c = V + θ c, (29) but we do not need to impoe aumption on thi covariance. The objective of thi ection i to derive an expreion relating net trade at the ectoral level to the value of the Pure Price Index. Since net trade alo depend on trade cot, we alo want thi expreion to depend on ummary meaure of trade cot in the ector. To that end, we define ome additional variable. Let y c = Y c / P c 0 Y c0 be the hare of country c inworldincome,andletr c = 1/G 1 σ P nc (ep c ) 1 σ be the hare of country c in the term (G ) 1 σ = P P ³ 1 σ, c 00 nc00 ep c00 which i common for all countrie and i thu denoted omitting the country upercript. In the free-trade equilibrium with thoe pure price and number of varietie, r c i alo the hare of country c in world expenditure (in ector ). We define a ummary meaure of outbound trade cot for country c a τ c,out = X c 0 y c0 ³ τ cc0 1. (30) The outbound average trade cot i a weighted average, acro countrie, of the bilateral cot of exporting from country c to other countrie (including itelf). The following Propoition decribe the main reult of thi ection. Propoition 2 Under Aumption 6, country c ectoral net trade can be approximated (via a Taylor expanion) a a linear function ofthepurepriceindexandthicountry outbound average trade cot, T c /Y c ' Ψ + γ ln P e co + γ μ τ c,out + b Z θ c, (31) ³ 1 σ γ =(1 σ η )b < 0, Ψ = b ln (Y o )+ln ep o + A + Z V, μ = (σ 1) (σ +η 1) > 0, A =ln X Y c 0 (G c0 c 0 ) +(σ 1 σ 1) X X ³ r c00 y c0 τ c00 c 0 1 c 0 Proof. See Appendix. Propoition 2 provide a imple expreion for the relationhip between net trade, pure price and trade cot. It formalie the idea that the urplu in a country ectoral net trade hould be larger the lower are it pure price. In addition to pure price, trade cot alo influence net trade. In particular, conditional on pure price, higher outbound trade barrier for country c imply a more negative trade balance. c 00

16 Etimating Cro-Country Difference in Product Quality 16 Equation (31) doe not include an expreion for inbound average trade cot due to our ue of a Taylor approximation around a free-trade equilibrium. For intuition regarding the abence of inbound trade cot, uppoe that under free trade country c impoe a bilateral tariff on the import from one country. That tariff ha an obviou negative impact on the net trade of the targeted country, which i captured by an increae in the targeted country outbound average tariff. On the other hand, the impoition of thi tariff raie the market hare of all other countrie elling in the dometic market (including c) via an increae in the price index G c. Note that country c benefit from it tariff increae a much a it would benefit from a tariff increae in any other country with the ame income. Thi ymmetry i due to the fact that under free trade country c ha the ame market hare in each country. For the ame reaon, foreign countrie benefit from country c tariff a much a they would benefit from a tariff increae in any other country with the ame income (including themelve). The improvement in the non-targeted countrie net trade i captured by an increae in the term A S, which i contant acro countrie. A increae for the targeted country a well, but in thi cae the increae in net trade i more than offet bythenegativeimpactofthetariff (via an increae in the outbound average trade cot). 21 The effect of trade cot on net trade characteried in Propoition 1 are conditional on pure price. Thi implie that, while they appropriately adjut the relationhip between net trade and pure price, they do not provide a comparative tatic aement of the impact of trade cot on net trade. Change in thoe cot will typically affect pure price in general equilibrium, implying an indirect effect on net trade not captured in equation (31). Equation (31) can be interpreted a a relative demand function, where net trade i the quantity variable, the Pure Price Index i the price variable, and the trade cot are demand hifter. The firt term capture movement along the demand curve: higher pure price of country c in ector are aociated with a worening of thi country net trade poition in that ector. The econd term capture movement of the demand curve. Conditional on pure price, higher outbound trade cot hift thi curve to the left. Before concluding thi ection, we note that our aumption of contant quality and elaticitie of ubtitution acro product categorie within ector highlight an aggregation trade-off in our methodology. While thee aumption are more likely to be atified for more diaggregate ector, data on countrie global net trade become more carce, and meaurement error likely increae, with diaggregation. 5. Empirical Implementation and Reult In thi ection we ue the reult of Propoition 1 and 2 to etimate product quality for the United State top trading partner. Our etimation trategy proceed in two tage. In the firt tage, baed on the reult of Section 3, we ue data on export unit value and quantitie to derive an etimate of each country Impure Price Index. In the econd tage, uing the reult of Section 4, we ue information on countrie global net trade and trade 21 Away from the free-trade equilibrium, inward tariff hould have a higher impact on the net trade of the country impoing it, a thi country command a higher relative market hare in the dometic market. In our empirical analyi, we control for inbound tariff to capture thi effect.

17 Etimating Cro-Country Difference in Product Quality 17 cot to infer movement in countrie pure price, and trip thee movement away to extract etimate of product quality from the firt-tage reult. We begin by decribing our data ource and outlining our etimation trategy. We then preent Quality Index etimate for the All Manufacturing ector Data The firt tage of our etimation require product-level export price for every country. Thee price are derived from product-level U.S. import data available from the U.S. Cenu Bureau and compiled by Feentra et al. (2002). The databae record the cutom value of all U.S. import by ource country from 1972 to Import are recorded according to thouand of finely detailed even-digit Tariff Sytem of the United State (TSUSA) categorie (1974 to 1988) and ten-digit Harmonied Sytem (HS) categorie (1989 to 2001). We focu here on product in All Manufacturing, i.e., product in SITC aggregate 5 through 8. The U.S. trade data include information on both quantity and value for many good. We compute the unit value, or price, of product from country c, p c, by dividing import value (v)byimportquantity(q c ), c p c = v/q c. c 22 Example of the unit employed to claify product include doen of hirt in apparel, quare meter of carpet in textile and pound offolicacidinchemical. Product-level trade data are noiy due to both aggregation bia and meaurement error. 23 Aggregation bia i minimied by uing detailed data, but i likely to remain. We therefore trim the data along two dimenion before uing them to compute Paache and Lapeyre indexe. The firt trim involve dropping country-year-product obervation with value le than $10,000 or quantity equal to 1. The econd trim eliminate country-pairyear-product obervation when the relative quantity or the relative price of the countrypair-product i either below the 2nd percentile or above the 98th percentile of all countrypair-product obervation in that year. The firt trim get rid of unuual and unrealitic import while the econd trim dicard unreliable country comparion. The econd tage of our etimation require meaure of trade balance and trade cot at the ectoral level. We meaure countrie ectoral trade balance relative to GDP by dividing nominal dollar-denominated trade flow data from the World Trade Flow databae compiled by Feentra et al. (2004) with GDP data from the World Bank World Development Indicator databae. For the real exchange rate we rely on verion 6.1 of the Penn World Table (i.e., PPP/XRAT). Ideally, our etimate of trade cot between countrie would include meaure of tranportation cot, tariff and non-tariff barrier a well a other cot due to language barrier, etc. Here, due to data contraint, we focu on the former. 24 We meaure bilateral tranport cot uing the U.S. import data, which record both the cutom-inurance-freight (cif) and 22 Availability of unit value average about 80 percent over the year in our ample. 23 See, for example, GAO (1995) and Schott (2004). 24 Our technique will benefit from the ongoing development of dataet uch a TRAINS that record etimate of countrie tariff and non-tarriff barrier. Though we are exploring the ue of TRAINS in our etimation, the parene of it coverage prior to the late 1990 everely retrict the ample ie of the econd tage of our etimation.

18 Etimating Cro-Country Difference in Product Quality 18 free-on-board (fob) value for mot import flow. We etimate ad valorem tranport cot per mile for indutry in year t by regreing the relative value pent on cutom, inurance and freight on import from country c on the ditance the export have travelled, cif c t fob c t fob c t = δ t D c,us + c t (32) where D c,us repreent the great circle ditance in mile between the United State and country c. In our etimation below, we et τ cd t equal to b δ t D cd. For each country, we compute average outbound trade cot by weighting detination countrie according to X their³ hare of world GDP. We alo calculate average inbound trade cot a τ c,in = w c0 τ c0 c 1, where we weight ource countrie according to their hare w c0 of world c 0 export in indutry. We report quality etimate for the top 45 non-opec U.S. trading partner for the period 1980 to Thi ample wa choen to yield a relatively long and balanced panel. We exclude year prior to 1980 becaue trade i dominated by a relatively mall group of high-income countrie. We exclude year after 1997 becaue of ignificant outlier in the trade balance data between 1998 and Etimation Strategy Firt Stage: Etimation of the Impure Price Index In the firt tage of the etimation trategy, we ue the reult of Propoition 1 to etimate each country Impure Price Index, P bco, where country o i the numeraire country. 26 The idea of the identification trategy i a follow. For generic country pair c and d, the etimated indexe P b co and P b do implicitly determine a bilateral index P b cd = P b co / P b do.thi index hould atify the Paache and Lapeyre bound for that country pair, a outlined in Propoition 1. Similarly, for C trading partner, the etimation of C 1 Impure Price Indexe, P bco c 6= o, implicitly determine C(C 1) bilateral indexe, P bcd c, d, which hould atify the bilateral Paache and Lapeyre price index bound for all country pair. If the Paache and Lapeyre bound were oberved without error, etimation would entail earching for an interior olution to the et of retriction impoed by the bound acro country pair. Here, in light of evidence that import data (mainly quantitie) are mirecorded on cutom document (GAO 1995), we intead allow for the poibility that the true Paache and Lapeyre indexe are oberved with error. Denote the true Paache and Lapeyre indexe by H cd and L cd, repectively. We aume that the oberved indexe, H cd and L cd, vary from the true indexe by a multiplicative error, ln H cd =lnh cd and ln Lcd =lnl cd. We alo aume that each error +ζ cd h, +ζ cd l, i ditributed normally, ζ cd h, N(0,ψ/wcd ) and ζ cd l, N(0,ψ/wcd ), and that the error 25 We are currently invetigating thee outlier and plan to extend the analyi to 2001 once they are verified. 26 The choice of numeraire i made without lo of generality. In the reult preented below, Switerland (CHE) i the numeraire.

19 Etimating Cro-Country Difference in Product Quality 19 for each bound are independent both of each other and of error term for other bilateral pair. 27 Note that we weight the tandard deviation of the error ditribution by w cd.inthe reult below, thi weight i et equal to the quare root of the number of categorie that countrie c and d export in common to the United State. Thi weight i meant to increae the contribution to the likelihood of country pair with a relatively large number of export in common. Satifying the inequality contraint of Propoition 2 for a given pair of countrie implie: ln P cd ln H cd = ζ cd h, ln Hcd ln P cd (33) ln P cd ln L cd = ζ cd l, ln Lcd ln P cd. (34) We etimate the et of index number b P co, c 6= o, and the variance parameter b ψ,fora given year t, by maximiing the likelihood that the true Paache and Lapeyre bound contain the etimate Second Stage: Etimation of Product Quality Variation in etimate of countrie Impure Price Indexe contain information about pure price and product quality. Propoition 2 demontrate that countrie pure price, a ummaried by the Pure Price Index, determine their ectoral trade balance. In the econd tage, we ue the reult of that propoition to trip away the pure-price component of the Impure Price Index. Incorporating ln P e cd =lnp cd ln λ cd from equation (7), and neglecting the error ariing from the linear approximation decribed in the proof of Propoition 2, we can rewrite equation (31) a T c t/y c t = Ψ t + γ ln P b t co + γ μ τ c,out t γ ln λ co t + b Z θ c t + γ κ co t (35) where κ co =lnp co ln P b co i the etimation error in the firt-tage etimate, and ubcript t indexe time period. Equation (35) highlight the fact that countrie unoberved product quality relative to the numeraire country (λ co t) i part of a compound error term that alo include the etimation error in the firt tage (κ co t) and the idioyncratic component of the covariance between exce variety and pure price (θ c t) fromequation(29). Weaumethat both κ co t and θ c t are uncorrelated with P b co. However, auming that the quality component of the error term (ln λ co t) i uncorrelated with the regreor ln P bco i untenable. Developed countrie, which tend to have higher export price, are alo likely to produce higher quality. (Thi preumption i confirmed later by our reult.) To deal with thi endogeneity problem, we firt pecify a time path for the evolution of product quality relative to the bae country: ln λ co t = α co 0 + α co 1t + ε co t (36) 27 Our aumption about the normality and independence of the error repreent a potentially trong implification. Error acro country pair with one country in common are likely to be correlated a they are contructed uing imilar information. The within-country-pair Paache and Lapeyre error are alo likely to be correlated: a high negative Paache error will coincide with a high poitive Lapeyre error. We are currently working on relaxing thee aumption. t