A Tale of Two Tails: Productivity Distribution and the Gains from Trade

Power Law in COVID-19 Cases in China

“…Indeed, there are more flexible forms of the Pareto distribution—often with an extra parameter and/or of mixture form—that allow for capturing extreme upper‐tail (and lower‐tail) probabilities more closely. Such generalized, or, composite, distributions have been shown to improve upon the benchmark power law distribution in fitting empirical data (see, for instance, Giesen et al, 2010 ; Ioannides & Skouras, 2013 ; Luckstead & Devadoss, 2017 ; Nigai, 2017 ; Patel & Schoenberg, 2011 ). The main goal of the present study is to determine whether a power law generally approximates the upper tail COVID‐19 cases in China, which has an implication for understanding tail risk properties of COVID‐19, and not the investigation of various distributions within the power law family, which is beyond the scope of this research.…”

Unobserved heterogeneity in the productivity distribution and gains from trade

“…While these composite distributions can be constructed based on many individual parametric distributions, applications mostly focus on lognormal distributions with Pareto tails. The “inverse Pareto‐lognormal‐Pareto” distribution has been applied in the city size literature (Ioannides and Skouras 2013, Luckstead and Devadoss 2017), while the “lognormal‐Pareto” version was applied by Nigai (2017) to the firm‐size literature (Kondo et al 2018). Dewitte (2020) generalizes the implementation of the piecewise composite distributions to allow for any underlying density in three‐ and two‐piecewise composite distributions, focusing mainly on Pareto‐tailed piecewise composites.…”

“…Also, the propagation of firm‐level volatility to the aggregate level relies mainly on a Pareto approximation of the right tail of the productivity distribution (Gabaix 2011, di Giovanni et al 2011, Carvalho and Grassi 2019). In the international trade literature, it is recognized that different choices for the productivity distribution significantly affect gains from trade (GFT) estimates (Head et al 2014, Nigai 2017, Bee and Schiavo 2018) and alter the channels through which trade affects welfare (Arkolakis et al 2012, Bas et al 2017, Melitz and Redding 2015, Fernandes et al 2018).…”

“…Others build on the idea that a single distribution cannot adequately capture the heterogeneity in productivity. This results in combinations of distributions such as the double Pareto‐(Arkolakis 2016), double Pareto‐lognormal (Sager and Timoshenko 2019) or lognormal‐Pareto (Nigai 2017). Nevertheless, Dewitte (2020) demonstrates that none of the distributions that are currently considered can provide a sufficiently good fit to the data.…”

Trade Flows and Exchange Rates: Importers, Exporters and Products

“…11 Calibrated to the U.S. data, Melitz and Redding (2015) set the Pareto shape parameter for firm productivity to be 4.25, and Bernard, Redding and Schott (2009) set it equal to 4. Estimating using French firm level data, Nigai (2017) found that a Pareto shape parameter would take a value of 1.9. Lower values of k correspond to greater firm heterogeneity.…”