Four Essays on the Gravity Model

Abstract

For the first time in empirical economic research, Jan Tinbergen, one of the first Nobel laureates in economics, adapted and applied Newton’s gravity equation to international trade flows. His research was published as a book: Shaping the World Economy: Suggestions for an International Economic Policy (1962), with August Heckscher as a secondary coauthor. Since then, the gravity model has become a major workhorse in empirical studies in international economics in particular, though its theoretical justification remains somewhat tenuous. This dissertation contributes four essays all related to the gravity model. Essay One deals with two almost universal observations in a countless number of empirical studies that employ the gravity model. The first observation is that the income (or GDP) of both the importing country and the exporting country has a positive effect on the importing country’s imports. The second observation is that the exporting country’s GDP has a greater effect than the importing country’s GDP on its import. While theoretical discussions of this first observation exist in economic literature, none exists regarding the second observation. Starting from the macroeconomic equilibrium condition for open economies, this essay derives a theoretical outcome consistent with the first and second observations. Though the outcome is in linear form, it still justifies the log-linear gravity model since in general there are sign and order agreements, under certain conditions, between the coefficients of a linear model and those of the corresponding log-linear model. Essay Two provides a theoretical justification for the relevance of the gravity model to the transnational terrorism flows in two approaches, assuming the household production of illegal products. The first approach presents a qualitative justification for the relevance of the gravity model. The second approach provides a more rigorous quantitative justification for the gravity model, based on a modified ellipse function, by deriving the mathematical results that show, under certain conditions, both the source and host countries have a positive income effect on transnational terrorism, with the source country’s income effect greater than that of the host country. Essay Three derives an aggregate form of gravity model that can indirectly estimate the coefficients of the underlying bilateral gravity model, which is useful especially when the bilateral data on transnational terrorism are either unavailable or questionable in quality. Using a sample of aggregate panel data on transnational terrorism flows among G-8 countries (G-7 plus China) for a sixteen-year period (1996-2011), we find that the aggregate gravity model performs well in the sense that it produces empirical results consistent with what would be expected of the underlying bilateral gravity model when regressed on a bilateral data. Essay Four develops a new approach to testing whether a gravity model is correctly specified by carrying out a two-way linear restriction test. In doing so, we use two equivalent gravity models: the import gravity model and the trade volume gravity model. We demonstrate that there is a set of linear restrictions that relate the two coefficient vectors, which can be used to test for specification error. Since there are two unknown vectors of coefficients, as opposed to the usual one, we replace either unknown vector with its consistent estimator as its proxy. Monte Carlo experiments show that this approach with the consistent proxy is quite promising in testing whether a gravity model is correctly specified, under-specified, or over-specified.