Comparison of welfare gains in the Armington, Krugman and Melitz models : insights from a structural gravity approach

How large are the estimated gains from trade from a reduction in trade costs in the heterogeneous firms Melitz (M) model compared with the Armington (A) and Krugman (K) models? Surprisingly little is known beyond the one-sector model. This paper analyzes this question using a global trade model that contains ten regions and various numbers of sectors (1-10). Following Arkolakis and others (2012), the analysis holds the local trade response constant across the model comparisons based on a structural gravity estimate. Various model features and scenarios are introduced that are important to real economies, almost none of which has been examined across the three market structures with a constant trade response. In response to global reductions in iceberg trade costs, in all the multi-sector models, the ranking of global welfare gains is Melitz < Krugman < Armington; and the Krugman model captures between 75 and 95 percent on the additional gains above the Armington model that are estimated by the Melitz model. However, for individual regions, there are numerous cases of reversed welfare rankings. id est, Melitz < Krugman < Armington. For unilateral increases in tariffs, welfare gains are typically estimated with the Armington model, but welfare losses with monopolistic competition models. The paper constructs a multi-sector Feenstra ratio for the Dixit-Stiglitz variety externality and calculates changes in the terms-of-trade. These parameters provide economically intuitive explanations of the general pattern of results and exceptions. The paper concludes that gains from the reduction of trade costs for the world are: Melitz > Krugman > Armington. For individual regions, however, the welfare ranking of the Armington, Krugman and Melitz market structures is model, data, parameter and scenario dependent. The results highlight the need for data and structural considerations in policy analysis