Ghosh Supply-Driven Model
Also known as: Ghosh Model, Supply-Side Input-Output Model, Allocation Coefficient Model, Output-Side I-O Model
The Ghosh model is the supply-side counterpart to the Leontief demand-driven input-output system, introduced by Ambica Ghosh in 1958. Rather than fixing the recipe of inputs per unit of output, it fixes allocation coefficients — the share of each sector's output sold to every downstream buyer — and asks how a change in the supply of primary inputs (value added) propagates forward to total output. Solving x' = x'B + w' gives x' = w'(I − B)^{-1}, where the Ghosh inverse G = (I − B)^{-1} plays the forward-looking role that the Leontief inverse plays for demand.
Key highlights
- Captures forward propagation of supply-side shocks that the demand-driven Leontief model cannot represent.
- Provides forward-linkage indicators that complement Leontief backward linkages for identifying key sectors.
- Mathematically linked to the Leontief inverse by a simple diagonal transform, so it reuses the same data.
- Natural framework for analyzing resource-supply expansions, bottlenecks, and primary-input disruptions.
Intuition
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How it works
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When to use it
Use the Ghosh model when the relevant shock originates on the supply side — a resource discovery, a primary-input shortage, an export-supply expansion, or a disruption to value-added availability — and you want to trace its forward propagation to downstream output. It is the standard tool for forward-linkage analysis and supply-disruption assessment. Be aware that the strict quantity interpretation (more supply mechanically forcing more output) is economically implausible because it implies inputs are freely substitutable; many analysts therefore read the Ghosh model as a price model or use it strictly for linkage measurement, where it is well grounded.
Strengths & limitations
- Captures forward propagation of supply-side shocks that the demand-driven Leontief model cannot represent.
- Provides forward-linkage indicators that complement Leontief backward linkages for identifying key sectors.
- Mathematically linked to the Leontief inverse by a simple diagonal transform, so it reuses the same data.
- Natural framework for analyzing resource-supply expansions, bottlenecks, and primary-input disruptions.
- The literal quantity interpretation implies implausible input substitutability and is widely criticized as economically untenable.
- Allocation coefficients can be as unstable across time as technical coefficients, undermining forecasts.
- Many regard it as legitimate only as a price model or for linkage measurement, restricting its use.
- Shares the input-output limitations of fixed coefficients, coarse aggregation, and base-year dependence.
Common pitfalls
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Applications
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Frequently asked
How does the Ghosh model differ from the Leontief model?
The Leontief model is demand-driven: it fixes technical coefficients (inputs per unit of output) and solves for the output needed to meet final demand. The Ghosh model is supply-driven: it fixes allocation coefficients (the distribution of a sector's sales across buyers) and solves for the output generated by primary-input supply. One propagates shocks backward to suppliers, the other forward to customers, and the two inverses are linked by a diagonal transform G = x-hat^{-1} L x-hat.
Why is the Ghosh quantity interpretation controversial?
Taken literally, more primary-input supply forcing proportionally more output implies that intermediate inputs are perfect substitutes — a sector could expand using only extra labor or capital regardless of its other inputs. This contradicts the fixed-recipe logic of production, so many economists argue the Ghosh model is defensible only as a price model or for measuring forward linkages, not as a literal supply-driven quantity model.
What are forward linkages and how does the Ghosh model measure them?
A forward linkage measures how strongly an increase in one sector's output stimulates the sectors that buy from it downstream. The Ghosh model quantifies this through the row sums of its inverse G = (I − B)^{-1}: a large row sum for sector i means a unit increase in its supply induces a large total expansion of output across its customers, marking it as a strong forward-linkage (supply-pushing) sector.
Sources
- 1.Ghosh, A. (1958). Input-output approach in an allocation system. Economica, 25(97), 58–64.
- 2.Miller, R. E., & Blair, P. D. (2009). Input-Output Analysis: Foundations and Extensions (2nd ed.). Cambridge University Press.ISBN 9780521739023
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ScholarGate. (2026, June 22). Ghosh Supply-Driven Model. ScholarGate. https://scholargate.app/economics/ghosh-supply-model