The consumption-real exchange rate anomaly with extensive margins

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 effect due to changes
in the number of product varieties, 2) statistical inefficiency 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 effect. This provides a realistic correlation between
data-consistent real exchange rates and consumption.