Relating Output and Volatility in a Model of International Risk-Sharing with Limited Commitment

I study the constrained efficient allocations of a simple model of risk sharing and capital flows across countries assuming that each country cannot commit to fully repay its contract obligations. In the model, the degree of risk sharing and the amount of investment are interdependent. It is shown that, when individual rationality constraints are binding, the variance of consumption in any given country across states of nature (iid across countries) may be a non monotonic function of income: low in the early stage of development, high in an intermediate range and converging to zero as income converges to a high income level. A monotonically decreasing consumption variance can only obtain if the social welfare function assigns equal weights to all countries (equal treatment). The model also shows that a structure of competitive financial markets with appropriate borrowing constraints may not be sufficient to decentralize the constrained efficient allocation. A supernational authority forcing a specific redistribution of income within poorly capitalized countries may be necessary for decentralization.