Behavioral Characteristics of Applied General Equilibrium Models with Variable Elasticity of Substitution between Varieties from Different Sources

As the recent developments in applied general equilibrium (AGE) analysis enabled us to incorporate the Melitz-type monopolistic competition and heterogeneous firms (Zhai (2008), Balistreri and Rutherford (2013), Dixon, Jerie, and Rimmer (2016), and Akgul, Villoria, and Hertel (2016)), people's attention is now directed to the re-estimation of the elasticity of substitution between varieties from different sources, which fits to an estimated value of the Pareto shape parameter for the productivity distribution of firms. In this situation, a controversy arises on the question whether the incorporation of endogenous changes in productivity might bring significantly large welfare gains from trade (Balistreri, Hillberry, and Rutherford (2011), Arkolakis, Costinot, and Rodriguez-Clare (2012), Melitz and Trefler (2013), and Melitz and Redding (2014)). While Dixon, et al. (2016) emphasized that the Melitz-type trade specification may not lead a substantial revision of the welfare estimates obtained with the models such that based on pure competition and the Armington-type specification, Oyamada (2014) and Itakura and Oyamada (2016) suggest that the strength of the preference for variety (PfV), which might be exaggerated in most of the AGE models with the Krugman- and Melitz-type specifications (Ardelean (2006)), plays an important role in determining the extent of welfare effects. The purpose of this research is to present another approach to handle the PfV effect endogenizing the substitution elasticity as an increasing function of the total number of varieties that are available in the destination region/country. The model alternatively incorporates the Krugman- and Melitz-type trade specifications, and is calibrated to the GTAP 9A database for 2011. The original 140 countries/regions and 57 commodities/activities are respectively aggregated to three. The regions consist of the Asia-Pacific, the North and South Americas, and the European Union and the Rest of the World. The three sectors are the primary industries, manufacturing, and services. The manufacturing sector is assumed to be imperfectly competitive with increasing returns to scale, while the other two are characterized by constant returns to scale. The primary industries sector uses a sector specific factor, such as land and natural resources, in addition to capital, labor, and intermediate goods in its production process. The services sector provides a fraction of its output as the international shipping supply. Simulation experiments with a special focus on the key parameters that defines the endogenous elasticity revealed the following characteristics of the model: (1) endogenizing the substitution elasticity as an increasing function of the total number of varieties, based on the intuition that additional varieties fill in gaps between existing varieties, drastically inflates the potential effects of trade liberalization; (2) the reaction of a model with the Melitz-type specification to a given shock is different from the one with the Krugman-type, because the former may independently determines the levels of domestic and exported varieties so that more efficient resource allocation is possible; (3) the gains from liberalizing trade are not always larger with the Melitz-type specification than the ones obtained with the Krugman-type when a policy change leads to reductions in number of firms entered in the domestic or international markets; and (4) there are likely to be points where the volumes of effects obtained with the Melitz-type exceed the ones with the Krugman-type.