Supply Function Competition and Exporters: Nonparametric Identification and Estimation of Productivity Distributions and Marginal Costs

In this paper we develop a structural model in which exporters are competing in supply functions and study the nonparametric identification and estimation of productivity distributions and marginal costs in this framework using disaggregated bilateral trade data. Our model is able to reconcile the existence of multiple sellers, multiple prices, and variable markups that we observe in data and also incorporates features such as strategic pricing and incomplete information. Our identification and estimation methodology gains insights from methodologies used in empirical auctions. Our identification and estimation methodology makes an important contribution to the empirical auction literature by showing that the underlying structure is identified nonparametrically even if we do not observe the entire schedules, but only the transaction points instead; whereas the methodology in the literature of empirical auctions depends heavily on the fact that the entire bid/supply schedule is observed. Moreover, in view of the recent studies in international trade that have shown the sensitivity of the gains from trade estimates to the parametrization of productivity distributions, maintaining a flexible structure for productivity distributions is very important. We apply our model to the German market for manufacturing imports for 1990 using disaggregated bilateral trade data, which consists only of trade values and traded quantities. We recover the destination-source specific productivity distributions and destination-source specific marginal cost functions nonparametrically. Our empirical results do not support the distributional assumptions that are commonly made in the international trade literature such as Fréchet and Pareto. In particular, we find that the productivity distributions are not unimodal; low productivities are more likely to occur as expected, but there is not a single mode. Our results provide important insights about cross country and cross destination differences in productivity distributions, trade costs and markups.