Shadow Offshoring and Complementarity in Product Space
The Usual Suspects: Pareto and Log-Normal Distributions of Firms' Productivity
Firms differ in size and productivity with important implications for trade policy and measuring gains from trade. Distribution of firms’ productivities is then a central object in a model with heterogeneous firms. I introduce a new way to estimate the shape parameter of the Pareto distribution for firm productivity using the data on firm-level imports to the US. I provide my estimates for about 600 US industries at the HS-4 level under assumptions of both CES and translog utility functions and offer few alternative specifications. I improve this estimator by allowing for the case of bounded Pareto distribution, making it robust to misspecification. In order to check the validity of distributional assumptions, I provide a new way to test them. My first finding is that it is important to allow parameters of productivity distributions to vary by industry. I find that on aggregated level, firms' productivity distribution is log-normal rather than Pareto, while on the disaggregated level for most industries the distribution is Pareto rather than log-normal and bounded Pareto rather than unbounded.
I propose a simple and computationally feasible algorithm to solve a firms' problem for a large class of sequential production models of offshoring. These models allow for production chain of any length, any number of sourcing countries and arbitrary structure of production and trade costs. I show that in this class of models, allocation decisions are interdependent and this interdependence generates a new channel of proximity-concentration trade-off. The presence of trade costs makes firm cluster its production in certain countries, while trade liberalization allows firms to fragment their production more and exploit productivity differences between countries more efficiently. Then I present a general equilibrium heterogeneous firms model in which every firm solves the allocation problem described above. In this model the distribution of firms' productivities is endogenous with respect to trade costs: trade liberalization leads to a distribution that stochastically dominates the old one, thus leading to increase in welfare. I use the model to decompose the welfare gains from trade liberalization by two channels: cheaper intermediate inputs and more efficient production structure. I apply the model to the data and study the case of China joining WTO. I use simulated maximum likelihood technique to calibrate the model and find that more efficient production structure accounts for approximately 25% of gains from trade.
Work in Progress
Costs of Redrawing the Map: Evidence from the Treaty of Versailles