INTRODUCTION
Production functions detail the relationship between an Industry’s inputs and its Output. In effect, they trace the backward linkages, or the interconnectedness of an Industry to other Industries from which it purchases inputs to produce its Output and to Institutions to which it pays Labor Income, Taxes, and more. IMPLAN uses the Leontief Production Function (LPF), also known as the Fixed-Proportions Production Function and assumes that inputs and outputs increase proportionally to one another and that the same quantity of inputs is needed per unit of output.
Each Industry in IMPLAN has a unique LPF that reflects the mix of inputs required for each Industry, including labor. IMPLAN has developed these LPFs using national-level data. IMPLAN then combines this national-level data with local economic information and inter-county trade flow data to develop regional LPFs. Thus, IMPLAN Industry LPFs reflect the Industry demand that is sourced locally. Read more about the data sources in IMPLAN Data Sources.
This article defines the Leontief Production Function in IMPLAN, briefly discusses sources of leakage, and summarizes how they are used in Economic Impact Analysis.
INDUSTRY LPF BASICS
IMPLAN uses the Leontief Production Function, also known as the Fixed-Proportions Production Function. It assumes that inputs and outputs increase proportionally to one another and that the same quantity of inputs is needed per unit of Output. In other words, if Output increases by 10% input requirements will also increase by 10%. Read Assumptions of I-O for more important information about the Leontief Production Function and Input-Output analysis.
The LPF of an Industry in IMPLAN determines how each Industry will allocate Output. Industries purchase Commodities from other Industries (and from itself!) to operate their business. These purchases are known as Intermediate Inputs.
Industries also have employees and pay Labor Income (composed of Employee Compensation and Proprietor Income). They also pay taxes (Taxes on Production and Imports less Subsidies) and realize profits (Other Property Income). These combine to give us Value Added. Value Added components can also be called Factor Income.
In equation form:
Output represents an Industry’s total value of production in a given year in Producer Prices. Annual production can be measured by either total revenue (sales) or total expenditures for a business. Note that measuring total revenue differs by Industry type to account for applicable margins and net changes to inventory.
Intermediate Inputs (II) are an Industry’s purchase of non-durable goods and services that are used to produce other goods and services.
Employee Compensation (EC) is the total cost of employees to the employer, and is the sum of Wage and Salary Income plus supplements and payroll taxes. It is also referred to as fully-loaded payroll.
Proprietor Income (PI) is the Industry’s current-production income of sole proprietorships, partnerships, and tax-exempt cooperatives. It is also referred to as income (profit or loss) to self-employed individuals and/or unincorporated business owners.
Other Property Income (OPI) is the Industry’s gross operating surplus less the proprietor's income. This includes consumption of fixed capital (CFC), corporate profits, and net of business current transfer payments. More commonly referred to as the income (profit or loss) by incorporated businesses.
Taxes on Production & Imports net of Subsidies (TOPI) is the Industry’s tax liability net of subsidies, such as general sales and property taxes, that are chargeable to business expenses. Note, however, that TOPI does not include all taxes paid by an Industry. For example, employee and employer contributions to social insurance are a part of Employee Compensation and corporate profits taxes are part of Other Property Income.
The LPF components in this article are for U.S.-based Products. Learn more about the LPFs for the Canada Provincial and International Products in Concepts of Valuation in National Economic Accounts.
THE LPF IN THE SAM
The five components of the LPF (EC, PI, OPI, TOPI, and II) can be found in the IMPLAN Social Accounting Matrix (SAM). In relation to Industries, the SAM details all Industry transactions, including Industry demand for Commodities and how each of the Industry Factors of Production (EC, PI, OPI, and TOPI) are distributed to Households, Government, other Institutions, and other regions (Trade).
Industry LPFs actually play a critical role in the development of Social Accounting Matrices (SAMs), of which IMPLAN produces annually for every zip code, county, and state in the U.S. These SAMs provide a complete picture of the economy and can be used to conduct Economic Impact Analysis. Industry LPFs are important because they provide the framework for understanding how Industries and Institutions are interconnected. The availability of data on the components of Industry LPF, specifically Employee Compensation and Total Value Added, are critical to the data development process as described in Constructing the IMPLAN SAM.
THE LPF IN ECONOMIC IMPACT ANALYSIS
Economic Impact Analysis is designed to show the ripple effects of a given economic activity in other Industries and geographies through input purchases, labor payments, and trade, also known as its multiplier effects. An Industry’s LPF plays a critical role in the analysis. Production in a given Industry supports demand for production in other Industries throughout the economy, both due to supply chain spending (Intermediate Inputs) and spending by workers (Labor Income). An Industry’s expenditures are derived from the I-O and Social Accounting Matrix (SAM) model.
Read more about multipliers in Economic Effects and Multipliers.
SOURCES OF INDUSTRY LEAKAGE
Not all inputs required by the Industry can be sourced from within the local economy, some must be imported from other regions. This applies not only to the purchase of Intermediate Inputs, but also to payments for labor. This is known as leakage.
IMPLAN accounts for this Industry leakage by incorporating Commodity Trade Flows and EC Commuting Flows. Commodities can be imported from outside of the region (but within the U.S.) or from outside of the U.S. These are reflected by Regional Purchase Coefficients (RPCs). Similarly, employees can work for an Industry within the region but live outside of the region (in-commuters). Note however, that leakage related to labor payments only applies to Employee Compensation. There is no leakage for Proprietor Income as all proprietors are assumed to be located within the region.
The remaining components of Output, Taxes on Production and Imports less Subsidies (TOPI) and Other Property Income (OPI), are calculated for the Industry and region in the SAM, but are considered leakages in Economic Impact Analysis as they do not generate additional multiplier effects. This is due to the fact that IMPLAN does not know how, where, or when the Government will use the fiscal revenue generated through taxes paid by Industries. Thus, TOPI is treated as leakage. Additionally, OPI is treated as leakage because IMPLAN assumes that profits (typically corporate profits) will go to recipients outside of the region.
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Written September 26, 2019
Updated September 30, 2024