NBER WORKING PAPER SERIES UNDERSTANDING INTERNATIONAL PRICE DIFFERENCES USING BARCODE DATA. Christian Broda David E. Weinstein

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1 NBER WORKING PAPER SERIES UNDERSTANDING INTERNATIONAL PRICE DIFFERENCES USING BARCODE DATA Chrisian Broda David E. Weinsein Working Paper hp:// NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachuses Avenue Cambridge, MA May 2008 The auhors wish o hank he NSF (gran # ) and he Federal Reserve Bank of New York for providing financial suppor for his projec. We would like o hank he Direcor of Research a he FRBNY, Joseph Tracy, for his early suppor of his projec. We would also like o hank ACNielsen s vice-presiden of Pricing Research Frank Piorowski, Ivan Rocabado, and Maura Elhbrech for heir careful explanaion of he daa. Jean Imbs, Sam Korum, Virgiliu Midrigan, Haroon Mumaz, Moren Ravn, Helene Rey, and Serena Ng provided excellen commens on an earlier draf. Jesse Handbury provided us wih ousanding research assisance. In addiion, we would like o hank he Global Financial Markes Iniiaive a he Universiy of Chicago GSB and he Cener for Japanese Economy and Business a he Columbia Business School for research suppor. The views expressed herein are hose of he auhor(s) and do no necessarily reflec he views of he Naional Bureau of Economic Research. NBER working papers are circulaed for discussion and commen purposes. They have no been peerreviewed or been subjec o he review by he NBER Board of Direcors ha accompanies official NBER publicaions by Chrisian Broda and David E. Weinsein. All righs reserved. Shor secions of ex, no o exceed wo paragraphs, may be quoed wihou explici permission provided ha full credi, including noice, is given o he source.

2 Undersanding Inernaional Price Differences Using Barcode Daa Chrisian Broda and David E. Weinsein NBER Working Paper No May 2008 JEL No. F1,F15,F31 ABSTRACT The empirical lieraure in inernaional finance has produced hree key resuls abou inernaional price deviaions: borders give rise o flagran violaions of he law of one price, disance maers enormously for undersanding hese deviaions, and mos papers find ha convergence raes back o purchasing power pariy are inconsisen wih he evidence of micro sudies on nominal price sickiness. The daa underlying hese resuls are mosly comprised of price indexes and price surveys of goods ha may no be idenical inernaionally. In his paper, we revisi hese hree sylized facs using massive amouns of US and Canadian daa ha share a common barcode classificaion. We find ha none of hese hree main sylized facs survive. We use our barcode level daa o replicae prior work and explain wha assumpions caused researchers o find differen resuls from hose we find in his paper. Overall, our work is supporive of simple pricing models where he degree of marke segmenaion across he border is similar o ha wihin borders. Chrisian Broda Universiy of Chicago Graduae School of Business 5807 Souh Woodlawn Avenue Chicago, IL and NBER cbroda@chicagogsb.edu David E. Weinsein Columbia Universiy, Deparmen of Economics 420 W. 118h Sree MC 3308 New York, NY and NBER dew35@columbia.edu

3 I. Inroducion Daa limiaions have prevened researchers from comparing he prices of idenical goods sysemaically wihin and across borders. This resricion has led researchers o infer he exen of marke segmenaion from he behavior of price indexes, aggregae prices of goods ha may no be idenical inernaionally, and a non-random selecion of paricular goods (e.g. Big Macs). Mos papers in his lieraure have emphasized hree key resuls abou inernaional price deviaions: borders give rise o flagran violaions of he law of one price (LOP), disance maers enormously for undersanding hese deviaions, and convergence raes back o purchasing power pariy (PPP) are inconsisen wih he evidence of micro sudies on nominal price sickiness (c.f., Rogoff (1996)). In his paper we revisi hese hree sylized facs using massive amouns of US and Canadian barcode daa. Our findings sugges ha none of hese convenional facs survive scruiny of micro daa. The law of one price in is absolue form holds as well across he border as i does wihin counries, disance coefficiens are five o en imes larger in aggregae daa han in micro daa, and raes of price convergence wihin and across borders are fas and compleely in line wih micro sudies. In shor, he daa is supporive of simple pricing models where he degree of marke segmenaion across he border is similar o ha wihin borders. While he use of micro daa in inernaional pricing has become more widespread (see Akeson and Bursein (2008), Gopinah and Rigobon (2007) and Goldberg and Verboven (2001) for imporan applicaions), comparing idenical goods inernaionally has remained a challenge. We ake advanage of he fac ha he US and Canada share a common barcode sysem o compare prices of a vas number of producs. Using daa wihin and across 10 ciies in he US and 6 regions in Canada we revisi he main facs in inernaional pricing. Our daa includes around 40 percen of all expendiures on goods in consumpion, and is also vasly richer a he micro level han ha used in naional saisics. 1 Moreover, unlike all prior work, we have boh price and quaniy daa, which les us form heory based, as opposed o ad hoc, indexes of PPP. One imporan feaure of he daa is ha i les us compare he exen of inernaional marke segmenaion wih segmenaion wihin counries. We confirm he early finding by Isard (1977) ha he LOP is flagranly violaed in inernaional daa. However, we can show ha ha he LOP is also flagranly violaed across ciies in he same counry. Thus, he observaion ha 1 For example, our daa conains 700,000 price quoes for he US in a ypical year. By conras he sample is only 5 percen as large. 2

4 an idenical can of soda sells a differen prices in differen counries is no very informaive abou border barriers because prices vary subsanially across space even wihin borders. Obviously, he more ineresing quesion is how much larger are inernaional violaions han domesic ones. Here we find he answer o be no much. In heir seminal work, Engel and Rogers (1996) compare border barriers wih regional ones by expressing he widh of he border in erms of disance equivalens. Using barcode daa and he same mehodology as hey do, we find he disance-equivalen border effec o be 3 miles roughly wha one migh expec if rucks crossing o border had o sop briefly o fill ou some paperwork. In oher specificaions he widh of he border rises o a few hundred miles, bu never anyhing close o he ens of housands of miles found in he original paper and in subsequen work (e.g., Parsley and Wei (2001)). Our second conribuion is o explain why micro daa reveals small border effecs bu aggregae daa reveals much larger impacs. We begin by demonsraing ha if we form price indexes using our barcode daa and hen replicae Engel and Rogers (1996), our resuls are quie similar o heirs. Clearly, somehing abou aggregaing micro daa causes he border effec o appear larger. We argue ha a vas amoun of informaion abou marke segmenaion across space is los when one uses price indexes. In paricular, because aggregae indexes collapse he large wihin-counry idiosyncraic variaion of relaive goods prices while preserving he variaion due o exchange rae movemens, hey make he cross-counry variaion appear much larger han he wihin counry variaion. Thus, aggregaion of individual goods prices mechanically serves o amplify he measured impac of he borders on prices. In our daa, his uninended consequence of aggregaing individual prices ino disaggregae produc caegories is enirely responsible for he large size of he border when using price index daa. We also find a iny border effec when we look a deviaions in he LOP. Here we compare inernaional LOP deviaions wih hose wihin he US afer conrolling for disance. Our finding is paricularly surprising given ha he impac of disance on he price deviaions of idenical goods is only abou one enh as high as ha obained using price index daa. This underscores he role ha composiional effecs have in explaining he relaionship beween price dispersion and disance previously found in he lieraure. We documen ha he se of common goods across ciies varies sysemaically across space and borders and herefore unless all individual prices wihin he index move ogeher, price indexes will appear o deviae across 3

5 space and borders simply due o he fac ha he underlying weighs and goods are differen. We nex documen ha he underlying prices wihin indexes vary enormously across ime even for narrowly defined produc caegories, e.g. fresh eggs. This implies ha he majoriy of he increased dispersion in aggregae prices ha we observe as he disance beween ciies rises is no he resul of acual deviaions from he LOP bu raher from composiional effecs in he se of goods used o compue ciy-specific price indexes. Finally, we urn our aenion o undersanding wha Rogoff (1996) has ermed The PPP Puzzle : he fac ha inernaional price adjusmen occurs a much slower raes han wha one would expec from micro daa. We firs use our barcode daa o confirm ha convergence raes o long-run levels are fas using disaggregae daa bu slow o non-exisen using aggregae daa formed from our barcode daa. Once again, he quesion arises of why he aggregae resuls differ so much from hose using micro daa. We show ha srong non-lineariies in he response o shocks are behind Rogoff s puzzle. We confirm on our disaggregae barcode daa he finding ha convergence raes are highly non-linear (see, for example, Obsfeld and Taylor (1997) and Parsley and Wei (1996)). Large relaive price deviaions disappear very rapidly bu small ones are quie persisen. This implies ha when calculaing he average convergence speed for individual goods OLS pus a large weigh on observaions wih big price deviaions which converge rapidly. By conras, when he daa is aggregaed, large negaive and posiive price deviaions cancel each oher and a larger weigh is given o observaions where price deviaions are small. We show ha he pervasiveness of he non-linear responses can explain all he differences in he raes of convergence found a he aggregae versus disaggregae level. In paricular, we also show ha in our daa heerogeneiy of he convergence coefficien across goods does no generae a quaniaively imporan aggregaion bias. 2 The srucure of he paper is as follows. In Secion II we provide a review of he heory and he empirical lieraure on inernaional pricing. In Secion III we describe he daa and preview some of he main resuls and in Secion IV we examine he widh of he border a he aggregae and micro level and explain he sources of he differen resuls. In Secion V we examine he issue of convergence raes o PPP wihin and across he border boh a he aggregae 2 A number of papers have examined wheher heerogeneiy of he convergence coefficien across goods can explain his aggregaion bias and have found mixed success. Mos prominenly Imbs e al (2005) sugges ha heerogeneiy in he coefficiens across goods is imporan o explain he PPP puzzle, while Chen and Engel (2005), Parsley and Wei (2007), Reidel and Szilagyi (2005), and Choi, Mark and Sul (2007) find oherwise. 4

6 and micro level. In Secion VI we provide an explanaion for he difference in convergence raes beween differen levels of aggregaion. II. Theory and Lieraure Review The empirical lieraure on inernaional pricing is vas, and i is useful o have an organizing framework for undersanding he prior work. We find i useful o wrie down he simple predicion of he heory of he LOP in is exac form and hen conras hese equaions wih heir approximae forms, i.e. he equaions ha are esimaed in he lieraure. The difference beween boh forms will be insrucive in undersanding where he problems in he exising ess of his heory lie. Unforunaely, he empirical lieraure has no been consisen in is usage of erms like LOP and PPP, especially when narrow aggregaes of producs are compared. In order o avoid any confusion, we will use he erms LOP and PPP in he same way as in Rogoff (1996) i.e. if he prices of a good in wo differen locaions are compared, we will refer o ha as a es of LOP, and if wo price aggregaes are compared, we will refer o ha as a es of PPP. 3 Absolue LOP saes ha he price of an idenical good should be he same across locaions when denominaed in a common currency. Formally, his suggess ha P uc (i.e. he price of good u in ciy or region c in ime ) can be wrien as (1) P = E ' P ' uc cc uc where P uc is he price of he good in a differen region or counry and E cc is he exchange rae which equals uniy if he wo ciies or regions are in he same counry. Tess of equaion (1) have been exremely limied. Previous sudies have found ha commodiies ha are raded on organized exchanges, e.g. gold, end no o have large deviaions in he LOP. For he handful of goods ha have also been sudied, auhors have ypically found large deviaions from he LOP. Examples include he work on Big Macs by Cumby (1996), 3 One of he drawbacks of his approach is ha we will refer o some papers as ess of PPP even hough he auhors refer o heir work as ess of LOP. This is regreable, bu because many of he resuls in his paper urn crucially on wha exacly is being esed, we feel i necessary o be precise abou our erminology. 5

7 IKEA sales by Haskel and Wolf (2001), and The Economis magazine by Ghosh and Wolf (1994). A second class of sudies has sough o es wha migh be called Approximae Absolue LOP: (2) Puc = Ecc' Pu ' c' where goods u and u belong o a similar produc caegory bu are no idenical goods. Since differen goods are being compared, ess based on equaion (2) (as opposed o equaion (1)) canno disinguish violaions in he LOP from violaions of he assumpion ha good u and good u ener ino consumer uiliy idenically. For example, ineresing recen work based on he Eurosa daabase (c.f., Crucini, Telmer, and Zachariadis (2005) and Crucini and Shinani (2006)) es his form of he LOP. However, i is difficul o know how much of an observed violaion in he LOP is due o he fac ha borders preven arbirage from eliminaing price differenials for goods like lady s boos and how much is due o he sample of lady s boos varying across counries. 4 Concern over his unobserved heerogeneiy has moivaed researchers o examine Relaive LOP, which we define as follows: (3) Δ puc =Δ ecc ' +Δpuc', where lower case leers refer o naural logarihms of he upper case leers, and he Δ s refer o ime differences. Tess of equaion (3) relax he assumpion ha prices mus converge o he same level (perhaps due o a consan rade barrier), and only es wheher prices end o remain a consan level apar. The micro sudies in he lieraure have ypically worked wih an equaion ha migh be ermed Approximae Relaive LOP: (4) puc ecc ' pu ' c' Δ =Δ +Δ. The major advanage of using equaion (4) relaive o equaion (3) is ha i correcs for any unobserved heerogeneiy ha causes good u and good u o ener ino consumer uiliy differenly. This is wha moivaed Parsley and Wei (1996) o use his form of he LOP in heir pioneering sudy of urban prices in he US. Differencing he daa does no come wihou a cos., 4 While effors o compare goods of comparable qualiy are usually highlighed in survey manuals, he comparison of idenical goods is generally impossible. 6

8 One can easily imagine ha he heerogeneiy beween wo differen goods conains a consan componen and a ime varying componen. To he exen ha he ime varying componen is small, esimaing equaion (4) will be similar o esimaing equaion (3), bu if differen goods experience very differen shocks across ime, i is easy o see how equaion (3) migh hold closely bu equaion (4) migh be violaed severely. Much of our heory only requires average prices o equilibrae; hence we urn our aenion o PPP. We can derive Absolue PPP by weighing equaion (1), summing and hen aking logs o produce: (5) ln wuc Puc = ln Ecc ' + ln wucpuc' u Ic u Ic. Alernaively, one can firs ake logs of equaion (1) and hen sum o produce (6) w ln ( P ) = ln E + w ln ( P ) uc uc cc ' uc uc' u Ic u Ic. There are wo imporan feaures of equaion (5) and (6). Firs, here is no inellecual conen o equaions (5) and (6) ha is no capured in equaion (1). If equaions (5) and (6) hold bu equaion (1) does no, his simply is a saemen ha here is a weighing scheme ha can cause he deviaions in equaion (1) o cancel. Second, assuming he Absolue LOP holds, Absolue PPP will hold only if one uses he same weighs in boh locaions. 5 Given he daa limiaions o find price levels across counries, he lieraure has in general ended o focus more on Relaive PPP. The heoreical version of Relaive PPP can be wrien down by firs differencing equaion (5): (7) Δ ln wucpuc =Δ ln Ecc ' +Δln wuc Puc ' u Ic u Ic However, all previous work on PPP has focused on wha migh be ermed Approximae Relaive PPP: (8) Δ ln wucpuc =Δ ln Ecc ' +Δln wuc ' Puc ' u Ic u Ic'. 5 I is hard o classify sudies like Goldberg and Verboven (2001, 2005) and Luz (2004) ha have examined varians of equaion (2) and (6) in which he prices are aggregaed ogeher using hedonically adjused price indexes. 7

9 Prominen sudies include Isard (1977) Giovannini (1988), and Kneer (1989, 1993) on average impor prices, and Engel (1993), Froo, Kim, and Rogoff (1995), and Rogers and Jenkins (1995) on price indexes. There are hree imporan differences beween equaion (8) and equaion (7). Firs, equaion (7) may hold bu equaion (8) will no if he price changes of he se of goods I c and I c are differen because of idiosyncraic shocks. Second, equaion (7) may hold bu equaion (8) may no if he log price changes of goods u and u do no equal he simple price changes. 6 Third, equaion (8) may no hold because he weighs on he lef hand side do no equal hose on he righ. This las criique is paricularly imporan because saisical agencies make no effor o insure ha inernaional or even urban price indexes use he same weighs and/or goods. Finally, Engel and Rogers (1996) seminal work deserves special menion. Working around he limiaions of exising price daa hey have insrumened a useful es based on he variance raio of price changes. In he simples form, one can imagine aking he variance of equaion (3) and seeing if he variance is larger when c and c are in differen counries relaive o when hey are in he same counry. However, insead of aking he variance of equaion (3), Engel and Rogers are forced o work wih he variance of equaion (8). In secion IV we explore he uninended consequences of heir ess of (3) based on he relaive volailiy of he erms in equaion (8). The foregoing analysis provides a simple roadmap for undersanding he way his paper is srucured. Firs we will examine he LOP and PPP in heir absolue and relaive exac forms using housands of barcode producs boh wihin and across borders. Nex, every ime we find a difference beween our resuls and hose of oher papers ha have examined hese relaionships in heir approximae forms we will invesigae wheher we can replicae he resuls and pinpoin o he assumpion ha gives rise o he failure or anomaly. This enables us o no only do precise esing bu also undersand he previous lieraure. 6 For example, some CPI indexes are based on Laspeyres and ohers incorporae on geomeric averages. 8

10 III. Daa Descripion III. A. Overview A major difference beween his paper and prior work is ha we bring barcode daa o bear on he quesion of inernaional price differences. We use hree daases ha are exracs of ACNielsen s Homescan daabase. The Homescan daabase is colleced by ACNielsen in he Unied Saes and ACNielsen Canada in Canada. In each counry Universal Produc Code (UPC) scanners are given o a demographically represenaive sample of households. In he US, approximaely 60,000 households in 23 ciies receive hese scanners and approximaely 15,000 households in 6 regions receive hem in Canada. Households hen scan in every purchase hey make. If he purchase is made from a sore wih ScanTrak echnology, he prices of each good are downloaded direcly from he sore s daabase. If he good is purchased elsewhere, e.g. on he inerne, he household direcly eners he price. As such, he daabase provides us wih a vas array of goods wih barcodes. The majoriy of hese goods are in he grocery, drug, and mass merchandise secors. Because he full daase is exremely expensive, we purchased hree exracs ha we will make use of in his sudy. The firs one is he daabase ha we will refer o as he US Naional Daabase and was used in Broda and Weinsein (2007). In his exrac, we had ACNielsen collapse he ciy and household dimension of he daabase, and hus we have price and quaniy daa on every UPC purchased by he US sample of households for every quarer beween 2001:Q1 and 2003:Q4 a he naional level. This daabase conains informaion on approximaely 700,000 goods each year. The second daabase, we refer o as he US Cross-Secional Daabase, is new. In his daabase, we have household level daa on every purchase in he fourh quarer of 2003 by a subsample of 3,000 households evenly divided across 10 US ciies. In each ciy, he households were randomly seleced from he full sample so ha heir demographic characerisics mach hose of he ciy as a whole. Finally, he hird daabase, which we shall call he Canadian Regional Daabase, is also new. ACNielsen Canada provided us wih average price and quaniy daa by region in Canada for every quarer beween 2001:Q1 and 2004:Q4. Table 1 describes he basic saisics of each of hese hree differen daabases. As one can see from he able, our daa provides a much richer breakdown of prices for his sample of goods han is available in naional saisics. 9

11 These daabases have hree key feaures ha lend hemselves o he sudy of pricing in differen markes. The firs is ha we idenify differen goods using barcodes. Since companies only use one barcode per good, when we compare goods inernaionally, we can be confiden ha we are comparing precisely he same goods (see Table A1 in he appendix for examples of he level of deail in our daabase). Second, we can also compare variaion of prices across ciies wihin and across borders. This les us precisely examine he border effec in levels; somehing no one has done before. Third, because we have boh price and quaniy daa, we know exacly how o weigh he goods when building price indexes, which allows us o examine he role ha composiional effecs play in sudies ha use naional saisic daa. III.B. Daa Preview Before plunging ino he economerics, i is useful o examine he raw daa o obain some inuiion for how prices vary across regions and ime. The firs poin ha is imporan o conemplae is he vasness of barcode informaion ha is included in our daabase. In he US Naional and Canadian Regional Daabase here are 700,000 and 490,000 UPCs available, respecively. Even wihin narrow produc caegories, consumers have access o an enormous number of differen goods. We made use of he US Naional Daabase o examine how many UPCs were sold in each of he 123 Produc Groups in he US. In he ACNielsen classificaion sysem, a produc group is a highly disaggregaed subse of he oal daabase. For example, fresh eggs, ice, and milk are all differen produc groups. We plo a hisogram of he coun of he number of UPCs per produc group in Figure 1. The firs hing ha is immediaely apparen from he figure is he vas number of UPCs per produc group. Wih he excepion of a few produc groups yeas, meal sarers, road sal, canning supplies, and conracepives all producs in he US are comprised of over 200 differen UPCs. The ypical produc group has 2700 differen UPCs. Even relaively homogeneous goods like fresh eggs are comprised of 2275 differen varieies. The simple fac ha here are many UPCs per produc group would be an inellecual curiosiy if i weren for he fac ha he degree of sample overlap varies sysemaically wih variables of ineres. In Figure 2, we plo he share of UPCs ha are common beween ciies in he US and regions in Canada and he disance beween hose wo locaions. For exposiional purposes, he bilaeral ciy daa is shown in hree differen plos: comparisons wihin ciy pairs in 10

12 he US, wihin region pairs in Canada and beween ciies in he US and regions in Canada. The paern observed in each of hese plos is unmisakable: as disance beween ciies rise, he share of common idenical goods beween ciies falls. Wihin he US, he share of common goods across ciies is over 28 percen beween New York and Philadelphia he closes ciy pair in our daa and is less han 18 percen for goods beween New York and Los Angeles he wo ciies furher apar. Wihin Canada, Onario and Quebec share almos 60 percen of goods while Briish Columbia and Mariimes share less han 45 percen of he goods. 7 In Table A3 in he appendix we show regressions of he share of common goods in erms of he simple coun of he number of goods and in value erms agains bilaeral disance beween ciies. Despie he large sample of goods ha are included in each ciy, only around 25 percen of he UPCs are common beween any wo ciies in he US. While his probably undersaes he rue degree of overlap in he US because some UPCs migh no have been purchased by he sample households included in our daa bu did exis in he ciy, i underscores he imporance of composiional effecs when comparing prices of similar produc caegories across ciies wihin a counry. Our sample of over 50,000 UPCs per ciy is around 40 imes larger han hose used by he Bureau of Labor Saisics when compuing regional price indexes. 8 This suggess ha he amoun of overlap in ciy or regional price indexes in naional saisics daa is quie small. Figure 2C shows he imporance of composiional effecs across he border. A large number of he producs sold in he US are no sold in Canada in idenical form. In he ypical bilaeral ciy/region comparison beween he US and Canada only 7.5 percen of he goods are common, his is less han one hird he common se of goods available beween ciy pairs of equal disance wihin he US (Figure 2A and 2C are direcly comparable). This means ha he composiion of a random sample of goods sold in he US is likely o differ subsanially wih he composiion of a sample of goods sold in Canada. By he same oken, more proximae locaions have more similar consumpion bundles han disan locaions. The fac ha price indexes across regions or counries are largely composed of differen goods would no be a problem for undersanding he LOP or PPP if goods wihin caegories are fairly homogenous. In his case, one could have a reasonable degree of confidence ha similar 7 The levels of he share of common goods wihin ciies are no direcly comparable beween Figures 2A and 2B. This is because our daa is based on differen household sizes per ciy/region in he US and Canada, and because regions in Canada include several large ciies. 8 The BLS collecs around 34,000 price quoes (for he same caegories included in our daabase) over 23 differen ciies. This implies ha hey collec around 1,260 price quoes per ciy. 11

13 goods would have similar prices or a leas hese prices would move ogeher. In Figure 3, we plo he kernel densiy of quarerly UPC relaive price changes and quarerly UPC relaive price changes afer conrolling for produc group-ime fixed effecs. 9 Formally, le p ugc, be he log price of UPC u ha belongs o produc group g in ciy c and period. We denoe he relaive log price of a UPC wih respec o a region or ciy c as q ugcc, = p ugc, p ugcc,. Boh prices are expressed in US dollars when ciy c and c are in differen counries. 10 For simpliciy, we drop he c subscrip when we use Onario, Canada s larges region, as he reference region. The red line in Figure 3 shows he disribuion of Δq ugc, for all UPCs in all ime periods in Canada. The blue line shows he kernel disribuion of Δq ugc, where q, = q, q, ugc ugc gc, where q gc, is he average relaive price differenial beween UPCs in group g, ciy c, in ime. The blue disribuion shows he log relaive price change of a paricular UPC in a paricular ciy and ime once i has been purged of common group-ciy-ime effecs. As one can see from he plo, here is enormous dispersion of prices wihin produc groups as boh disribuions lie almos on op of each oher. In oher words, common produc-group and ime facors play a iny role in explaining he observed ime-series volailiy of UPC prices. The sandard deviaion of he UPC specific componen of prices is close o 15 percen, which is almos idenical o he sandard deviaion of he raw price changes. If we focus our aenion on a relaively homogeneous good like fresh eggs, he sandard deviaion falls o 10 percen, bu i is prey clear ha one canno even rea a relaively homogeneous good like fresh eggs as a single iem. 11 The preceding analysis suggess ha even hough goods may have idenical prices, goods caegories migh exhibi very differen average prices and price changes. Forunaely, he use of UPC daa means ha we can be precise abou he prices ha we are comparing. In Table 2, we compare he prices of individual UPCs across ciies and regions in he fourh quarer of In he firs panel, we focus on he US. Since we have daa for 10 ciies, we can make 45 bilaeral comparisons of prices across ciy pairs. The middle and lower panels examine all bilaeral 9 The ime series properies of disaggregaed daa have been examined exensively in Broda and Weinsein (2007) and Klenow and Kryvsov (2007), so here we will jus review a few key sylized facs uncovered in hose papers. 10 We adjus Canadian prices downwards by 7 percen because Canadian prices are inclusive of he VAT. 11 These numbers imply ha here is vasly more volailiy in he raw price daa han in exchange raes. The ypical quarerly exchange rae change among developed economies wih flexible exchange raes is less han 2 percen (see Calvo and Reinhar (2004)). The large volailiy of he raw price daa relaive o exchange rae daa has an imporan implicaion for examining convergence. I implies ha a large share of he flucuaions in he prices of individual goods across counries is likely o come from UPC specific shocks ha are ignored a he aggregae level. 12

14 comparisons beween regions in Canada and beween ciies in he US and regions in Canada. As he firs column indicaes, we ypically have 10,616 prices of common UPCs for every ciy pair in he US, 25,094 goods in he ypical bilaeral region comparison wihin Canada and 1,531 idenical goods beween bilaeral pairs across counries. Columns 2-3 of Table 2 presen medians, averages, and sandard deviaions of bilaeral ciy comparisons for several sample saisics (in Table A3 in he appendix we presen all ciy pair comparisons). In Column 2, we firs compued he median price differenial for each ciy pair. In Column 3, we compue he sandard deviaion of log relaive prices of he same UPCs consumed in each ciy pair. The able shows ha he ypical price differenial beween ciy pairs in he US is 0, wih a sandard deviaion of (upper panel). We repea he same exercise for Canadian regions and obain very similar resuls (middle panel). These resuls sugges ha he ypical price differenial does no vary much across ciies. 12 The ypical difference in prices of idenical goods does seem o rise as we cross borders, bu he rise is quie modes (lower panel). The median price difference in he 4 h quarer of 2003 for a given UPC in a US ciy relaive o a Canadian region is only 1.9 percen higher on average. 13 We presen he sandard deviaion of he log relaive prices in Column 3. The able reveals ha he ypical sandard deviaion of log price differences beween any wo ciies is 22.3 percen in he US and 18.7 percen in Canada. These numbers reveal somehing very imporan abou he LOP: even wihin a counry he sandard deviaion of prices of idenical goods is ypically 20 percen. To pu his number in perspecive, consider he resuls of Froo, Kim, and Rogoff s [1995] sudy of inernaional violaions of he law of one price. In ha sudy, hey concluded, he volailiy of law of one price deviaions is boh remarkably high (ypically on he order of 20% or more per year for mos commodiies in mos cenuries) and remarkably sable over ime. The imporan fac o bear in mind is ha he LOP deviaions ha hese auhors found inernaionally are approximaely he same magniude as hose we observe wihin counries. In oher words, he prices of individual goods vary subsanially across space regardless of wheher wo regions are in he same counry or no. 12 This finding is presen in our daa in all quarers for which we have regional Canadian daa. 13 This resul, however, is no robus o he ime period being sudied, as large cumulaive exchange rae movemens over his period have made absolue PPP flucuaions vary from around 15 percen o 2 percen. 13

15 This poin nowihsanding, we can see ha he dispersion of prices of individual goods vary slighly more when crossing he border. The lower panel of Table 2 shows ha he sandard deviaion of prices of idenical goods across he border is ypically 26.7 percen, roughly 4 percenage poins larger han wihin he US and 8 percenage poins larger han wihin Canada. Resuls are similar using he ypical absolue price difference beween ciies. One can also inspec he imporance of he border visually in Figure 4. Here we plo he kernel densiies of all relaive prices across ciies wihin he US, wihin Canada, and beween he US and Canada. As he plo makes clear, prices in he US are a bi higher han prices in Canada, and here is evidence of greaer dispersion in inernaional prices han in domesic prices, bu he disribuions are no radically differen. Raher he border seems o add a small amoun o he very large wihin-counry dispersion in prices across ciies. This creaes some ension wih he resuls of Engel and Rogers (1996), and is a poin ha we will need o explore more sysemaically. In sum, he sample saisics reveal a number of imporan lessons for undersanding inernaional pricing. Firs, here are a vas number of goods in he marke and he composiion of consumpion varies sysemaically wih disance and across borders. This implies ha one mus ake grea care abou how samples are consruced when comparing relaive price movemens across space and borders. Second, he prices of hese goods vary subsanially even for narrowly defined commodiies. This implies ha absolue deviaions in he LOP will be quie sensiive o wheher precisely he same goods are compared. Third, one should no equae he inernaional violaion of he law of one price wih a barrier a he border. The daa srongly suggess ha here are subsanial violaions of he law of one price wihin counries and ha hese violaions are of similar magniudes as inernaional violaions. Fourh, here is vasly more volailiy in individual price quoes han in price indexes. This means ha much of he price variaion is eliminaed when one focuses on price indexes. As we will see in he nex few secions, each of hese sylized facs will play a key role in undersanding why absolue price convergence holds and why i has been so hard o find evidence in favor of i. 14

16 IV. The Widh of he Border Redux In order o undersand he magniude of inernaional deviaions of he LOP, we need o hink of a benchmark. One of he simples and mos compelling reasons why prices may differ spaially is ha i is difficul o ranspor goods. Thus, one migh expec smaller LOP deviaions in close ciies han in disan ciies. In heir seminal work, Engel and Rogers [1996] developed his concep furher by expressing border effecs in erms of disance a convenion we will adop here. A simple way of compuing he widh of he border is o regress a measure of he price dispersion on he log of disance and a dummy variable ha is one if he price difference is compued for a good purchased in ciies ha are locaed in differen counry. In his case one can compue he widh of he border by dividing he border coefficien by he disance coefficien and hen exponeniaing. In Table 3, we presen he resuls for a similar regression as ha in Engel and Rogers. The only difference is ha we use wo differen measures of price dispersion. Firs, we look a a price variance measure: he square of he log price difference of a UPC 2 2 purchased in wo differen ciies, i.e. ( qugcc', ) ( pugc, pugc', ) = ; second, we look a he absolue log price difference paid for he same UPC in wo ciies, i.e. qugcc', = pugc, pugc',. Specifically, we run he following regression: (9) ( ) 2 q = α + β ln dis + γborder + ε ugcc', c cc' cc' ugcc', (10) qugcc', = αc + β ln discc' + γbordercc' + εugcc', where α c are ciy dummies, and sandard errors are clusered by ciy pair. The widh of he border adoped by Engel and Rogers is given by exp( ˆ γ / ˆ β ), where circumflexes indicae esimaed parameers. One of he problems of his approach is ha his measure of he border is uniless, and hence one canno sricly inerpre i in erms of a mileage equivalen. 14 However, he coefficien can be inerpreed in erms of he relaive disance beween any wo ciies. 15 This poin 14 For insance, wheher we measure disance in inches or in miles would imply he same γ and β coefficiens. 15 This can mos easily be undersood in erms of an example. Suppose here are hree ciies: A, B, and C. Le q ugac, and q ugbc, be he absolue relaive price differences beween ciy pairs AC and BC, respecively. If he disance beween ciies A and C is 2 log unis more han he disance beween ciies B and C and he border coefficien is 2, 15

17 nowihsanding we will sick wih convenion for he purposes of comparabiliy wih prior research and someimes express he widh of he border in erms of miles. A imes we will focus on he magniude of he border coefficien, which is a less colorful, bu more meaningful measure of he border. The resuls of his exercise are presened in Table 3. The firs panel presens he raw regression resuls and he second panel presens resuls in which we weigh he observaions by he sales of he UPC. 16 The weighed regression resuls are probably more reasonable because he forces of goods arbirage are probably much greaer for a good wih a large amoun of sales han for a good ha is only purchased by a few people. In all regressions, disance conribues significanly o price dispersion and here is a posiive and significan border effec. This is comforing because our priors srongly sugges ha borders and disance inerfere wih he law of one price. Wha is mos ineresing in he able, however, is our esimae of he impac of he border. If we look a he regressions wih he absolue log price difference as he dependen variable, we see ha he border inroduces a price wedge of seven percen beween he US and Canada. We can obain some sense of how small his is compared o prior work by compuing he widh of he border. In he unweighed regressions, he widh of he border ranges from 720 miles o 328 miles depending on he specificaion. By conras he poin esimae in Engel and Rogers was 75,000 miles for all goods and 3.8 million miles for food a home he caegory closes o our sample of goods. Similarly Parsley and Wei (2001) esimae ha he widh of he border vis à vis Japan is 43 quadrillion miles. Of course, he unweighed esimaes are likely o oversae he border for he reasons we have highlighed above. If we urn o he weighed regression resuls, we find ha ha widh of he border ranges beween 36 and 106 miles. In oher words, Canada is no locaed midway beween he Earh and he Moon i s really jus a few miles norh of Buffalo. We show in Figure A1 in he appendix ha his resul is robus o he quarer we use. The fac ha we find he border effec o be so small srikes us as boh deeply comforing and confounding. On he one hand given Canada s proximiy o he US, he exisence of a Free hen he impac of crossing he border would have he same impac on absolue relaive price differences as comparing relaive prices in ciy B wih hose in ciy A. Noe ha he criical facor driving he widh of he border is no he disance from B o C bu he relaive differences from C of A and B. Thus, if here were wo addiional ciies A and B ha were wice as far from C as A and B respecively, he border effec would have an idenical impac on relaive prices as ravelling from A o B. 16 We use he average value of consumpion of each UPC beween ciy pairs as a weigh. 16

18 Trade Agreemen, and he similariy of he economies suggess ha we should expec small border effecs. However, i is puzzling why we should find such a small border effec when so many oher sudies have no. One possible explanaion harks back o our earlier discussion of he heerogeneiy of producs wihin produc caegories. If caegories like fresh eggs are very heerogeneous, hen a baske of fresh eggs in one counry is likely o conain very differen eggs han a baske of eggs in anoher counry. We have already seen ha his composiional effec becomes more imporan wih disance and when one crosses a border. We can now examine he imporance of his effec in hree sages. Our firs ask is o demonsrae ha carefully aggregaing he daa does no affec he esimaes of he border effec. In order o do his, we need o be precise abou wha goods and weighs are used o compue ciy price indexes. We firs define I gcc as he se of commonly consumed UPCs in ciy pair cc ha belong o produc group g. We firs consruc a common weighed index as a Geomeric index of he relaive prices of common goods wihin every produc group in every bilaeral ciy pair: (11) Common Weigh Index gcc' 1 ( s ) 2 ugc + sugc ' P ugc = u I P gcc ' ugc' where s ugc is he share of expendiure in produc group g on UPC u in ciy c in ime. Noe ha he log of equaion (11) can be expressed in erms of he acual log price difference of a UPC s s q. 1 purchased in wo differen ciies ln(common Weigh Index ) = 2 ( + ) gcc' u I ugc ugc' ugcc', gcc ' The wo key characerisics of his index is ha i only uses prices for common UPC across ciies and i only depends on he average share of consumpion in he wo ciies and no on he ciy specific expendiure shares. The second index we consider is he ciy-specific index: (12) Ciy-Specific Weigh Index gcc' = ( Pugc ) u Igcc ' ( Pugc' ) u Igcc ' In conras o he common-weigh index, he ciy-specific index can vary wih he marke shares of expendiures in wo locaions even if he average expendiure level is he same. The disincion is imporan because i les us examine wheher simply allowing he weighs of sugc sugc '. 17

19 common goods o vary has an effec on he resuls. We would expec disance o have a differen effec on his index if composiional effecs are imporan. Finally we form an all-goods price index defined below: (13) All-Goods Index gcc ' = ( Pugc ) u Igc ( Pugc' ) where I gc is he se of UPCs available in ciy c and produc group g. The major difference beween his equaion and equaion (12) is ha we now allow all goods in each ciy o ener he index, no jus he common ones. Our basic ess involve re-esimaing he regressions in equaions (9) - (10) using he log of he price indexes a he produc group level insead of he log price differences of individual UPCs o see wheher he simple ac of aggregaion creaes a problem. As one can see in he firs panel of Table 4, simply using common goods price indexes has almos no impac on our measure of he border. The esimaed border effecs do no move by much and he widh of he border says wihin 100 miles of he esimaes ha we obained wih he UPC-level daa. However, i is imporan o remember ha he daa used by researchers o examine border effecs is no based on a common se of goods, bu raher on non-overlapping samples of he goods available in each counry. Panels 2 and 3 in Table 4 can help us undersand he impac of using price indexes o assess he border effec. The second panel shows he impac ha composiional effecs hrough ciy-specific weighs can have on he disance and border coefficiens. The impac of disance on he square log price differences is over 5 imes larger han in he firs panel and he border dummy jumps by a facor of 3. The difference beween he wo panels can be raced direcly o composiional effecs. The prices of disaggregaed goods caegories may vary a lo even if he underlying prices hardly vary a all. The border dummy also rises o almos 3 imes is value when common-weighs are used. Since composiional effecs end o raise boh he log disance and border coefficiens he impac on he widh of he border is no srongly affeced by using ciy-specific weighs. The imporance of disance and he border rises dramaically when we use an index composed of all goods. Now he disance and border coefficiens rise by a leas an order of magniude. Ineresingly, when goods ha are specific o each ciy are included, he widh of he border dummy jumps o lierally asronomical values. Mos of his is driven by an enormous u Igc ' sugc sugc '. 18

20 jump in he border coefficien. The widh of he border ranges from 23 million miles o 7.9 billion miles depending on he specificaion. The difference beween his se of resuls and he previous one arises solely from he fac ha he composiion of goods wihin a produc group differs across he border sufficienly o affec he average price. This large border effec resuls in apparen rejecions of he law of one price or PPP because he Canadians drink RC Cola and Americans drink Coca-Cola. While one may hope ha RC Cola and Coca-Cola move ogeher in he ime series, here are many reasons o worry ha his may no be he case. A he very leas, one can see ample reasons why LOP migh hold precisely, bu he way in which aggregae indexes are formed produces failures of PPP. This esablishes ha i can be very misleading o esimae deviaions from he law of price or PPP using even highly disaggregaed produc caegories. This explanaion, however, is unsaisfacory o explain he resuls of Engel and Rogers (1996) because hose resuls are based on he ime-series volailiy of price indexes as opposed o he dispersion of price levels. For insance, if prices in a produc group all move ogeher, i is possible for he levels o deviae across regions bu he ime series no o show a large border effec. In order o examine wha role is played by aggregaion in he resuls by Engel and Rogers we exploi he fac ha we have ime series daa a he UPC level in he US Naional Sample and for each of six Canadian regions in he Canadian Regional Sample. Following Engel and Rogers, for each region pair, we compue he sandard deviaion of he relaive log price changes of he goods common o ha pair. In paricular, we calculae ugcc', ugcc', ugcc', 1 sd q ugcc ', ( Δ ) where Δ q = q q. This is he same saisic ha Engel and Rogers use in heir sudy bu compued a he UPC level raher han a he produc group level. We hen regress hese sandard deviaions on he log of disance beween he regional pairs (couning he US as anoher region) and a border dummy, using he average disance beween he Canadian region and our sample of ciies as a proxy for he Canadian region s disance o he US. Tha is, we jus use his ime-series proxy for marke segmenaion as he dependan variable in regression (9). The resuls from his exercise are presened in Table 5. A firs glance, he resuls are quie similar o hose of Engel and Rogers (1996) we find ha he sandard deviaion of relaive inflaion raes rises wih disance and jumps discreely a he border. This resul is suggesive of rade coss and border effecs maering for price arbirage. However, wha is mos sriking is he magniude of he border. While Engel and Rogers found a border effec of 3.8 million miles for 19

21 he food a home secor, we find a more modes border ha is 3 miles wide. Thus he UPC level daa also suggess much smaller relaive border effecs even when we use he same proxy for marke segmenaion as Engel and Rogers. Bu why do hese resuls differ so much? Before we begin our invesigaion of he cause for he much smaller border effec, i is useful o firs focus on why i is likely ha disaggregaed daa would produce differen resuls. The major difference beween Engel and Roger s use of price indexes and our use of UPC level daa is ha price indexes are averages of individual price quoes. We have already seen in our analysis of he sample saisics ha individual price movemens exhibi enormous volailiy in he ime series bu here is no much difference in he average price level across ciies. Thus, averaging he prices of UPCs ogeher ends o eliminae much of he idiosyncraic variance of UPCs and leaves us wih only he relaively small levels of variance of average prices across ciies. Inernaionally, however, he impac of exchange rae flucuaions is no compressed by averaging because he impac is common o all UPCs in a counry. This causes he border coefficien o fall less slowly han he disance coefficien. Since we divide by he disance coefficien when compuing he border effec, ceeris paribus, his will end o make he border appear wider. We can see his formally by conducing he following exercise. We can decompose he change in he relaive price as follows: (14) Δ qugcc' = δcc' + δe + εugcc', where he δ s correspond o ciy pair and exchange rae shocks, and ε ugcc is he idiosyncraic shock o a UPC. Similarly if wo ciies are in he same counry, we decompose he price movemen using he same erms wih he excepion ha δ e = 0. If we assume ha all hese erms are independen, hen we can wrie (15) ( ) Var Δ qugcc' = σ cc' + σe + σε in he case when he ciies are in differen counries and 2 2 (16) ( Δ ) = σ + σ Var q ε ugcc' when he ciies are in he same counry. In his case he border effec (expressed in erms of raios of variances insead of sandard deviaions) would be cc ' 20

22 (17) ( qugcc' ) Inernaional ( Δqugcc' ) Var Δ σ + σ + σ = Var Domesic cc' e ε 2 2 σcc' + σε However, if here are n UPCs in a produc group and we firs average he daa before compuing he variances, he raio of he variances will be (18) Var Var ( Δqugcc ' ) Inernaional ( Δqugcc' ) Domesic σ ε σcc' + σe + = n, 2 2 σ ε σ cc' + n which is sricly larger han he expression given in equaion (17) for n > 1. This suggess ha if one compues border effecs by comparing he variances of relaive prices using price indexes, one will end o find larger effecs han if one uses he underlying micro-daa. Moreover in daases like ours, where he variance of he idiosyncraic shocks is likely o be large and he variance of bilaeral ciy-pair shocks small, one would expec his effec o be subsanial for large n. In Table 6, we examine his aggregaion bias by running he same regressions ha we ran in Table 5, bu firs pooling he UPC level daa o form produc group averages and hen compuing he sandard deviaions in he movemens of he produc group level prices. We presen wo ses of resuls based on he wo differen ways of pooling he daa given by equaions (11) and (13). As one can see from he upper panel of his able, he coefficien on he border dummy quadruples and he widh of he border rises subsanially (relaive o Table 5). Averaging he daa causes he widh of he border o rise o 1000 o 100,000 miles depending on he specificaion. Alhough hese numbers are much larger, hey are sill smaller han he ypical border effecs of millions, if no quadrillions of miles, ha ofen appear in sudies. The lower panel of Table 6 shows he widh of he border based on aggregae ciy-specific price indexes. A key disincion beween hese aggregae prices and hose used in he upper panel is ha each producgroup index is an average of a much larger number of UPCs han in he upper panel. This is because he share of common goods across he border is less han 5 percen he size of he sample of goods in each region in Canada. As we noed earlier, his suggess ha we migh expec o see even larger border effecs if we jus formed indexes based on he se of UPCs consumed wihin a ciy in a paricular produc group. We verify ha using indexes based on all. 21