Approximate Aggregation

This paper revisits the approximate aggregation result of Krusell and Smith (1998). For the stochastic growth model with inelastic labor supply and uninsurable shocks to employment, those authors found that the mean was sufficient to forecast future prices; since prices are known functions of only aggregate capital, the fact that the mean evolves independently of the rest of the distribution rendered it the only relevant piece of information contained in the cross-sectional distribution. I compute the implications of the algorithm for many features of the cross-sectional distribution, finding that the model produces distributions which feature independent central moments. What this means is that the usual statement 'Only the Mean Matters' really should be augmented with the phrase 'for the Evolution of the Mean,' as the mean does not provide any useful information for those higher-order moments. Nonlinear statistics computed from the distribution barely depend on the mean and do not influence its evolution, so that again the mean fails to provide sufficient information to track all the implications of the model. I next consider the possibility of self-fulfilling equilibria, in which the idea that agents make decisions based on limited information that somehow results in only those variables mattering. I test this idea in two ways. First, holding the behavior of every agent constant except one (who is of measure zero), I consider whether that household could benefit in terms of forecasting accuracy by using the information contained in higher-order moments and statistics; I find that projecting the forecasting error on a wide spectrum of variables fails to uncover even one that has a signficant impact on the accuracy of the forecast for next period's mean. Second, I allow for some or all of the households in the economy to explicitly use those higher-order statistics for forecasting, again finding no argument for doing so. Even when only a fraction of households use additional information, so that their forecasts are statistically more accurate than the ones who do not, they do not tend to get systematically wealthier over time. These tests suggest strongly that self-fulfilling equilibria are not a feature of this economy. In the last section of the paper, I consider three economies in which there is cross-sectional heterogeneity in the marginal propensity to save out of wealth. Krusell and Smith (1998) point to the relative homogeneity of the MPS as an important feature for generating approximate aggregation. I show that homogeneity is not really sufficient, as each of the example economies feature large cross-sectional dispersion in MPS but nevertheless nearly aggregate. The key feature is rather a low amount of variation in this distribution over the business cycle -- in no economy does there occur significant movements in the distribution of MPS with respect to changes in the aggregate state