Size, openness, and macroeconomic interdependence

The curse of dimensionality, a problem associated with analyzing the interaction of a relatively large number of endogenous macroeconomic variables, is a prevailing issue in the open economy macro literature. The most common practise to mitigate this problem is to apply the so-called Small Open Economy Framework (SOEF). In this paper, we aim to review under which conditions the SOEF is a justifiable approximation and how severe the consequences of violation of key conditions might be. Thereby, we use a multicountry general equilibrium model as a laboratory. First, we derive the conditions that ensure the existence of the equilibrium and study the properties of the equilibrium using large N asymptotics. Second, we show that the SOEF is a valid approximation only for economies (i) that have a diversified foreign trade structure and if (ii) there is no globally dominant economy in the system. Third, we illustrate that macroeconomic interdependence is primarily related to the degree of trade diversification, and not to the extent of trade openness. Furthermore, we provide some evidence on the pattern of global macroeconomic interdependence by calculating probability impulse response functions in our calibrated multicountry model using data for 153 economies.