comparison, following Arkolakis et al. (2012), we hold the trade response in each scenario constant across the three market structures based on a structural gravity estimate. Like Costinot and Rodriguez-Clare (2014), our results are numerical. This allows us to assess not just the qualitative differences between the estimated gains from trade from the market structure, but also the quantitative differences. In particular, we answer the question of whether the Krugman model captures most of the gains from trade above the Armington model. That is, what is the relative importance of the variety externality in the Krugman model compared to the selection effect in the heterogeneous firms model in producing larger estimated gains above the perfectly competitive Armington model? We employ a ten-region model of global trade built on the GTAP 9 dataset. All of our exercises are comparative static without moving to autarchy.

To stay close to the earlier literature, we first replicate the Arkolakis _et al_ . (2012) equivalence result from a global ten percent reduction in iceberg trade costs, in a one-sector model. We then progressively introduce real features of the data. We find that trade imbalances alone are insufficient to break the equivalence result of Arkolakis _et al_ . (2012) in their one-sector model. We then introduce three features that break the welfare equivalence: (i) labor-leisure choice in a one-sector model;<sup>3</sup> (ii) intermediate demand in a single sector; and (iii) multiple (four) sectors with intermediate demand based on the data.<sup>4</sup> Next, we show that intermediate demand based on data as opposed to a single aggregate and a lower elasticity of substitution both make a significant difference in the comparative results across the models.<sup>5</sup> In table 5, we investigate variations in primary factor assumptions: single primary factor; three primary factors with and without a specific factor and labor-leisure choice.<sup>6</sup> Next, we expand our model

> 3 In addition to Balistreri _et al.,_ (2011), see also Adao, Arkolakis and Esposito (2017).

4 Arkolakis, Costinot and Rodriguez-Clare (2012) first showed that both multiple sectors and tradable intermediates broke the welfare equivalence between monopolistic competition and the Armington model, but only tradable intermediates led to unambiguously larger welfare estimates.

5 Costinot and Rodriguez-Clare (2014) incorporated intermediates in a multi-sector model, but they assumed an aggregate intermediate good. So all their sectors use intermediates in the same proportion in that model. Further, they did not test for sensitivity of the results to the elasticity of substitution for intermediates. We find that these assumptions have a strong impact: the former increases the relative gains of the monopolistic competition models and the latter reduces them.

6 Costinot and Rodriguez-Clare (2014, 200-223) evaluated the impact two factors of production, but only in their autarchy exercises and with common cost shares across countries for the two factors. They report that there are virtually no Heckscher-Ohlin effects in their Armington model, but one could question how general that result is when factor cost shares are identical across all regions. Further, they do not report results in the monopolistic competition models with multiple primary factors of production; so we do not have comparable results for the Krugman or Melitz models.

Costinot and Rodriguez-Clare (2014, 231) indicate that we cannot generalize from autarchy exercises to trade policy exercises. In an Armington model, they find opposite results regarding the impact of multiple sectors between their autarchy exercise and a forty percent tariff increase. They conclude that “one should be careful when extrapolating from the autarky exercises ...to richer comparative static exercises. Models that point towards larger 2