the regional nearest neighbor tests and by the first order nearest neighbor measures.

Transcription

1 Research Notes and Commenfs 399 the regional nearest neighbor tests and by the first order nearest neighbor measures. It is probable that a model designed specifically to describe the pattern of business centers within cities is required. Such a model may result from the integration of different clustering processes for low order centers or clustering processes for low order centers and deterministic processes for larger centers. Further developments of disturbances on a central place model could offer alternative approaches. LITERATURE CITED 1. ARTLE, R. Studies in the Structure of the Stockholm Economy. Stockholm: The Business Research Institute of the Stockholm School of Economics, CURTIS, J. T. and R. P. MCINTOSH. The Interrelation of Certain Analytic and Synthetic Phytosociological Characters, Ecology, 31 (1950), DACEY, M. F. An Empirical Study of the Areal Distribution of Houses in Puerto Rico, Transactions, I.B.G., 45 (1968), DACEY, M. F. and TUNG, T. The Identification of Randomness in Point Patterns, Journal of Regional Science, 4 (1962), GETIS, A. Temporal Land-use Pattern Analysis with the Use of Nearest Neighbor and Quadrat Methods, Annals, Association of American Geographers, 54 (1964), 391r KING, L. J. A Quantitative Expression of the Pattern of Urban Settlements in Selected Areas of the United States, Tidjschrijt voor Econ. en SOC. Geograjie, 53 (1962), MCCONNELL, H. uadrat Methods in Map Analysis, Discussion Paper 3 (Department of 8 eography, University of Iowa, 1966). 8. ROGERS, A. A Stochastic Analysis of the Spatial Clustering of Retail Establishments, Journal of the American Statistical Association, 60 (1965), A Note Concerning the Development of a Geographic Model of International Trade Maurice H. Yeates International trade can be studied as a special form of interaction in that it involves analysis of movements between places that are politically independent as well as physically separated. Trade between countries is affected not only by the size or purchasing power of the countries, but also by political decisions reflected in multi-lateral and bi-lateral trade agreements. This paper is concerned with demonstrat- Maurice H. Yeates is associate professor of geography at Queen s University, Kingston, Ontario.

2 400 Geographical Analysis ing that the volume of trade between countries can be explained by a modification of the well-known gravity model. There have been many studies by economists of a theoretic [I, 3 61 and econometric [7] nature concerning international trade. Some of these studies, particularly those of Beckerman [2] and Linneman [4] have incorporated into their analyses the effects of distance and economic wealth. They have not, however, incorporated these variables along with trade groups into a model relating to interaction in general. Trade, Mass, and location One measure of particular importance as far as the magnitude of flows is concerned is the mass of the countries involved. As a model is to be developed with respect to a particular country (country A), this refers to the variation in mass among country A s m purchasing partners. In this analysis total national income is used as an operational definition of mass, as it indicates the disposable income available in country j in monetary terms. All other things being equal, it is expected that the countries with the greatest purchasing power will be the most important trading partners. This factor has, however, to be counter-balanced by a second which refers to the varying location of the m trading partners with respect to A. Those countries closest to A should incur lower transport charges for comparative shipments than those further away. They would, therefore, be more competitive. It is extremely difficult to obtain transport costs for international trade as many different types of transport media may be used. In this study, distances along the arcs of great circles connecting the capital of country A with the capitals of the m trading partners will be used to represent relative location and the average transport cost of goods being shipped to or from Country A. The Empirical Model The relationship between volume of trade (imports and exports summed) and the two variables outlined above can be expressed in the form of a multiple regression model. Each variable has been transformed into the common logarithms in order to normalize the data. The model has been empirically examined with respect to a number of arbitrarily chosen countries, which are: Sweden, Canada, Italy, France, the Republic of South Africa, and the United Kingdom. The

3 Research Notes and Comments 407 TABLE 1 PARAMETERS AND CORRELATION COEFFICIENTS PERTAINING TO THE TRADE PATTERN OF SELECTED COUNTRIES* REGPESSION COEFXICIENTS COUNTBY INTEIICEPT NI Distance R Sweden Canada France Republic of S. Africa Italy (1) Italy (2) United Kingdom International trade data from United Nations Yccrrbook of International!Trade Sblislics, 1066 and All data are for 1964 except Italy (2) which are for parameters of the models and the multiple correlation coefficients (R) are listed in Table 1. It is interesting to note that the model provides a reasonable explanation for variations in volume of international trade with respect to most of the countries. The only exceptions are France and the United Kingdom. Examination of the residuals for these countries indicates a much greater trade flow with former colonies and commonwealth countries. A second interesting feature of Table 1 is that the signs of the regression coefficients behave consistently and predictably. All countries tend to have greater volumes of trade with those countries with the largest total national incomes, and the volume of trade increases exponentially, except for France and the United Kingdom where the regression coefficients are less than unity. As far as distance is concerned, the regression coefficients support the postulate that the volume of trade decreases with distance. The distance effect is particularly strong (regression coefficients greater than unity) with respect to Canada, Sweden, and South Africa. m A General Trade Model Thus, from the empirical examples cited, it would seem that the model presented above provides a reasonable statement of some geographic patterns of international trade. The empirically developed multiple regression model can be recalled as follows: where, TRADEAj = the volume of trade (in thousands of U.S.

4 402 Geographical Analysis dollars) between country A and her jth trading partner ; NIj = the total national income (in thousands of U.S. dollars) of the jth trading partner; DAj = the distance (in miles) along the arc of a great circle connecting the capital of country A with the capital of the jth trading partner; and a, b, and c are empirically determined constants. In antilogarithmic form this model becomes This model is similar to the generalized gravity model of flows between one place and many other places [6]. Trading Groups and International Trade It has been mentioned that an examination of the residuals indicates that a major reason for the rather low correlations obtained in the cases of France and the United Kingdom were the greater than expected flows to former colonies. For the United Kingdom these greater than expected flows are the result of a myriad of commonwealth preferences, or special trade treaties, and a similar situation exists with respect to France and her former colonies. The effect of special multi-lateral trade agreements of this type can be examined within the framework of the general model outlined above by the use of nominal variables [S]. The results of the addition of nominal variables to delimit these former colonies are listed in Table 2. It can be observed that the multiple correlation coefficient increases markedly. The associated regression coefficients are positive for both countries, and these can be interpreted as representing positive increments to the constant a TABLE 2 PARAMETERS AND CORRELATION COEFFICIENTS PERTAINING TO THE TRADE PATTERN OF FRANCE AND THE UNITED KINGDOM 1954 REGRESSION COEPPICIENTS Preference COUNTRY INTERCEPT NI Distance Bloc R m France United Kingdom

5 Research Notes and Comments 403 if a trading partner is in the group defined by the binary coded variable. Thus, in the case of France, the equation for former colonies is, TRADEpj = ( ) (Nlj) (Dpj), and for the rest, TRADEpi = (Nlj) (Dpj). In case of the United Kingdom, the equation for the commonwealth preference countries is, TRADE.Kj = ( ) (Nlj) (DuKj) and for the rest, TRADEuKj = (Nlj) (DuKj). Thus it is possible to include within the general model the effect of trading groups, as it can be assumed that the effect of these is subsumed within the proportionality constant of the gravity model. Conclusion The purpose of this note has been to demonstrate that the voluminous international trade data available to the economic geographer can be analyzed successfully within the framework of a general model concerning interaction. The success of the results should encourage further research along these lines. It is possible, for example, to conceive a disaggregation of the data into commodity groupings to determine the effect of distance and trading groups on the flow of individual items. It is hoped that a note of this kind will stimulate more meaningful research into the geography of international trade. LITERATURE CITED 1. BALASSA, B. Changing Patterns in Foreign Trade and Payments. New York: W. W. Norton & Co. Inc., BECKERMAN, W. Distance and the Pattern of Intra-European Trade, The Review of Economics and Statistics, 38 (1956), CHIPMAN, J. A Survey of the Theory of International Trade, Econometnca, 33 (1965), , ; 34 (1966), LINNEMAN, H. An Econometm c Study of International Trade Flows. Amsterdam: The North Holland Press, 1966.

6 404 Geographical Analysis 5. OHLIN, B. Interregional and International Trade. Cambridge : Harvard University Press, OLSSON, G. Distance and Human Interaction. Philadelphia, Pa. : Regional Science Research Institute, 1965, p PRAIS, S. J. Econometric Research in International Trade: A Review, Kvklos. 15 (1962) Sv&, D. B.. The Use of Dummy Variables in Regression Equations, Journal of the American Statistical Association, 52 (1957), Local Structure in the Town Populations of lowa M. F. Goodchild Attempts to identify a central place hierarchy in the observed town populations of an area have been largely unsuccessful. Studies which have claimed a measure of success have either assumed the population levels of the hierarchy, or at least assumed the number of levels. Berry et al. [I] identified a hierarchy in functions and functional units, and demonstrated a close relationship between population and number of functions, but reported no study of a population hierarchy. The line of search for a population hierarchy must be to look for nodality in the town population frequency distribution. The number of nodes is unknown: any fitted model must therefore include it as a variable, together with the node populations. For such a search to have any degree of statistical significance, the study would require a large number of towns, and consequently would cover a large geographical area. Over such an area, social, economic and technological factors might vary considerably, changing the absolute levels, if not the form, of any central place town population hierarchy. Berry et al. [I] have suggested that this is the reason for the apparent lack of success of such studies. This study considers the hypothesis that, although the absolute levels of the hierarchy may vary spatially, an analytic relationship is maintained between them. Specifically, two tests concerning the differences and ratios of population are discussed. Tests The tests define local scale by considering relationships only between nearest neighbors. The first test involves takiig population M. F. Goodchild is assistant professor of geography at the University of Western Ontario, London, Ontario.