The double EMG distribution and trade elasticities

Abstract

Using Brazilian export data that, unlike many trade data sets, have a full record of small export sales, this paper reconsiders trade elasticities and the welfare gains from trade. Using the Brazilian data, this paper provides novel evidence on the properties of the distributions of log-export sales and shows that the double exponentially modified Gaussian (EMG) distribution parsimoniously captures these properties. Using the double EMG distribution in a standard monopolistic competition model of trade, this paper demonstrates that data truncation, which is prevalent in many data sets, leads to an upward bias in measuring the partial elasticity of trade with respect to variable trade costs. This bias subsequently leads to the underestimation of the gains from trade by 1% to 9% depending on the extent of data truncation, a range that is commensurate with typical economic growth and large booms.Résumé. Double distribution gaussienne modifiée de façon exponentielle (EMG) et élasticités commerciales. En s'appuyant sur les données relatives aux exportations brésiliennes consignant, contrairement à de nombreux autres ensembles de données, tous les volumes de ventes à l'exportation y compris les plus petits, cet article réexamine l'élasticité des échanges et les bienfaits sociaux en découlant. Grâce à ces données, l'article offre un nouvel éclairage sur les propriétés des distributions relatives aux ventes à l'exportation consignées, et montre que la double distribution gaussienne modifiée de façon exponentielle (EMG) ne reflète que partiellement ces propriétés. En utilisant cette double distribution dans un modèle commercial standard caractérisé par une concurrence monopolistique, cet article démontre que la troncature des données, fréquente dans de nombreux ensembles de données, génère des erreurs systématiques par excès lorsque l'on mesure l'élasticité partielle des échanges par rapport aux coûts commerciaux variables.

Welfare and trade elasticity with multinational production

“…Therefore, our model delivers elasticity measures, both for exports and affiliates, that are not constant and depends on bilateral trade costs despite the Pareto assumption. This result relates to recent papers highlighting the limit of the unbounded Pareto and adopting alternative productivity distributions, as Sager and Timoshenko (), Nigai (), Bas, Mayer, and Thoenig (), Bee and Schiavo (), and Head, Mayer, and Thoenig ().…”

Firm Growth Through New Establishments

“…Notice also that, when Φ is a log-normal distribution,H is a convolution of a Pareto distribution and a log-normal distribution analyzed in Reed (2001), and more recently, Cao and Luo (2017) and Sager and Timoshenko (2018). Therefore, we offer an alternative micro-foundation of this convolution distribution with endogenous establishment growth rate, relative to the micro-foundation in Reed (2001) with exogenous growth rate.…”

“…. , where G is the CDF of the convolution between a normal distribution and an exponential distribution (see Sager and Timoshenko (2018) for more details on this type of distribution):…”

On the U.S. Firm and Establishment Size Distributions

“…We also use the Akaike information criterion (AIC), which 5 See Reed (2001) for the stochastic growth processes that can yield such distribution. Sager and Timoshenko (2017) also rationalize this distribution using a model with Pareto productivity shocks and lognormal demand shocks. 6 Clauset et al (2009) discuss this issue in detail and also provide a Monte Carlo simulation to show that the lognormal distribution can approximate a Pareto very closely when evaluated with the regression analysis approach used in Axtell (2001) and Gabaix (2009).…”

“…Fernandes et al (2015) propose to model the firm productivity distribution with a lognormal distribution to match the empirical evidence on the importance of the intensive margin of trade. Sager and Timoshenko (2017) show that a convolution of lognormal and Pareto fits best using Brazilian export sales data. Nigai (2017) shows that a mixture of lognormal and Pareto fits the firm productivity distribution of French firms the best and that its adoption affects the estimation of the gains from trade.…”