Linking Trade Data from Different National Statistical Offices Through a Private Set Intersection

National Statistical Offices (NSOs) collect extensive data on the international activities of firms within their borders. However, they typically lack information about the foreign partners with whom these firms trade. Linking import data from one NSO to corresponding export data from a partner NSO could significantly enhance statistics on firms’ international operations. While technically feasible, such linkage is legally constrained by strict privacy laws. Private set intersection (PSI) protocols may help address privacy concerns but require unique identifiers to avoid linkage errors. To overcome this limitation, we propose a PSI protocol with three innovations. First, we estimate the rates of linkage error by modeling the number of links from a given record. Second, we adjust an estimated population mean according to the estimated linkage accuracy. Lastly, our adjustment explicitly accounts for this accuracy without assuming a particular relationship among the target variables.