21 THE INTENSIVE MARGIN IN TRADE and Mayer (2014), and _σ_ = 5 from Bas et al. (2015), so _θ_<sup> ̄</sup> = 1 _._ 25) (see footnote 19); and finally and _θ_ ̄ = 1 (as in Zipf’s Law).

Table 9 reports the results of this simulation exercise. Two broad patterns emerge from the table. First, the simulated IME decreases with _θ_<sup> ̄</sup> . This is because the effect of granularity on the IME is stronger when there is more dispersion in productivity levels. Second, the simulated IME is highest when productivity is less correlated across destinations, again because this gives granularity more room to generate a covariance between average exports per firm and total exports. For our estimate of _θ_<sup> ̄</sup> ( _θ_<sup> ̄</sup> = 2 _._ 4) and with no demand shocks (so there is perfect correlation in firm-level productivity across destinations), the simulated IME of 0.001 is quite low. The highest simulated IME occurs for the case in which _θ_<sup> ̄</sup> = 1 and there is no correlation between the product of demand shocks and productivity across destinations. In this case the simulated IME is 0.33, not too far from our preferred estimate based on the data of 0.4. But we think of this as an extreme case because _θ_<sup> ̄</sup> = 1 is far from the estimates that come out of trade data, and because of the implausible assumption that firm-level exports are completely uncorrelated across destinations. A low _θ_<sup> ̄</sup> also implies that, in contrast to the data, virtually all of the action behind a positive IME comes from the superstar firms. To see that, we calculate average simulated exports per firm in each percentile and use those to estimate an IME per percentile. We plot the resulting 100 IME estimates in Figure 8 along with the corresponding IME estimates based on the actual data. The IME based on the actual data is increasing with a spike at the top percentile. Granularity and the Pareto distribution fail to reproduce this pattern in the simulated data, since the corresponding IME is much smaller than in the data for most percentiles. The IME in the simulated data is almost zero for small percentiles and is relatively high for a small number of top percentiles. We conclude that granularity does not offer a plausible explanation for the positive estimated IME in the data.

# **4. The Intensive Margin in the Melitz-Lognormal Model**

In this section we depart from the assumption of a common Pareto distribution of firm-level productivity and instead assume a lognormal distribution.<sup>25</sup> In the theory section we start by showing how this can lead to a positive IME in a simple Melitz model, and then propose a maximum-

> 25One could consider combining a lognormal distribution with a Pareto distribution on the right tail, as in Nigai (2017). We have used Nigai’s Matblab code on our data to estimate the point of truncation (percentile) where the lognormal ends and the Pareto begins. We find that for 75% of country pairs with more than a hundred exporters the point of truncation occurs after the 99th percentile, and for the median country pair the truncation point is at the 99.9%. In light of these results, in the rest of the paper we focus on the case in which productivity is described by a fully lognormal distribution.