Gravity, PPML, and Heterogeneous Effects (with Xinbei Zhou)

The gravity equation is the most popular empirical tool among trade economists. Two of the most common approaches to estimating it are the ordinary least squares (OLS) and Poisson Pseudo-Maximum Likelihood (PPML), with PPML often being preferred to OLS because it does not lead to a bias if the error term of the regression is heteroskedastic. We show theoretically and document in a series of Monte-Carlo simulations that in case the trade elasticity is not constant between country pairs, OLS and PPML estimates of the gravity equation have a different interpretation: OLS estimate is the average elasticity and PPML is the elasticity of average. Furthermore, we employ the gravity dataset and show that more than 100% of the difference between PPML and OLS estimates of distance elasticity is explained by the difference in the interpretation of the coefficients. The bias of OLS estimates associated with the error term heteroskedasticity accounts for 8% of the difference between the estimates and has the sign opposite to what was previously found in the literature.

Costs of Redrawing the Map: Evidence from the Treaty of Versailles

**Working Papers******

Vladimir Tyazhelnikov

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. Distributions of firms’ productivities are then a central object in models 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 estimates for about 600 US industries at the HS-4 level under assumptions of both CES and translog utility functions and offer a few alternative specifications. I improve this estimator by allowing for the case of a 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 an aggregated level, firms' productivity distribution is log-normal rather than Pareto. On the disaggregated level for most industries the distribution is Pareto rather than log-normal and bounded Pareto rather than unbounded.

Shadow Offshoring and Complementarity in Product Space (with Edwin Jiang)

We develop a two-country quantitative model of international production of a complex good that consists of multiple parts. Production of those parts exhibit some degree of comlplementarity and consequently, decisions on production locations are interrelated. We use this model to generate a new measure of offshoring that, unlike conventional measures, accounts not only for total costs of parts produced abroad but also for what parts are produced there and how similar these parts are between each other. We use the World Input-Output Database to estimate the model for the case of US production and find that this measure of offshoring is a significantly better predictor of welfare consequences of trade liberalization than standard measures of integration.

**Work in Progress******

Production Clustering and Offshoring (revise and resubmit at *American Economic Journal: Microeconomics)*

I introduce a quantifiable model of international production that allows for a production chain of any length, any number of sourcing countries, and weak assumptions on the structure of production and trade costs. Furthermore, the production process does not have to be perfectly sequential, and the final goods can be made from any number of independent subchains. I show that in this model allocation decisions on different stages of production are interdependent, which generates a new channel of proximity-concentration trade-off. The presence of trade costs makes firms cluster their production in certain countries, while trade liberalization allows firms to fragment their production more and exploit productivity differences between countries more efficiently. I then present a general equilibrium heterogeneous firms model in which every firm solves the allocation problem described above. In this model, the distribution of firms' productivity with respect to trade costs: trade liberalization leads to a distribution that stochastically dominates the old one, thus leading to an increase in welfare. I use the model to decompose the welfare gains from trade liberalization through two channels: cheaper intermediate inputs and a more efficient production structure. I apply the model to the data and study Chinese joining the WTO. Using the simulated maximum likelihood technique to calibrate the model, I find that a more efficient production structure accounts for approximately 12% of gains from trade.

Oligopoly and Oligopsony in International Trade (under review) (with Luca Macedoni)

We study the effects of international trade on firms' oligopsony power in inputs markets. Combining international trade data with measures of market concentration, we find that higher oligopsony power is associated with higher unit prices of export goods, and this effect is much larger than the effect of oligopoly power in final goods markets. We build a theoretical model of international trade in which firms are oligopolists in the market for final goods and oligopsonists in the market for inputs. Trade liberalization in one market reduces firms' market power in such market, but it has the opposite effect in the other market. In particular, international trade between oligopolists in final goods markets causes oligopsony power to increase. Calibrating our model for the US, we find that the reduction in domestic markups generated by international trade are 30-50% lower due to the presence of oligopsony power.