Paradox in deviation measure and trap in method improvement—take international comparison as an example

Due to the problem of "true value agnostic" in the measurement of the real world, people believe that the existing methods can be closer to the true value by improving them. Therefore, they are willing to excessively affirm the more advanced method and deny the relatively "traditional" method. Taking the exchange rate method and purchasing power parity method commonly used in international economic comparison as examples, this paper generalizes the problems revealed by the exchange-rate-deviation index and concludes that there are at least three paradoxes in the deviation measurement of different methods. These paradoxes are the paradox of behavior significance, the paradox of comparative object, and the paradox of measurement result. The reason is that there is a cautionary trap in the improvement or innovation of measurement methods in reality. Sometimes the improved method is not necessarily better than the unimproved method. People tend to prefer advanced technology and methodology, but the problem of statistical input and related statistical benefits need to be considered in practical measurement. In fact, these basic problems still exist in some of the methods of economic statistics that we regard as common sense. When learning or introducing new methods, scholars do not absolutize the existing methods and conclusions. They should pay attention to critical experience, avoid the trap of improvement methods, and seek real improvement or innovation.