The Conditions of Dynamic Aggregation

Abstract

Accounting consistency and predictive sufficiency are different properties. An official aggregate can continue to measure exactly what its rules define while ceasing to contain the information needed to predict subsequent economic dynamics. This paper develops a framework for identifying when that divergence occurs.

Economic interaction can affect aggregation in three different ways. Dispersion erases local variation. Common exposure aligns agents through shared signals, technologies, constraints, or institutions. Strategic complementarity strengthens alignment when agents respond to one another’s expected actions. The balance among these forces determines whether conventional macroeconomic aggregates remain dynamically sufficient, whether distributions, networks, or histories must be added, or whether a low-dimensional description survives only in a different set of coordinates.

The paper distinguishes dimensional failure from coordinate failure. Dimensional failure occurs when the inherited economic state is too small and requires additional variables. Coordinate failure occurs when the economy may still be represented parsimoniously, but the established variables are no longer the most informative way to organize it. This distinction separates growing economic complexity from the obsolescence of inherited classifications.

The paper translates the framework into an applied diagnostic protocol. It proposes testing whether candidate information improves out-of-sample prediction, examining how sufficiency changes across forecast horizons, and comparing augmented models with alternative representations of matched effective complexity. These comparisons distinguish missing information from obsolete coordinates while limiting the advantages that larger or more heavily tuned models would otherwise receive.

Institutions play two roles. They shape adjustment speeds, strategic feedback, and common exposure, but they also define the boundaries through which economic activity is measured. The paper therefore distinguishes passive coordinate lag from strategic perimeter leakage. Passive lag arises when economic activity changes faster than administrative classifications. Strategic leakage arises when regulated actors alter the measured object in response to the measurement or regulatory rule itself.

A formal perimeter-leakage result shows that when a regulated actor can meet a measured target through either genuine reduction or relocation outside the regulated boundary, relocation increases as genuine reduction becomes relatively more costly. If the relocated activity retains economic or systemic effectiveness, the measured statistic can improve faster than the underlying condition. In the limiting case, the reported proxy can improve while effective coupling worsens.

National accounting and financial regulation illustrate the framework. The historical treatment of research and development shows how productive activity can precede its recognition in official coordinates. The movement of credit activity between banks and nonbank institutions shows how improvement within a regulatory perimeter may differ from change in the effective financial network.

The paper is conceptual and analytical. It develops a common language and an empirical testing strategy for determining when established aggregates remain useful, when the economic state must be enlarged, and when the coordinate system itself should be replaced.