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
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