Approximate aggregation revisited: higher moments do matter

Abstract

This article addresses the ‘approximate aggregation’ result by Krusell and Smith (1998) who show that in a heterogeneous-agent model it is possible to obtain near-perfect forecasts disregarding distributional information. While this fact is generally interpreted causally, the forecasting model is misspecified and thus unfit for inference. Approximate aggregation does not hold in the baseline economy of Krusell and Smith (1998) when inferences are drawn from an econometric model showing no evidence of misspecification: the higher moments of the wealth distribution are important for the aggregate dynamics.

Keywords:

• approximate aggregation
• incomplete markets
• household heterogeneity
• forecasting and inference

JEL Classification:

• E10
• E25
• C52

Acknowledgement

The author would like to thank G. W. Evans for his insightful comments.

Notes

¹ In the following, I will refer to such worker and investor as the benchmark ones.

² This is seen directly from Krusell and Smith (1998). The coefficients on the agents’ forecasting specification are different among the two phases of the business cycle only by magnitudes between 10⁻² and 10⁻³. These differences imply approximately the same forecasts in both expansions and recessions and hence, the approximate aggregation logic would imply that aggregate shocks do not matter.

³ This conclusion also attains if the full measure of agents forecasts according to the second specification of Table 1.

⁴ First differencing does not solve the problem of autocorrelated residuals.