International Trade & Spatial Econometrics
Anderson-van Wincoop Gravity & Multilateral Resistance
Compute structural bilateral trade X_ij = (Y_i * Y_j / Y_W) * (t_ij / (Pi_i * P_j))^(1 - sigma) and expose naive Tinbergen border-puzzle bias.
Why bilateral trade depends on RELATIVE barriers t_ij / (Pi_i * P_j), not t_ij alone!
Jan Tinbergen’s (1962) empirical gravity equation modeled bilateral exports X_ij from country i to j using economic mass (Y_i * Y_j / Y_W) and bilateral trade cost t_ij^(1 - sigma) (sigma > 1), omitting third-country remoteness! James Anderson and Eric van Wincoop (2003) resolved the famous McCallum Canada-US border puzzle by proving general-equilibrium CES trade equals X_ij = (Y_i * Y_j / Y_W) * (t_ij / (Pi_i * P_j))^(1 - sigma), where outward Multilateral Resistance Pi_i and inward Multilateral Resistance P_j summarize average barriers each partner faces with the REST of the world!
Verify on two geographically remote neighbors with Y_i = 200 (B2), Y_j = 300 (B3), world GDP Y_W = 10,000 (B4 -> frictionless benchmark 6.00), CES elasticity sigma = 5 (B5 -> exponent 1 - sigma = -4), bilateral cost t_ij = 1.25 (B6), outward resistance Pi_i = 1.50 (B7), and inward resistance P_j = 1.50 (B8): naive Tinbergen gravity (assuming Pi_i = P_j = 1) predicts just 6.00 * 1.25^(-4) = 2.4576, whereas structural Anderson-van Wincoop gravity recognizes relative barrier 1.25 / 2.25 = 5/9 < 1 and predicts 6.00 * (9/5)^4 = 62.9856 — 25.63x larger because high third-country barriers channel regional trade inward!
| Gravity Model Specification (Y_i=200, Y_j=300, Y_W=10k, sig=5) | Formula | Predicted Bilateral Flow |
|---|---|---|
| Frictionless Benchmark (t_ij=Pi_i=P_j=1) | (Y_i * Y_j) / Y_W | 6.0000 |
| Naive Tinbergen Gravity (Ignores MR) | (Y_i * Y_j / Y_W) * t_ij^(1 - sigma) | 2.4576 |
| Structural AvW Gravity (Pi_i=P_j=1.50) | (Y_i*Y_j/Y_W) * (t_ij/(Pi_i*P_j))^(1-sig) | 62.9856 (25.63x Naive!) |
Anderson-van Wincoop Structural Bilateral Gravity Flow X_ij Formula
Validate Y_W >= Y_i + Y_j > 0, CES elasticity sigma > 1, bilateral barrier t_ij >= 1, and positive multilateral resistance indices Pi_i, P_j > 0.
=LET(y_ex, B2, y_im, B3, y_wd, B4, sig_c, B5, t_bi, B6, pi_out, B7, p_in, B8, IF(OR(y_ex <= 0, y_im <= 0, y_wd < y_ex + y_im, sig_c <= 1, t_bi < 1, pi_out <= 0, p_in <= 0), "Invalid Gravity Input", ROUND((y_ex * y_im / y_wd) * POWER(t_bi / (pi_out * p_in), 1 - sig_c), 4)))Multilateral-Resistance Redirection Amplification Factor (Pi_i * P_j)^(sigma - 1) Formula
Measure the exact omitted-variable bias ratio X_structural / X_naive = POWER(Pi_i * P_j, sigma - 1).
=IF(OR(B5 <= 1, B7 <= 0, B8 <= 0), "Invalid Gravity Input", ROUND(POWER(B7 * B8, B5 - 1), 4))Try the example
Use the original values or change them to test your understanding.