Input-Output Analysis
Also known as: Leontief Model, Inter-Industry Analysis, I-O Analysis, Input-Output Model
Input-output analysis is a quantitative framework for representing the interdependence between the industries of an economy, introduced by Wassily Leontief in 1936. It records the flows of goods and services between sectors in a transactions table, derives fixed technical coefficients describing how much each industry buys from every other industry per unit of output, and inverts the resulting linear system to trace how an exogenous change in final demand ripples through the entire production structure.
Key highlights
- Captures the full chain of direct and indirect inter-industry effects in a single, exact matrix inversion, avoiding double counting.
- Built directly on official national accounts, giving it an empirical, internally consistent accounting foundation.
- Transparent and reproducible: multipliers can be decomposed and audited sector by sector.
- Readily extended to satellite accounts for employment, energy, emissions, and water, making it a workhorse for environmental and regional analysis.
Intuition
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How it works
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When to use it
Use input-output analysis when you need to quantify the economy-wide ripple effects of a change in final demand, a new investment, a policy shock, or a supply disruption, and you have access to an inter-industry transactions table (often published by national statistical offices every few years). It is the standard tool for impact assessment of large projects, regional economic studies, environmental and carbon footprint accounting, and supply-chain analysis. It assumes fixed input proportions, no capacity constraints, no price responses, and constant returns to scale, so it is best for short-run, demand-driven impact questions rather than long-run analyses where substitution and prices matter — for those, a computable general equilibrium model is more appropriate.
Strengths & limitations
- Captures the full chain of direct and indirect inter-industry effects in a single, exact matrix inversion, avoiding double counting.
- Built directly on official national accounts, giving it an empirical, internally consistent accounting foundation.
- Transparent and reproducible: multipliers can be decomposed and audited sector by sector.
- Readily extended to satellite accounts for employment, energy, emissions, and water, making it a workhorse for environmental and regional analysis.
- Assumes fixed technical coefficients and linear, constant-returns technology, ruling out input substitution and economies of scale.
- Demand-driven and price-free: it cannot model supply constraints, capacity limits, or how prices reallocate resources.
- Coefficients are fixed at the table's base year and become outdated as technology and trade patterns change.
- Tables are costly to compile and are published infrequently and at a coarse sectoral aggregation, masking heterogeneity within sectors.
Common pitfalls
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Applications
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Frequently asked
What is the difference between input-output analysis and a computable general equilibrium (CGE) model?
Input-output analysis uses fixed technical coefficients and a linear, demand-driven structure with no prices, so output responds proportionally to final demand. A CGE model embeds the same accounting structure but adds optimizing agents, flexible substitution between inputs, market-clearing prices, and resource constraints, allowing it to capture substitution and reallocation effects that the linear I-O model holds fixed. I-O is the calibration starting point; CGE is the behavioral extension.
What does the Leontief inverse actually represent?
Each entry ℓ_ij of the Leontief inverse (I − A)^{-1} is the total output that sector i must produce, directly and indirectly, to deliver one unit of sector j's product to final demand. It equals the infinite sum I + A + A² + A³ + …, where each term is a successive round of inter-industry requirements, so the inverse compactly captures the entire supply-chain cascade.
Why are output multipliers often criticized in impact studies?
Multipliers measure gross output generated per unit of final demand, not net welfare gains, and they assume idle resources, no price changes, and no crowding out. Used uncritically — for example by ignoring import leakages or applying national coefficients to a small region — they systematically overstate the true economic benefit of a project, which is why careful analysts adjust coefficients and report assumptions explicitly.
Sources
- 1.Leontief, W. W. (1936). Quantitative input and output relations in the economic system of the United States. The Review of Economics and Statistics, 18(3), 105–125.
- 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). Input-Output Analysis. ScholarGate. https://scholargate.app/economics/input-output-analysis