Empirical research in international trade is constrained by the absence of a reliable, exhaustive data base on bilateral trade flows among regions. The United Nations data base on bilateral merchandise trade flows among countries is the most complete source of such data. However, it is notably unreliable. The purpose of this paper is to report on a statistical procedure for estimating systematic reporting biases, by region, for this particular data base. This serves two purposes. First, it offers a concrete quantification of one dimension of the reporting problem. Secondly, with these reporting biases in hand, it is possible to "adjust" the data. That is, one can create a set of bias-corrected trade flows. The proposed procedure capitalizes on the fact that the UN bilateral trade data base contains two observations on every trade flow, at any point in time. Our statistical model seeks to explain the discrepancy between reported exports from country i to country j at time T, and reported imports by j from i at T. Systematic discrepancies are attributed to c.i.f./f.o.b. margins and reporting biases by the two countries in question. We estimate the model using trade flows among OECD countries over the period 1962-1987. Merchandise trade is grouped into eight categories. Preliminary results indicate that the reporting of Japanese import flows and U.S. export flows are unbiased. Both exports from, and imports to Australia exhibit statistically significant reporting biases. In particular, exports are systematically underreported (by 11.5%), while imports are systematically overreported (by 4.4%). A similar pattern exists for New Zealand, while the opposite is true of the European Community. Canada, on the other hand, appears to overreport both exports and imports. Some of these results may be due to the simple approach which we have taken to modeling the transportation and insurance margins. Future research will attempt to improve this aspect of the model. We will also attempt to estimate reporting biases for non-OECD regions.