Research Note on "International Consumption Risk Sharing with Incomplete Goods and Asset Markets"

Perfect risk sharing requires both, frictionless goods as well as frictionless asset markets. To analyze the consequences of both type of frictions for consumption risk sharing across countries, the model by Ghironi and Melitz (2005) is extended to allow for international trade in equities. The model features fixed costs of exporting as well as variables iceberg costs when shipping goods. Financial markets are incomplete, as only two assets are traded, which cannot span all the uncertainty caused by potential shock scenarios. In models with incomplete asset markets, two well known problems arise. First, the steady state portfolio allocation in a non-stochastic steady state is indeterminate since assets are perfect substitutes. And, second, as noted by Schmitt-Grohé and Uribe (2003) among others, even transitory shocks may have permanent effects on wealth. This, in turn, may lead to non-stationary responses of the endogenous variables. To deal with these issues, quadratic portfolio costs on asset holdings as in Ghironi, Lee, and Rebucci (2007) are introduced. Besides introducing frictions in asset markets, these costs help to pin down the steady state portfolio allocation and induce model stationarity. This research note gives technical details on the solution of the model. In the following section, the basic setup of the model as well as the main variables and equilibrium conditions of the model are briefly summarized. Section 3 solves for the steady state levels of the endogenous variables.