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Black markets can reduce the effects of distortionary regulations by reallocating scarce resources towards those who value them the most. The illegal nature of black markets however creates transaction costs that reduce the gains from trade. We take a partial identification approach to infer gains from trade and transaction costs in the black market for Beijing car license plates which emerged following their recent rationing. We use optimal transport methods to non-parametrically estimate a lower bound on the volume of unobserved black market trade under weak assumptions using comprehensive car sales data. We find that at least 11% of the quota of license plates is illegally traded. We next infer gains from trade and transaction costs and tighten the bounds on the volume of trade under further assumptions on black market transactions. The inferred size of the transaction costs suggests severe market frictions: between 61% and 82% of the realized gains from trade are lost to transaction costs, while between 7% and 28% of the potential gains from trade are realized in the black market.