Models of heterogeneous firms with selection into export market participation generically exhibit aggregate trade elasticities that vary across country-pairs. Only when heterogeneity is assumed Pareto-distributed do all elasticities collapse into a unique elasticity, estimable with a gravity equation. This paper provides a theory-consistent methodology for quantifying country-pair specific aggregate elasticities when moving away from Pareto, i.e. when gravity does not hold. Combining two firm-level customs datasets for which we observe French and Chinese individual sales on the same destination market over the 2000–2006 period, we are able to estimate all the components of the bilateral aggregate elasticity: i) the demand-side parameter that governs the intensive margin and ii) the supply side parameters that drive the extensive margin. These components are then used to calculate theoretical predictions of bilateral aggregate elasticities over the whole set of destinations, and how those elasticities decompose into different margins. Our predictions fit well with econometric estimates, supporting our view that micro-data is a key element in the quantification of aggregate trade elasticities.