Aggregation across each nation: aggregator choice and macroeconomic dynamics

We study the implications of trade aggregation in an infinite-horizon economy with multiple countries. Specifically, we ask whether there is a role for alternatives to the Armington aggregator in the workhorse open-economy macroeconomics model. We show analytically that the first-order dynamics of the model are entirely captured by a few sufficient statistics, so that the precise choice of functional form for the trade aggregator is irrelevant. This irrelevance result has the following implications. For given steady-state trade elasticities and expenditure shares, any aggregator that is homogeneous of degree one is equivalent to the Armington aggregator at first order. Similarly, aggregators that are homogeneous of arbitrary degree are equivalent to a simple generalisation of the Armington aggregator, for given steady-state trade elasticities and expenditure shares. In models with more than two countries, alternative aggregators can play a role by allowing for steady-state differences in bilateral trade elasticities across different country pairs, which the Armington aggregator rules out.