Modern trade theory for CGE modelling: the Armington, Krugman and Melitz models

The Armington specification of international trade, based on product differentiation at the country level, has been at the heart of computable general equilibrium (CGE) modeling for 40 years. Starting in the 1980s with the work of Krugman and more recently Melitz, trade theorists have preferred specifications in which product differentiation is assumed at the firm level. We draw out the connections between the Armington, Krugman and Melitz models by deriving them as successively less restrictive special cases of an encompassing model. We then investigate the optimality properties of the Melitz model, demonstrating that a Melitz general equilibrium is the solution to a global, cost-minimizing problem. This raises the possibility that envelope theorems can be used in interpreting results from a Melitz model. Next we explain the Balistreri-Rutherford decomposition in which a Melitz general equilibrium model is broken into a set of Melitz sectoral models combined with an Armington general equilibrium model. Balistreri and Rutherford see their decomposition as a basis of an iterative approach for solving Melitz general equilibrium models. We see their decomposition as a means for interpreting Melitz results as the outcome of an Armington simulation with additional shocks to productivity and preferences variables. The paper is written for CGE modelers and others who want to gain access to modern trade theory. This theory would not be of interest to CGE modellers if there we no prospect for empirically determining parameter values. Consequently we explain how parameters are being estimated for Melitz models. Also with CGE modelers in mind, we describe our computational experience in solving a Melitz general equilibrium model using GEMPACK software. With GEMPACK, Melitz general equilibrium solutions can be computed directly without the Balistreri-Rutherford iterative process. However, the Balistreri-Rutherford decomposition plays a key role in our interpretation of welfare results. Their decomposition allows us to express the welfare result for the effects of a tariff change in a Melitz general equilibrium model as the sum of five components computed from an Armington model: the employment effect; the terms of trade effect; the tax-carrying-flow or efficiency effect; the production technology effect; and the conversion technology or preference effect. The first three of these components are familiar from Armington models. The last two factors are additions to Armington supplied by Melitz. A striking feature in our computations is that these last two components are approximately offsetting, leaving the Melitz welfare result close to that which could be obtained from an Armington model. We conjecture that the offsetting feature is an envelope implication. That our computed welfare effects of a tariff change in a Melitz general equilibrium model depend almost entirely on Armington mechanisms (terms-of-trade and efficiency effects) suggests that results from a Melitz model might be more generally equivalent to those from an Armington model. Initially we test this idea by comparing tariff results from Melitz and Armington models built with identical databases and with identical values for the inter-variety (or Armington) substitution parameter, s. In this test, the Melitz results imply that tariff increases have much more restrictive effects on trade flows and larger welfare effects in absolute terms than the Armington results. It is tempting to interpret this as meaning that the Armington specification leads to under estimates of the restrictiveness and welfare effects of tariffs. However, we don’t think that such an interpretation is legitimate. To us, it demonstrates that s = x in a Melitz model doesn’t mean the same thing as s = x in an Armington model. 5 Potentially, it is possible to observe the response of trade flows to tariff changes. Let’s assume for the sake of argument that a Melitz model with s = x correctly produces these responses. Can we build an Armington model on the same database as that of the Melitz model which also correctly produces the trade flow responses? Through a series of computations in an admittedly simple framework, we find that the answer is yes. There exists an Armington model with s > x that is closely equivalent in terms of trade responses and welfare effects to a Melitz model with s = x. Conditional on this result being substantiated in further research, we conclude that: (a) Melitz is really a micro-foundation story for Armington; and (b) that CGE modellers can embrace Melitz without throwing away their Armington-based models.