33 THE INTENSIVE MARGIN IN TRADE

# **5.2. Counterfactual Analysis in the Estimated Full-Lognormal Melitz Model**

For our counterfactual analysis we need a set of countries for which we have _λij_ , _hij_ , _Xj_ and _Yi_ , as well as _gij_ for all _i_ and _j_ in that set. Since we assume (see Section 4) that the variances of _φi_ and _fij_ differ by origin but not by destination, then _gij_ = _gi_ for all _i_ and _j_ . We have estimated _gi_ for a set of 37 EDD countries, and we can infer the implied _Ni_ for all those countries, so we can include any subset of those countries in our analysis.<sup>35</sup> We then construct _hij_ using data for _Nij_ and _hij ≡Hij_ ( _Nij/Ni_ ). Finally, we also need _Xij_ and _Nij_ for _i_ = _j_ . Following the approach proposed by Ossa (2012), we construct _Xii_ as manufacturing value-added in country _i_ from the World Development Indicators divided by 0.25, which is close to the average share of manufacturing value-added in gross production from the World Input-Output Database (WIOD) for the set of covered EDD countries in 2007. We set _Nii_ = _Ni_ , which would be true if there are no fixed costs for domestic sales.

We conduct our counterfactual analysis for a world composed of the 12 Latin American countries and China, for which we have estimated the full lognormal model.<sup>36</sup> We do not consider the whole EDD dataset for computational reasons. This is because some of the country pairs in the whole EDD dataset trade very little and this makes our welfare calculations imprecise (since we need to use numerical approximation to compute some of the integrals).

We are interested in comparing the counterfactual implications of the full Melitz-lognormal model with those of the Melitz-Pareto model. We proceed in three steps. First, we allow for some change in trade costs and compute the counterfactual implications using the estimated full Melitz-lognormal model. We consider four different trade costs shocks: a 1%, a 5%, a 10%, and a ˆ 25% uniform reduction in international trade costs – formally, ˆ _τij_ = _τ ∈{_ 0 _._ 99 _,_ 0 _._ 95 _,_ 0 _._ 9 _,_ 0 _._ 75 _}_ if _i_ = _j,_ while ˆ _τii_ = 1. Second, we use these results to estimate the trade elasticity by running the OLS regression This leads to four values of the trade elasticity, one for each _τ_ ˆ. Following ACR, we use these values as estimates of the shape parameter of the Pareto distribution in the Melitz-Pareto model, ˆ ˆ which we denote by _θτ_ ˆ for _τ ∈{_ 0 _._ 99 _,_ 0 _._ 95 _,_ 0 _._ 9 _,_ 0 _._ 75 _}_ .<sup>37</sup> Finally, for each trade cost shock _τ_ we

> 35To see how we get _Ni_ , note that the estimated model provides us with a probability that a random firm from some origin is selling to at least one of the 15 destinations we consider. Since we observe the total number of exporters to those destinations, we can infer the total number of firms from which they are drawn. The more detailed procedure is described in the Online Appendix D.

> 36Our procedure implicitly assigns trade flows between these countries and countries outside of this group to domestic transactions.

> 37We get _θ_ 0 _._ 99 = 4 _._ 5; _θ_ 0 _._ 95 = 4 _._ 49; _θ_ 0 _._ 9 = 4 _._ 47; _θ_ 0 _._ 75 = 4 _._ 43.