Gravity with gravitas: comment
They showed that computing the border effect requires solving a non-linear system of multilateral price indexes. This note shows that the non-linear system can be solved analytically, such that a numerical approximation is no longer needed. The exact solution yields a reduced-form log-linear gravity equation that can be estimated using standard econometric techniques.
After estimation, the calculation of treatment effects like the border effect is straightforward. Using the same data and assumptions, I find that the border effect for Canada is half as large as reported by Anderson and Van Wincoop.