Official international economic statistics are generally considered accurate and meaningful gauges of cross-border flows of trade and capital. Most data users also assume that the quality of the underlying data keeps improving over time. Through an extensive review of the national accounting literature, archival research, two dozen interviews with high-level statisticians, and a series of data quality tests, we evaluate this common view for the primary source of data on trade and capital flows: the International Monetary Fund's Balance of Payments (BOP) Statistics. Our assessment paints a less rosy picture: reported figures are far less accurate than they are typically imagined to be and often do not correspond to the theoretical concepts with which users associate them. At the same time, measurement quality deteriorates over time as the transnationalization of economic production gradually undermines the validity of BOP statistics. Our findings raise serious questions about the widespread use of these numbers, with their deceptive pretense to accuracy, in scholarly research and public debate about the international political economy.