Is gravity linear

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The Gravity Model Specification for Modeling International Trade Flows and Free Trade Agreement Effects: A 10-Year Review of Empirical Studies (2010, background): “Theoretical considerations on the proper use and deviations from the gravity model have been a topic of considerable interest in the literature (examples include Feenstra et al. [87]; Anderson and van Wincoop [28]; Henderson and Millimet [80]).”
Intra-national trade costs: Assaying regional frictions (2019, background): “With no variation in intra-regional costs, the effect of border cost variation alone is measured by (26) and hence that portion of ln ÛTBij in (23).”
Ethnic Networks, Information, and International Trade: Revisiting the Evidence (2009, methodology): “Using nonparametric tests, Henderson and Millimet (2008) recommend estimation of the gravity model in levels.”
Natural Disasters and the Effect of Trade on Income: A New Panel IV Approach (2011, unknown): “Santos Silva and Tenreyro (2006) provide a justification of the validity of the conditional mean assumption; see also Henderson and Millimet (2008) on the advantages of the Poisson model in gravity models.”