Now that we have the basic framework of input-output analysis in hand, let's move a little closer to the format in which data is now accumulated at the national level and from which we estimate the parameters of regional models.
This format was developed in the 1960s by Richard A. Stone at Cambridge and adopted as a standard by the United Nations. Stone later received the Nobel Prize in Economics for his work in national income accounting (which includes input-output accounting). Statistics Canada (the statistical agency in Canada) pioneered in applying this format starting with their 1960 table; the Input-Output Division of the U.S. Department of Commerce produced their 1972 table in the new format. As a result, most of the state and regional models produced today are based on this format and data source.
This format is called the "commodity-by-industry" format, and sometimes the "rectangular" system. It is rectangular in that the commodity dimension may be greater than the industry dimension (which poses a problem when the direct-requirements matrix must be square to provide a solvable system). It originated with a realization that firms, grouped in industries, buy commodities and that we have trouble grouping commodities into industries. Firms often produce several commodities. They are classified into industries according to their primary products; their remaining products are secondary. An accounting scheme has to manage this problem.
I had the pleasure of building three input-output systems in Nova Scotia (1974, 1979, and 1984) during the period when the computing world moved from mainframes to desktops. The system fits exactly with the new U.S. system. Chapters 8 and 9 parallel Chapters 4 and 5 in organization and content. My intention is to make the transition to the more complex modern system easier as well as to economize on the writing chore.(DPA Group Inc. and Schaffer 1989)
The Nova Scotia input-output tables represent a complete set of social accounts for the Province. As is common with most social accounts, it is double entry in nature, but it has been organized in matrix form rather than as the traditional T-accounts. This section presents a brief schematic review of the accounting framework. In addition, the interpretation of the Nova Scotia tables is demonstrated with a set of highly aggregated (five-industries) tables which duplicate the format of the more detailed tables produced in the Nova Scotia Input-Output Study itself.
The Nova Scotia input-output tables follow the form of the Canadian tables. They are of the "rectangular form" and show substantially more of the commodity detail of industry purchases than do tables of the "square" form commonly used in the United States and elsewhere. As shown in Illustration 7.1, the tables comprise six matrices. Three sets of accounts are evident in these matrices and the comments which follow are intended to identify the accounts in the tables.
For each commodity used and/or produced in the Province, accounts representing supply and demand can be constructed. Thus, the shaded row in Illustration 7.2 presents the demand side of the supply-and-demand equation for a particular commodity. It
shows both the intermediate uses, or demands, expressed by domestic industries for the commodity, as recorded in Matrix 2, and the final uses, or demands, by consuming sectors for the commodity, as recorded in Matrix 1. These consuming sectors include local consumers and investors, governments, and non-local users. Total demand is the sum of total industry demand and total final demand.
The supply side of the equation for a commodity is represented in Illustration 7.2 by the shaded column, which traverses Matrix 5 and Vector 6. In Matrix 5, this column identifies the domestic industrial origins of the commodity; Vector 6 identifies imports of the commodity. The column sum is total supply, which is equal to total demand.
The inputs and outputs of industries can also be traced in this system. Illustration 7.3 moves the shaded column and row to represent inputs and outputs of a particular industry. The outputs of the industry can be seen in the shaded row. This row records the values of the various commodities produced by the industry. The column in Illustration 7.3 records the production technology of the industry in terms of commodities purchased in Matrix 2 and of payments to "primary" inputs (i.e., labor, return to capital, etc.), or factors of production, in Matrix 3. Since the payments to inputs include profits, or the residual receipts by owners of establishments in the industry, total inputs equal total outputs for the industry.
The incomes and expenditures of "primary" sectors (e.g. household, government, etc.) of the economy can also be traced through the system. The shaded row and column in Illustration 7.4 are illustrative. The shaded row represents the incomes of a "primary" sector such as households or a government. As seen in Matrix 3, these incomes are paid by industries which use the services of the factors of production owned or provided by the sector. In addition, transfers of incomes from other "primary" sectors are recorded in Matrix 4. With the exception of wages and salaries paid by households, governments, and outside employers these "transfers" are non-market in nature and represent such items as taxes, savings, welfare payments, intergovernmental transfers, and surpluses and deficits.
In accounting for gross provincial product, the row sums of Matrix 3 represent incomes of domestic factors as paid by the private, or industrial, sectors of the economy. The addition of incomes earned by households from the primary sectors in Matrix 4 completes the income side of gross provincial product. This tabulation of incomes represents value added in the economy.
The shaded column in Illustration 7.4 represents the final expenditures by a primary-input sector. In Matrix 1, the commodity detail of such expenditures is shown, and in Matrix 4, the transfers (including wages and salaries) to other primary sectors are recorded. The sum of these commodity purchases and transfers is total expenditures, which is equal to total receipts by the sectors.
The expenditures side of the gross provincial product account consists of the sum of total
purchases of goods and services by domestic primary sectors, household incomes received from
these sectors, and gross commodity exports less industry imports (or net exports).
With this overall scheme in mind, consider now the format of the actual tables. Small, highly aggregated (5-industry) versions of the tables are used as illustrations.
The commodity flows table combines the use, final demand, and associated income matrices (Matrices 1, 2, 3 and 4) of Illustration 7.1. (In the national tables, the two equivalent tables are described as the "use matrix" (example Matrices 2 and 3) and the "final demand matrix" (example Matrices 1 and 4). Table 7.1 is the aggregated commodity flows table. The boundaries between the various matrices are marked by a row for total commodity inputs and a column for total industry demands. This table is a complete description of commodity purchases by all Nova Scotia industries, all domestic and government consumers, and all non-local purchasers.
Note that the commodity flows table does not distinguish between commodities produced domestically and those imported from outside the Province. The table which embodies this distinction is called the "provincial flows table" and is presented in the next chapter as the first stage in developing the input-output model.
The commodity origins table combines the domestic origin matrix (5) and the imports vector (6) of Illustration 7.1 (In the national tables, the equivalent table is called the "make matrix"). Table 7.2 is an aggregated commodity origins table for Nova Scotia which is consistent with the aggregated flows table.
Note that the origins table records more than just the origins of commodities. It also includes a complete tabulation of supply and demand for each commodity used in Nova Scotia. The last seven columns of the table summarize the commodity accounts of the Province. The demands recorded here are the same as the demand totals found in Table 7.1. Also note that the industry accounts are represented by the column totals found in both tables. Total industry inputs are in Table 7.1 while total industry outputs are in Table 7.2.
For ease of production and in reading, columns represent industries and rows represent commodities. This convention requires that the domestic origins matrix and the imports vector be transposed from their original form in Illustration 7.1.
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