The Linear Algebra of Economic Geography Models

We provide sufficient statistics for nominal and real wage exposure to productivity shocks in a constant elasticity economic geography model. These exposure measures summarize the first-order general equilibrium elasticity of nominal and real wages in each location with respect to productivity shocks in all locations. They are readily computed using commonly-available trade data and the values of trade and migration elasticities. They have an intuitive interpretation in terms of underlying economic mechanisms. Computing these measures for all bilateral pairs of locations involves a single matrix inversion and therefore remains computational efficient even with an extremely high-dimensional state space. These sufficient statistics provide theory-consistent measures of locations’ exposure to productivity shocks for use in further economic and statistical analysis.