This paper investigates a consumption-real exchange rate anomaly from the open macroeconomics literature known as the Backus-Smith puzzle . We both analytically and quantitatively examine how an expansion of trade along extensive margins can contribute to the puzzle's resolution. Our argument is based on 1) a wealth e¤ect due to changes in the number of product varieties, 2) statistical ine¢ ciency in measuring the number of product varieties, and 3) market incompleteness. Contrary to complete asset markets which, in general, feature overly strong risk sharing properties, changes in the number of product varieties under incomplete markets may produce a wealth e¤ect under high trade elasticity. Since statistical agencies systematically fail to capture the welfare impact arising from that changes, data-consistent terms of trade and real exchange rates tend to appreciate due to this positive wealth e¤ect. This provides a realistic correlation between data-consistent real exchange rates and consumption.6 I would like to thank the editor and two anonymous referees for their valuable comments. I gratefully acknowledge Philippe Martin for his advice and encouragement. I would like to also thank Nicolas Coeurdacier, Hideaki Hirata, Jan Kranich, Eiji Ogawa, Eiji Okano and Robert Kollmann for providing comments and insightful discussions. I thank all seminar participants at the Universities Rennes1, Paris1, Hitotsubashi, the 13th T2M conference, the 14th SMYE, the 25th EEA meeting and the 13th macroeconomic conference in Tokyo. The paper is based on the second chapter of my Ph.D. dissertation.