This paper investigates the role of shocks to U.S. productivity and demand in driving the real value of the dollar, and the dynamics of the U.S. trade balance. Using sign restrictions based on robust predictions by standard theory, we identify shocks that increase domestic labor productivity and output in manufacturing (our measure of U.S. tradables), relative to an aggregate of other industrial countries including the rest of the G7, while driving down (up in the case of demand) the relative price of tradables (in accord to Harrod-Balassa-Samuelson effects). Consistent with previous results based on different methodologies, we find that positive productivity differentials raise U.S. consumption and investment relative to the rest of the world, and deteriorate net exports; both the U.S. real exchange rate and the U.S. terms of trade appreciate in response to these shocks. Demand shocks also appreciate the dollar, but have negligible effects on absorption and the trade balance. These findings question a common view in the literature, that a country's terms of trade deteriorate when its tradables supply grows, providing a mechanism to contain differences in national wealth even if productivity level do not converge. They also provide an empirical contribution to the current debate on the adjustment of the U.S. current account position. Contrary to widespread presumptions, productivity growth in the U.S. tradable sector does not necessarily improve the U.S. trade deficit, nor deteriorate the U.S. terms of trade, at least in the short and medium run.