The Emprcal Economcs Letters, 7(5): (May 008) ISSN 1681 8997 Blateral Trade Flows and Nontraded Goods Yh-mng Ln Department of Appled Economcs, Natonal Chay Unversty. 580 Snmn Road, Chay, 600, Tawan Emal: yxl173@mal.ncyu.edu.tw. Abstract: Ths paper develops a monopolstc competton model wth nontraded goods whch provdes an explanaton for why the real volume of trade s much lower than predcted by Helpman and Krugman's (1985) model. Furthermore, t explans the phenomenon that the volume of trade among hgh-ncome countres s relatvely larger than the volume of trade between hgh-ncome and low-ncome countres. We also derve a testable gravty equaton from ths model. A sample of 1995 ncludng 118 countres s examned. Our results show that evdence from the data s consstent wth the predcton of ths model. Further, the goodness-of-ft ncreases as nontraded goods are consdered. Keywords: Blateral Trade Flows; Gravty Equaton; and Nontraded Goods JEL Classfcaton: F10, F1 1. Introducton In the last few decades, the most mportant development n the theory of nternatonal trade s the monopolstc competton model. Helpman and Krugman (1985) proposed a model n whch monopolstcally compettve frms produce dfferentated goods usng an ncreasng return to scale technology (IRS) and all ndvduals have dentcal homothetc preferences and a love for varety. Ther model provdes an explanaton for the phenomenon of large volumes of trade among smlar countres wth a factor-proportons vew of ntersectoral trade flows, whch could not be explaned by the tradtonal Heckscher-Ohln (HO) theorem. In Helpman and Krugman's model, t s assumed that the economy has free trade, balanced trade, no transport cost, all tradeable goods, and dentcal producton technology across countres. The monopolstc competton model yelds the followng equaton to predct the volume of blateral trade, YY j M j = = s jy (1) Yw where M j s the mports of country from country j, Y ( Y j ) s the gross domestc Y j product (GDP) of country (j), Y w s the total world ncome, and s j = s the share of Y w
The Emprcal Economcs Letters, 7(5): (May 008) 470 country j n total world ncome. Equaton (1) means that the blateral trade flows are postvely related to the product of countres' GDPs, whch s the smplest form of gravty equaton. However, the volume of trade n the real world s much less than the amount predcted by equaton (1). For example, the volume of trade n the world s about 5,14 bllon U.S. dollars, whch s much lower than the predcted number, 5,033 bllon US dollars n 1995. Obvously, the blateral trade flows are overestmated by Krugman and Helpman's model. Many possble factors could reduce the blateral trade flows. For example, hgh transport cost could decrease the volume of trade. Most countres do not have completely free trade. Further, not all goods n the real world are tradeable such as servces, educaton, and housng. All of these facts wll reduce the volume of trade. However, most of the semnal studes do pay attenton to the nfluence of transport cost. The gravty equaton, n general, shows that the volume of blateral trade s not only postvely related to both ncomes, but also negatvely related to the dstance between the two trade partners, n whch the dstance s used as a proxy varable for transport costs. The study of the gravty equaton s probably the most successful emprcal work n nternatonal trade. The model was frst ntroduced by Tnbergen (196) and Anderson (1979) was the frst to derve the gravty equaton theoretcally. Anderson (1979) assumed that preferences are Cobb-Douglas (or CES) and the goods are dfferentated by countres of orgn, whch s called the Armngton assumpton. Bergstrand (1985) used CES preferences over Armngton-dfferentated goods to develop a general equlbrum model of world trade, thus yeldng a reduced-form gravty equaton for blateral trade nvolvng prce ndces. In ths paper, the assumpton that all goods are tradable s relaxed. I ncorporate nontraded goods n a monopolstc competton model. Ths model tres to provde an explanaton of why the real volume of trade s much lower than predcted. The ntuton s qute smple. It s because the countres do not have so many goods that are tradable n the real world. An estmable gravty equaton can be derved from ths model. Moreover, snce ths model ncorporates nonhomothetc preferences, t also can explan the phenomenon that the volumes of trade among the ndustralzed countres are relatve large to the volumes of trade between developed and less-developed countres, whch was proposed by Lnder (1961) and Markusen (1986). Markusen (1986) proposed a nonhomothetc model to explan the dfference between the volume of W-E trade and the volume of N-S trade. Unfortunately, hs model does not offer a testable model to predct the volume of trade from hs model. However, n the extenson of hs paper, Hunter and Markusen (1988)
The Emprcal Economcs Letters, 7(5): (May 008) 471 proposed a nonhomothetc model and estmated a lnear expendture system (LES) to show that the demand s nonhomothetc. The remander of ths paper s organzed as follows: n Secton, we set up the model and derve the gravty equaton wth nontraded goods. Secton 3 descrbes the data sets used n ths study. The emprcal results are gven n Secton 4. They strongly support the predcton of ths model n a sample of 118 countres n 1995. Secton 5 concludes.. The Model In ths secton, the model s set up. Consder an open economy whch has balanced trade, no transport costs, and wth dentcal producton technologes. There are m countres and two types of goods, tradeable goods ( x k ) and nontraded goods ( z ). The tradeable goods x are dfferentated manufactured goods whch are produced wth producton ( ) k technologes wth ncreasng returns to scale. The nontraded good s a homogeneous commodty and s produced wth a constant returns to scale (CRS) technology. It s assumed that all ndvduals consume tradeable goods as well as nontraded goods. Consumers have the followng dentcal nonhomothetc preferences, whch are gven by ( x ) u( z) α 1 k k + 0 < 1 U = α where u () s a strctly concave functon. < α () All ndvduals maxmze ther utlty subject to ther ncome. Snce the subutlty functon for dfferentated goods s homogeneous of degree one, we can use a two-stage budgetng procedure to solve ths utlty maxmzaton problem. The consumer's problem can be rewrtten as: Max U = ℵ + u( z), (3) s.t. P ℵ + p z z = I. α 1 k where I s ndvdual ncome, ℵ = ( ) α goods, P k k x s the quantty ndex for dfferentated ( α 1) α α ( α 1) = k p k s the prce ndex for ℵ, p z and p k for good z and x, respectvely. If we consder ℵ as the numerare, the utlty can be consdered as a quas-lnear utlty functon. Accordng to the property of quas-lnear utlty functon, the consumpton of z s constant whch s determned by () z p z u = (4) P
The Emprcal Economcs Letters, 7(5): (May 008) 47 for all consumers f the ncome s bg enough. There s no ncome effect for z. Increasng ndvdual ncome does not change the quantty of demand for good z at all, and all the extra ncome goes entrely to the consumpton of dfferentated goods. Let z = z satsfy equaton (4) whch means that z s the demand quantty of notraded good for every consumer n every country and thus s ndependent of ndvdual ncome and the prces of the dfferentated commodtes. Furthermore, t s also assumed that the ndvdual's ncome n every country s bgger than z. Due to ths specal property of the nonhomothetc preference, the producton of nontraded good for country s Z = nz and s produced frst n country, where n s the populaton of country. In addton, the dfferentated manufactured goods are produced and freely traded. Just lke the mperfect competton model proposed by Helpman and Krugman (1985) and Helpman (1987), a number of frms produce one dfferentated commodty n a monopolstcally compettve market. Also, all frms are equpped wth dentcal IRS technology, and free entry leads to zero proft n equlbrum. In ths model, the volume of trade s dfferent from the result of Helpman and Krugman (1985) but smlar. Snce ths property of nonhomothetc preference s love for varety for dfferentated goods, each country wll demand all foregn varetes accordng to the country's share of world value of dfferentated goods. Therefore, the value of dfferentated goods that country mports from j, denoted M, s X X j M j = (5) X w where X j s the value of a dfferentated good produced n country j, and X w = j X j s the world output of dfferentated goods. Let Y = X + Z denote the GDP of country. Rearrangng equaton (5), M j can be rewrtten as ( Y Z)( Yj Z j) j( Yj Z j) j ( Y nz )( Yj n jz ). M j = = X w Takng natural logarthms of both sdes of equaton (6), t follows that M X Y nz = + Y n z ln ( j ) ln ( w ) ln (( )( j j )) ( Xw) YY j Yjnz Yn jz nn j( z ) where ln ( X w ) s a constant. ( ) = ln + ln +, (7) (6)
The Emprcal Economcs Letters, 7(5): (May 008) 473 In order to derve an estmable gravty equaton, t s necessary to lnearze the last term of equaton (7). Applyng the frst order Taylor seres approxmaton at z = 0, t yelds the followng estmable gravty equaton: where ln n Y + n Y j j ( M ) = ln( X ) + ln( Y Y ) z + ε j w j Y Y j ( ) ( ) 1 1 = c + ln Y + ln Y j + Z + ε (8) Y Y j y s per capta ncome of country, ε s the dsturbance term. Comparng the new gravty equaton to the conventonal gravty equaton, there s a new tem, 1 1 + z, n ths model. It shows that the blateral trade flow s not only related y y j to the GDP of both countres, but also related to the demand for nontraded goods and the per capta ncomes n both countres. Accordng to the above equaton, blateral trade flow decreases f the consumpton of nontraded goods ncreases or the per capta ncome decreases. It explans that the volume of trade between two rch countres s larger than that between two lower-ncome countres. 3. Data There are three databases used n ths study. The world blateral trade flows data s orgnally obtaned from the CD-ROM World Trade Flows, 1980-1997, wth Producton and Tarff Data. The data used to test ths model s from the year of 1995. There are 18 countres or regons n ths database. In Feenstra (000), t ndcated that the man source for blateral trade data s the Unted Natonal Statstcal Offce. Another data set used n the study s the GDP and per capta ncome data whch s downloaded from Harvard Unversty, CID (Center for Internatonal Development). The GDP and per capta ncome are PPP-adjusted. In Gallup and Sachs (1999), t ndcated that most of the GDP and per capta ncome data are from the World Bank. For countres whch are mssng n the World Bank, the data s obtaned from CIA (1996, 1997). In order to compare ths nontraded goods model and the conventonal gravty model, a dstance data set s also employed. The dstance data set s downloaded from Purdue Unversty. Ths data set contans 137 countres and t provdes the dstance between captal ctes n klometers. Combnng the above three data sets, there are 118 countres employed n ths paper.
The Emprcal Economcs Letters, 7(5): (May 008) 474 4. Emprcal Results In ths secton, the gravty equatons derved from the nonhomothetc model are estmated by usng the above data set. Based on equaton (8), the gravty equaton can be specfed as the followng two forms ( ) α β ( ) β ( ) 1 1 ln M j = + 1 ln Y + ln Y j z + + ε (9) y y j where α, β and z are the coeffcents to be estmated. Theoretcally, αˆ s expected to be negatve, z should be postve, and 1 ˆβ and ˆβ should be around 1. In order to demonstrate the advantage of ths new model, the conventonal gravty equaton s also to be estmated, whch s ( M ) α + β ln( Y ) + β ln( Y ) + ε ln 1 (10) j = j Ordnary Least Square (OLS) estmaton s employed to estmate the above regressons. The estmaton results are shown n Table 1. There are 13,806 observatons n ths sample. In Table 1, t shows all of the estmated coeffcents n equaton (9) and (10) are sgnfcant at 1% sgnfcant level. The most mportant s that all of the sgns of the estmated coeffcents concde wth our expectaton. In partcular, ẑ s around $1,053 n ths model, whch means that all ndvduals consume at least about $1,053 goods produced by ther country every year. It can be found that the estmated coeffcents of GDPs n Equaton (9) are sgnfcant closer to unty than n Equaton (10) whch means that ths new model has a theoretcal advantage. Ths nontraded goods gravty equaton s more consstent wth the data than the conventonal gravty model. The R of Equaton (9) s about 0.60, whch s bgger than the R n Equaton (10). That shows that the goodness-of-ft of ths new model s better than the conventonal model. Next, ths paper examnes the performance of ths model when a dstance term exsts and compare the tradtonal gravty equaton wth a dstance term. The results are also gven n Table 1 where Equaton (9 ) and Equaton (10 ) are Equaton (9) and Equaton (10) wth dstance term, respectvely. The δ s the coeffcent of the dstance term n each model. Just lke the results above, the sgns of estmated coeffcents are as expected and sgnfcant. We also can fnd that the estmated coeffcents of GDPs are also much closer to unty than the result of Equaton (10 ).
The Emprcal Economcs Letters, 7(5): (May 008) 475 Table 1: Estmaton Results Coeffcent Equaton (9) Equaton (10) Equaton (9 ) Equaton (10 ) α -1.78-6.6-9.63-15.40 (0.317) (0.35) (0.416) (0.361) β 1.51 1.68 1.5 1.71 1 (0.017) (0.015) (0.016) (0.014) β 1.14 1.3 1.15 1.34 (0.017) (0.015) (0.016) (0.014) z 1053.34 1163.45 (47.7) (44.606) δ -1.41 (0.034) -1.36 (0.034) R 0.603 0.588 0.647 0.630 Note: Standard errors are gven n parentheses 5 Conclusons In ths paper, we tred to provde an alternatve explanaton of why the real volume of trade s much less than the volume predcted by Helpman and Krugman's model. We consder nontraded goods as an mportant mpact on blateral trade flows. Furthermore, ths model explans why the volume of trade between N-S s much less than the volume among developed countres. We developed a model wth nontraded goods and nonhomothetc preferences and derved an estmable gravty equaton. The model tres to make a connecton to brdge the gap between theory and emprcal work on the role of nontraded goods. Ths model fnds that blateral trade flows are not only related to the GDP of two countres, but also related to the per capta ncome of the two countres. The ndvdual consumpton level of nontraded goods can be estmated, whch s also related to blateral trade flows. In the emprcal work of ths study, we employed a sample of 1995 data wth 118 countres to test ths model. The emprcal results are consstent wth the expectatons from ths model. References Anderson, J., 1979, A theoretcal foundaton for the gravty equaton, Amercan Economc Revew. 69, 106-116. Bergstrand, J., 1985, The gravty equaton n nternatonal trade: some mcroeconomc foundatons and emprcal evdence. Revew of Economcs and Statstcs, 67, 474-481. CIA, 1996, The World Factbook. Washngton, D.C. Central Intellgence Agency.
The Emprcal Economcs Letters, 7(5): (May 008) 476 CIA, 1997, The World Factbook.http://www.odc.gov/ca/publcatons/factbook/ndex.html. Feenstra, R., 000, World trade flows, 1980-1997, wth producton and tarff data, Workng Paper, Unversty of Calforna, Davs. Gallup, J. and Sachs, J., 1999, Geography and economc development, Workng Paper, Harvard Unversty. Helpman, E., 1987, Imperfect competton and nternatonal trade: evdence from fourteen ndustral countres. Journal of the Japanese and Internatonal Economes, 1, 6-81. Helpman, E. and Krugman, P., 1985, Increasng Returns, Imperfect Competton, and Foregn Trade. Cambrdge: MIT Press. Hunter, L, 1991, The contrbuton of nonhomothetc preferences to trade. Journal of Internatonal Economcs, 30, 345-358. Hunter, L. and Markusen, J., 1988, Per capta ncome as a bass for trade. In R. Feenstra (eds.), Emprcal Methods for Internatonal Trade, Cambrdge: MIT Press. Lnder, S., 1961, An Essay on Trade and Transformaton. New York: Wley and Sons. Markusen, J., 1986, Explanng the volume of trade: an eclectc approach. Amercan Economc Revew, 76, 100-1011. Tnbergen, J., 196, Shapng the World Economy: Suggestons for an Internatonal Economc Polcy. New York: Twenteth Century Fund.