Exact Aggregation of Economic Growth Rates: From Accounting Sums to the Mean of Individual Weighted Rates

Abstract Macroeconomic aggregation of growth rates faces a structural tension: the simple arithmetic mean of heterogeneous individual growth rates does not reconstruct the global macroeconomic rate G . Institutional accounting approaches—whether through additive contributions G=∑Δi/X0 or through “weighted averages” G=∑giwi —guarantee exact macro closure, but transform individual variations into shares of the aggregate, thereby preventing direct statistical analysis of the underlying distribution. Conversely, cross‑sectional analysis based on raw individual rates gi ignores the structural weight of each entity and generates severe scale biases. To overcome this dichotomy, the article introduces a new univariate metric: the Weighted Aggregable Rate rwi. This metric reconciles accounting rigor with distributional analysis. The rwi ensures exact macroeconomic aggregation by simple arithmetic mean, G=1/N∑rwi, thus legitimising the use of standard cross‑sectional operators of dispersion and asymmetry (variance σ2rw , skewness γ1 ). These moments allow us to deconstruct the “superposition states” inherent in the macro rate, discriminating between growth dynamics—diffuse, concentrated or compensating—that were previously conflated within a single aggregate. Applied to real and constructed data on national accounts, public finances, employment and inflation, this framework dispels the holistic illusion of macroeconomic aggregates. It also operationalises granular cross‑sectional analysis, providing central banks and statistical institutes with a robust tool for the early detection of systemic vulnerabilities. Keywords: Macroeconomic aggregation; Weighted aggregable rate; Granular hypothesis; National accounting; Morphology of growth; Macroprudential stability.JEL codes: C43, E01, E60, O47.