Introduction

To more accurately measure transportation services, the Bureau of Transportation Statistics (BTS) of the U.S. Department of Transportation and the Bureau of Economic Analysis (BEA) of the U.S. Department of Commerce, jointly developed the Transportation Satellite Accounts (TSAs)¹. The TSAs supplement the U.S. Input-Output (I-O) Accounts by explicitly measuring the contribution of in-house transportation. In-house transportation consists of transportation services undertaken to support the activities of a business in a nontransportation industry. For example, a grocery company may employ its own transportation to move foodstuffs from distribution centers to local markets. In-house transportation also includes household transportation conducted using a private automobile.

In-house transportation is not separately measured in the I-O Accounts. A portion of in-house transportation is captured under for-hire transportation when it is provided by an establishment, owned and operated by a nontransportation enterprise, and large enough to be identified as a separate establishment producing primarily transportation services (e.g., fleet truck transportation owned by a grocery store chain to move food stuffs from distribution centers to local stores). Transportation provided by smaller scale establishments within nontransportation enterprises and transportation incidental to a business establishment (such as delivery service provided by a local furniture store) are not measured as transportation in the standard I-O accounts (the I-O accounts would capture the value added by these types of in-house transportation under the industry to which the establishment provides services)². In the supplementary I-O accounts, the BEA reassigns some of the secondary products to industries in which the products are primary³. This reassignment, however, does not provide a complete or separate measure of in-house transportation services. The I-O accounts provide no measure of household transportation. As such, the most prominent data sources on industry providers of transportation services do not fully capture all transportation activities.

To provide an explicit measure of in-house transportation, the TSAs rearrange the I-O accounts⁴. In rearranging I-O data, the TSAs maintain the following I-O accounts approach:

• Classification of industries and commodities using the I-O industry and commodity classification system and the special definitions and conventions in the I-O accounts, with the only exception made to form in-house transportation as a new industry and a new commodity.
• The reassignment – or using I-O terminology, the “redefinition” – of secondary products to industries in which they are the primary products. Reassignment in the TSAs involves moving all intermediate and value-added inputs of in-house transportation from the industry in which production is secondary to the newly defined in-house transportation industry.
• Valuation of transactions in producers’ prices.

The TSAs additionally maintain the following measures made in the I-O accounts:

• Transportation costs (the costs to move commodities from producers to intermediate or final users) and trade margins.

The 2002 TSAs differ from previously released TSAs in that they provide a measure of household transportation conducted using private automobiles. Inclusion of household transportation requires expanding GDP by the value added by household transportation since this value is not already captured in the I-O accounts.

The TSAs differ from the I-O accounts in that they separately measure in-house transportation related to business activities and provide a measure of household transportation. In the TSAs, in-house transportation is treated as a separate industry where the only output is in-house transportation service. Business related in-house transportation service covers both the operation of an industry’s own aircraft, railcars, trucks, and/or water vessels to move the industry’s intermediate inputs or output. This coverage differs from that for for-hire transportation in the I-O accounts. In the I-O accounts, the use of for-hire transportation by an industry includes only transportation expenses associated with moving intermediate inputs to the industry, plus the expenses for certain direct transportation services. For example, if a for-hire truck carries wheat from a farm to a mill, the I-O use table credits this activity to the mill, even though the farm may have purchased the transportation service. However, if an in-house truck of the mill transports the wheat from the farm, the TSAs use table shows the mill as providing the services and credits the activity to the farm only when an in-house truck of the farm transports the wheat to the mill. Household in-house transportation covers transportation provided by households for their own use through the use of an automobile.

Estimation of in-house transportation services related to business in the TSAs involves the following:

• Identifying the transportation related inputs. The TSAs define a set of inputs unique to or mostly used for transportation by a specific mode. These inputs, derived from the underlying items in the I-O accounts, are called “transportation-related inputs” (TRIs). The TRIs used to derive in-house transportation estimates for the four modes included in the TSAs (air, rail, truck, and water).
• Developing industry distribution weights. Distribution weights were developed to distribute the total value of in-house transportation to industries. The weights assign a larger portion of the value of in-house transportation to industries that employed a larger share of transportation workers.⁵
• Distributing TRIs. TRIs were aggregated from the item to the commodity level after removing the component used for nontransportation purposes, such as gasoline used for heating or for operating machinery, and the component used for transportation modes other than the one for which the TRI was selected, such as gasoline used for transportation modes other than trucking. The resulting estimate of in-house transportation then was distributed across industries by applying the distribution weight matching to the TRI, e.g., the share of fuel consumed by industries for trucking was used to distribute the in-house value of motor gasoline.  
• Estimating inputs. Transportation activities require inputs not unique or primary to transportation. For example, office supplies and accounting services are shared by transportation and all other production activities. The TSAs assume nontransportation industries use these nontransportation related inputs in the same proportion as for-hire industries.⁶

Estimation of in-house transportation services related to households in the TSAs involves the following:

• Re-arranging and expanding the I-O framework of the TSAs. Household purchases of passenger cars (classified as consumer expenditures in the I-O accounts) will be reclassified as fixed private investments and an estimate of their depreciation will be added to the I-O framework. Household purchases of inputs related to operating automobiles (classified as consumer expenditures in the I-O accounts) will be reclassified as an input to the household production of transportation services. Labor inputs for HPTS will be estimated and added to the I-O framework.

The above steps are explained in greater detail in the sections following along with details on how to form the four final components of the TSAs: the make, use, direct requirements, and total requirements tables. These explanations apply to the 2002 benchmark TSAs developed by BTS.

2002 TSAs

Overview of Methods

As a satellite account to the 2002 benchmark I-O accounts, the 2002 TSAs provide a systematic and consistent framework and dataset for conducting analytical studies on the role of transportation in the economy, both on an industry and commodity basis. The 2002 TSAs cover all activities related to the use of vehicles (such as aircraft, railcars, trucks, and water vessels by nontransportation industries and automobiles by households) and related structures (such as airports, railroad stations, highways, and port facilities). The 2002 TSAs present detailed industry use of transportation services for the seven for-hire transportation industries reported in the U.S. I-O accounts and for the created in-house transportation industry (see table 1). The created in-house transportation industry covers air, rail, truck, and water transportation services produced by nontransportation industries to carry out business activities and by households through the use of private automobiles.

The TSAs measure the magnitude of in-house transportation services by estimating the inputs used by each nontransportation industry in the 2002 benchmark I-O accounts for its in-house transportation activities related to business activities and by estimating the inputs to the production of household transportation using an automobile. To do this, the TSAs rearrange the I-O accounts using data on transportation from other sources. The major data sources are identified in table 2.

Estimating In-house Transportation by Nontransportation Industries for Business Activities

Rearrangement of the I-O data with the supplemental data sources listed in table 2 occurs in the following steps. These steps are used to estimate in-house transportation conducted by nontransportation industries for business activities:

1. Identifying transportation-related inputs (TRIs). The TSAs define a set of inputs unique to or mostly used for transportation by a specific mode. These inputs, derived from the items in the I-O accounts, are called “transportation-related inputs” (TRIs).
2. Developing industry distribution weights. Distribution weights were developed to distribute TRI commodities to industries. The weights assign a larger portion of TRI commodities to industries with a larger stock of transportation vehicles (aircraft, railcars, trucks, and water vessels).
3. Estimating and distributing the value of in-house transportation. TRIs were aggregated from the item to the commodity level after removing the component that is part of final demand; the component used for nontransportation purposes, such as gasoline used for heating or for operating machinery; and the component used for transportation modes other than the one for which the TRI was selected, such as gasoline used for transportation modes other than trucking. The resulting value is the dollar estimate of the commodity used for in-house transportation purposes. The value was distributed across industries by applying the distribution weight matching to the TRI, e.g., the share of fuel consumed by industries for trucking was used to distribute the in-house value of motor gasoline.
4. Estimating inputs to in-house transportation production. Transportation activities require inputs not unique or primary to transportation. For example, office supplies and accounting services are shared by transportation and all other production activities. The TSAs assume nontransportation industries use these nontransportation related inputs in the same proportion as for-hire industries.
5. Post-processing. Adjustments were made after estimating nontransportation related inputs to ensure that the value of the transportation and nontransportation component of each commodity used by an industry equals that in the I-O use table before rearrangement.

Each of the steps above is explained in detail below.

TRIs derived from the items table of the detailed IO accounts must be distributed across industries as the IO tables themselves do not show the value of items used by industries, only the value of commodities. Distribution is performed using distributional weights. The weights assign a portion of TRIs (aggregated to the commodity level after determining the modal value of each item) to each industry based on the industry’s employment of transportation workers (aircraft, railcars, trucks, and water vessels) relative to the total stock across all industries¹⁰. Specifically, the weight for industry j relative to all industries (j=1,…,n) within mode k is:

〖industry weight〗_jk=〖employment〗_jk/(∑_(j=1)^n▒〖employment〗_jk )

As the industry weight indicates the proportion of the stock used by an industry within a given mode, the sum of all weights within a mode equals one.

Three types of weights were created are shown in table 5. Weights were not developed to distribute TRIs that are commodities themselves because the amount used by industries is shown in the IO use table.

The specific steps involved in creating the weights follow.

Industry employment of transportation workers were from the Bureau of Labor Statistics Employment Projections Program. This program provides industry by occupation and occupation by industry data biennially. The 2002 TSAs use 2002 industry by occupation data. Employment of: aircraft pilots and flight engineers; heavy and tractor-trailer truck drivers; light truck or delivery service drivers; and captains, mates, and pilots of water vessels was extracted. The extracted data was used to develop the four types of weights shown in table 5. The weights represent the fraction of the total number of transportation workers related to mode, k, employed by an industry, i, in the I-O accounts. Data for federal general government, federal government enterprises, State and local general government, State and local government enterprises are excluded and weights were not calculated for these industries. These industries were not considered to make and use in-house transportation in the same way as all other intermediate industries.

〖weight〗_i= 〖employment〗_k*∑_i▒〖1/employment〗_ik
where i=IO industry and k=transportation mode

For TRIs that are commodities, the value of in-house transportation is taken directly from the IO use table. For each industry in the IO use table, the value of in-house transportation is the value of the TRI commodity used to produce industry output. Assume, for example that the commodity railroad rolling stock manufacturing is the selected TRI (as in the 2002 TSAs). If an industry consumes 3000 dollars of railroad rolling stock manufacturing and then in-house value of rail transportation is 3000 dollars.

The value of in-house transportation for TRIs that are not commodities themselves is estimated by: (1) removing the component used for nontransportation purposes, such as gasoline used for heating or for operating machinery and the component used for transportation modes other than the one for which the TRI was selected, such as gasoline used for transportation modes other than trucking; (2) aggregating the resultant value from the item to the commodity level; and (3) then subtracting the producers’ value of the commodity (from the I-O use table) used by the relevant for-hire transportation, as shown below.

in-house value = mode value – producers’ value (for TRI commodity used by for-hire mode k)

The resulting estimate of in-house transportation then was distributed across industries by applying the distribution weight matching to the TRI, e.g., the share of fuel consumed by industries for trucking was used to distribute the in-house value of motor gasoline. In-house values were distributed only across industries that used a given TRI commodity and had a positive weight.  

Transportation activities require inputs not unique or primary to transportation. For example, office supplies and accounting services are used within an industry to produce transportation and all other activities. The TSAs assume nontransportation industries use these nontransportation related inputs in the same proportion as for-hire industries. This is performed through the development of a transportation input structure table (TIST) for each mode. The TIST table contains iTIST values which indicate, for each mode, how much of a nontransportation related commodity¹¹ was used to generate in-house transportation services. iTISTs were calculated by multiplying the sum of the in-house transportation value (calculated in the previous step) by a ratio, with the type of ratio being applied depending on whether the commodity is an intermediate or a value-added commodity. Both ratio types assume that private transportation uses inputs in the same proportion as for-hire transportation.

For all nontransportation related intermediate commodities used by for-hire mode k, the ratio is the value of the nontransportation related input i (Rik) to the total value of all TRIs used by the for-hire mode (Dk1). General ratios are not prepared for value-added commodities in this step as they are estimated during post-processing.

Within mode k, the resultant general ratios for all commodities except value-added commodities were applied to the sum of in-house transportation for industry j (Ijk) to find the iTIST for commodity i (iTISTijk) in the I-O use table. This process is shown in table 7 for selected nontransportation related commodities used in air transportation

No modification was made in this step to reflect whether the in-house value was derived from a TRI classified as an item versus a commodity as none was needed.

1. Identifying transportation related inputs

   A transportation related input (TRI) is an item unique or primarily used to generate transportation services in a specific mode of transportation. Typically, a TRI is a nondurable good (i.e., a good consumed within a year), such as fuel and tires, that comprises a relatively high proportion of the total value used by a for-hire transportation mode. Some goods account for a high proportion of the total value used by a for-hire transportation mode but do not make good TRIs, as they are not used exclusively for transportation and/or by the mode. For example, the item “automotive repair and maintenance” accounts for a high proportion of total inputs, but it may not be used exclusively for transportation as it includes repair garages. As such, the purchase of the item may indicate the purchase of a good for nontransportation purposes from a repair garage. For instance, inland marine insurance is not a good TRI for water transportation, as it includes insurance purchased by nontransportation industries to cover the movement of freight purchased from for-hire transportation industries. Similarly, some goods are a collection of goods, not all of which are good TRIs. Good TRIs are representative and widely used by for-hire transportation and nontransportation industries for transportation services. Thus, items like airplane propellers are not selected as TRIs, for while needed for transportation, they are not purchased as frequently or by as many industries as items like fuel.

   In the 2002 TSAs, one or more TRIs were selected from the I-O item control table for each mode included in estimating in-house transportation services (air, rail, truck, and water). The selected TRIs are identified in table 3. All, with the exception of the TRI used to estimate in-house rail transportation, comprise a relatively high proportion of the total value of the commodity to which they belong. The selected rail TRIs comprises the entire commodity and hence the commodity name itself is listed as the TRI in table 3.

   The following steps (a) and (b) are performed for each TRI that is an IO item; the steps are not performed for TRIs that are commodities.

   1. Developing split factors for transportation related inputs

      For each item in the TRI master list (table 3), the producers’ value includes both the nontransportation and the transportation related value of the item and includes both the component used in the intermediate portion and the final demand portion of the IO use table. The intermediate value is derived by multiplying the producers’ value by a share privately obtained from the Bureau of Economic Analysis that is a proportion of the item used for intermediate production. To extract the transportation value from this, a split factor was applied to each.

      transportation value = producers’ value* intermediate share * split factor

      The split factor is the proportion of the TRI commodity used for transportation. The split factors for the 2002 TSAs are shown in the table 4. Split factors for motor gasoline, light fuel oils (referred to as distillates), and liquefied refinery gases items used in truck transportation were derived from industry energy use information⁷ . All other split factors were set to 1 as the item was deemed to be used exclusively in transportation. All split factors are specific to the TRI; hence, for each TRI, one minus the split factor equals the proportion of the TRI commodity used for nontransportation purposes.

   2. Developing modal shares for transportation related inputs

      As many of the TRIs are used by more than one transportation mode, a modal share was applied to the transportation value.

      mode value = transportation value * modal share.

      The modal share indicates the proportion of the TRI used by a specific transportation mode (for both for-hire and in-house transportation services). For fuel items, modal shares were derived from data on fuel use by mode⁸. The modal shares are the same across fuel items belonging to the same commodity as item specific fuel use data by mode is not available. All non-fuel related TRIs for trucking were derived from vehicle miles of travel data⁹. Given the non-specificity of this data, the modal shares for non-fuel related TRIs for trucking are the same across items for a given commodity and across multiple commodities. For the remaining TRIs, the modal share was set to one as the item was deemed to be used exclusively by the mode.

2. Developing industry weights
   1. Industry weight creation for all modes:
3. Estimating and distributing the value of in-house transportation
4. Estimating inputs used in producing in-house transportation For the for-hire mode 481000 (air transportation), the procedure for calculating the aforementioned ratios is shown in table 6 for several commodities, which are used by the for-hire air industry but are not on the TRI master list. The values are example values and not actual values from the 2002 TSAs.
5. 1. Calculating trade margins and transportation costs After calculating the iTIST values, industry by commodity margin and transportation cost ratios were applied to the iTIST values to find the markup on the commodity when delivered to its final use. The margin and transportation cost ratios are expressed in terms of the producers' value for commodity i and industry j . As the I-O table already contained a wholesale and retail trade adjustment commodity, both were removed before applying the margins to the iTIST.
   2. Appending margins to iTIST table The calculated margins and transportation costs were appended to the iTIST table.
6. Post-processing.
   No modification was made in the following steps to reflect whether the in-house value was derived from a TRI classified as an item versus a commodity as none was needed.
   1. Calculating the nTIST The iTIST tables calculated in the previous step were summed across mode to create the combined TIST table. The resulting TIST values were subtracted from the producers' value of the commodity (from the I-O use table) to find the portion of the commodity used in providing services other than transportation, which is called the nTIST.
   2. Balancing the TIST table After calculating nTIST values, adjustments were made to ensure that the nTIST values were positive for all commodities used by industries with a positive producers' value. Adjustments were made per the following formula which distributes the net shortfall across each mode according to the original proportion of in-house transportation that each mode accounts for.

      iTISTNEW = iTISTORIGINAL + (nTISTORIGINAL * (iTISTORIGINAL/combinedTISTORIGINAL))

      To verify that the iTIST values were updated appropriately, the values were summed across modes to create a new TIST table, in which the summed iTIST values were subtracted from the producers' value to calculate a new nTIST value.

   3. Calculating value added by in-house transportation related to business activities For value added commodities used by a for-hire mode k, the ratio is the value of value-added commodity i (Rik) to the value of all intermediate commodities (Dk2). The value-added ratio is calculated for each for-hire mode and is applied to the sum of the preceding iTIST values (after balancing) for each industry.
   4. Re-calculating the nTIST and re-balancing the TIST table The estimated values from step c are appended to the balanced TIST table (prepared in step b above). The iTIST values in this new table were summed across modes to create the combined TIST table. The resulting TIST values were subtracted from the producers' value of the commodity (from the I-O use table) to find the portion of the commodity used in providing services other than transportation, which is called the nTIST. Adjustments were made to ensure that the nTIST values were positive for all commodities used by industries with a positive producers' value, as in step b.

Estimating In-house Transportation by Households

Estimating household production of transportation services (HPTS) through the use of private automobiles and adding HPTS to the TSAs requires estimating the value of intermediate inputs used by households for user-operated transportation activities and the value-added inputs for HPTS. This is consistent with the I-O framework of the TSAs.

Table 8 lists the primary data sources used in the above two steps for estimating HPTS.

1. Estimating the intermediate inputs for HPTS
   Inputs for household production of transportation services can be classified into two major components: ownership inputs and operating inputs. Both are counted as final uses within personal consumption expenditures (PCE) in the I-O accounts and hence need to be reclassified in order to estimate the value of HPTS. Ownership inputs are reclassified as fixed private investment in the final use portion of the I-O use table and operating inputs are reclassified as intermediate inputs into HPTS, which is added as an industry and commodity to the intermediate portion of the I-O use table. Table 8 lists the PCE and input classification.
2. Estimating the value-added by HPTS
   The value-added by HPTS can be defined as the sum of the value of labor services, indirect taxes, and other value added (primarily the value of capital services).

   1. Labor services:
      The I-O accounts do not count the value of unpaid labor; therefore, the value of time spent driving is set to zero.

   2. Indirect taxes:
      Assumed to be zero because of a lack of detailed data. Indirect taxes such as license fees are not presented explicitly in the I-O accounts which the current TSAs are based.

   3. Other value added:
      Two components: return to capital and annual depreciation of household-owned vehicles. The return to capital is assumed to be zero since households are a non-profit sector. Annual depreciation in relation to household-owned automobiles will be obtained from the Bureau of Economic Analysis fixed asset tables.

Creating the TSA tables

The final step in the TSAs involves the production of the make, use, direct requirement, and total requirements tables. The steps for creating these tables are outlined below.

With regards to household production of transportation services, the following cells equal zero:

All of the aforementioned cells take a zero value as in-house transportation services are provided only by nontransportation industries for their own use.

For the in-house transportation and all other rows, the sum of all entries equals the total output of the commodity. Similarly, the sum of all entries in each column equals the total output of the corresponding industry. The sum of the total commodity output column is the I-O use value increased by the value of in-house transportation output.

1. Creating the TSAs make table
   The TSA make table is formed by adding five additional columns and a five additional rows to the I-O make table containing the values of the five in-house modes. The value at the intersection of the in-house transportation column and row for each mode k produced to conduct business activities equals the total output of in-house transportation from the iTIST table for mode k; the value for all other cells in the in-house transportation column and row equal zero. In all remaining cells, the cell value is the same as in the 2002 I-O make table. The value at the intersection of the in-house transportation column and row for household transportation is the sum of the intermediate inputs and the value added (total output) by household production of transportation services through the use of automobiles. The resulting make table is shown in table 9.

2. Creating the TSA use table
   The TSAs use table is an I-O use table modified to show estimates of transportation related inputs. The estimates of transportation related inputs to produce business related in-house transportation are derived from the adjusted iTIST tables and added as additional columns and rows to the matrix formed from the nTIST values in the adjusted TIST table. The resulting matrix is appended to the final-demand portion of the I-O use table (as altered so as to estimate household transportation) to form the TSA use table. The estimates of transportation related inputs to produce household transportation are those taken from the final use portion of the I-O use table and those calculated in the preceding section on estimating the value added h household production of transportation services. The resulting TSA use table is shown in table 11.

   In the TSA use table, inputs for for-hire transportation industries are all zero because these industries, by assumption, do not have any in-house transportation activities. In the in-house transportation row for business activities, the following cells equal zero:

   • • The cell at the intersection of the in-house transportation row and column (the use of in-house transportation services to support in-house transportation activities), and
     • The cell at the intersections between the in-house transportation row and the for-hire transportation columns (the use of the in-house transportation services to support for-hire transportation activities)
   • • The cell at the intersection of the in-house transportation row and column (the use of in-house transportation services to support in-house transportation activities) takes a value of zero.
     • The cell at the intersections between the in-house transportation row for household transportation and each intermediate industry.

Concluding Remarks

The methodology presented here for the Transportation Satellite Accounts (TSAs) is complete but suffers from several weaknesses. Many of these weaknesses can be attributed to assumptions used by the Bureau of Economic Analysis in the I-O accounts, including the assumption that:

These assumptions in part contribute to the following weaknesses in the TSAs: 

Other weaknesses in the TSAs include the following:

Not all of the weaknesses in the TSAs can be corrected, particularly those that arise from assumptions in the I-O accounts.

The 2002 TSAs improve upon previous TSAs by:

¹ The original TSAs were designed by the MacroSys Research and Technology under a subcontract with AMTI (Contract No. SK-97-2). The first version, using the 1992 benchmark I-O accounts, was delivered at the end of April 1997 and the second version, using the 1996 benchmark I-O accounts, was completed in the year 2000. Revisions were to the original method made by the Bureau of Transportation Statistics to produce TSAs from the 1997 benchmark IO accounts.

² For information on how the treatment of transportation in NAICS differs from that in the Standard Industrial Classification System (SIC), see the section “Changes in Method in the 1997 TSAs and Comparability” in this report.

³ For information on the treatment of secondary products in the 1997 U.S. I-O accounts, see: Lawson, Ann M. et al., “Benchmark Input-Output Accounts of the United States, 1997,” Survey of Current Business, December 2002, pg 27. 

⁴ The U.S. I-O accounts are the foundation for the TSAs. The TSAs make no attempt to verify or correct any problems that may exist in the I-O accounts.

⁵ The weights used in the 1997 TSAs were developed from data on the stock of transportation vehicles (aircraft, railcars, trucks, and water vessels). Because of the difficulty in acquiring this data, the 2002 TSAs were developed from data on the employment of transportation workers, published biennially by the Bureau of Labor Statistics as part of the Employment Projections program: http://www.bls.gov/emp/

⁶ Adjustments were made after applying the for-hire relationship to ensure that the value of the transportation and nontransportation component of each commodity used by an industry equals that in the I-O use table before rearrangement. 

⁷ U.S. Department of Energy, Energy Information Administration, Annual Energy Review 2008, tables 5.13a-5.13d.

⁸ U.S. Department of Energy, Oak Ridge National Laboratory, Transportation Energy Data Book: Edition 28. Light fuel oils are referred to as diesel in this publication.

⁹ U.S. Department of Transportation, Federal Highway Administration, Highway Statistics. Reported in U.S. Department of Transportation, Bureau of Transportation Statistics, National Transportation Statistics: Chapter 1, section C, table 1-32 [as of April 2010].

¹⁰ Stock values are used rather than flows because there are not readily available flow estimates indicating the intensity in which industries use transportation in their production process. It is assumed that employing a larger number of transportation workers implies that an industry uses a larger share of the related transportation mode in producing output. The actual employment values are not used; rather, the number of employed persons is used to create shares that indicate an industry's relative use of a mode.

¹¹ Nontransporation commodities are commodities in the IO table not classified as for-hire transportation

¹² The received 2002 I-O use table did not balance with the make table. As a result, the margin ratios were derived from the summary I-O use table (after redefinition) on the BEA website. As the online table contains less detail than that in the received table, industries and commodities were grouped (per the NAICS I-O table released by the BEA with the 2002 Benchmark I-O data made available online) and iTIST values summed together before applying the ratios. To ensure correct groupings, the received make table (for which the total value equaled the total value of the I-O make table on the BEA website) was matched to the summary make table (after redefinition) on the BEA website.

¹³ For more information on the derivation of the industry-by-commodity total requirements table, see: Handbook of Input-Output Table, Compilation and Analysis (New York: United Nations, 1999).

¹⁴ When deriving the TSAs industry-by-commodity total requirements coefficients, the underlying I-O assumptions were maintained. This includes the assumption that the technology and relative prices defining the relationships between producers and consumers within a given year remain constant. For more information, see: U.S. Department of Commerce, Bureau of Economic Analysis, “Concepts and Methods of the U.S. Input-Output Accounts,” September 2006.

¹⁵ As mentioned in the discussion, these are identities which are not calculated as part of the total requirements table. 

1. The direct requirements table comes from the TSA use table. The coefficients a_ij in the table are derived by dividing the TSA use value for each commodity i used by industry j by the total output for the industry:

   (a_ij= 〖TSA use value〗_ij)⁄(∑_(j=1)▒〖TSA use value〗_ij )

   The coefficients for industry j sum to unity. Coefficients are calculated for all industries in the TSAs use table but not for the components of final use or GDP. The resulting table is shown in table 12.

   The values in the table are calculated per the method used by the U.S. Department of Commerce, Bureau of Economic Analysis (June 2008)

   The following describes the method.

   Derivation of the total requirements table used the following mathematical procedure, which involves the following identities¹⁴:

   1. Creating TSA direct requirements table The TSAs direct requirements table shows the direct requirement coefficients for each commodity and industry. These values are the amount of a commodity (on a row) required by an industry (on a column) to produce a dollar of the industry's output.
   2. Creating TSA total requirements table
      The TSA total requirements table shows the commodity by industry total requirements coefficients. These coefficients show the production directly and indirectly required to deliver a dollar’s worth of goods and services to consumers and other final users. Each column shows the commodity delivered to final users, and each row shows the demand for an industry’s output in response to a dollar increase in the final demand for the commodity. The last row shows the sum of all the changes in industry outputs that are required to deliver a dollar’s worth of goods and services to final users. Because each of these sums is a dollar multiple of the initial dollar spent of an industry’s output, the sum often is referred to as an “output multiplier”. These multipliers can be used to estimate the impact of changes in the final demands of commodities on total industry output.¹² Hence, the table shows the interdependence among producers and consumers in the economy and can be used to derive estimates of the direct and indirect effects of changes in final demand on for-hire and in-house transportation industries and commodities. For instance, the table can be used to analyze the relative effects on transportation and nontransportation industries from an increase in government expenditures on transportation or from a change in the composition of fixed investment that results from a change in business activity.¹³

   1. We arrive at the commodity-by-commodity total requirements table through the following:

      From (1) and (3) we derive

      And from (2) and (4) we derive

      Substituting (6) in (5) and solving for q, we obtain

      Where (I- B*D)^(-1) is the commodity-by-commodity total requirements matrix

      We arrive at the industry-by-industry total requirements table through the following:

      Substituting (5) into (6) and solving for g, we obtain.

      Where (I- D*B)^(-1) is the industry-by-industry total requirements matrix

      We arrive at the industry-by-commodity total requirements table through the following: Substituting (6) into (7)

      Where D * (I- D*B)^(-1) is the industry-by-commodity total requirements matrix

      Only the commodity-by-commodity and industry-by-commodity total requirements table was published for the TSAs.

      1. B=U*g ̂^(-1)
      2. D=V*q ̂^(-1)
      3. q=U*i+e
      4. g=V*i
      5. q=B*g+e
      6. g=D*q
      7. q=(I- B*D)^(-1)* e
      8. g=(I- D*B)^(-1)* D* e
      9. g=D * (I- D*B)^(-1)* e
   1. There are no economies or diseconomies of scale in the production process. In other words, there is a direct, linear relationship between inputs consumed by an industry and the level of output of an industry within a single year. This assumption is contrary to most production functions in economics, which are non-linear in nature, as well as to most industrial organization theory, which assumes that some industries are more economically competitive and hence do not use commodities in the same proportion as less competitive industries.
   2. Each industry produces a single commodity with a unique input structure. The commodity is assumed to be homogenous and hence to possess no distinguishing qualities or features.
   3. Changes in price do not affect the proportion of inputs used. The level of inputs changes only in response to a change in final demand.
   4. Inputs are not substitutable. This means that within a given technology there is one preferred set of input ratios that will continue to be preferred regardless of final demand quantities.
   1. The assumption that production processes are linear and exhibit constant returns to scale even though likely to vary across industries, for the reasons discussed above. 
   2. The assumption that larger employment numbers are an indicator of greater in-house transportation production and consumption.
   3. Reasonability in the scale of inputs to other inputs when preparing the general ratio. The general ratio is constructed under the assumption that the inputs are related and that production processes are constant.  
   1. Split factors and modals shares are commodity, not item specific. TRIs comprising the same commodity are assumed to be used in transportation and by a specific transportation mode in the same proportion even though they are different items.
   2. The TSAs do not incorporate measures of capital stocks. This problem, however, can be corrected with estimates from the Transportation Infrastructure Capital Stocks Accounts (TICSAs). 
   • Using a single data source is used to distribute the in-house value of air, rail, water, and truck transportation and
   • Providing an estimate of the value added by household production of transportation services.