Endnotes

¹See Devarajan and Robinson (2005) on the influence of CGE models on trade policy and Kehoe (2005) for a critical review of CGE analyses of NAFTA.

²Chaney (2006) estimates the distorted gravity equations based on a simplified version of the Melitz (2003) model, and finds strong support for it in both sectoral trade data and the stylized facts on firm-level trade. Bernard, Jensen and Schott (2006) use firm level US manufacturing data to examine the effects of changing trade costs on firms' entry and exit behavior and changes in average productivity. They find that lowering trade costs in a sector increases the probability of firm death or entry into export markets in that sector. The existing exports expand as trade costs decline. Moreover, industry aggregate productivity and within-plant productivity rises as trade costs fall.

³Some CGE models incorporate ad hoc assumptions about trade-productivity externalities, such as linking productivity to export performance or imported intermediate and capital goods. See, for example, de Melo and Robinson (1992), Lewis, Robinson and Wang (1995) and World Bank (2001).

⁴See Helpman, Melitz and Yeaple (2004) and Falvey, Greenway and Yu (2006) for an extension of the Melitz model to asymmetric countries.

⁵This is the standard Spence-Dixit-Stiglitz preference function, which implies love of variety in utility. Some recent empirical investigations have lent support to the love of variety effects in international trade. See Broda and Weinstein (2006) and Ardelean (2007).

⁶Since there is a one-to-one correspondence between φ and ω, we will look at the distribution of φ instead of the distribution of ω below.

⁷The death shocks that force firms to exit are assumed to be independent of firms' productivity. Natural disasters, new regulations and major changes in consumer tastes could be the causes of these shocks.

⁸See footnote 9 of Melitz (2003).

⁹See Melitz (2003) for detailed exploration and proof of these properties.

¹⁰The centripetal forces and multiple equilibria are central themes of new economic geography models which analyze industry's location decisions in the context of imperfect competition and economies of scale. See Fujita et al (1999).

¹¹See Bernard and Jensen (1999, 2004), Roberts and Tybout (1997) and Clerides et al (1998) for empirical evidence on selection into export markets. The electronic component sector in the People's Republic of China and some Southeast Asian countries may be good counterexamples for selection into export markets. As part of the global supply chain and regional production network, a large proportion of their products are exported and some of their firms are fully export-oriented.

¹²The modeling of household behavior follows the LINKAGE model. See van der Mensbrugghe (2005).

¹³The assumptionã>ó-1 ensures that the size distribution of firms has a finite mean.

¹⁴For the sake of comparability, I do not use the GTAP values of Armington elasticities in manufacturing and services sectors in the standard homogeneous firm CGE and instead use the same values of the substitution elasticity between differentiated varieties in the firm heterogeneity model as shown in Table 1.

¹⁵To ensure that the new model generates additional gains from a trade expansion in comparison with the conventional model, I raise the Armington elasticities in the standard Armington CGE model by 33% and run the tariff reduction simulation. Compared to the Melitz CGE model, the Armington CGE model with high elasticities predicts a similar expansion in global real exports, but 23% lower global welfare gains. I am grateful to Peter Dixon for suggesting this simulation.

¹⁶Real exports are defined as the sum of each firm's exports, i.e. they are measured "at the factory gate" and are not augmented by variety effects.

¹⁷See, for example, Oliveira-Martins, Scarpetta and Pilat (1996).

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