  This paper introduces a causal machine learning approach to investigate the
impact of the EU-Canada Comprehensive Economic Trade Agreement (CETA). We
propose a matrix completion algorithm on French customs data to obtain
multidimensional counterfactuals at the firm, product and destination levels.
We find a small but significant positive impact on average at the product-level
intensive margin. On the other hand, the extensive margin shows product
churning due to the treaty beyond regular entry-exit dynamics: one product in
eight that was not previously exported substitutes almost as many that are no
longer exported. When we delve into the heterogeneity, we find that the effects
of the treaty are higher for products at a comparative advantage. Focusing on
multiproduct firms, we find that they adjust their portfolio in Canada by
reallocating towards their first and most exported product due to increasing
local market competition after trade liberalization. Finally, multidimensional
counterfactuals allow us to evaluate the general equilibrium effect of the
CETA. Specifically, we observe trade diversion, as exports to other
destinations are re-directed to Canada.
