Michael Jerie

Modern Trade Theory for CGE Modelling: The Armington, Krugman and Melitz Models

This paper is for CGE modelers and others interested in modern trade theory. The Armington specification of trade, assuming country-level product differentiation, has been central to CGE modelling for 40 years. Starting in the 1980s with Krugman and more recently Melitz, trade theorists have preferred specifications with firm-level product differentiation. We draw out the connections between the Armington, Krugman and Melitz models, deriving them as successively less restrictive special cases of an encompassing model. We then investigate optimality properties of the Melitz model, demonstrating that a Melitz general equilibrium is the solution to a global, cost-minimizing problem. This suggests 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 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 it as a means for interpreting Melitz results as the outcome of an Armington simulation with additional shocks to productivity and preferences variables. With CGE modelers in mind, we report computational experience in solving a Melitz general equilibrium model using GEMPACK.

Armington, Krugman and Melitz as Special Cases of an Encompassing Model

This chapter is built around a general, theoretical, multi-country model of production, pricing and trade by firms in the widget industry. We refer to this as the Armington, Krugman, Melitz Encompassing (AKME) model. We explain the Armington, Krugman and Melitz models and the relationships between them by showing that they are successively less restrictive special cases of AKME. All CGE modelers are familiar with the Armington model in which country of origin distinguishes one widget from another and firms play no role. For Krugman and Melitz, widgets are distinguished by firm rather than country. However, before these models can be taken into the CGE framework, the firm dimension must be eliminated. “Typical” firms must replace individual firms. Defining a typical firm in each country for Krugman is straight forward. While different firms produce distinct varieties of widgets, all widget firms in a given country have the same productivity and face the same demand conditions. Consequently, any widget firm in a country will do as typical. For Melitz, there is a richer specification of inter-firm heterogeneity. While firms in a given country face the same demand conditions, they can have different productivity levels. This makes identification of the typical firm challenging. We show how Melitz defines multiple typical firms, one for each trading link. Throughout the chapter we explain the modeling strategy in non-technical terms but we do not shirk the mathematics, particularly for Melitz. Understanding the mathematics is essential for accurate translation of Melitz into the CGE framework and for interpreting results.

Calibration and Parameter Estimation for a Melitz Sector in a CGE Model

This chapter is about giving numbers to parameters and unobservable variables in a Melitz CGE model. We start by describing how a Melitz model can be calibrated. This is the process by which unobservable variables (preference and fixed cost variables, δ’s, F’s and H’s) are evaluated so that for given parameter values (inter-variety substitution elasticities and productivity distribution parameters, σ and α) the model reproduces base-year data. We find that for a Melitz model there are multiple legitimate calibration possibilities but that the choice between these does not affect simulation results. Then, we review the method that Balistreri et al. (2011) have pioneered for estimating parameters in a Melitz model. This method combines calibration and estimation. Rather than setting initial values for unobservable variables to reproduce base-year data, Balistreri et al. impose theoretically preferred structures on the unobservable variables. These structures are incompatible with precise calibration, but pave the way for estimation. Parameters can be estimated by choosing the values that allow calibration to base-year data that is as close as possible subject to meeting the preferred structural constraints on the unobservable variables. Balistreri et al.’s approach is likely to be a starting point for many potentially fruitful calibration/estimation efforts.

Converting an Armington Model into a Melitz Model: Giving Melitz Sectors to GTAP

This chapter describes how to convert an existing Armington CGE model into a Melitz CGE model with minimal changes to the original Armington model. The main task is to add equations to the bottom of the Armington model to form what we call an Armington-to-Melitz or A2M system. With an A2M system, industries can be switched between Armington and Melitz treatments by closure swaps. We use BasicArmington (a simple Armington model) to explain how to create an A2M system. Then we apply the method to a 10-region, 57-commodity version of the frequently applied policy-oriented GTAP model to create a GTAP-A2M system. Using this system, we compare the effects under Armington and Melitz assumptions of a tariff imposed by North America on imports of wearing apparel (Wap). To facilitate the comparison, we decompose the welfare effects for each region into parts attributable to changes in employment, terms of trade and scale-related efficiency. This helps us to understand how each of these factors operates under Armington and Melitz, but it does not give us an intuitive explanation of their net outcome. To explain net outcomes for welfare effects by region we set out an intuitive overarching theory. We check its validity by back-of-the-envelope (BOTE) calculations using GTAP data items and selected simulation results. BOTE calculations enable us to cut through the maze of complications in CGE models to locate, for any specific result, the essential underlying ingredients.

Melitz Equals Armington Plus Endogenous Productivity and Preferences

This chapter continues the exploration from Chap. 2 of the relationship between the Melitz and Armington models. We find that the principal results from a Melitz model can be obtained from an Amington model with additional equations that endogenize factor productivity for industries and preferences by households between goods obtained from different supplying regions. In short, Melitz equals Armington plus endogenous productivity and preferences (M = A+) This idea comes out of the algorithm devised by Balistreri and Rutherford (BR 2013) for solving general equilibrium models that contain Melitz sectors. As we describe in this chapter, the BR algorithm involves: solving Melitz sectors one at a time with guessed values of economy-wide variables; passing productivity and preference results from the Melitz sectoral computations to an Armington general equilibrium model; solving the Armington model and passing results for economy-wide variables back to the Melitz sectoral computations. We don’t think an algorithmic approach such as this is necessary for solving Melitz general equilibrium models. Nevertheless the basic insight encapsulated in the (M = A+) equation is of considerable interest. It means that the results from a Melitz general equilibrium model for the effects of a trade reform can be interpreted as the sum of the effects in an Armington model of the reform and particular productivity and preference changes. With this interpretation, CGE modelers can draw on 40 years’ experience with Armington models to help them understand results from Melitz models. We illustrate this in Chap. 6.

Introduction: What’s in the Book and How to Read It

This book is for people who want to understand modern trade theory, particularly the Melitz model. We lay out the theory from first principles and relate it to earlier theories of Armington and Krugman. For some readers, this will be sufficient to satisfy their requirements. However, the book goes further and shows how Melitz theory can be embedded in computable general equilibrium (CGE) models and how results from these models can then be interpreted.

Illustrative GEMPACK Computations in a General Equilibrium Model with Melitz Sectors

One way to learn about the theoretical properties of a model is to construct and apply a simple numerical version. This is also a good preparation for creating policy-relevant models. Here we describe MelitzGE, a simplified Melitz general equilibrium model implemented with stylized data. Using MelitzGE we start by conducting simulations for which the results can be known a priori. Test simulations such as these check the coding of models. They can also expose theoretical properties. For example, a MelitzGE test simulation of the effects of a uniform 1% world-wide increase in employment shows a uniform increase in consumption of more than 1%, determined by the substitution elasticity σ. Sorting out why this is so helps us understand how love of variety and scale operate in Melitz. Next we conduct tariff simulations. Using the Balistreri-Rutherford decomposition discussed in Chap. 5, we find that Melitz love-of-variety and productivity effects tend to cancel out leaving welfare determined by phenomena familiar from Armington: terms-of-trade and efficiency effects. Recognition that these effects depend on tariff levels and trade-flow sensitivity to tariff changes leads to an investigation of the equivalence between Armington and Melitz models when calibrated to produce similar trade sensitivities. The GEMPACK code for our computations is in an appendix. As illustrated in this chapter and the next, GEMPACK is ideal software for Melitz-style CGE modelling. Nevertheless, readers will not need to be familiar with GEMPACK or follow the GEMPACK code to understand the chapter.

Optimality in the Armington, Krugman and Melitz Models

Every student of welfare economics is aware of propositions suggesting, perhaps with caveats, that free trade (zero tariffs) in a world of pure competition generates a Pareto optimal or efficient outcome. In this chapter we investigate what can be said about efficiency in the worlds of Krugman and Melitz where industries are monopolistically competitive with prices exceeding marginal costs. We find that the complications introduced by Krugman and Melitz do not prevent free trade from delivering intra-sectoral efficiency: under free trade a Melitz worldwide widget industry satisfies any given levels of widget demands across countries with cost-minimizing worldwide selections of firms, output per firm and trade volumes. However, monopolistic competition in some industries combined with pure competition in others introduces inter-sectoral inefficiency, with possibilities for Pareto improvements by allocating resources away from industries that are purely competitive toward those that are monopolistically competitive. Working with the Dixit–Stiglitz model we show that inter-sectoral welfare costs associated with mixed market structures (pure and monopolistic competition) are likely to be small in an empirical CGE setting. Conclusions reached in this chapter concerning intra and inter-sectoral efficiency are helpful for interpreting results from CGE simulations with Armington, Krugman and Melitz features. For example, Melitz intra-sectoral efficiency with zero tariffs means that envelope theorems are applicable. As we will see in Chaps. 6 and 7, this helps us to understand the circumstances under which Melitz and Armington models produce similar welfare results for the effects of tariff changes.