Input-Output & Social Accounting Matrix Structure


Input-Output (I-O) modeling is based on the work of Nobel Prize winner Wassily Leontief. The foundational concept is that everything in an economy is interconnected through buy-sell relationships. The interconnectedness of industries is represented and measured through an Input-Output (I-O) Table.  A Social Accounting Matrix (SAM) expands upon the I-O Table to include other economic agents such as Households and Government. I-O Tables and SAMs are static matrices that trace monetary flows throughout a region for a given period of time.

An I-O model captures industry-to-industry transactions, while a SAM is an extension of and I-O model that captures industry-to-industry, industry-to-institution, and institution-institution transactions and transfers, thereby encompassing all market and non-market monetary flows in a region for a given period of time. Many national governments aggregate and record these monetary flows and produce national accounts that provide detailed information about all aspects of the economy. In the United States, the benchmark I-O accounts are produced every five years by the Bureau of Economic Analysis. 

A core tenet of SAM models is that transactions or transfers are recorded and accounted for by both parties (the buyer and the seller in a market or the recipient and the funder in a non-market) in a region. Consistent with basic financial accounting, receipts must equal expenditures. That is, the SAM must balance. 

I-O models quantify the backward linkage effects of production, estimating economic impacts by analyzing which goods, services, and labor needs are required to produce products or services. These secondary demands are quantified as effects to industries in the selected region. Economic activity associated with the modeled Event that does not generate additional effects in the defined region are treated as a leakage. Leakages occur by way of taxes, savings, profits, imports, and commuting. Input-Output analysis does not look at forward linkages in terms of how an industry’s production is used as an input for other production or for final use, also known as downstream effects.

Industries and Institutions

A SAM captures all monetary flows in a region and traces monetary flows between two general types of economic agents: (1) industries and (2) institutions. 

Industries are a group of establishments engaged in the same or similar types of economic activity. Industries produce and sell goods or services, also known as products or commodities. Industries also purchase raw materials and services from other industries, pay for labor, pay taxes, and generate profits. Institutions are entities that create final demand in an economy. Final demand reflects the total value of goods and services sold to final users. In IMPLAN, institutions include households, government institutions (federal, state, and local), capital, inventory, and trade. 

Simplified SAM

Figure X illustrates the 4 major components of a simplified SAM. These components are : 

  • Intermediate Input / Output: This matrix traces the monetary flow or transactions between industries. The rows represent Intermediate output or total value of an industry’s production that is used as inputs for other industries (as opposed to final demand). The columns represent Intermediate Input (II), or the total value of purchases of non-durable goods and services that are used to produce other goods and services.   
  • Final Demand: This matrix traces the monetary flow between industries and institutions. More specifically, Final Demand is the value of goods and services produced and sold to final users to meet demand, whether it is local demand or an export. It captures industry production that is consumed by households and government institutions as well as capital investment, additions to inventory, and exports less the value of imports and sales by institutions (i.e., deletions from inventory and other institutional sales).
  • Value Added: This matrix traces the monetary flows between industries and institutions as a result of industry production, outside of the demand for raw material inputs. Value Added encompasses the payments made to labor and payments to government in the form of taxes. It also includes profits. By definition, Value Added is the difference between an industry’s total output and the cost of its Intermediate Inputs and it is a measure of the contribution to GDP.
  • Transfers: The final matrix is known as the transfer matrix and it traces the monetary flow between institutions. Inter-institutional transfers include transfers from businesses to households (interest and dividend payments), transfers from people to government (payment of taxes), and transfers from governments to people (social security, unemployment compensation, and other refunds and benefits). Inter-institutional transfers also include the capital accounts. For businesses, this includes investment and borrowing. For households, this is net savings. Government capital accounts show surplus and deficits. In such transactions there is no well-defined market value being exchanged in return for the payment; for example, while taxes are used to fund government services, these government services do not have a market value since they are not purchased in a market setting.

Example of a Balanced SAM

The requirement of a balanced SAM is best illustrated from the perspective of an industry. Industries produce and sell goods or services, also known as commodities, to: (1) other industries that use them as inputs for their own production or (2) final users of the product, such as households or other institutions. 

Focusing on the receipts side of the equation, an industry’s total value of production, or output, consists of these two parts: Intermediate Output (IO) and Final Demand (FD). Intermediate Output (IO) includes production consumed by other industries as one of their inputs into their production and Final Demand  (FD) includes production consumed by households and other institutions.

Output = Intermediate Output (IO) + Final Demand (FD)

In order to produce those goods and services, industries require inputs and make operational expenditures. They purchase raw materials and services from other industries, pay for labor, and pay taxes. 

On the expenditures side of the equation, an industry’s output can be measured by the industry’s costs of production. Intermediate Inputs (II) includes expenditures for inputs from other industries and Value Added (VA) includes expenditures on labor, taxes, and includes measures of profit. 

Output = Intermediate Inputs (II) + Value Added (VA)


Written August 30, 2023