Origin of Departure from LLN

Understanding the Departure from LLN

By coming down this path, we are able to see the origin of the departure from the Law of Large Numbers (LLN) and describe the situation formally in terms of the parameters of populations of agents. This exploration requires re-analyzing certain conceptions established in previous research and considering new perspectives.

The interpretation of 'postponement' in LLN as firm-to-firm comovement, and the neat relation that allows us to balance it against the magnitude of self-variance shown by agents, are connections worth exploring further in new studies.

This paper is now slowly coming to a closure, first by including some additional results which may be useful, such as moments of log levels of quantiles, and in subsequent sections by testing robustness to generalizations regarding size distributions. We will cover the accounting of extensive margins and explore the elements of cross covariance matrices.

In our empirical setting, $\hat{\sigma}$ is large enough to let fat-tail micro shock distributions be qualitatively different from log-normals in some respects. For example, in the range of parameters characterizing our population of French traders, there is clear delayed convergence of averages when the number of agents is large, as we have observed.