← All parts of this equation

Equation 10 · Part 14 · Selection Accounting: The Price Equation Runs the Economy

Denominator: HHI

Var⁡(Sel)=σ2∑isi2(zi−zˉ)2,Ne=1HHI\operatorname{Var}(\mathrm{Sel}) = \sigma^2 \sum_i s_i^2 (z_i - \bar z)^2, \qquad N_e = \frac{1}{\mathrm{HHI}}
HHI\mathrm{HHI}

What this part means

The complete quantity below the fraction bar; it must be nonzero for this division.

Its job in the formula

HHI occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

The passage around this formula

Every one of those covariance terms is a realized statistic computed on one historical sample path, and molecular evolution learned the hard way not to trust such statistics without a baseline: Kimura’s neutral theory showed that most measured molecular substitution is drift, not selection, and the field has required a null model ever since before crediting any pattern to adaptation. Proposition 4 supplies the economic equivalent. Assume market shares move by pure noise, uncorrelated with productivity — no firm is being selected for or against — and the expected value of the measured selection term is exactly zero. Its variance is not zero, and it has a closed form: Var⁡(Sel)=σ2∑isi2(zi−zˉ)2,Ne=1HHI\operatorname{Var}(\mathrm{Sel}) = \sigma^2 \sum_i s_i^2 (z_i - \bar z)^2, \qquad N_e = \frac{1}{\mathrm{HHI}}.…

Read this part in the article →

Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

Open the illustrated fractions: division written vertically guide →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.