Stochastic Discount Factor Approach to International Risk-Sharing:A Robustness Check of the Bilateral Setting

This paper presents a robustness check of the stochastic discount factor approach
to international (bilateral) risk-sharing given in Brandt, Cochrane, and Santa-Clara
(2006). We demonstrate two main inherent limitations of the bilateral SDF
approach to international risk-sharing. First, the discount factors are not uniquely
determined in the bilateral framework and crucially depend on the partner country
included in the calculations. Second, the deviations between the discount factors
obtained in this way (the imprecision in the measurement of marginal utility
growth) are larger for countries whose stock market excess return shocks are
relatively less important. In order to account for some of these criticisms, we
extend the bilateral into a three-country setting. Although the trilateral framework
demonstrates that the (final) results for the international risk-sharing index are
quite robust to the number of countries used in their calculation, it does not
resolve the inherent incoherence found in the bilateral SDF approach.