The Identification of Reporting Accuracies from Mirror Data

Summary Mirror data are observations of bilateral variables such as trade from one country to another, reported by both countries. The efficient estimation of a bilateral variable from its mirror data, for example when compiling consistent international trade statistics, requires information about the accuracy of the reporters. This can be obtained from the simultaneous estimation of the accuracy of multiple reporters, from all mirror data. This estimation requires an identifying restriction. For example, in one of the proposed models this restriction prevents the model to be indifferent between (a) all reporters reporting correctly and (b) all reporters over-reporting with the same percentage. Two models are presented. First, a model with country-specific mean reporting errors is discussed shortly. This model has been discussed elsewhere without a convincing solution of the identification problem. Such a solution is presented here, assuming symmetry. Second, a model is presented with country specific reporting error variances, in the form of a generalized linear model (GLM). This model supplies the weights for the traditional method of optimally combining inconsistent data: weighted with the reciprocal of their error variance. Here also a symmetrical identifying restriction is used. In this way, this paper paves the road for the production of harmonized statistics by international agencies. A small data set on international trade is used as an illustration.