Addendum to: International Trade, Technology, and the Skill Premium

In this Addendum we set up a perfectly competitive version of the model and conduct a range of comparative static exercises under simplifying assumptions. Compared to the model described in Section 2 of our main paper, we assume that there is a large number of …rms in each variety (!; j) in each country and that within a country all …rms have access to the same productivity z. This implies that …rms will price at marginal cost, exactly as in Eaton and Kortum (2002), henceforth EK. Throughout this Addendum we maintain the following simplifying assumptions: 1. There are two countries, I = f1; 2g 2. Trade costs are symmetric, = 12 = 21 3. The elasticity of substitution between sectors is one, = 1 4. Trade is balanced, which implies Yi = PiQi 5. All sectors are tradeable, i = 1 for all i and JM = J In what follows we only write the equations that di¤er between the model presented in Section 2 and the perfectly competitive model presented here. Denote by cin (!; j) the unit cost of all country i variety (!; j) …rms supplying country n. Under perfect competition, the price of variety (!; j) in country n is pn (!; j) = min i fcin (!; j)g , exactly as in EK. Pro…ts in each variety are zero with perfect competition and constant returns to scale. Hence, with balanced trade, the budget constraint in each country n satis…es PiQi = siHi + wiLi. Hicks-Neutral Technology In this section we study a special version of the model: a standard H-O model extended to incorporate withinand across-sector productivity heterogeneity. We …rst show that our framework captures the key mechanisms of the H-O model: comparative advantage is shaped by cross-country di¤erences in endowment ratios, a country is a net exporter in its comparative advantage sector, and trade raises the relative wage of a country’s abundant factor. Unlike the standard H-O model, in which countries share identical technologies, comparative advantage is also shaped by productivity heterogeneity in our model. Second, we show how the extent of productivity heterogeneity shapes the response of relative wages to trade liberalization. Burstein and Vogel (2011) derive these results in a version of the model with monopolistically competitive …rms similar to the one studied in Bernard, Redding, and Schott (2007). In addition to assumptions 1-5 made above, we also make the following assumptions: