This seminar will focus on the estimation of gravity models, which are important theoretical spatial models.
The gravity models are generalization of the natural gravity model in physics but they are generalized to have interactions with n regions instead of just two regions.
A gravity model in trade concerns flow variables. The first gravity model has been proposed by Anderson (1979) and subsequently generalized by Anderson and Wincoop (2003). However, their gravity model is formulated under the assumption that the supply of traded quantity is predetermined in each country.
Their later assumption of inelastic supply of traded quantity seems too strong.
Subsequentially, in order to relax such restrictions. Behrens et al. (2012) propose a dual utility approach with the assumption that the supplied trade quantity is the amount such that the profit of a country will be reduced to zero (due to competition). Based on the duality of utility function, Behrens et al. (2013) has derived a gravity model with flows from other regions as explanatory variables determined as Nash equilibria, so one may regard such a formulated gravity model as a nonlinear spatial autoregressive flow (SARF) model.
Behrens et al. (2013) has provided a linear SARF model, which approximates at a particular point of a parameter so that one might have a linear SAR-type model for estimation. That linear SAR flow model has been studied and estimated in Behrens et al. (2013) and Lee and Yu (2022).
While Behrens et al. (2013)’s linear SARF model is of special interest, but in this project, we would like to consider the estimation of the structural nonlinear spatial interactions gravity equation and may compare it with the linear approximated model in order to investigate whether a linear approximated SARF model would be appropriate or not. [But the empirical study has not yet been done in those days.]
In order to justify the estimates of the nonlinear gravity model, due to its nonlinearity feature, nonlinear spatial asymptotic theory of spatial mixing and spatial near-epoch dependence (SNED) features could be the important theories in order to study asymptotic properties of those estimates.
In this project, we will attempt to investigate asymptotic properties of the quasi-maximum likelihood estimates for the nonlinear flow model.
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