Equation 4 · Part 2 · Selection Accounting: The Price Equation Runs the Economy
subscript
subscript
What this part means
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
Its job in the formula
A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.
Full expression→subscript→Article meaning
The passage around this formula
The change in mean log productivity splits into a covariance between a firm’s relative fitness — its share-growth factor — and its productivity, plus a share-weighted average of each firm’s own productivity change, weighted by how much it grew. The first term is selection: value reallocated toward whoever is already ahead. The second is transmission: value created inside units that already exist. This holds for any partition of any economy in any period. It is exact bookkeeping, not a behavioral model, and it carries no error term to hide behind.
Learn the underlying idea
A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.
Open the illustrated subscripts: which member of a family? guide →
Sources cited in the article section
- [8] Dynamic Olley-Pakes Productivity Decomposition with Entry and Exit ↗
- [6] The Dynamics of Productivity in the Telecommunications Equipment Industry ↗
- [7] Aggregate Productivity Growth: Lessons from Microeconomic Evidence ↗
These citations provide research context; check each source for the exact claim it supports.