DISCUSSION PAPER DRD82 I~TRA-INDUSTRY SPECIALIZATION: A :-fULTI -COl'!\TRY PF.RSPECTI VE Bela Bi1lassa June 1984 Development Research D~partment Economics and Researc~ Staff World Bank . f - .. · .. ·- The views presented here are those of the author, and they should not be interpreted as reflecting those of the World Bank INTRA-INDUSTRY SPECIALIZATION: A HULTI-COUNTRY PERSPECTIVE Bela ~lassa * (with a Technical Appendix by Luc Bauwens) June 1984 * Professor of Political Economy at the Johns Hopkins University and Consult~ntfto the World Bank. The paper was prepared in the framework of the world Bank's research project "Changes in Comparative Advantage in Manufactured Goods" (RPO 672-41). The author is greatly indebted to Luc Bauwens for his suggestions on alternative estimation procedures and for carrying out the arduous task of estimation; Mr. Bauwens also made very useful comments on the previous drafts of the paper. Valuable comments were further - · received at seminars held at the Johns Hopkins University, the Un~versit~ de Pa~is I (Sorbonne) and the World Bank. Finally, thanks are due tg,L~nda · · Pacheco and Marcus Noland for data collection and to Jerzy Rozans~ for generating the trade data. However, the a~thor alone is responsible for the opinions expressed in the paper that should not be interpreted to represent the views of the World Bank. ------------------------- Abstract This paper has tested various hypotheses as to the determinants of intra-industry trade in thirty-eight developed and developing countries exporting manufactured goods. The econometric estimates for the entire group of countries show that the extent of intra-industry trade increases with the level of economic development (GNP per head), the size of domestic markets (GNP), and the openness of national economies. The ex~stence of trading partners with common borders and geographical proximity further cont.ibutes to intra-industry trade. These hypotheses have also been confirmed for the developing country group. And while similarities in regard to trade odeftttl;Ton'a~d "the. existence of border trade, as well as intercorrelation be~t1le<'gr'oss national product and per capita GNP, have reduced the statistical significance of the regression coefficients for these variables for the developed country group, the equation has a high eAplanatory power. . f - - · · - ----------------------------------.- ............ INTRA-INDUSTRY SPECIALIZATION: A MULTI-COUNTRY PERSPECTIVE Bela Balassa Since the time this author firdt introduced the concept of intra- industry -- as compared to inter-industry -- trade (Balassa, 1966), a vast literature has developed on the subject. Efforts at the measurement of the extent of intra-industry specialization, i.e. rt~ relativ~ importance within a country's total trade, have been complemented by research on: the theory of intra-industry trade and its determinants. 1/ The present paper investigates the determinants of intra-industry specialization in a cross-country framework, by tnttlg ·.the" aoutltrt' aathe unit of observation. It sets out to explain the exten~_of int~&-t~dostry trade in countries exporting manufactured goods by reference to country characteristics affecting such trade. This is a neglected area as most contributions have examined the effects of commodity characteristics on intra-industry specialization. Exceptions ate Loertscher and Wolter (1980) and Havrylyshyn and Civan (1983), to which reference will be made below. Section I of the paper will consider a variety of possible hypotheses that may be put forward to explain the extent of intra-industry trade in a cross-country' framework. Section II will describe the methods and data used · in the process of estimation. Section III and IV, respectively, will provide - the empirical results for all f the countries under study and for the developed .. : and developing country subgroups, respectively. Section V will provLde a · brief overview of the principill firidings. _ · · 1/ The expressiun::: "intra-industry trade" and "intra-industry specialization" will be used interchangeably In the paper. - 2 - I Staffan Burenstam Linder (1961) was the first to suggest that, at higher levels of economic development, international trade will increasingly involve the exchange of differentiated products; i.e. intra-industry specialisation. Following Linder, one may formulate the hypothesis that the .. extent of intra-industry trade will be positively correlated with the level of · economic, development. In turn, starting with ¥:ugman (1919) and Lancaster (1980), a number of writers have emphasized r~e role of economies of scale in intra-industry trade. They have shown that, in the e\'ent of product dUf~q~~..1on~, : economies of scale will give rise to intra-industry speCialization between countries with identical resource endow~ents, production functiona, an~ tastt!s. Subsequently, 'Krugman (1980) hu concluded that, in the event of transportat:Lon costs, a country with a larger domestic market will be a net exporter of differentiatee productD subject to economies of scale and a country with a smaller docestic market will be a net exporter of standardized products subject to constant return'i to Bcale. Special cases aside, there will nevertheless be intra-indu~try trade in the products subject to economies of scale, ,with larger countries accounting for a relativ~ly high proportion of this trade. " Correspondingly, it may be hypothesized that the extent of intra- industry trilde will be positively correlatecl with the size of domestic f ... markets. - - Krugman (1980) has further shown t"t, in a model of product · different lation under economies of scale, '.11th trade taking place between two identical countries, the introduction of transportation costs in the form of a uniform It·ss in transit per unit of product will n'lt affect the number of - 3 - firms or output t>er fif:: in either country. However, the prices of i~ported goods will rise relative to the prices of domestic goods in both countries, thereby leading to a decline in the volume of intra-industry trade. Thus, one may hypothesize that the extent of such trade will be negatively correlated with transportation costs. In a model of intra-industry trade incorporating specific capital and constant returns to sCdle, Falvey (1981) has concluded that the \olume of this trade will vary inversely with the level of trad~ restrictions. In analogy to transportation costs, this conclusion can be extended to the case of intra- industry trade in products subject to economies of scale. forward the hypothesis that the extent of intra-indust:ry t~il1·· ·*W, be negatively correlated with the level of trade restrictions. Grubel and Lloyd have suggested that, in countries sharing a common border, intra-industry trade may occur "in products which are functionally homogeneous but differentiated by location" (1975. p. 75). Correspondingly, it can be hypothesized that the extent of intra-industry trade will increase in a country that shares a common border with its trading partners. Finally. this author has examined the relative importance of intra- industry trade in the framework of integation arra~gements in Western Europe (1966 and 1975) and in Latin America (1979). In the following, it will be hypothesized that economic integration tends to increase the extent of intra- ~ . f industry trade. · II Tn the present paper, the hypotheses put forward to explain the .-.- . extent of intra-industry trade in particular countries have been tested in a cross-country iraw~~v~!~. !hi~ has involved explaining intercountry - 4 - differences in the extent of intra-industry trade by simultaneously introducing the described hypotheses in the estimating equations. The investigation has been limited to manufactured goods that are characterized by product differentiation and are subject to economies of scale, with the exclusion of natural resource products whose trade is much · influenced by the availability of such resources in individual countries. The · commodity classification scheme utilized has been established on the basis of the United States Standard Industrial Classification, 2! with 4-digit SIC categories merged in cases when the economic characteristics of the products in question were judged to be very similar. :! The investigation covers 38 countries whose manufactured exports exceeded $300 million in the year 1979 and accounted for at least 18 percent of th~ir total exports. This benchmark has been chosen in order to avoid spurious correlations between the extent of intra-industry trade and the level 1/ The investigation excludes foods and beverages (SIC 20), tobacco (SIC 21), lion-ferrous metals (SIC 333), as well as several 4 digit categories covering textile waste, preserved wood, sawmill products, prefabricated wood, veneer and plywood, wood pulp, dyeing and tanning extracts, fertilizers, adhesives and gelatin, carbon black, petroleum refining and products, asbestos and asphalt products, cement and concrete, lime, gypsum products, cut stone products, and 1apidary work. It ,also excludes ordnance (SIC 19), for which comparable trade data are not available. In turn, all SITC categories in · classes 5 to 8 were included in the Loertscher-Wolte~ study and these classes _less iron and steel (68) in the Havrylyshyn-Civan study. ~ 'f 62/ This contrasts with investigations by other authors, including the studies _:Sy Loertscher-Wolter and Havrylyshyn-Civan, which used the 3-digit Standard ~International Trade Classification for this purpose. The 3-digit SIT. scheme ;is to a considerable extent arbitrary and cannot be regarded as an · economically meaningful ~lassification. -- In earlier work by the author, a combination of 3-and 4-digit SITC items has b~en used to establish an economically meaningful classification scheme (1966). The use of an industry classification scheme utilized in the present paper is, however, superior to this trade classification scheme. - 5 - of economic development through the inclusion of countries which hardly export any manufactured goods. ~ The investigation pertains to the year 1971. The index of intra- industry trade for a particular country (1IT j ) has been derived as in (I), where ~j~ and Mj~' respectively, refer to the adjusted exports and imports of commodity i by country j. The formula makes adjustro.ent for the imbalance in total trade, when Xj stands for total exports and M for total imports. j !.! The index takes values from 0 and 1 as the extent of intra-industry trade increases. 31 Xji Mji f IXj~ - M~il t y:- - R- j j (I) lIT - 1 - · l'~ j X M t (xji + "Ji) f Xj ( ji + ji) H'j 1/ Loertscher-Wolter limited their investigation to the OECD countries while Havrylyshyn-Civan included a numher of low income countries that export little mpnufactured goods. In the 62 country saaple u~ed. by these authors, the share of manufactured products in total exports did not reach 1 percent in Nigeria, the Central African Republic, Sudan, and Algeria while manufactured goods account for over 70 percent of total exports in most of the developed countries. f 2i A consistent adjustment procedute was first proposed by Aquino (1978). However, while Aquino adjusted for %he imbalance in trade in manufactured goods, in the present investigatio~djustment has been made for the imbalance in total trade, so as to allow for tnter-industry specialization between primary and manufactured goods (Balassa, 1979). -- The .\quino adjustment is used in the Loertscher-Wolter and Havrylyshyn-Ci\'8' studies. 3/ I am indebted to Carl Christ for suggesting the trallsformation of equation (I) shown here. - 6 - The level of development has been defined as GNP per head (YIP). A dummy variable for developed and for developing countries has also been tried, but it has given poor statistical results. At any rate. the use of a continuous variable that recognizes the existence of gradation over the scale of economic development is preferable to a dummy variable that provides a binary classification. · Market size has been represented by the gross national produc~ (Y). While the domestic consumption of manufactured goods would have been a more appropriate measure of the size of domestic market for these products. the necessary data are not available for several countries a.a4~.rM!·'!;9\i~je1::·t -"to"","·· considers ble error for others. At the same time, from availa.bl.- -1>{\f.ol'..zaa~LQa_ it appears that the consumption of manufactured goods and the gross national product are highly correlated. Transportation costs have been introduced in the form of a variable for propinquity. This has been defined as the weighted average of the inverse of distance (0) between country j and partner country k, the weights being the gross national product (Y) of the partner countries In recent years, developed countrtes have made increased use of import restrictions that are the principal measures of protection in most . developing countries. Estimates of the tariff equivalent of these measures are few and far between and, at any rate, their use is appropriate o~y under 'f competitive conditions. This being the case, an indicator of trade -· 6 orientation has used to represent the level of trade restrictio~ be~ .. · · Trade orientation has been defined in terms of deviations of actual from hypothetical values of per capita exports. Hypothetical values have been derived from a regression equation that, in addition to the per capita income - 7 - and popul~tion variables utilized in early work by Chenery (1960), includes variables representing the availability of mineral resources and distance from foreign markets. The latter two variables have been included on the expectation that, ceteris paribus. the availability of mineral resources and propinquity will raise per capita exports. l! Mineral resource availability has been represented by the ratio of mineral exports (Xm) to the gross national product. while propinquity has been defined as stated above. The results are reported in equation (2), with t- values shown in parenthesis. As is apparent. the equati~n has a high explanatory power and all the regression coefficients 3re significant at thel percent level. using a one-tail test. (2) log -0.1864 + 0.9212 log (Yj/P ) - 0.3541 log P j j (-0.38) (15.02) (-6.38) Y iJ -2 + o 02510 X m/ y + 0.0598 \ k jk R =< 0.9404 (2.91) j j (2.06) ~ tY k In turn. the border trade variable has been given a value of 1 for · countries that have a common border with at least one cf the trading partners under consideration. Dummy variable~ have also been introduced for membership » l! The described procedure has first been utilized in aa1assa, 1983; a distance variable has been added in the present paper. While population appears in the terms shown on the two sides of the equation, as in Chenery's original formulation, this should not affect the appropriateness of using deviations from hypothetical values as an indicator of trade orientation. - 8 - in the European Common Market and the tatin American Free Trade Area, aa well as for Singapore that has considerable entrepot trade. III Three alternative estimation procedures have been used: ordinary least-squares, nonlinear lealt-squares utilizing a logistic function, and the logit analysis of the same logistic function with weighted least-squares. J! The three alternative estimation procedures have given similar results 1n terms of t,e statistical significance of the variables and the explanatory power of the regression equations, indicating the robustness of the estimates. 11 The best statistical results are reported in Table ~-, The regression coefficients of income per head, the gross national.. product, the trade crientation vdriable, the proximity variable, and the Singapore dummy are all statistically significant at the 1 percent level in every equation while the border dummy is significant at least at the 5 percent level. However, the dummy variables for economic integration are not significant at even the 10 percent level in any of the equations, when combined with the above variables, and they have been dropped from the estimating equations. J! As noted in the Teshnical Appendix, the use of the latter estimation procedure has involved~redefining the dependent variable of the regression equation. The logistil function is more appropriate in the present case as the dependent variable_takes values between 0 and 1; use has also been made of ordinary least-Bquares~_however, in part to test the sensitivity of the results to the choice ~ the estimation procedure and in part for comparahility with other studies. 2/ This has also been the case in using the logit procedure with ordinary :reast-squares, the results of which are not reported here in order to economize with space. - 8A - Table 1 Estimates of Intra-Industry Trad~ for Countries Exporting ~anufactured Products (regression coefficients with t-values in parenthesis) Ordinary" Nonlinear Logit Analysis with Least Squares Least Squares Weighted Least Squares Constant 0.116 (5.26) -1.604 (8.45) -1.530 (8.10) Proximity 0.141 (5.12) 0.611 (4.60) 0.550 (4.02) Border Owr.my 0.098 (2.90) 0.469 (2.01) 0.532 (2.42) Per Capita GNP 0.061 (4.10) 0.311 (4.34 ) 0.347 (4.20) GNP 0.054 (4.84) 0.204 (l.80) 0.219 0.81) Trade Orientation 0.128 (4.52) 0.612 (4.28) 0.600 0.85) Singapore Dummy 0.333 0.95) 1.413 ()".~/·'!' 1.,311 0.361 tt 2 0.8911 0.9184 0.8394 c 0.0610 0.0659 0.0613 N 38 38 38 Note: For definition of variables and explanation of methodology, see text and Technical Appendix. The proximity, per capita GNP, and GNP variables have hen scaled in terms of 10,000 miles, 1,000 dollars, and 100,000 dollars. respectively, and have been expressed in nat~ral logarithr"s. · I f ... - · · · - ----------------------------------- - 9 - The coefflc:tent r,f det;!rmiMtion is 0.90 using ordinary least- squares, 0.98 utilizing nonlinear least-squares, and 0.£4 applying the logit procedure with weighted least-squares. tn turn, the residual standard deviations, estimated as the sum of squares of the residuals divided by the · number of observations, are 0.067, 0.066, and 0.067 in the three case., · t I respectively. ~ The plots obtained with the three alternative estimation procedures are also very similar and show uniformly small deviations from the regression line. Figure 1 provides the resul ts under nonlinear [e."'_ ,.leD;8't;w~",a.. estimatiC'!l. As in the case of the othH two met1fods ()f_.e.~.1mat1on, upward. deviations are r~latively more pronounced for tnd4a. Mexico, Austria and France while downward devlations are larger for Greece, SWitzerland. and Germany. The deviations mal be attributed to random errord rather than to t'.conomic caus~s:; given their smallness, a formal analysis of the residuals has not been attempted. fable 2 comp~re8 the results obtained in the P~vrylyshyn-Civan study by ordinary least-squares with estimates derived using t~e same specification in the present study. The regression equations explain tgree-fourths of the variance of the index of intra-industry trad~ in both cases and, with one · · 1/ For a discussion on the comparability of goodness of fit measures, see the Technical Appendix. - 9A. - , I .... I I ". I I I I · ;:) . ..· I I "I I ,:, I I ;:) I I , .n I .., " I I · ;:) I I I I ., '0 · :::l :\ .n ':) . ':) · ". I · , I :I ......" ... .. .... ,. C ' I I , ... I .t\ ::I ... 10:3 .. l '0· ..... I · c ..... ~~ - o c. CII .... :too .::a · :i- ::) II ... t; ~h .. . Q .... .n I: "'" 110 .. . ::1011 · -- i;.1 !' ,:, ... :- .. 1:! ., ., =- ....= ~ - ::I · '::I ~ 1 ..... :- a ... a- ::I " ..:I ' .::l II . =- '" ..... ;:)· ..· (01\ ., .. ::I .. f 1'\ · · :) · · .... .J ., ..... · GNP J!../ 0.0015 (0.08) -0.0084 (0.91) -0.0003 (0.04) 0.0021 (0.28) 0.0432 d (1.02) > Trade Orientation 0.1045 (2.84) 0.1076 ('\.Il) 0.1216 (4.04) Export Concentration -0.2343 (2.74) -0.6517 (1.44) -0.3656 (0.99) -0.2997 (0.86) -0.2398 (0 .. 7q~ EEC Dummy 0.2683 (5.29) 0.2247 (3.78) 0.1259 (2.30 0.1177 (2.29) 0.0442 (0.87) NIC Dummy 0.1668 (4.15) 0.0936 (1.98) 0.0723 (1.86) 0.0569 (1.51) 0.0226 (0.66) Singapore Dummy 0.2063 (2.20) 0.3293 (1.62) R2 0.7663 0.7397 0.8305 p.8r;03 0.R868 N 62 38 38 ~8 ' 3R Nutes: (a) For definItion of variables. see text and Table 1 (b) Gross domestIc product In the Havrylyshyn-Civan study (c) For complra'bll1ty with the present study the coeffIcIent valu«~6 have been divided by 100. with the exception of tho per capita Income variable where the same Icaiing was used In the twu cases. (d) Expressed In logarithmIc terms · - 11 - associated with a low level of intra-industry specialization. Also, the choice made among low-income countries Involves a considerable degree of arbitrariness, and the selection of a different set of countries might have given rise to different results. By contrast, the present study covers all countries that fulfil the stated criteria. In turn, the poor performance of the domestic market varlable (GOP in the Havrylyshyn-Civan investigation and GNP in the present study) is explained by its introduction in an untransformed form. As shown in Table 2, this variable is highly significant statistically if expressed in logarithmic terms, which compresses the extreme observations and reduces t~'va~iaQility of GNP that is quite large compared to the variability of the index of intra- industry trade. At the same time, the level of statistical significance of the EEC and the NIC dummies declines if the proximity, border trade, and the Singapore dummy variables are introduced in the estimating equations of the present study. ~ And, these dummy variables are not significant statistically at even the 10 percent level if the ~rket size variable is expressed in logarithmic terms. . . . It appears, then, that the use of EEC and NIC dummies involves a misspecification as they pick up the statistical impact of other variables. This conclusion -is of particular interest as far c+ the Common Market is ·conce7ned as it indicates that membership in the ~C adds little to the · · ·effects of proximity and border trade on intra-industry specialization when l! The exclusion of the trade orientation variable does not change this result as this variable is uncorrelated with the other explanatory variables, it having been obtained from the residuals of equation (2). - 12 - the domestic market variable is expressed i~ logarithmic terms. It further appears that the ~IC dummy largely picks up the impact of Singapore#s entrepot trade. Finally, the model specification of the present study has successfully included a policy variable in its effects on intra-industry ~ specialization that i~ absen~ from the Havrylyshyn-Civan study. The result. obtained with this variable indicate that increased openness, reflecting liberal trade policies, leads to greater intra-industry trade. At the same time, the specifications used in the present study have permitted explaining a higher proportion of the variance of the extent of intra-indU8~ry~tr~e.eve~ though the countries under consideration represented a more homogeneous group than in the Havrylyshyn-Civan investigation. IV It has been noted that, in contradistinction with the Havrylyshyn- Civa~ investigation, this study has been limited to countries exporting manufactured products, thereby reducing the heterogeneity of the observations. It has further been noted that the inclusion of a dummy variable for developed and for developing countries has given poor statistical results. * At the same time, interest attaches to caking separate estimates for developed and for developing country subgroups. The separation of developed and developing economies has been effected by taking their 1973 pef capita incomes as the benchmark. Countries - · with per capita incomes of $2250~r · higher have been classified as developed · - - 13 - and countries with per capita incomes of $2030 or lower as developing. with no country being between these two benchmarks. 1/ The separation of the countries under study into two groups does not affect the explanatory power of the regression equation as represented by the coefficient of determination. under the n~nlinear least squares procedure. For the developing country sample, this result obtains also 'under ordinary least squares estimation while the coefficient of determination is higher in this case if logit analysis with weighted least square is .sed. But the explanatory power of the regression is lower for the developed country sample under both the ordinary least squares and the logit procedures. 21 "~" In turn, the residual standard deviation is uniformly lower for the . developing country sample and, to a much lesser extent, the developed country sample than for all countries taken together (Tables 1 and 3). At the same time, as explained in the Technical Appendix, it is the latter procedure rather than the coefficient of determination that permits comparisons of the goodness of fit under the different estimation procedures. Notwithstanding the high explanatory power of the regression equations as countries exporting manufactured products have been divided intu developed and developing country groups, increased intercorrelation among the .. explanatory variables and s~aller variations in the values they take. have ! . reduced the statistical significance of the individual regression - .. .. -------------------------------------- · 1/ Cf. Annex to Figure 1. 2/ Clair. Gaussens. and Phan (1984) used ordinary least squares in an equation pertaining to intra-industry trade among developed countries. The explanatory power of the regression equation was approximately the same as in the present study. .. Table J Estimation of Intra-Industry Trade for Developed and for Developing Countries Exporting Kanufactured Products Developed Countries Developing Countries OrdInary Nonlinear Logit Analysis with Ordinary Nonlinear Logit Analysis with L.east Squares Least Squares Weighted Least Squares Least Squares Least Squares Weighted Least Sq~res Constant 0,1276 (1.08) -1.~872 (J.21) -1.~141 (2.97) 0.2204 (3.99) -1.J648 (J.21) -1.2727 (2.8J) Proximity 0.1~27 (2,41) 0.6236 (2.2~) 0.6408 (2.28) 0.1414 (l.99) 0.6708 (J.02) 0.7021 (2.89) Border Dummy 0.0268 (0.27) 0.1423 (0.33) 0.0880 (0.20) 0.0762 (2.2~) O. ~187 (1.81) 0.~087 (1.64) Per CapIta GNP 0.1219 (1. ~~) O.~254 (1.61) 0.4879 (1.4~) 0.0198 (0.99) 0.1093 (0.14) 0.1388 (0.l8) CNP 0.0209 (0.80) 0.0813 (0.48) 0.08~1 (0.76) 0.0911 (~.25) 0.5101 (4.22', 0.~4l8 (4.22) Trade OrIentation 0.2J41 'lU~)"" 1'1.1302 (1.42) 0.9730 (l.21) 0.148~ (5.29) 0.9036 (4.10) 0.8891 (4.18) 51 ngapore Dummy 0.4570 (6.03) 2.205 (4.9',) 2.2578 (4.60) R2 0.1340 0.9886 0.7463 0.8690 ... .... 0.9681 0.9124 >- 0.0643 0.0624 0.0645 0.0446 0.01.89 O.O~O~ " N 18 18 . 18 20 20 20 Note: See Table 1. · - 14 - coefficients. This is the case, in particular, in the developed c:>untry group where the gross natLonal product and GNP per capita are highly correlated and there is little variation in several of the other variables. Thus, the domestic market variable is nelt significant in any of the equations estimated for the developed country group, and the statistical significance of the per ca~ita income variable barely approaches 10 percent. And while the proximity variable is statistically significant at the 5 percent level in all the equations, the horder variable is not significant at sll. The latter result is explained by the fact that, apart from Australia and Japan, all developed countries have trading partners 'with ccimm.on" bCJr 'racJr. . ",U'u between 0 and 1. There is no guarant~·hb;"'ever, that the pred~ values of the regression equation will fall within this range when linear ~I) or log- linear fanctions are used while such an outcome is ensured if a logistic function is chosen as in (II). l! The latter may also be transformed into (III), provided that the index of intra-industry trade is not exactly 0 or 1, which is the case for all the countries under consideration as indeed it is expected to be if the estl~Ate pertains to individual ccuntries. Under (III), the dependent variable (known as the logit of lIT) can vary between - - and +.- , and the regression equation is linear (in-every case, Xj is defined as the vector of the explanatory variables). . ... . t - .. · · · - l! The author is Researcher at the World Bank. 2/ Other possible choices include the normal distribution function and the Gompertz curve, but they are not as convenient as the logistic function. - 19 - Despite its possible disadvantages, (I) has been estimated by ordinary least-squares (OLS) that has been used by several researchers on intra-industry trade. l! In turn, (II) has been estimated by the use of nonlinear least-squares (~1.S) 2/, while (III), ~',~1\"'rt:at.f.ma't.e.cl. \)>> a.r.d.1nary - ~ least-squares as well as weighted least-squares (Wl.S)~, The La'H"e1!" aethod has been recommended for minimum chi-square estimation of the logit model in the case of multiple observations. 11 It has been applied by Loertacher and Wolter (1980) in the case of intra-industry trade, using to weight the explanatory variables. ~ This method has also be~n used in this study, although questions arise about the theoretical justification for II In fact, the predicted values fall between 0 and 1 in the present study. 21 It should be noted that, in this case, NLS is equivalent to the maximum likeUhood e'stlmation (MLE) of (II) under the assumption that the disturbances are normal. However, such an assuaption would be highly questionable, since by construction the disturbances can only take values between -1 and +1. MLE .could be performed by assuming that the disturbances have a truncated normal ;distribution, or a sfmmetrical beta distribution. Further research on this ·topic is in progress. ~ In a model such as (III), IIT j is an observed proportion, say nj/~j' where . j is the number of observations corresponding to xi' and nj is the number of ·successes". Then if mj is large, the disturbance term of (III) has expectation 0 and variance I/m1' IIT i . (I-IIT j ). The correction for heteroscedasticity thus requires divIding all the (dependent and explanatory) variables by the standard deviation of the disturbance and then applying OLS to the weighted data (Xaddala, 1983, Chapter 2.8). ~ However, they neglected to weight the dependent variable. - 20 - this form of heteroscedasticity in the present context, and the results obtained show little evidence of its existence. Next, we indicate how to interpret and compare estimates of the coefficients under the different specifications. Let Djk(x) denote the partial derivative of IIT j with respect to Xjk (the k-th variable of Xj)' while Ejk (x) denotes the corresponding elasticity. Then, under (I), while if x jk - In Zjk' Under (II) and (ill), Dj~ (z) - ~Aj/zjk. Ejk (z) ~ ak~ . . - · where Aj ~ exp -~'xj/(1+exp-a'Xj)2. : ,6 - - ·- - 21 - When a derivative or an elasticity depends on j, one can compute theE at the sample mean of the relevant variables. 1/ This has been done in the following example, with comparisons made for elasticities of the regression results reported in Table 1, when a subscript * indicates that the elasticity was computed at the 6ample mean. OLS NtS LOGIT(WLS) LOGlT(OLS) proximity 0.361* 0.611 0.550 0.557 'f, per capita GNP 0.156* 0.377 0.)47 0.414 GNP 0.138* 0.204 0.219 0.249 trade orientation 0.023* 0.043* 0.048* 0.047* Finally, we consider how to compare the goodness of fit of the different estimation methods. The R2 is the natural measure in the case of OLS applied to specification (I). In the case of NLS, we compute the ratio of the sums of squares of the predicted values and of the dependent variable, but this ratio is not strictly co~parable to the R2 of OLS, because the sum of . squares in the denominator is the variance of lIT in the case of OLS. For th~ logit specification (III) by OLS or WLS, the R2,s are not comparable with those of OLS and It"LS, since the depende'nt variable is not the same j they f -are not comparable between~lOgit by OLS and by WLS either because the depend;it variable is weighted in the latter case but not in the former. - 1/ An alternative method is to compute the sample me~n of the derivatives or elasticities evaluated at the sample values. - 22 - An alternative procedure is to compare the four methods in terms of the standard deviation of the residuals of lIT. This standard deviation is obtained in a straightforward way in the cases of OLS with (I) and NLS with (11). In regard to (Ill), one has to use the estimates of a obtained by applying OLS or WLS to (III) in the right-hand side of (II) in order to ( compute the deviations between the two sides of (II). The resulting standard deviations will necessarily be greater than the standard deviation of OLS, since the latter method directly minimizes the sum ~f squares with respect to lIT, whereas the logit procedures m1nimi%&~§~~S '0 of squares with respect to the ·f logit of lIT. The results are shown in Tables 1 and 3 · · - . · · - - 23 - SOCRCES Aquino, Antonio (1978), "Intra-Industry Trade and Intra-Industry Specfalization as Concurrent Sources of International Trade in Manufactures," Weltwitschaftliche. Archiv 114 (2), 275-96. Balassa, Bela (1966), "Tariff Reductions and Trade in Manufactures Among Industrial Countrie.," American Economic Review 56 (3), June, 466-73. (1967), Trade Liberalization &mon Industrial Countries: Ob ectives -a-n~a~Al~t-e-rnatlves. 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