Section 3: Estimating Multifactor Productivity in Truck Transportation, 1987-2003

Section 3: Estimating Multifactor Productivity in Truck Transportation, 1987-2003


This analysis utilizes two versions of the growth-accounting methodology to calculate multifactor productivity (MFP) in the trucking industry in the United States. The initial methodology used is the basic growth-accounting of sources of economic growthwhich includes weighted growth rates of production inputs, with the weights being the share of the input in total industry costs/output. This methodology was initially used in macroeconomic analyses of sources of growth, by analysts such as E. Denison1 and J.W. Kendrick2 who also used it to analyze productivity at the sectoral and industry levels. The more recent version of the methodology has been usedin a somewhat different and, what might be called, an enhanced formby government agencies, such as the Bureau of Labor Statistics (BLS), to estimate multifactor productivity at the sectoral and industry levels.3 This version utilizes the Tornqvist formula in the calculations. The basic growth-accounting methodology is presented in Appendix A, while the enhanced methodology using the Tornqvist index is presented in Appendix B.

The section which follows defines productivity (labor and MFP) and describes its benefits (increases). The subsequent section describes the data used and their characteristics, the calculations, and the results of the calculations by using the two methodological approachesthe basic growth-accounting methodology and the enhanced methodology.

Defining Productivity

Labor productivity is defined as output per unit of labor, and is calculated by dividing output by a measure of the labor input (number of employees or labor hours). Increases in labor productivity reflect the effect of two basic factors: 1) increased use of capital in productionwhich increases the amount of capital per worker, and 2) technological progress, which can include a number of factors, and is discussed at a later point under multifactor productivity.

Multifactor productivity (MFP) refers to the productivity of all the inputs used in the production process. Multifactor productivity is a more comprehensive measure of productivity than labor productivity, or other single-factor productivity measures. It indicates the overall production efficiency of an industry; it relates to increases in industry output that are not accounted for by increases in the inputs.

For estimating MFP at the industry level, the output measure used is total output (rather than value added). The inputs used for analysis are: labor, capital, and intermediate inputs. The labor input is measured in terms of numbers of workers or labor hours; while the capital input includes structures, equipment, inventories, and land (in a broad definition of capital). Intermediate inputs include purchased electricity, fuels, materials, and services. The weights used to estimate the contribution of each input to output are their shares in the total costs of the industry.

With regard to the capital input, one notes that reproducible tangible capital and land are two distinct factors of production. There are differences between reproducible capital (structures and equipment) and land. For one, structures and equipment are man-made. They are an output of a production process. Land, on the other hand, is not man-made; it is a natural resource. Moreover, structures and equipment depreciate over time as they are used in production; land does not depreciate over time (at least for practical purposes).

Benefits of Productivity Increases

Productivity, or productivity changes, can affect a company in an industry and a number of companies in the same industry. Thusly, a change in the productivity of the truck transportation industry would affect the productivity of the transportation sector. A change in the productivity of a sectorsuch as transportationwould, in turn, affect productivity of the U.S. economy.

The initial and basic result of a productivity increase, at the firm or industry level, is a reduction in costs and an increase in profits (total revenues minus total costs). Thus, the productivity increase benefits directly the affected industry. Subsequently, the increase in profits can be followed by lower prices of the industryparticularly when there is competition among the producers of the industry. Competition is affected by the number of producers in the industry, among other things. The higher the number of producers in the industry, the more the expected competition in the industry. Another impact of productivity increases (increase in profits) could be an increase in the labor compensation (wages and fringe benefits) of the workers working for the affected firm/industry, if the company/ industry shares part of the productivity gain with the workers.

All three of these impacts of a productivity increase result in higher incomes in the economy. In the case of the business enterprise, there is a direct increase in its profit/income. If part of that profit goes to the stockholders of the firm, in the form of higher dividends, their incomes would increase. Moreover, a portion of the higher profit can be kept by the company in the form of retained earnings with which to finance future investment that can lead to higher levels of productivity. In the case of labor, there could be an increase in the income of workers (labor compensation). In the case of the consumers/users of the services of the industry, if prices of that service decrease, there is an increase in the real incomes of the consumers. These are the basic benefits of productivity increases, and the reasons why productivity increases are desirable from the perspective of the company, industry, and the economy. A recent study has assessed the impact of productivity increases in air transportation. 4

There can also be second-round effects as when labor uses its higher income to increase its consumption of various goods and services in the economy. This increased consumption stimulates sales of various products/services and subsequent production of other industries, with possible increases in employment and incomes there. Thus, the benefits of an initial productivity increase can have a ripple effect in the industry and affect positively other industries and the economy.


The data used for the analysis were obtained primarily from the Bureau of Economic Analysis (BEA), U.S. Department of Commerce. This source provides most data series needed for the estimation of trucking MFP. The industry analyzed is the Truck Transportation industry, represented by NAICS 484 (North American Industry Classification System). This industry consists of: NAICS 4841General Freight Trucking and NAICS 4842Specialized Freight Trucking. In turn, NAICS 4841 includes: 48411 (Local), and 48412 (Long Distance). NAICS 4842 includes: 48421 (Used Household and Office Goods Moving); 48422 (Local); and 48423 (Long-Distance).

The data used for the trucking industry refer to for-hire trucking, whereby businesses, or households, hire trucking firms to provide transportation of goods. These data do not include in-house trucking, whereby a business, such as a grocery chain, engages its own trucks and truck drivers to transport its goods. Presently, sufficient data for in-house trucking are not available to include this segment in the estimation of MFP.5

The analysis is initially carried out for the period 1998-2003. The choice of the initial period was affected by data availability. The primary data series, obtained from BEA, include data on gross output, labor, capital, and intermediate inputs. Data on output, capital, and intermediate inputs are available, under NAICS, from 1987. However, labor data under NAICS are available only from 1998. Consequently, estimates of MFP are initially calculated for the 1998-2003 period. Subsequently, labor data under NAICS are extrapolated back to 1987, allowing for calculations on trucking MFP to be carried out for the 1987-2003 period.

In the first phase of calculations, estimates are developed for MFP in truck transportation without land. The second phase of calculations includes a measurement of the land input and its incorporated in the estimation of MFP.


Gross output in trucking is measured in terms of receipts of the industry. Output includes shorthaul and long-haul trucking. Data on gross output are available in current prices and in chain-type quantity indexes.

Labor Input

The main data for the labor input are in terms of full-time-equivalent workers (FTE). Part-time workers are converted (by BEA) into full-time equivalents. The labor data do not make a distinction for different types of labor. In this regard, it is noted that BLS, in its work on productivity (labor and MFP), also considers labor to be homogeneous and additive, with no distinction made between hours of different groups of employees.6 There are also data available on labor compensation of FTE employees in truck transportation. Thus, the MFP estimates are based on labor data of full-time equivalent employees. In truck transportation, there are also self-employed truckers; these are not included in full-time equivalent employees. The services of self-employed truckers would be included in intermediate inputs, which include purchased services. The services of selfemployed truckers are obtained by trucking firms through contractual arrangements.


Capital stock data refer to structures and equipment (including software). They are available in current prices and in Chain-Type Quantity Indexes for Net Stock. Net capital stock excludes the depreciation of capital from gross capital stock. Capital stock data of BEA do not include land (or inventories of unsold goods).

Intermediate Inputs

Intermediate inputs include purchases of electricity and other energy inputs, purchases of materials, and purchases of services. The latter would include the services of self-employed truckers. Data for intermediate inputs are available, from BEA, in the GDP-by-Industry accounts and in the Input-Output accounts. In the GDP by Industry accounts, intermediate inputs are obtained as the difference between independent estimates of gross output and value added (value of sales minus value of purchases of inputs). In the Input-Output accounts, intermediate inputs are obtained from a combination of source data for industry purchases and indirect techniques, and value added is the residual.7 The value added of a firm/industry is the value of its sales revenue minus the value of its purchases of intermediate inputs. This analysis uses data from the GDP-by-Industry accounts since that database presents a comprehensive and consistent set of data for variables used in the calculations. A tabulation in Appendix Table C indicates that data on intermediate inputs and gross output, from the two sources, since 1998 are the same for truck transportation. This is consistent with the objective of BEA to create integrated annual I-O and GDP-by-Industry accounts. These integrated accounts are only available starting in 1998. Prior to 1998, there were substantial differences in the measure for intermediate inputs from the two BEA sources (Yuskavage, 2001).

Weights of Inputs

The labor weight was obtained by relating labor compensation (wages and fringe benefits) to industry gross output, in current prices (labor compensation/ output). The weight for intermediate inputs was obtained in a similar manner: by relating the cost of these inputs to industry gross output. The weight of the capital input was obtained as a residual, for the first phase of calculations, by subtracting the combined percentage shares of labor and intermediates inputs from one (representing total industry costs).

The annual weights for the inputs used for the calculations with the basic growth-accounting approach are presented in Appendix D.


Land is one of the primary inputs of industry output. Land is non-reproducible capital while structures and equipment are reproducible capital. Data on land are not available from BEA. BEAs estimates of structures (values) are based on data collected by the U.S. Census Bureau. These data pertain to new structures and include the cost of construction and of site preparation for construction projects. Construction data for Census exclude land acquisition. Consequently, BEA data on fixed assets include the cost of new structures with site preparation, but do not include the cost of the land on which the structures are built.

The initial sets of estimates of trucking MFP are calculated without a measurement for land. The land input is estimated and incorporated in the MFP calculations in the second set of estimates. Its magnitude is estimated by the approach used by BLS in their estimation of industry MFP (Duke, et. al., 1992). The methodology and data for measuring the land input are discussed in a later section (MFP Calculations with Land).

Calculations: Basic Growth-Accounting Methodology

Calculations: 1998-2003

Estimates of MFP in trucking, from 1998 to 2003, are shown in Table 1. These estimates are based on the basic growth-accounting methodology, using annual growth rates of inputs, weighted by their share in total industry cost/output. The inputs are labor, capital, and intermediate inputs. Land is not included.8

The estimates indicate that for the first three years of the period of analysis, multifactor productivity in truck transportation declined (negative rates), while it grew at positive rates during the last two years.

With regard to changes in output and factor inputs, the data show that over the 1998-2003 period, output in trucking grew at positive rates for the first two years; however, those rates became negative in the last three years of analysis. Changes in employment in trucking were similar to changes in output, with initially positive rates of growth followed by negative ones. Similar patterns can also be observed for capital and intermediate inputs. Changes in the factor inputs over time resulted in a positive combined weighted growth rate during the first two years of the period of analysis; the growth rate turned negative during the last three years of analysis.

Inputs in the trucking industry decreased over the period of analysis and this was accompanied by decreasing output. However, in the last two years of analysis, MFP increased while trucking output continued to decline. This increase of MFP, which accompanied declining output, indicates increasing efficiency in the utilization of industry resources.

Calculations: 1987-2003

It was mentioned previously that data under NAICS are available for the 1987-2003 period for gross output, and for the inputs of capital and intermediate purchases. However, labor data for trucking, under NAICS, are available only for 1998-2003. This factor defined the time frame for calculations presented in the previous section.

This section uses extrapolated labor data for trucking to expand the analysis to the 1987-2003 period. Labor data are available for trucking under NAICS for 1998-2003, whereas labor data (employment and labor compensation) are available for trucking and warehousing, under SIC 42, for the period 1987-2000.9 There are three years of data overlap between NAICS and SIC labor data. Consequently, the ratio of labor under NAICS to labor under SIC, in 2000 (the most recent year), was used to extrapolate the NAICS trucking employment and labor compensation back to 1987. These calculations are shown in Appendix E. These labor data were then used to calculate MFP in trucking over 1987-1998.

The results of the calculations are presented in Table 2. They indicate that MFP in trucking experienced a mixed record of performance over the period of analysis. The years in which trucking MFP experienced positive growth rates are observed mostly in the first part of the period of analysisin the late 1980s and early 1990s. The last two years of analysis (2002, 2003) also show positive growth rates. Negative MFP growth rates are observed during the late 1990s, and 2000 and 2001.

With regard to individual components of the trucking MFP framework, one observes (Table 2) that gross output grew at positive rates during the period of analysiswith the exception of the last three years (2001-2003). Labor also increased at positive rates for most years over time, while during the last two years (2002, 2003), it experienced negative growth rates.

Capital data do not indicate a consistent trend over time: years of positive growth rates are followed by negative growth rates. Years in which capital in the industry had negative growth rates include the last three years of analysis. The intermediate inputs also do not show a consistent trend over time. In most of the years, these purchases experienced a positive growth rate, while in the last three years, they had negative growth rates.

In summary, the data and calculations indicate that the trucking industry was increasing in activity/ output and inputs in the first half of the period of analysisthe late 1980s and early 1990s. Multifactor productivity also increased over this period. This situation changed significantly during the late 1990s and in 2000 and 2001. During this period, trucking experienced decreases in output, factor inputs, and multifactor productivity. However, during the last two years of analysis2002 and 2003MFP in trucking increased. During the same period, output and factor inputs decreased. This implies increasing efficiency in the utilization of the available inputs in the industry.

Calculations with the Tornqvist Index

Calculations: 1987-2003

Calculations are also carried out by the use of the Tornqvist index methodological framework. In this case, the inputs of labor, capital, and intermediates purchases are aggregated into a chained Tornqvist index (See Appendix B). Data on gross output are available in terms of a chain-type quantity index. Estimates of trucking MFP levels are obtained by relating the combined input index to the quantity output index. Growth rates of MFP are calculated starting with 1989. The results of the calculations are presented in Table 3.

The index numbers in column 3 of the table indicate increases and decreases of trucking MFP levels over time. One does not observe a persistent trend. The growth rates (column 4) provide a picture that is clearer to interpret. These growth rates again indicate that MFP in trucking grew at positive rates during the late 1980s and the first half of the 1990s. This changed in the second half of the 1990s and the first two years of the 2000s, when one observes negative growth rates of MFP. In the last two years of analysis, 2002 and 2003, trucking MFP is again observed to grow at positive rates.

One also observes that these growth rates of trucking MFP are quite similar to those obtained by using the annually-weighted growth rates of inputs (basic growth-accounting methodology), presented in Table 2. The two sets of MFP growth rates are compared in Appendix Table F. For some years, the two sets of growth rates are the same; while for other years, the growth rates differ somewhat. Therefore, the calculations indicate only small differences in the results from the two versions of the estimating methodology. Consequently, it appears that these two methods are relatively good substitutes for each other.

MFP Calculations with Land

This section presents estimates of the quantity and cost share for land used in truck transportation, and includes that factor input in calculating MFP for the industry. The data for output, capital, and intermediate inputs have been described previously. The data for the labor input used refer to FTE employees; and the data for labor compensation were obtained from the BEAs Input-Output accounts. The data on FTEs are compatible with the Input-Output data on labor compensation (for the labor cost share).

The land used by the trucking industry for this study relates to privately owned land; this includes land used for terminals, maintenance facilities, office buildings, parking lots, etc. It does not include land used for public capital, such as highways. This is similar to the measurement of land by BLS for industry studies of multifactor productivity. The land used for public capital, such as highways, in trucking MFP will be assessed in an upcoming study.

This study estimates a land stocks index by using an approach similar to that of BLS, with some modification. In estimating the land input for MFP calculations, that agency uses a result from a study by Manvel (1968). According to that study, the value of industrial land in 1966 accounted for 24% of the total value of industrial land and structures in 1966. Consequently, in BLS industry studies of MFP, an industrys wealth stock of structures in 1966 is multiplied by the ratio 0.24/0.76 (land/ structures) to estimate the value of land for the industry in 1966. This estimate is then extrapolated backward and forward, in correspondence with changes in the gross value of structures stocks in constant dollars (of the industry). The gross structures stocks are the capital stocks without deductions for depreciation. In this regard, the position is taken that land does not depreciate, since its service life is (for practical purposes) infinite and its ability to provide services over time does not decline. The resulting land estimate is in constant dollars since the calculation uses the constant dollar value of structures as the extrapolator.10 One notes that a measurement in constant dollars implies a measurement in quantity terms, since the effect of price changes is taken out.

This study uses the quantity index of the net structures stocks of the trucking industry for extrapolation, instead of the gross structures stocks. This has been affected by two considerations. First, BEA has stopped producing estimates of gross capital stocks; consequently, a NAICS-based gross structure stock index for the trucking industry is not available from that source. In addition, the Manvel estimates of the 1966 values for land and structure were based on data of locally-assessed taxable real estate. Since property assessments are expected to reflect the physical and economic conditions of the properties assessed, the land-tostructures ratio can be interpreted as the relationship between the values of land and depreciated structures. Therefore, the net stock of structures would seem to be appropriate for the estimation of land stock.

A complication in measuring land stocks is that the BLS procedure requires the structures (wealth stock) of the trucking industry, in constant prices, to be available for 1966; however, the BEA structure series (quantity index), under NAICS, is available only from 1987 to 2003. SIC data (value and quantity), however, are available from BEA that go back to 1966.11 Consequently, this study extrapolates NAICS data for structures by using SIC data for structures for the SIC industry Trucking and Warehousing. Moreover, there are data on structures available for overlapping years between the SIC and NAICS series. Consequently, the ratio between the two series (in current prices) for 1987 and 1988 (the earliest overlapping years) was used to extrapolate the NAIC series backward to 1966. This results in an estimate of the land value, in current prices, used in 1966 by truck transportation. This value is the same as the value of land in 1966 dollars (i.e., constant prices). This value in constant dollars is subsequently extrapolated forward by the movement of the NAICS Structures stock (quantity) for truck transportation.

The estimated land input is then combined with the structures and equipment stock index, by Tornqvist aggregation, and this results in a capital input index of reproducible and non-reproducible capital. The capital input index is approximated by the capital stock index. The results of the calculations on the land input (land index) are shown in Appendix G.

Weights of Inputs

The weights of the inputs used in the estimation of industry MFP are the cost of each input (labor, capital, land, and intermediate inputs) in the total costs of the industry. The total costs of the industry are the combined cost of each factor input.

Data on costs for labor and intermediate inputs are available in the BEA GDP-by-Industry accounts. Labor compensation is the labor cost, including wages and fringe benefits. The value of total intermediate inputs is the total intermediate input cost. Total industry costs are measured as gross industry output, in terms of revenues, minus indirect business taxes (sales taxes).

The weights for structures, equipment, and land are estimated in this study. These three types of capital assets comprise the capital input of the industry. This study measure total capital costs (of the capital assets) in the trucking industry by the industrys gross operating surplus. The gross operating surplus consists of pre-tax income and depreciation of fixed capital assets.

To provide a simple description of the concepts:

  1. Profit or Income before (corporate income) taxes = Total revenuesTotal costs;
  2. Depreciation = amount deducted from income for wear of fixed capital assets
  3. Gross operating surplus = Income (before tax) + Depreciation.

This gross operating surplus is taken as the cost of industry capital. This would be the cost of capital for the use of structures, equipment, and landthat is, the total costs of the industry and it would be the overall weight for the industry capital input.

The calculations take structures and equipment as one segment of industry capital (reproducible capital) and land as another segment (non-reproducible capital). Structures-equipment and land are eventually combined into a capital index; consequently, one needs the cost of these asset classes, to be used as weights in the aggregation. In this regard, total capital costs (gross operating surplus) of truck transportation are allocated between structures-equipment (costs) and land (costs).

This allocation is based on two assumptions, needed for the calculations of land costs: The source data (BEA) provide data on values; however, one needs data on costs to calculate land costs. The two assumptions are:

1. The share of structures value in the total value of structures and equipment (available BEA data) is the same as the share of structures cost to total costs of structures and equipment.

structures value (BEA) over structures and equipment cost = stuctures cost over structures and equipment cost

2. The ratio of the land cost to the cost of structures (net of depreciation) is the same as the ratio of the land value to the structures value.

land value (manvel) over structures value (manvel) = land cost over structures cose(net)

With the above assumptions, the estimation of the land cost is estimated by obtaining values for the relevant variables in the relationships shown above. Initially, the cost of structures is separated from total capital costs (gross operating surplus). The cost of structures is net of depreciation; the structures cost is used to estimate the land cost, and land does not depreciate. The land cost is assumed to be equal to 0.24/0.76 times the cost of structures (net of depreciation). The steps in the estimation of land cost are described in Appendix H. The weights used for the inputs in the calculations that include land are shown in Appendix I.

Results of MFP in Truck Transportation

The estimated levels and growth rates of MFP for truck transportation, with a measurement for land, are calculated for the period of analysis and various subperiods. The results are presented in Table 4. The annual growth rates show that MFP in trucking grew at positive rates during 1988 to 1994, and in 1996. It grew at negative rates in 1995, and during 1997 to 2000. In the last 3 years of analysis, 2001 to 2003, truck MFP again grew at positive rates.

The growth rates for longer periods summarize changes in truck MFP over time. Over the entire period of analysis, truck MFP increased at an annual rate of 0.8%. The period of analysis can be subdivided into three subperiods: 1987-1995, 1995-2001, and 2001-2003. The calculation results indicate that during the first subperiod (1987-1995), truck MFP increased at an average rate of 2.0% per annum. In contrast, during the second subperiod, of 1995-2001, MFP decreased at an annual rate of -0.8%. During the last subperiod (20012003), truck MFP again increased, at an annual rate of 1.1%.

In addition, it is possible to compare the MFP results shown in Table 4 with those of a recent study by Triplett and Bosworth (2004). They estimated MFP for the SIC industry Trucking and Warehousing, for a shorter period than of our analysis. Growth rates of those calculations are presented in Table 5 along with BTS-estimated growth rates of the NAICS Truck Transportation industryfor the two periods shown. In comparing the two sets of MFP results, one notes a general consistency between the BTS results and those of Triplett-Bosworth even though there is, at least, a difference in industry coverage. According to both sets of results, the trucking industry shows positive growth rates of MFP during 1987 to 1995; they become negative growth rates during 1995 to 2001.

From another perspective of assessing the MFP results, one also notes that the MFP estimates in Table 3 are quite similar to the results shown in Table 4. The estimates in the former table do not include a measure for the land input while the results of the latter table do. Thus, it would appear that the inclusion of the land input does not make a noteworthy difference to the MFP results. This, however, would seem to be related to the methodology used in this study for the measurement of land. The approach used essentially tied the land measurement to the magnitude, and change, in the stock of structures. That is, changes in land followed changes in the structures. This eliminated the effect of actual changes in the land input that might have been substantially differentin some yearsfrom changes in the structures. In future work, it is planned for the measurement of land to be carried out by a different approach.

Two Points

There are two points to note with respect to the estimated MFP for truck transportation. First, as pointed out, the official statistics of trucking output include the output of firms whose primary output is trucking. They do not include data for in-house trucking. Therefore, such data are not available for this analysis.

Second, there is the matter of contracted services. Trucking services are sometimes contracted out by truck carriers to single owner-operators of trucks. That activity would be an intermediate purchase by the trucking firm. Consequently, the activity would be counted in the gross output of truck transportation. On the input side, the activity would be counted as an intermediate input. This measurement would not affect the estimation of MFP, since the activity is measured in both the output and input sides.

1 Denison, 1974 and 1967.

2 Kendrick, 1973.

3 Bureau of Labor Statistics, 1983; Duke et al., 1992.

4 Apostolides, 2006.

5 BTS has been doing work in estimating the output of in-house trucking. However, other data needed for the estimation of MFP are not available.

6 Bureau of Labor Statistics, 1983.

7 Yuskavage, 2001, p. 7.

8 The weight of land would be included in the weight of capital since the weight of capital is derived as a residual (from 1.00) after accounting for the weight of labor and intermediate inputs.

9 Information on this issue was provided by BEA staff.

10 Communications with BLS staff, Office of Productivity and Technology.

11 The data were kindly provided to BTS by BEA staff, Fixed Asset Accounts.