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43 IV . On the theory and application of Gravity Models 4.1 Introductio n Gravity models have become predominant in the last four decades in empirical analy- sis of bi later al trade and foreign inves tments . The rst appli cation s (Ti nber gen, 1962; Pölyhönnen, 1963; Pulliainnen, 1963; Linnemann, 1966), however, preceded the theo- retical explanation for the empirical success. It is obvious that the pure formal resemblance between the Newtonian gravity equa- tion and the one used in empirical economic studies is not an adequate explanation of why gravity models have become such popular tools for trade modeling. That is why before the estimation of such a model it is important that I shortly review the most important theoretical explanations behind gravity models and establish a link between empirics and theory. Cha pte r 4 i s st ruc tur ed a s follows: Fir st, in s ect ion 4.2, I br iey ref er to the most important studies that so far have attempted to provide a theoretical basis for gravity models. Section 4.3 reviews the 1985 article of Bergstrand in detail, in which he derives a generalized form of the gravity equ ation. In Section 4.4 I summarize the crucial problems associated with the estimation of gravity models. Finally, in section 4.5, the gravity model is ada pte d to a sin gle -countr y pers pec tive, and I brie y dis cuss the consequences of suc h an approach. 4.2 Theoretical explanations of the gravity models The application of gravity equations to empirical analysis of international trade was  pioneered by Tinbergen (1962), Pölyhonnen (1963), Pullianinen (1963), and Linneman (1966). These early gravity equations generally took the following (log-linearized) form: (4.1) where IM ij is the imports from country i to j, Y  x  ,   P  x denote the aggregate income and the population of country x, and  Dist ij is the geographical distance between i and j. The coef cie nt s α 1 and α 2 are expected to be positive, while α 3 , α 4 , α 5 are expected to be negative in empirical studies. In other words, the volume of foreign trade between two countries is directly proportional with their incomes, but inversely proportional with the geographical distance. Also, one may expect that larger countries trade less in relative terms and consequently the ceteris paribus impact of population should also be negative. As equation (4.1) suggests, the gravity equation was developed for cross-sectional analysis. Gravity equations applied to panel data analysis appeared in the 1980s only, but made the traditional cross-section approach obsolete in a few years. The main reason for 

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