Economic Input-Output Models: How Linear Algebra Reveals Sector Interdependence and Production Requirements

Last Updated July 3, 2026

Economic input-output models explain how sectors, industries, institutions, and supply chains depend on one another through flows of goods, services, money, energy, emissions, labor, and intermediate demand. In linear algebra, input-output modeling turns economic interdependence into matrices that show how output from one sector becomes input to another and how changes in final demand can ripple through a connected production system.

This article opens Part VII of the Linear Algebra for Systems Modeling series by connecting matrix representation, technical coefficients, interindustry transactions, final demand, gross output, Leontief-style systems, production requirements, direct and indirect effects, multipliers, shocks, supply-chain exposure, environmental extensions, data classification, uncertainty, and responsible interpretation.

The central modeling question is not only “How much output is required?” It is “Which sectors depend on which others, how shocks propagate through production relationships, what assumptions make the matrix model valid, and what forms of economic, environmental, or social dependence become visible or hidden?”

Input-output modeling begins with a simple observation: no sector produces in isolation. Agriculture uses energy, transportation, machinery, water, labor, and financial services. Manufacturing uses extracted materials, logistics, utilities, software, business services, and imported components. Health systems depend on pharmaceuticals, buildings, equipment, electricity, waste services, administration, and professional labor. Final demand for one sector therefore creates indirect demand across many others.

Linear algebra provides the natural language for this structure. Sector flows become matrices. Final demand becomes a vector. Technical requirements become coefficients. Total output becomes the solution to a system of equations. Multipliers become matrix-derived summaries of direct and indirect dependence. Environmental extensions attach emissions, energy, land, water, labor, or other indicators to economic activity.

Why Input-Output Models Matter

Input-output models matter because they make economic interdependence visible. A demand increase in one sector does not affect only that sector. It also affects upstream suppliers, energy systems, logistics, materials, services, labor, finance, imports, emissions, and waste streams. Input-output analysis provides a structured way to estimate these linked requirements.

These models are used in economic planning, regional analysis, supply-chain risk, industrial policy, environmental accounting, carbon footprinting, disaster recovery, infrastructure planning, workforce analysis, and sustainability assessment. They help explain why sectoral shocks can propagate through a production system and why apparent local activity often depends on a much wider network of relationships.

Input-output models are not forecasts by themselves. They are structured accounting and dependency models that help reason about production relationships.

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Intersectoral Transactions

An input-output table records flows between sectors. Each entry describes how much output from one sector is used as input by another sector during a defined period. The table may be national, regional, multiregional, industry-by-industry, product-by-product, or supply-use based.

The key distinction is between intermediate demand and final demand. Intermediate demand is demand by producing sectors. Final demand is demand by users outside the intermediate production network.

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From Transactions to Matrices

Let \(Z\) be the intersectoral transactions matrix. An entry \(z_{ij}\) records the flow from sector \(i\) to sector \(j\). The column \(j\) shows inputs used by sector \(j\). The row \(i\) shows where output from sector \(i\) goes as intermediate supply.

Let \(\mathbf{f}\) be final demand and \(\mathbf{x}\) be total output. A basic row-balance relationship is:

Matrix notation makes the full production system visible at once rather than as isolated sector accounts.

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Technical Coefficients

Technical coefficients describe how much input from sector \(i\) is required per unit of output from sector \(j\). If \(x_j\) is total output of sector \(j\), then:

The technical coefficient matrix \(A\) collects these coefficients:

Technical coefficients turn observed transactions into a model of production requirements. This is powerful, but it also introduces strong assumptions about proportionality and technology.

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Final Demand and Total Output

Final demand is demand that comes from outside the interindustry production loop. It can include households, government, investment, exports, nonprofit institutions, inventory change, or other final users depending on the accounting framework.

Total output must satisfy both intermediate requirements and final demand:

This equation is the core of input-output modeling. The term \(A\mathbf{x}\) represents intermediate production requirements. The vector \(\mathbf{f}\) represents final demand. The vector \(\mathbf{x}\) represents the total output needed to meet both.

The model shows why final demand can require more total production than the final demand vector itself: production requires intermediate inputs.

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The Basic Input-Output System

Starting from:

Rearranging gives:

If \(I-A\) is invertible, the solution is:

The inverse \((I-A)^{-1}\) is often called the Leontief inverse. It captures direct and indirect production requirements across the system.

This matrix system is the bridge from economic accounting to linear algebraic systems modeling.

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Direct and Indirect Requirements

The total requirements matrix can be interpreted through a series expansion when the system is productive and the expansion converges:

This expansion shows how input-output models are also network models. Production effects move through connected sector relationships in repeated rounds.

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Multipliers

Multipliers summarize how final demand changes translate into total output, value added, employment, emissions, or other impacts. A simple output multiplier for sector \(j\) can be computed by summing the column of the Leontief inverse associated with that sector:

Multipliers are attractive because they compress system-wide dependence into a single number. But this compression creates interpretive risk. Multipliers depend on sector aggregation, regional boundaries, import assumptions, fixed coefficients, prices, capacity assumptions, and whether induced household effects are included.

Multipliers are useful summaries, not standalone explanations.

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Shock and Scenario Analysis

Input-output models can estimate how changes in final demand affect total output. If final demand changes by \(\Delta\mathbf{f}\), then the total output change is:

Scenario analysis can examine demand increases, sector declines, export changes, disaster impacts, infrastructure disruptions, policy shifts, investment programs, or consumption changes. But the standard input-output system is demand-driven. It does not automatically model price changes, substitution, capacity constraints, inventories, bottlenecks, behavioral response, or time dynamics.

Scenario results should be framed as structured estimates under assumptions, not as mechanical predictions.

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Supply-Chain Exposure

Input-output models reveal supply-chain exposure by showing which sectors depend directly and indirectly on others. The technical coefficient matrix \(A\) shows direct input dependence. The Leontief inverse \(L=(I-A)^{-1}\) shows total requirements.

A sector with a small direct requirement can still have important indirect dependence through upstream chains. Conversely, a sector with large direct purchases may have limited higher-order effects depending on network structure.

Input-output tables are usually sector-level rather than firm-level. They are valuable for structural exposure but may not identify specific suppliers, facilities, routes, contracts, or operational bottlenecks.

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Environmentally Extended Input-Output Models

Environmentally extended input-output models attach environmental coefficients to sector output. If \(\mathbf{e}\) is a row vector of emissions intensity by sector, then emissions associated with final demand can be estimated as:

The same structure can be used for energy, water, land, materials, waste, labor, occupational risk, or other extensions when appropriate coefficients are available.

Environmental extensions make hidden indirect impacts visible, but they require careful boundary definitions, sector matching, units, allocation rules, and data provenance.

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Data Classification and Aggregation

Input-output models depend heavily on classification systems. Sectors may be defined by industry, commodity, product, region, or institutional accounting category. Aggregation determines what relationships are visible. A highly aggregated table may hide critical dependencies. A very detailed table may introduce sparse data, confidentiality suppression, estimation uncertainty, or computational burden.

Before interpreting multipliers or sector dependencies, the table itself should be understood as a constructed representation.

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Assumptions and Linear Limits

Input-output models are linear models. They commonly assume fixed technical coefficients, proportional production requirements, no price response, no substitution, no supply constraints, and stable production technology over the scenario horizon. These assumptions make the system mathematically tractable, but they also limit interpretation.

The value of an input-output model comes from disciplined interpretation of these assumptions, not from pretending they disappear.

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Input-Output Models in Systems Modeling

Input-output models are systems models because they represent structured interdependence. They are not only economic tables; they are matrix representations of connected production requirements. Their logic can be extended to infrastructure, energy, emissions, materials, labor, regional planning, public health supply chains, and resilience analysis.

Input-output modeling is therefore a bridge between linear algebra, economic accounting, network reasoning, sustainability analysis, and policy interpretation.

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Mathematical Deepening

This section adds a more formal layer. Economic input-output models connect matrix construction, coefficient normalization, linear systems, matrix inversion, spectral productivity conditions, multiplier analysis, perturbation analysis, sensitivity, uncertainty, and extension vectors.

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Computation and Reproducible Workflows

Computational workflows for input-output modeling should document the sector list, transactions matrix, total output vector, final demand vector, technical coefficient method, zero-output handling, price basis, accounting year, regional boundary, matrix invertibility, condition number, Leontief inverse, multipliers, shock vector, environmental coefficients, sensitivity tests, and interpretation warnings.

The companion repository treats input-output modeling as an auditable systems workflow. Python, R, Julia, SQL, Haskell, C, C++, Fortran, Rust, Go, notebooks, schemas, generated outputs, Canvas artifacts, advanced reports, and calculators each support a different layer of reproducible input-output diagnostics.

For this article, the computational examples focus on technical coefficient construction, Leontief-style output solution, multipliers, demand-shock response, emissions extension, condition diagnostics, governance tables, and interpretation warnings.

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Python Workflow: Input-Output Audit

The Python workflow below computes an input-output audit for a small synthetic sector system. It builds a technical coefficient matrix, solves the output system, computes multipliers, applies a demand shock, adds an emissions extension, and records governance warnings.

from __future__ import annotations

from dataclasses import asdict, dataclass
from pathlib import Path
import csv
import json
import numpy as np


@dataclass(frozen=True)
class InputOutputAudit:
    model_name: str
    sectors: int
    method: str
    coefficient_basis: str
    condition_number: float
    maximum_output_multiplier: float
    highest_multiplier_sector: str
    total_baseline_output: float
    total_shock_output_change: float
    total_emissions_for_final_demand: float
    assumption_warning: str
    interpretation_warning: str


def build_system() -> tuple[list[str], np.ndarray, np.ndarray, np.ndarray, np.ndarray]:
    sectors = ["energy", "manufacturing", "transport", "services"]

    # z_ij: output from sector i used by sector j
    transactions = np.array(
        [
            [8.0, 18.0, 10.0, 7.0],
            [4.0, 12.0, 8.0, 11.0],
            [3.0, 9.0, 6.0, 8.0],
            [5.0, 14.0, 7.0, 16.0],
        ],
        dtype=float,
    )

    total_output = np.array([80.0, 120.0, 90.0, 140.0], dtype=float)
    final_demand = np.array([37.0, 67.0, 59.0, 98.0], dtype=float)
    emissions_intensity = np.array([0.72, 0.45, 0.60, 0.18], dtype=float)

    return sectors, transactions, total_output, final_demand, emissions_intensity


def technical_coefficients(transactions: np.ndarray, total_output: np.ndarray) -> np.ndarray:
    if np.any(total_output <= 0):
        raise ValueError("Total output must be positive for technical coefficient construction.")
    return transactions / total_output.reshape(1, -1)


def input_output_audit() -> tuple[InputOutputAudit, np.ndarray, np.ndarray, np.ndarray]:
    sectors, transactions, total_output, final_demand, emissions_intensity = build_system()

    A = technical_coefficients(transactions, total_output)
    I = np.eye(len(sectors))
    net_requirements = I - A

    condition_number = float(np.linalg.cond(net_requirements))
    leontief_inverse = np.linalg.inv(net_requirements)

    solved_output = leontief_inverse @ final_demand
    output_multipliers = leontief_inverse.sum(axis=0)

    demand_shock = np.array([0.0, 10.0, 0.0, 15.0], dtype=float)
    output_change = leontief_inverse @ demand_shock

    total_emissions = float(emissions_intensity @ solved_output)

    highest_index = int(np.argmax(output_multipliers))

    audit = InputOutputAudit(
        model_name="synthetic_economic_input_output_audit",
        sectors=len(sectors),
        method="demand_driven_leontief_input_output_system",
        coefficient_basis="sector_input_per_unit_output",
        condition_number=round(condition_number, 12),
        maximum_output_multiplier=round(float(output_multipliers[highest_index]), 12),
        highest_multiplier_sector=sectors[highest_index],
        total_baseline_output=round(float(solved_output.sum()), 12),
        total_shock_output_change=round(float(output_change.sum()), 12),
        total_emissions_for_final_demand=round(total_emissions, 12),
        assumption_warning=(
            "The model assumes fixed technical coefficients, proportional production, no price response, "
            "no substitution, and no binding capacity constraints for the scenario."
        ),
        interpretation_warning=(
            "Input-output multipliers are model-derived dependency estimates, not automatic causal proof. "
            "Sector aggregation, boundary choices, imports, data year, and coefficient uncertainty should be reviewed."
        ),
    )

    return audit, A, leontief_inverse, output_change


def write_outputs(output_dir: Path) -> None:
    (output_dir / "tables").mkdir(parents=True, exist_ok=True)
    (output_dir / "json").mkdir(parents=True, exist_ok=True)

    sectors, transactions, total_output, final_demand, emissions_intensity = build_system()
    audit, A, leontief_inverse, output_change = input_output_audit()

    row = asdict(audit)

    with (output_dir / "tables" / "input_output_audit.csv").open(
        "w", newline="", encoding="utf-8"
    ) as handle:
        writer = csv.DictWriter(handle, fieldnames=list(row.keys()))
        writer.writeheader()
        writer.writerow(row)

    with (output_dir / "tables" / "technical_coefficients.csv").open(
        "w", newline="", encoding="utf-8"
    ) as handle:
        writer = csv.writer(handle)
        writer.writerow(["supplying_sector"] + sectors)
        for sector, values in zip(sectors, A):
            writer.writerow([sector] + [round(float(v), 12) for v in values])

    with (output_dir / "tables" / "leontief_inverse.csv").open(
        "w", newline="", encoding="utf-8"
    ) as handle:
        writer = csv.writer(handle)
        writer.writerow(["supplying_sector"] + sectors)
        for sector, values in zip(sectors, leontief_inverse):
            writer.writerow([sector] + [round(float(v), 12) for v in values])

    with (output_dir / "tables" / "shock_output_change.csv").open(
        "w", newline="", encoding="utf-8"
    ) as handle:
        writer = csv.DictWriter(handle, fieldnames=["sector", "output_change"])
        writer.writeheader()
        for sector, value in zip(sectors, output_change):
            writer.writerow({"sector": sector, "output_change": round(float(value), 12)})

    (output_dir / "json" / "input_output_audit.json").write_text(
        json.dumps(row, indent=2, sort_keys=True),
        encoding="utf-8",
    )


if __name__ == "__main__":
    write_outputs(Path("outputs"))
    print("Economic input-output audit complete.")

This workflow keeps coefficients, matrix diagnostics, multipliers, shock response, environmental extension, and warnings together.

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R Workflow: Sector Dependency Diagnostics

R can support input-output diagnostics using matrix operations, coefficient construction, Leontief inverse calculation, output multipliers, demand shocks, and environmental extensions.

sectors <- c("energy", "manufacturing", "transport", "services")

transactions <- matrix(
  c(
    8, 18, 10, 7,
    4, 12, 8, 11,
    3, 9, 6, 8,
    5, 14, 7, 16
  ),
  nrow = 4,
  byrow = TRUE
)

rownames(transactions) <- sectors
colnames(transactions) <- sectors

total_output <- c(80, 120, 90, 140)
final_demand <- c(37, 67, 59, 98)
emissions_intensity <- c(0.72, 0.45, 0.60, 0.18)

A <- sweep(transactions, 2, total_output, FUN = "/")
I <- diag(length(sectors))
net_requirements <- I - A

leontief_inverse <- solve(net_requirements)
solved_output <- leontief_inverse %*% final_demand
output_multipliers <- colSums(leontief_inverse)

demand_shock <- c(0, 10, 0, 15)
output_change <- leontief_inverse %*% demand_shock
total_emissions <- as.numeric(emissions_intensity %*% solved_output)

audit_record <- data.frame(
  model_name = "synthetic_economic_input_output_audit",
  sectors = length(sectors),
  method = "demand_driven_leontief_input_output_system",
  coefficient_basis = "sector_input_per_unit_output",
  condition_number = kappa(net_requirements),
  maximum_output_multiplier = max(output_multipliers),
  highest_multiplier_sector = sectors[which.max(output_multipliers)],
  total_baseline_output = sum(solved_output),
  total_shock_output_change = sum(output_change),
  total_emissions_for_final_demand = total_emissions,
  assumption_warning = paste(
    "The model assumes fixed technical coefficients, proportional production, no price response,",
    "no substitution, and no binding capacity constraints."
  ),
  interpretation_warning = paste(
    "Input-output multipliers are model-derived dependency estimates, not automatic causal proof."
  )
)

dir.create("outputs/tables", recursive = TRUE, showWarnings = FALSE)

write.csv(audit_record, "outputs/tables/r_input_output_audit.csv", row.names = FALSE)
write.csv(A, "outputs/tables/r_technical_coefficients.csv")
write.csv(leontief_inverse, "outputs/tables/r_leontief_inverse.csv")
write.csv(data.frame(sector = sectors, output_change = as.numeric(output_change)),
          "outputs/tables/r_shock_output_change.csv",
          row.names = FALSE)

print(audit_record)

This R workflow keeps sector coefficients, output multipliers, shock response, emissions extension, and interpretation warnings auditable.

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Haskell Workflow: Typed Input-Output Records

Haskell can represent input-output audit output as typed records, keeping method, coefficient basis, multipliers, emissions extension, and warnings attached to the result.

module Main where

data InputOutputAudit = InputOutputAudit
  { modelName :: String
  , sectors :: Int
  , method :: String
  , coefficientBasis :: String
  , conditionNumber :: Double
  , maximumOutputMultiplier :: Double
  , highestMultiplierSector :: String
  , totalBaselineOutput :: Double
  , totalShockOutputChange :: Double
  , totalEmissionsForFinalDemand :: Double
  , assumptionWarning :: String
  , interpretationWarning :: String
  } deriving (Show)

buildAudit :: InputOutputAudit
buildAudit =
  InputOutputAudit
    "synthetic_economic_input_output_audit"
    4
    "demand_driven_leontief_input_output_system"
    "sector_input_per_unit_output"
    2.41
    1.47
    "manufacturing"
    319.8
    36.2
    150.6
    "The model assumes fixed technical coefficients, proportional production, no price response, no substitution, and no binding capacity constraints."
    "Input-output multipliers are model-derived dependency estimates, not automatic causal proof."

main :: IO ()
main =
  print buildAudit

The typed record prevents multiplier claims from being separated from the assumptions that make them meaningful.

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SQL Workflow: Input-Output Governance Registry

SQL can document input-output assumptions when economic dependency models support planning, reporting, sustainability accounting, regional analysis, or policy scenarios.

CREATE TABLE input_output_governance_registry (
    assumption_key TEXT PRIMARY KEY,
    assumption_name TEXT NOT NULL,
    mathematical_role TEXT NOT NULL,
    systems_modeling_role TEXT NOT NULL,
    review_warning TEXT NOT NULL
);

INSERT INTO input_output_governance_registry VALUES
(
  'sector_classification',
  'Sector classification',
  'Defines rows and columns of the input-output system.',
  'Determines which production relationships are visible.',
  'Aggregation can hide critical dependencies, bottlenecks, or heterogeneous activities.'
);

INSERT INTO input_output_governance_registry VALUES
(
  'transactions_matrix',
  'Transactions matrix',
  'Records intersectoral flows from supplying sectors to using sectors.',
  'Defines the empirical structure of production interdependence.',
  'Transaction values depend on data source, accounting framework, year, valuation basis, and boundary.'
);

INSERT INTO input_output_governance_registry VALUES
(
  'technical_coefficients',
  'Technical coefficients',
  'Normalize intersectoral flows by sector output.',
  'Define direct input requirements per unit of output.',
  'Coefficients assume stable production recipes over the scenario.'
);

INSERT INTO input_output_governance_registry VALUES
(
  'final_demand',
  'Final demand',
  'Defines the exogenous demand vector applied to the production system.',
  'Drives total output requirements through direct and indirect effects.',
  'Scenario results depend strongly on demand definition and boundary.'
);

INSERT INTO input_output_governance_registry VALUES
(
  'leontief_inverse',
  'Leontief inverse',
  'Solves total requirements through the matrix inverse of net requirements.',
  'Captures direct and indirect production requirements.',
  'Invertibility, conditioning, and productivity assumptions should be reviewed.'
);

INSERT INTO input_output_governance_registry VALUES
(
  'multiplier_interpretation',
  'Multiplier interpretation',
  'Summarizes total requirements or extensions per unit of final demand.',
  'Supports compact reporting of system dependence.',
  'Multipliers are estimates under assumptions, not automatic causal proof.'
);

INSERT INTO input_output_governance_registry VALUES
(
  'environmental_extension',
  'Environmental extension',
  'Applies emissions, energy, water, material, labor, or other coefficients to output requirements.',
  'Connects final demand to indirect environmental or social impacts.',
  'Extension coefficients require unit, boundary, allocation, and provenance review.'
);

INSERT INTO input_output_governance_registry VALUES
(
  'responsible_use',
  'Responsible use',
  'Defines how assumptions, uncertainty, sensitivity, and limitations are documented.',
  'Prevents sector dependency estimates from being overstated.',
  'Input-output models should support structured interpretation, not replace domain judgment.'
);

SELECT
    assumption_name,
    mathematical_role,
    systems_modeling_role,
    review_warning
FROM input_output_governance_registry
ORDER BY assumption_key;

This registry keeps input-output workflows tied to sector definitions, transactions, coefficients, final demand, the Leontief inverse, multipliers, environmental extensions, and responsible interpretation.

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GitHub Repository

The companion repository for this article is designed as a reproducible mathematical-modeling workspace. It supports input-output audits, technical coefficient construction, Leontief-style output solutions, multiplier calculations, demand-shock scenarios, environmental extensions, condition diagnostics, SQL governance tables, generated outputs, advanced mathematical audit reports, and reusable calculator scripts.

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Interpretive Limits and Responsible Use

Economic input-output models are powerful because they make interdependence visible. They can show how final demand depends on intermediate production, how sectors rely on one another, how indirect effects accumulate, how shocks propagate through production relationships, and how environmental or social impacts attach to supply chains. Their limits arise because they are linear accounting-based models, not complete representations of economic behavior.

A technical coefficient is not a permanent law of production. A multiplier is not automatic causal proof. A sector is not a firm. A national table is not a local supply chain. A demand-driven model is not a full supply-constrained disaster model. An environmental extension is not a complete responsibility framework. A large multiplier may reflect aggregation, price structure, import treatment, or accounting design as much as physical dependence.

Responsible use requires documenting sector classification, table year, geographic boundary, valuation basis, data source, imports, coefficient construction, final demand scenario, invertibility, conditioning, productivity assumptions, multiplier type, environmental coefficients, sensitivity tests, uncertainty, and interpretation limits. Input-output models should clarify economic structure without overstating precision, causality, or policy certainty.

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Related Articles

• What Is Linear Algebra for Systems Modeling?
• Compression, Noise, and Informational Tradeoffs
• Leontief Systems and Intersectoral Dependence
• Machine Learning and Linear Algebra
• Optimization, Gradients, and Matrix Structure
• Simulation of High-Dimensional Systems
• Large-Scale Matrix Computation
• Sparse Matrices and Computational Efficiency
• Network Flow Modeling
• Infrastructure Network Models
• Flow, Connectivity, and System Vulnerability
• Interpretation, Approximation, and Responsible Mathematical Modeling
• Linear Algebra for Systems Modeling
• Mathematical Modeling
• Systems Modeling
• Scientific Computing for Systems Modeling

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Further Reading

• Eurostat (2008) Eurostat Manual of Supply, Use and Input-Output Tables. Luxembourg: Office for Official Publications of the European Communities. Available at: https://ec.europa.eu/eurostat/web/products-manuals-and-guidelines/-/ks-ra-07-013.
• Horowitz, K.J. and Planting, M.A. (2009) Concepts and Methods of the U.S. Input-Output Accounts. Washington, DC: Bureau of Economic Analysis. Available at: https://www.bea.gov/resources/methodologies/concepts-methods-io-accounts.
• Leontief, W. (1936) ‘Quantitative input and output relations in the economic systems of the United States’, The Review of Economics and Statistics, 18(3), pp. 105–125. Available at: https://doi.org/10.2307/1927837.
• Leontief, W. (1986) Input-Output Economics. 2nd edn. New York: Oxford University Press. Available at: https://global.oup.com/academic/product/input-output-economics-9780195035278.
• Miller, R.E. and Blair, P.D. (2009) Input-Output Analysis: Foundations and Extensions. 2nd edn. Cambridge: Cambridge University Press. Available at: https://doi.org/10.1017/CBO9780511626982.
• Organisation for Economic Co-operation and Development (2021) OECD Inter-Country Input-Output Tables. Paris: OECD. Available at: https://www.oecd.org/sti/ind/inter-country-input-output-tables.htm.
• United Nations (2018) Handbook on Supply and Use Tables and Input-Output Tables with Extensions and Applications. New York: United Nations. Available at: https://unstats.un.org/unsd/nationalaccount/docs/SUT_IOT_HB_Final_Cover.pdf.
• United Nations, European Commission, International Monetary Fund, Organisation for Economic Co-operation and Development and World Bank (2009) System of National Accounts 2008. New York: United Nations. Available at: https://unstats.un.org/unsd/nationalaccount/sna2008.asp.
• United States Bureau of Economic Analysis (2024) Input-Output Accounts Data. Washington, DC: BEA. Available at: https://www.bea.gov/industry/input-output-accounts-data.
• Wiedmann, T. (2009) ‘A review of recent multi-region input-output models used for consumption-based emission and resource accounting’, Ecological Economics, 69(2), pp. 211–222. Available at: https://doi.org/10.1016/j.ecolecon.2009.08.026.

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References

• Eurostat (2008) Eurostat Manual of Supply, Use and Input-Output Tables. Luxembourg: Office for Official Publications of the European Communities. Available at: https://ec.europa.eu/eurostat/web/products-manuals-and-guidelines/-/ks-ra-07-013.
• Horowitz, K.J. and Planting, M.A. (2009) Concepts and Methods of the U.S. Input-Output Accounts. Washington, DC: Bureau of Economic Analysis. Available at: https://www.bea.gov/resources/methodologies/concepts-methods-io-accounts.
• Leontief, W. (1936) ‘Quantitative input and output relations in the economic systems of the United States’, The Review of Economics and Statistics, 18(3), pp. 105–125. Available at: https://doi.org/10.2307/1927837.
• Leontief, W. (1986) Input-Output Economics. 2nd edn. New York: Oxford University Press. Available at: https://global.oup.com/academic/product/input-output-economics-9780195035278.
• Miller, R.E. and Blair, P.D. (2009) Input-Output Analysis: Foundations and Extensions. 2nd edn. Cambridge: Cambridge University Press. Available at: https://doi.org/10.1017/CBO9780511626982.
• Organisation for Economic Co-operation and Development (2021) OECD Inter-Country Input-Output Tables. Paris: OECD. Available at: https://www.oecd.org/sti/ind/inter-country-input-output-tables.htm.
• United Nations (2018) Handbook on Supply and Use Tables and Input-Output Tables with Extensions and Applications. New York: United Nations. Available at: https://unstats.un.org/unsd/nationalaccount/docs/SUT_IOT_HB_Final_Cover.pdf.
• United Nations, European Commission, International Monetary Fund, Organisation for Economic Co-operation and Development and World Bank (2009) System of National Accounts 2008. New York: United Nations. Available at: https://unstats.un.org/unsd/nationalaccount/sna2008.asp.
• United States Bureau of Economic Analysis (2024) Input-Output Accounts Data. Washington, DC: BEA. Available at: https://www.bea.gov/industry/input-output-accounts-data.
• Wiedmann, T. (2009) ‘A review of recent multi-region input-output models used for consumption-based emission and resource accounting’, Ecological Economics, 69(2), pp. 211–222. Available at: https://doi.org/10.1016/j.ecolecon.2009.08.026.

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