Structural Parameters of Trade Models with Firm Heterogeneity

While various firm heterogeneity models of trade have recently emerged in the CGE literature, their mainstream adoption in trade policy analysis has been limited partly due to lack of available parameter estimates at the disaggregate sector level. The firm heterogeneity theory in quantitative trade models assume firm productivity as well as firm size distributions are characterized by power-laws, especially in the upper tail of the distribution where rare events such as exporting occurs. In recent empirical studies, it is reported that power-laws may not be suitable for the entire range of the distribution. Therefore, it is paramount to identify a minimum threshold above which the power-law provides a good fit for the data. This is especially important in estimating the structural parameters of the firm heterogeneity model for use in policy analysis as biased estimates may distort trade volumes and welfare responses. In this paper, we use maximum-likelihood and Kolmogorov-Smirnov (KS) statistic to estimate the minimum threshold for truncating the data which then allows us to estimate the shape parameter of firm size and productivity distributions based on power-law and ORBIS firm-level data. We then impute the elasticity of substitution across varieties that are appropriate to use in firm heterogeneity models of trade. We provide parameter values for productivity distribution and substitution elasticity for 19 GTAP manufacturing sectors.