The use of three-dimensional models as a tool to analyse migration flows has substantially increased during the last decade. These models are very popular in analysing economic phenomena related to the movement of goods and services, capital and people. In fact, while gravity models have been used extensively in the analysis of trade determinants, only due to the recent availability of time-varying origin-destination migration data, have multi-dimensional panel data models been applied in order to improve our understanding of migration flows. Recent contributions have also provided the micro-foundations of gravity models in the context of migration analysis and, nowadays, the literature is expanding by considering the role of different factors and policies under the framework provided by Random Utility Maximization (RUM) models. The aim of this chapter is to provide a survey of recent developments in multi-dimensional panel data models in the context of migration analysis, to identify the problems that researchers face when using these models and to review potential new directions in this field of research.
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