Are shocks to the terms of trade shocks to productivity?

International trade is frequently thought of as a production technology in which the inputs are> exports and the outputs are imports. Exports are transformed into imports at the rate of the price> of exports relative to the price of imports: the reciprocal of the terms of trade. Cast this way, a> change in the terms of trade acts as a productivity shock. Or does it? In this paper, we show that> this line of reasoning cannot work in standard models. Starting with a simple model and then> generalizing, we show that changes in the terms of trade have no first-order effect on> productivity when output is measured as chain-weighted real GDP. The terms of trade do affect> real income and consumption in a country, and we show how measures of real income change> with the terms of trade at business cycle frequencies and during financial crises.