Gravity trade model with firm heterogeneity and horizontal foreign direct investment

We develop a gravity trade model based on a theoretical analysis of heterogeneous firms that engage in horizontal Foreign Direct Investment (FDI) or exporting. The model allows firms' endogenous choice between exporting or FDI to impact the proportion of exporting firms and subsequently bilateral trade. Based on the theoretical results, we propose a three-stage estimation procedure: First, estimate firm selection into horizontal FDI; second, use predicted probabilities from the first stage in the estimation of firm selection into exporting; and third, use predicted probabilities from the previous two stages in the gravity estimation of bilateral trade. We apply this procedure to the European Union (EU) processed food industry, which engages in worldwide FDI and trade. We estimate a baseline model of a standard gravity equation, a two-stage model without FDI selection, and our proposed three-stage model and quantify bias corrections in the coefficient estimates of the trade friction variables in the baseline and two-stage gravity models. The bias corrections can be large. For instance, the inclusion of the proportion of Multinational Enterprises (MNEs) in the trade-selection equation leads to a sign reversal of the distance coefficient estimate and results in an upward bias correction of $173\%$. The three-stage gravity corrects a downward bias of $31\%$ in the coefficient estimate of distance in the baseline but an upward bias of $77\%$ in the two-stage method, which indicates that the two-stage method overcorrects the downward bias in the baseline gravity.