Törnqvist index¶
In economics, the Törnqvist index is a price or quantity index.
Core Idea¶
Törnqvist index is treated here as the recurring socialscienceshumanitiesarts identity summarized by this source-grounded definition: In economics, the Törnqvist index is a price or quantity index. In economics, the Törnqvist index is a price or quantity index. In practice, Törnqvist index values are calculated for consecutive periods, then these are strung together, or "chained". Thus, the core calculation does not refer to a single base year. There is research on which method to use based partly on whether price changes or quantity changes are more volatile.
Scope of Application¶
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Theory. The Törnqvist index is a superlative index, meaning it can approximate any smooth production or cost function. "Smooth" here means that small changes in relative prices for a good will be.
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Computation. For multifactor productivity calculations, the indirect method is used.
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Computation. The data used are prices and quantities in two time-periods, (t-1) and (t), for each of n goods which are indexed by i.
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Computation. In practice, Törnqvist indexes are often computed using an equation that results from taking logs of both sides, as in the expression below which computes the same Pt as those above.
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Computation. Quantity indexes are used in computing aggregate indexes for physical "capital" summarizing equipment and structures of different types into one time series.
Clarity¶
A clear use of Törnqvist index names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is In economics, the Törnqvist index is a price or quantity index. The strongest recognition evidence in the frozen account is: For example, a Törnqvist index summarizing labor input may weigh the growth rate of the hours of each group of workers by.
Manages Complexity¶
Törnqvist index compresses multiple socialscienceshumanitiesarts details into a stable diagnostic relation. The source shows both the central mechanism—in practice, Törnqvist indexes are often computed using an equation that results from taking logs of both sides, as in the expression below which computes the same Pt as those above.—and the practical consequence—if one needs matched quantity and price indexes they can be calculated directly from these equations, but.
Abstract Reasoning¶
- Type the carrier. Identify the socialscienceshumanitiesarts entities to which the claim applies.
- State the relation. Use the source-grounded identity: In economics, the Törnqvist index is a price or quantity index.
- Check operation and conditions. Törnqvist indexes are close to the figures given by the Fisher index.
- Demand recognition evidence. For example, a Törnqvist index summarizing labor input may weigh the growth rate of the hours of each group of workers by the share of labor compensation they receive.
- Test variation.
Knowledge Transfer¶
Within the home domain. Knowledge about Törnqvist index transfers literally when a new case preserves the same carrier type, relation, and recognition test. The Törnqvist index is a superlative index, meaning it can approximate any smooth production or cost function. "Smooth" here means that small changes in relative prices for a good will be associated with small changes in the quantity of it used. For multifactor productivity calculations, the indirect method is used. Beyond the home domain. No canonical parent is asserted for Törnqvist index.
Relationships to Other Abstractions¶
Current abstraction Törnqvist index Domain-specific
Parents (1) — more general patterns this builds on
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Törnqvist index is a kind of, typical Aggregation Prime
The Törnqvist index is a value-share-weighted geometric mean collapsing many price or quantity ratios into one chained index number.
Hierarchy path (1) — routes to 1 parentless root
- Törnqvist index → Aggregation → Micro Macro Linkage
Neighborhood in Abstraction Space¶
Törnqvist index sits in a moderately populated region (54th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.
Family — Financial Indices & Trading Indicators (15 abstractions)
Nearest neighbors
- Volume Index — 0.87
- Merton's portfolio problem — 0.87
- PRIX index — 0.86
- Value at risk — 0.86
- Substitution bias — 0.85
Computed from structural-signature embeddings · 2026-10-08