# I. Introduction

Paul Armington's seminal 1969 paper, "A Theory of Demand for Products Distinguished by Place of Production," showed that imports and domestically produced goods in the same sector could be imperfect substitutes, with the degree of substitutability captured by the elasticity of substitution, or Armington elasticity. This insight helped explain why we observe domestic and foreign goods in the same sector sold at different prices in the same country. It also enabled more realistic simulation results from computable general equilibrium (CGE) models where, otherwise, small changes in policies or terms of trade would lead to huge swings in countries' trade patterns (Deardorff 2006). The notion of product differentiation, which extends symmetrically to exports and domestic goods, has since underpinned trade-focused, computable general equilibrium models,<sup>2</sup> including the aggregate, compact version, the 1-2-3 model, and additionally recent open-economy macroeconomic models.<sup>3</sup> In this regard, Devarajan, Lewis, and Robinson (1990) used the Armington assumption to specify the 1-2-3 model that captured most of the results from more disaggregated models in a transparent and data-economizing way.<sup>4</sup> The 1-2-3 model has been extended to incorporate dynamics (Devarajan and Go 1998) and uncertainty (Devarajan et al. 2017) and used to analyze equilibrium exchange rates (Devarajan et al. 1993), trade policy (de Melo and Robinson 1992), welfare costs of taxation (Auriol and Warlters 2012), and poverty (Devarajan and Go 2003).

Alongside the widespread use of the Armington framework, there has been considerable effort in estimating the magnitude of Armington elasticities at the sectoral level. Bajzik et al. (2020) collected 3,524 estimates in their meta-analysis on the 50<sup>th</sup> anniversary of Armington's paper. Almost all of these estimates are for developed countries at the sectoral level. Meanwhile, many CGE models of developing countries, including the 1-2-3 model, have been built with the Armington elasticities exogenously specified rather than empirically estimated. The reason is that there has not been sufficient time-series data to estimate these elasticities econometrically (some African countries gained independence only in the 1960s). Yet, as Schurenberg-Frosch (2015) shows in her sensitivity analysis of the Armington elasticity, model results can be highly sensitive to the magnitude of the elasticity. Hilberry and Hummels (2013) put it more bluntly: "It is no exaggeration to say that [the Armington elasticity] is the most important parameter in modern trade theory." Furthermore, apart from a few studies like Devarajan, Go, and Li (1999), there are hardly any direct estimates of export elasticity. A few studies take a country’s exports as imports from its major trading partners, thus estimating it indirectly as export demand from the rest of the world through an Armington function. In the 1-2-3 model, however, the export elasticity derives from a constant elasticity of transformation (CET) of supply, which, as mentioned above, is symmetric with the Armington function for imports in a general equilibrium framework. Thus, estimating it directly is also possible.

In this paper, we estimate the Armington and export elasticities for the 1-2-3 model for 191 countries using data from 1970-2018. Of these, 128 are developing countries, including almost all the countries in Sub-Saharan Africa and many under-studied ones like Benin, the Republic of Congo, Niger, Fiji, Haiti, Kiribati, and Tajikistan. The list includes several microstates, such as Nauru, Tuvalu, and

> 2 de Melo and Robinson (1989) used an aggregate framework that anticipates the 1-2-3 model to derive the theoretical properties of product differentiation in CGE models. Later, Thierfelder and Robisnon (2003) discussed how the 1-2-3 model qualifies the results of trade theory with perfect-substitution between foreign and domestic goods.

> 3 The recent literature of open-economy macroeconomics using the Armington formulation includes the New Keynesian framework and the associated class of dynamic stochastic general equilibrium models. See, for example, Gali (2015), Uribe and Schmitt-Grohé (2017) and Végh (2013).

> 4 See also the next section and Devarajan and Robinson (2013) for a discussion of how the 1-2-3 model extends the tradability factor of the Salter-Swan framework and its relations to disaggregated CGE models in policy analysis of developing countries. Also, Devarajan, Lewis, and Robinson (1993) discussed its macro properties.

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