NC State Extension Publications


This note describes in greater detail the methodology used to estimate the economic contributions of North Carolina’s forest products industry. It is a companion piece to the bulletin North Carolina’s Forests and Forest Products Industry By the Numbers, where a variety of figures and statistics are provided on the management and conversion of standing timber into primary and secondary wood and fiber products.

IMPLAN and the Social Accounting Matrix

IMpact Analysis for PLANning (IMPLAN) is an economic impact modeling system that uses input-output (I-O) and social accounting analysis to quantify economic activities of an industry in a predefined region in terms of dollars added in to the economy and jobs produced (IMPLAN LLC 2015). Data are obtained from various government sources, including agencies and bureaus within the Departments of Agriculture, Commerce, and Labor. The IMPLAN system’s input-output model currently defines 536 unique sectors in the U.S. economy (which are North American Industry Classification System [NAICS] sectors, except in some cases where aggregates of multiple sectors are used) and uses its database to model inter-sector linkages, such as sales and purchases between forest-based industries and other businesses.

An input-output table quantifies transactions by how many dollars each sector makes (processes to sell) and uses (purchases). The table separates processing sectors by rows and purchasing sectors by columns; every sector is considered to be both a processor and purchaser. Summing each row quantifies an industry’s output, which includes sales to other production sectors along with those to exogenous final users. The demands of final users are comprised of household, federal, and state and local government demands; capital investments; inventory; and domestic and foreign exports. The total outlay of inputs, which are the column sums, includes local purchases from intermediate production sectors, value added[1], and exogenous institutions, along with imports from outside the study region. The column and row sums must balance.

Beyond the I-O framework are the nonmarket income flows occurring in a region, such as households receiving wages and benefits from industries, dividends from corporations, and/or transfer payments from government. A social accounting matrix (SAM) details these economic relationships via construction of submatrices in addition to that characterizing the traditional inter-industry flows found in an input-output table. Closing a SAM with respect to any of the exogenous account(s) described previously allows for capturing additional contributions due to the interactions occurring between sectors. For example, households’ effects are captured via their receipt of labor income and subsequent consumption of goods and services. A simplified SAM internalized, or endogenized, with respect to households and purged of imports is illustrated in Table 1.

Table 1. Schematic of a simplified regional social accounting matrix (adapted from Holland and Wyeth 1993).
Processing Sectors Purchasing Sectors Total Output
Agriculture Forest Products Financial Services Value Added Households Exogenous Accounts
Agriculture 8 2 2 7 11 30
Forest Products 2 1 1 1 13 18
Financial Services 6 2 1 11 7 27
Value Added 10 10 18 38
Households 19 0 0 19
Exogenous Accounts 4 3 5 19 0 9 40
Total Outlays 30 18 27 38 19 40 172

Industry production requirements are highlighted by matrix A; industry payments to value added are allocated to matrix V; the labor income portions of value added are in turn distributed to households via matrix Y; and household expenditures for goods and services are captured by matrix C. Any household distributions are described by matrix H. The partitioned SAM, endogenous with respect to households, can thus be described as

A 0 C
V 0 0
0 Y H

Intermediate and final uses define sector totals by

X = (I - S)-1 F

where X is the column vector of industrial output and income flows, I is an identity matrix of initial requirements, and S is the SAM expenditure matrix of column-normalized coefficients. Matrix S for our study of forestry and forest products in North Carolina was as described above for the partitioned SAM in Table 1, closed with respect to households. The variable F represents the column vector of exogenous final demands placed on the endogenous accounts (Miller and Blair 2009). Equation 2 can be extended to predict the total amount of sector activities required to supply any forecasted changes to the exogenous accounts’ final demands for a given point in time.

The term (I - S)-1 is the total requirements matrix of Type SAM multipliers, with the matrix’s elements defined as each column sector j’s total output requirements from an individual row sector i. Summing Forest sector j’s column elements would provide its Type SAM output multiplier. Forest sector employment, labor income, and value added multipliers are derived based upon their relationships to output.

The multiplier effects described by IMPLAN include the direct effects of forestry and forest products manufacturing, the indirect supply chain effects of producing forest-based outputs, as well as any induced effects generated by household consumption of goods and services in the region due to forest sector activities. Capturing additional economic activity via the induced effect drives interest in the application of Type SAM multipliers.

Type SAM multipliers indicate to what extent activity is generated across North Carolina’s economy due to forest-based production. The Type SAM employment multiplier for forestry and forest products was 2.060, which indicated that for every 1,000 forest sector jobs, forestry and forest products supported an additional 1,060 jobs elsewhere in the state. The Type SAM output multiplier was 1.587, meaning for every $1.0 million dollars of North Carolina forestry and forest products output an additional $587,000 of output was generated in other sectors.

[1] Value added in IMPLAN includes employee compensation, proprietor income, other property income, and taxes on production and imports (less subsidies). Employee compensation and proprietor income sum to labor income.

Contributions Analyses of Forestry and Forest Products in North Carolina

A contributions analysis describes the economic effects of the forest sectors within a modeled economy. The results define to what extent the economy is influenced by forestry and forest products industry activities (Hughes 2015). Changes to final demand, which are normally analyzed on a marginal or incremental basis, are not assumed here as in the traditional impact analysis. Based on the number of sectors comprising forestry and forest products in the state, multiple sector contributions analyses were conducted. The model was constructed using the National Trade Flows method, and the SAM multiplier specifications were set to households only.

Output was the basis by which contributions were assessed, but it needed adjusting to discount for sales and purchases internal to the forest sectors so that double counting could be avoided. This required six steps using IMPLAN and Microsoft Excel: 1) compile the matrix of detailed Type SAM output multipliers for the forestry and forest products sectors under study, 2) invert the matrix, 3) obtain the direct contributions vector by multiplying the inverted contributions matrix by the forest sectors’ outputs found in IMPLAN’s study area data, 4) build “industry change” activities and events within IMPLAN using the values from the calculated direct contributions vector for 2013 at a local purchase percentage of 100%, 5) allocate total forest-based employment, labor income, value added and output contributions to only the direct effect, and 6) validate total forest sector contributions match IMPLAN’s original study area data.

We modified IMPLAN’s ready-made model to better reflect our knowledge of timber income and forestry supporting activities in the state. We first replaced IMPLAN’s estimates for stumpage and delivered log output (IMPLAN sectors 15 and 16) with those published by North Carolina State University’s Extension Forestry for 2013 (Jeuck and Bardon 2014). Second, employee compensation to worker ratios were calculated for these two sectors using 2013 data from the U.S. Department of Labor, Bureau of Labor Statistics’ Quarterly Census of Employment and Wages (QCEW) to replace IMPLAN’s default values (USDL BLS 2015). We then verified the consistency of our modified employment totals for these two sectors with those found in the U.S. Department of Commerce, Bureau of Economic Analysis’s Total Full-Time and Part-Time Employment Table SA25N (USDC BEA 2015).

Lastly, IMPLAN sector 19 merges Support Activities for Forestry with services supporting crops and livestock production. To account for only the forest-based contributions in this sector, we calculated a ratio of forestry support activities employment (NAICS 1153) to total employment in NAICS 115 using 2013 data from the QCEW database (USDL BLS 2015). This ratio was multiplied by IMPLAN sector 19 output to provide us a representative output for Support Activities for Forestry. Employment, labor income, and value added multipliers were derived based upon their relationships to the estimated forest-based output.


Holland, D. and P. Wyeth. 1993. SAM multipliers: Their decomposition, interpretation, and relationship to input-output multipliers. Research Bulletin XB1027, Washington State University, Pullman, WA. 43 p.

Hughes, D.W. 2015. Economic impact analysis of South Carolina’s forestry sector, 2015: Contribution of forests and forest products to the South Carolina economy. South Carolina Forestry Commission, Columbia, SC. 21 p.

IMPLAN, LLC. 2015. 2013 IMPLAN 2013 North Carolina database. Huntersville, NC.

Jeuck, J. and R. Bardon. 2014. 2013 income of North Carolina timber harvested and delivered to mills. North Carolina State University Extension Forestry, North Carolina Cooperative Extension Service, Raleigh, NC. 2 p.

Miller, R.E. and P.D. Blair. 2009. Input-Output Analysis: Foundations and Extensions. 2nd Edition. Cambridge University Press, New York.

US Department of Commerce Bureau of Economic Analysis. 2015. Total Full-Time and Part-Time Employment Table SA25N.

US Department of Labor Bureau of Labor Statistics. 2015. Quarterly Census of Employment and Wages: North Carolina NAICS 1131, 1133, 115, and 1153.


Assistant Professor and Extension Specialist
Forest Biomaterials
Extension Associate
Associate Dean of Extension, Department Extension Leader & Professor
Extension Specialist and Associate Professor
Utilization and Marketing Forester
North Carolina Forest Service
Technical Development and Planning Branch Head
North Carolina Forest Service

Publication date: Feb. 24, 2016

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