258
SHIELDING THE POOR
Typical Consumption Path for Agent 1 under Three Cases
Note: The consumption path is for agent 1 given a sequence of realizations for autarky, perfect insurance, and implementable allocations. Source: Authors' calculations.
the ratio of the variance of idiosyncratic (net of aggregate) consumption and endowments. As we discussed above, this ratio is inversely related to the amount of idiosyncratic risk that is diversified in equilibrium. The variances are computed as the sample variances over a very long simulation. As can be seen from the first two columns of the table, for the case of an additive shock and the parameters considered, the introduction of an insurance scheme reduces the average welfare that can be obtained in an enforceable equilibrium. As should be clear from the discussion above, this result is not the only possible one. With different parameters, one would get an overall improvement. However, the mechanism through which this result comes about is quite clear from the table. Notice that the introduction of aggregate insurance increases the value of autarky (and of the first best allocation, for that matter). The increase in the value of autarky crowds out some private transfers, as is evident from the 20 percent reduction in average private transfers. This reduction more than compensates for the increase in welfare induced by the reduction in the variance of aggregate shocks. The amount of crowding out induced by the public transfer scheme is also evident in the increase in the ratio of variances (the ratio equals 1 under autarky and zero under perfect insurance). The story in the last two columns, however, is very different. The introduction of aggregate insurance in the additive case improves welfare. The average size
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FIGURE 10-4.