When A sells to B, does it cost more than B selling to A?

The gravity literature usually reports bilateral trade costs as a single symmetric number: the geometric mean of the two one-way iceberg factors. That averaging throws away the direction of the wedge. Here we invert the Head-Ries (2001) identity the other way round — keeping the asymmetry and discarding the level — to ask where the implied cost of shipping A-to-B differs sharply from the cost of shipping B-to-A. In 2023, across 3,020 country pairs with both-way flows above $50M, the median absolute direction gap is 10.0% of the ad-valorem tariff-equivalent and the 90th percentile is 27.7%. Directional costs are not a rounding error.

The identity, and what it costs to keep the direction

Head & Ries (2001), “Increasing returns versus national product differentiation as an explanation for the pattern of U.S.-Canada trade” (American Economic Review 91(4): 858-876), first showed that under CES preferences the product of the two one-way iceberg cost factors between any two countries is identified from trade data alone, without estimating multilateral resistances:

(1 + tau_AB) * (1 + tau_BA) = [ (X_AA * X_BB) / (X_AB * X_BA) ]^(1 / (sigma - 1))

where X_AB is gross exports A to B and X_AA is A’s intranational trade (production absorbed at home). Novy (2013), “Gravity Redux: measuring international trade costs with panel data” (Economic Inquiry51(1): 101-121), re-derives the same expression from the Anderson & van Wincoop (2003) gravity system and shows it holds for any well-behaved micro-foundation with trade separability. The ESCAP-World Bank database (Arvis, Duval, Shepherd, Utoktham & Raj, 2016, World Bank Economic Review 30(1): 144-164) reports the geometric mean of (1 + tau_AB)(1 + tau_BA) under that identity.

The asymmetry is what’s left when you take the ratio instead of the product. Under the same CES structure, the intranational and multilateral-resistance terms cancel, leaving a clean closed form:

(1 + tau_AB) / (1 + tau_BA)  =  ( X_BA / X_AB )^(1 / (sigma - 1))

The direction-of-bias object needs only the two observed bilateral flows. This is the decomposition Jacks, Meissner & Novy (2011), “Trade booms, trade busts, and trade costs” (Journal of International Economics 83(2): 185-201), exploit to track cost symmetry over two centuries. We use sigma = 8 throughout (ESCAP / Arvis convention); because the exponent 1/(sigma-1) only rescales the magnitude, the rank order of asymmetries across pairs is invariant to any value in the plausible interval sigma in [3, 12] surveyed in Head & Mayer (2014), “Gravity equations: workhorse, toolkit, and cookbook” (Handbook of International Economics, vol. 4, ch. 3). Intranational trade uses the standard output-minus-exports proxy: GDP (nominal, current USD) less gross exports, both in the same year. Where Anderson & van Wincoop (2004) note in their JEL survey on trade-cost measurement, “there is no direct measure of internal trade; the GDP residual is the workhorse”.

Where direction matters most

Asymmetry beyond what distance predicts

Geography is the first candidate explanation: long routes have more friction, so we might expect the direction gap to widen with distance purely mechanically. Disdier & Head (2008), “The puzzling persistence of the distance effect on bilateral trade” (Review of Economics and Statistics 90(1): 37-48), show that the distance elasticity of trade is remarkably stable across decades. We run the dual specification here — regress the log of the absolute asymmetry on log bilateral distance across all 2,514 qualifying pairs with a CEPII distance record — and report pairs whose asymmetry exceeds the distance-implied prediction.

How symmetric are trade blocs, really?

Preferential trade agreements are supposed to compress cross-border frictions uniformly for members. Baier & Bergstrand (2007), “Do free trade agreements actually increase members’ international trade?” (Journal of International Economics 71(1): 72-95), estimate an FTA roughly doubles bilateral trade after a decade. The question here is different: among member pairs, does direction symmetry also improve? EU27 (306 qualifying pairs), ASEAN (34), and Mercosur including Bolivia (9) are the three deepest-integration blocs with enough intra-bloc trade to estimate on the 2023 snapshot under the $50M floor.

Has the world become more direction-symmetric?

Jacks, Meissner & Novy (2011) trace the evolution of bilateral trade costs over 140 years and find the symmetric level fell steadily through the two globalisation waves. The direction question is under-studied. Below we re-run the Head-Ries asymmetry on every qualifying pair from 1995 to 2023 and report the annual median and 75th-percentile of |asymmetry|.

Cost asymmetry vs flow imbalance across the top pairs

A natural reader question: is the direction-of-bias just another name for the bilateral trade imbalance? The two are related by construction (both are ratios of X_AB to X_BA) but carry different economic content: the trade imbalance reports dollars, the Head-Ries asymmetry translates those dollars into an implied iceberg-factor wedge via the CES exponent 1/(sigma-1). Figure 5 plots the ad-valorem-equivalent asymmetry against the dollar gap (X_AB - X_BA) across the 20 pairs in Figure 1, letting readers see how a similar AVE wedge can sit on very different volumes.

Forward and reverse one-way costs by distance bin

Figures 1 through 5 report the direction of the asymmetry; Figure 6 recovers each one-way iceberg factor on its own by combining the product and ratio identities of Head & Ries (2001). With (1 + tau_AB)(1 + tau_BA) and (1 + tau_AB) / (1 + tau_BA) both identified from observed flows and intranational-trade proxies, tau_AB and tau_BA can be solved for individually. We then bin the 2023 universe by bilateral distance quintile (CEPII Gravity V202411) and report the mean forward and reverse AVE-equivalents in each bin.

Direction-of-bias by income-pair type

The Head-Ries asymmetry on a single pair is a compound of geography, policy, and the institutional gap between the two partners. If the gap is systematic — rich-country exports to low-income partners face lower regulatory friction than the reverse — the average asymmetry should differ across World Bank income tiers. Figure 7 buckets the 2023qualifying pairs by (exporter-tier)-(importer-tier) using the World Bank FY2023 income thresholds applied to CEPII gravity’s gdpcap (current USD per capita): high-income (HIC) above USD 13,845, upper-middle (UMIC) 4,466-13,845, lower-middle (LMIC) 1,136-4,465, low (LIC) at or below 1,135.

Direction-of-bias by dyadic gravity features

Common official language, common colonizer, and shared border are the workhorse dyadic dummies in CEPII Gravity (Mayer & Zignago 2011, CEPII Working Paper 2011-25; Head & Mayer 2014). They proxy informational and institutional alignment between two partners. If alignment compresses friction symmetrically, pairs sharing a feature should show smaller |asymmetry|; if alignment mostly cuts the symmetric level via Anderson & van Wincoop (2003) multilateral-resistance terms, the direction wedge should be roughly invariant. Waugh (2010), “International trade and income differences” (American Economic Review 100(5): 2093-2124), reads the cross-section of bilateral frictions as a structural North-rich / South-poor cost asymmetry; the contiguous-versus-non-contiguous comparison here is the dyadic-features analogue applied to the Head-Ries direction component.

Open questions and policy read

• Are directional costs a policy target? Anderson and Yotov (2016, American Economic Review 106(10): 2928-2962) show welfare gains from declining symmetric costs are large, but their decomposition cannot price the direction wedge. If institutional friction is one-sided (e.g., non-tariff barriers on reverse flows), targeted policy can compress the wedge in the absence of a full FTA.
• Specification sensitivity. Novy (2013) notes the direction-of-bias object is robust to sigma but not to the X_AA proxy. Moving from GDP-less-exports to output-less-exports (ICIO) would change levels in small open economies; the rank order across pairs is typically preserved.
• Policy read. FTAs compress the level, not the direction. Regulatory convergence (mutual recognition of standards, certification reciprocity) is the instrument for the direction component; Baier and Bergstrand (2007) estimate the level effect, not the symmetry effect.

Caveats

• Intranational-trade proxy. X_AA = GDP minus gross exports is standard (Head & Ries 2001; Novy 2013) but noisy for small open economies where that residual can dip below plausible values. Anderson and van Wincoop (2004) survey the alternatives; none dominates at world coverage.
• Sigma sensitivity. Absolute AVE levels scale with 1/(sigma-1). The rank order of pairs, the distance residuals in Figure 2, and the time trend in Figure 4 are invariant. The within-bloc comparison in Figure 3 is also invariant because all three blocs use the same exponent.
• Re-exports and transit. BACI harmonises to country of origin / final destination but transit and entrepot flows via Netherlands, UAE, Singapore, Hong Kong contaminate the asymmetry at the country level; several of the top residuals in Figure 1 reflect that.
• Coverage of the intranational benchmark. The GDP residual is undefined for economies missing a 2023 macro-GDP record in our vintage; such pairs drop out of Figure 1’s computation of tau_sym (shown in meta-row for context), but the asymmetry ratio itself only needs the two bilateral flows and is unaffected.

References

• Anderson, J. E., & van Wincoop, E. (2003). “Gravity with gravitas: a solution to the border puzzle.” American Economic Review 93(1): 170-192.
• Anderson, J. E., & van Wincoop, E. (2004). “Trade costs.” Journal of Economic Literature 42(3): 691-751.
• Anderson, J. E., & Yotov, Y. V. (2016). “Terms of trade and global efficiency effects of free trade agreements, 1990-2002.” Journal of International Economics 99: 279-298.
• Arvis, J.-F., Duval, Y., Shepherd, B., Utoktham, C., & Raj, A. (2016). “Trade costs in the developing world: 1996-2010.” World Bank Economic Review 30(1): 144-164.
• Baier, S. L., & Bergstrand, J. H. (2007). “Do free trade agreements actually increase members’ international trade?” Journal of International Economics 71(1): 72-95.
• Disdier, A.-C., & Head, K. (2008). “The puzzling persistence of the distance effect on bilateral trade.” Review of Economics and Statistics 90(1): 37-48.
• Head, K., & Mayer, T. (2014). “Gravity equations: workhorse, toolkit, and cookbook.” In Handbook of International Economics, vol. 4, ch. 3.
• Head, K., & Ries, J. (2001). “Increasing returns versus national product differentiation as an explanation for the pattern of U.S.-Canada trade.” American Economic Review 91(4): 858-876.
• Jacks, D. S., Meissner, C. M., & Novy, D. (2011). “Trade booms, trade busts, and trade costs.” Journal of International Economics 83(2): 185-201.
• Mayer, T., & Zignago, S. (2011). “Notes on CEPII’s distances measures: The GeoDist database.” CEPII Working Paper 2011-25.
• Novy, D. (2013). “Gravity redux: measuring international trade costs with panel data.” Economic Inquiry 51(1): 101-121.
• Waugh, M. E. (2010). “International trade and income differences.” American Economic Review 100(5): 2093-2124.