channels through which PTAs can increase bilateral trade. But it also begs the question of what those channels are.” This partly motivates the conclusion of Schiff and Winters (2003) that the real gains from regional trade initiatives come from deep integration.

Despite the evidence that tariffs miss the majority of the impacts of PTAs, the modern general equilibrium simulation analyses of regional trade agreements have focused on tariffs, and have produced rather small estimated welfare gains from preferential trade agreements (PTAs).<sup>2</sup> In this paper, in addition to tariffs, we consider deep integration via three broader trade costs channels through which PTAs may reduce trade costs: time in trade costs; non-tariff barriers on goods; and barriers to services.<sup>3</sup> We find that, across all three market structures, deep integration contributes substantially to welfare; but preferential tariff reduction contributes virtually nothing.

To capture the important commitments that countries make in modern PTAs in business services, we develop the first multi-sector numerical model of foreign direct investment (FDI) with heterogeneous firms that captures the key stylized facts regarding FDI, including the defining characteristics of the knowledge capital model (Markusen, 2002).<sup>4</sup> We apply our FDI model to business services, as these are the sectors in which FDI is most actively negotiated in international trade agreements. Our FDI firms produce in our host country (The Philippines); and, reflecting the literature on the proximity burden in services, the demand structure in the host country distinguishes between services provided with a local presence and foreign produced services. That is, the “proximity burden” literature notes that foreign services provided through FDI are better substitutes for host country domestically provided services than services provided cross-border (Francois and Hoekman, 2010). In our Krugman and Melitz versions, our FDI firms interact under monopolistic competition with endogenous productivity effects in the use of their outputs through the Dixit-Stiglitz mechanism from additional varieties of business services. As such, our model incorporates the economic theory and the substantial and growing empirical literature based on firm level data showing that foreign direct investment and the wide

> 2 See Caliendo and Parro (2015) and Caliendo _et al_ . (2017).  Limão (2016, pp.316, 319) concludes that he believes that the small estimates of the gains from PTAs from these simulation studies are explained by the fact that they only consider the tariff impacts of the PTAs.

> 3 The estimates of Hummels _et al_ ., (2007) and Minor (2013) show the trade facilitation costs alone (what they call the “time in trade” costs) are greater than tariffs as an obstacle to trade for most countries. The World Economic Forum (2012) found that the cost of trading is a more important obstacle to trade development than trade policies.

> 4 Arkolakis _et al_ . (2018) have recently produced an important single sector, heterogenous firms model on foreign direct investment, but do not compare the impacts to a Krugman or Armington style model. The model of Bernard, Jensen, Redding and Schott (2018) is a general theoretical model of heterogeneous multinational firms.

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