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Technical Note: DOCUMENTATION for the Transportation Services Index

July 2013

Bureau of Transportation Statistics (BTS)
Research and Innovative Technology Administration (RITA)
U.S. Department of Transportation


In fiscal year 2002, researchers from the State University of New York at Albany (Kajal Lahiri and Vincent Yao) and George Washington University (Herman Stekler) studied the relationships between transportation data and measures of the economy.   Support for this research was provided through a BTS research grant on "Leading Economic Indicators for the Transportation Industry."   One of the outcomes of the research was the creation of a set of indexes that reflected passenger, freight, and total transportation services output.   These indexes, which were originally designed to serve as coincident measures of the transportation sector of the economy, were recognized as valuable measures that BTS should produce and provide to the public.

To provide such a measure, BTS undertook development of this index of output in the transportation industry. The services produced by each subsector of the industry are measured in terms of physical outputs—ton-miles for freight modes and passenger-miles for passenger modes. These data are then deseasonalized, indexed, and combined to create the monthly index.

The Transportation Services Index, or TSI, is a monthly measure of the volume of services performed by the for-hire transportation sector. The index covers the activities of for-hire freight carriers, for-hire passenger carriers, and a combination of the two.  The TSI tells us how the output of transportation services has increased or decreased from month to month. The movement of the index over time can be compared with other economic measures to understand the relationship of transportation to long-term changes in the economy.

The freight transportation services index consists of:

  • For-hire trucking (parcel services are not included),
  • Freight railroad services (including rail-based intermodal shipments such as containers on flat cars),
  • Inland waterway traffic,
  • Pipeline movements (including principally petroleum and petroleum products and natural gas), and
  • Air freight.

The index does not include international or coastal steamship movements, private trucking, courier services, or the United States Postal Service.  

The passenger transportation services index consists of:

  • Local mass transit,
  • Intercity passenger rail, and
  • Passenger air transportation.

The index does not include intercity bus, sight-seeing services, taxi service, private automobile usage, or bicycling and other non-motorized means of transportation.

The components have been selected to give the best coverage possible of the for-hire transportation industry, subject to current limitations on the availability of monthly data. They are grouped to conform to the classifications used in the National Income and Product Accounts.

The purpose of this document is to provide insight into the calculation of the Transportation Services Index (TSI).  The document is divided into 6 sections: raw data, seasonal adjustment, indexing, weighting, aggregation and chaining, and final indexes.   It is hoped that this document will provide an understanding of each stage of the process, in an attempt to provide transparency for all that goes into the TSI.


The BTS staff gather monthly and annual data for each mode of transportation from a range of government and private sources.  The monthly data consist of the modal ‘quantities’ in our index: truck, rail freight (carloads and intermodals), water, air freight and pipeline (natural gas and petroleum) for the freight component, and air passenger, transit and rail passenger for the passenger component.  The ideal data would be either monthly ton-miles (for freight) or passenger-miles (for passenger) – but proxies are utilized when such monthly data do not exist. 

Annual data are gathered and used as weights in the index calculation.  The primary set of data are annual GDP value-added figures by mode, but annual revenue data for air (passenger and freight) and rail (passenger and freight) are also needed for the calculation of the weights.  Details of both the monthly and annual data are provided next.

Monthly Data
FREIGHT: Truck Tonnage

Name of Series

American Trucking Associations (ATA) Monthly Truck Tonnage Index (NSA)


Represents the freight volumes (tonnage) that motor carriers actually reported to ATA and is absent of any adjustment for recurring seasonal factors


ATA Monthly Truck Tonnage Report – BTS receives a hardcopy of the report every month; copies of the press release can be obtained at:

(703) 838-1799, Tiffany Wlazlowski at (703) 838-1717, Sean McNally at (703)838-1995, or Bob Costello-ATA VP @ (703) 838-1799

Data format

Index number with 2000 = 100, monthly, seasonally unadjusted

Publication date

3rd of every month for the data 2 months earlier


The current monthly data are preliminary, and the data for the previous month are revised.  All other data are final. 


The Index represents ATA membership.  The monthly Truck Tonnage Index is based on a survey of the total tons of intercity freight transported by motor carriers.  This includes both large and small truckload carriers, along with less-than-truckload carriers.

Comments from Data Source: American Trucking Association (ATA)

Index Methodology

“ATA has been producing the tonnage index since the early 1970s. The index starts in January 1973 and includes both a not seasonally adjusted (NSA) and a seasonally adjusted (SA) series. The index is set to 2000 equaling 100.0. Each month, ATA asks its membership the amount of tonnage each carrier hauled, including all types of freight. The indexes are then calculated based on those responses.

“The NSA index is assembled by adding up all the monthly tonnage data reported by the survey participants for the two latest months. A monthly percent change is calculated and then applied to the index number for the n-1 month (that is, a 5  percent rise between March and April tonnage reported means the index level for March is increased by 5 percent to calculate the April level.)

“As a policy to protect our participants, the sample size is not distributed and remains confidential. Even though the exact sample composition cannot be published either, the sample does contain a fairly proportional number of carriers to each segment of the industry, including LTL and TL (specialized, refrigerated, flatbed, dry van, and bulk/tank.).”

Data Entry

The current monthly values are copied (entered by keyboard) from the Monthly Truck Tonnage Report, a PDF that BTS receives monthly from ATA through an ATA membership.  The data can also be pulled from the monthly press releases.

FREIGHT: Railroad Monthly Carloads and Intermodals

Name of Series

Rail monthly carloads and intermodal


Two series – carloads and intermodals from
Weekly Railfax Rail Carloading Report, Atlantic Systems Inc.

Source or


At Atlantic Systems: Contact: Mark Schulberg
Phone: (646) 439-2198

Data format

Weekly data

Publication date

Since the data are  weekly, the monthly data are current


One year after latest week


Ton-miles—the movement of one ton of freight one mile.

Intermodal traffic—the movement of truck trailers or containers by
rail and at least one other mode of transportation, usually trucks.

Comments from Data Source:  Atlantic Systems, Inc. (Railfax):

What is Railshare

Railshare is a comprehensive database of North American rail traffic. The data are provided each Thursday by the Association of American Railroads. Atlantic Systems Inc. processes this information and redistributes the data in an easy to use format. Each week's report covers the seven day period ending the preceding Saturday. Rail traffic is disaggregated between carload (traffic moving in traditional freight cars such as box cars, tank cars and hoppers) and intermodal traffic (containers and piggyback service). Railshare provides commodity breakdowns for carload traffic; commodity detail for intermodal traffic is unavailable. Railroads originate and also move traffic jointly with other originating carriers. The carrier totals shown in Railshare aggregate all traffic handled by individual carriers. Market shares are calculated as total handlings by carrier divided by total U.S. originated rail traffic. Railshare graphs show four major breakdowns of rail traffic. Total traffic includes all carload and intermodal traffic; carload traffic is further divided between economically sensitive commodities (cyclical) and those that are less affected by the business cycle (baseline).

Data Entry

The two data series are provided by RailFax, who obtain the weekly rail freight data from AAR.  The website to contact Railfax is:

They provide a weekly report containing US originated total rail carloads and intermodal units. The report (formatted in an Excel file unless otherwise requested) contains data beginning with the first week of the last year (to cover any restatements that are issued) through the current week. The report will be issued on Thursday mornings, usually before 10:00 AM.  Below is an example of the data provided below.  Note that the data are from the RailShare database; ‘Total’ stands for Carload units and ‘TOFC’ stands for Intermodal units – to get the correct data, the request for data must be for the ‘Major US railroads ‘ carloads originated and intermodal units originated.

The weekly carloads and intermodal data are converted to monthly values through the ‘PROC EXPAND” procedure in SAS.

FREIGHT: Waterborne Trade

Name of Series

Monthly Tonnage Indicator for Internal U.S. Waterways


Internal waterway tonnage of coal, petroleum and chemicals, food and farm products, estimated from 11 key locks on 9 rivers


The Waterborne Commerce Statistics Center of the U.S. Army Corps of Engineers produces a monthly report:
Internal U.S. Waterway Monthly Tonnage Indicators, which can be found at:


Contact: Amy Tujague  
Phone: 504-862-1441   

Data format

Millions of short tons, monthly

Publication date

The middle of each month for the data 1 month earlier


The latest 12 months are preliminary


The data do not include waterborne traffic in the Great Lakes, coastal areas or deep-seas.  Data from the 2 MI locks and the 1 OH lock are not representative of the movement south of the MI-OH confluence.

Data Entry

takes you to the Navigation Data Center of the US Army Corps of Engineers.  From this page the link of Total Monthly Indicator takes you to:

From this page the link of Total Monthly Indicator takes you to:


from which the recent monthly data values are pulled.

FREIGHT: Air Revenue Ton Miles

Name of Series

Air Revenue Ton Miles of Freight and Mail (RTMFM)


Ton Miles of freight and mail transported by the air industry


Office of Airline Information (OAI)/  BTS / DOT:
T1 dataset used to produce the monthly Air Carrier Traffic Statistics Monthly


Contact: Jennifer Rodes
Phone: (202) 366-8513

Data format

Unit:  Thousand RTMFM (1 ton = 2000 pounds)

Publication date

Published the end of the month for the data two months earlier




This data currently includes system (domestic + non-domestic) for large certificated carriers (Majors + Nationals + Large and Medium Regionals) providing both scheduled and non-scheduled services)

Data Entry

The data above extracted from the OAIR (restricted) schema on Sybase, maintained by OAI. 

FREIGHT: Pipeline Movement

Name of Series

Pipeline Movement


Movement between PADDs by pipelines  plus Alaska field consumption  (and forecasts)


EIA’s Movements by Pipeline between PAD Districts:
Energy Information Administration (EIA), “Petroleum Supply Monthly,” and “Monthly Energy Review,” (Table 3.1)


Contact: Mike Conner
Phone: (202) 586-1795

Data format

Thousands of barrels

Publication date

Estimates release one month after


Adjustments are used to reconcile the national and PAD District level sums of the State data with the independently estimated U.S. and Alaskan figures shown in Table 3.1 of the Monthly Energy Review and with PAD District level figures published in the Petroleum Supply Monthly from two months earlier. Revised data without adjustments at the State, PAD District, and national levels are available in Navigator upon publication of the Petroleum Supply Annual. All PAD District totals and the U.S. total are estimates. In addition, the following states are estimates: Alaska, Alabama, Arkansas, Colorado, Illinois, Indiana, Michigan, Missouri, Ohio, Oklahoma, New York, Pennsylvania, Texas, Utah, Virginia, West Virginia, and Wyoming. 



Data Entry

The PADD to PADD movement is obtained at the following website:

The data are downloaded and copied from this to the Excel worksheet.

Source data for Alaska pipeline production:
[NB: 2% of Alaskan crude not included.]

Note that there is a table at the bottom of the page (which does include the most recent data). The data can also be pulled from the Excel file; the data are on the second worksheet:

FREIGHT: Natural Gas Consumption

Name of Series

Natural Gas Consumption


Current month consumption of natural gas


Natural gas navigator:



Monthly Energy Review
Contact: Marion King
Phone: (202) 586 - 8800

Data format

Measure Unit: BCF - Billion Cubic Feet

Publication date

Actual end of month for two months back; forecast provide most current month


Two months back are actuals


Estimates of gross withdrawals and marketed production for the lower-48 States are derived from submissions by well operators on the monthly Form EIA-914, “Monthly Natural Gas Production Report.”  Production volumes are collected specifically for Texas, Louisiana, Oklahoma, Wyoming, New Mexico, the Federal Offshore Gulf of Mexico, and the sum of all other States (except Alaska).  Gross withdrawals for the State of Alaska are obtained from summary reports posted by the State of Alaska, Oil and Gas Conservation Commission. Marketed production is estimated from gross withdrawals using historical relationships between the two, while taking into consideration recent disturbances to those relationships.

Data Entry

The data are pulled from the EIA website:

The Custom Table Builder, which can be pulled from the following webpage (at:
from which a table of the natural gas consumption can be built; the row of data would be US Natural Gas Consumption:

PASSENGER: Aviation Revenue Passenger Miles

Name of Series

Air Revenue Passenger Miles


One revenue passenger transported one mile


Office of Airline Information (OAI)/  BTS / DOT:
T1 dataset used to produce the monthly Air Carrier Traffic Statistics Monthly


Contact: Jennifer Rodes
Phone: (202) 366-8513

Data format

Unit:  Thousand RPM

Publication date

Published the end of the month for the data two months earlier




These data currently includes system (domestic + non-domestic) for large certificated carriers (Majors + Nationals + Large and Medium Regionals) providing both scheduled and non-scheduled services

Data Entry

The data above extracted from the OAIR  (restricted) schema on Sybase, maintained by OAI. 

PASSENGER: National Transit Ridership

Name of Series

Estimated unlinked passenger trips


Unlinked passenger trips are defined as the number of passengers who board public transportation vehicles


American Public Transportation Association (APTA)


Contact: Christie Dawson   
phone: 202-496-4848

Data format

Thousands of trips

Publication date

Available the first day of each quarter for the monthly data 2 quarters earlier


The data are revised – the same period, one year prior.  The latest three years are still considered preliminary. 


Does include ridership of commuter rail, heavy rail, light rail and others (e.g.: motor bus, van pools, etc.).

Comments from Data Source: American Public Transportation Association (APTA)


The Public Transportation Ridership Report is a quarterly report of transit passenger ridership for U.S. and Canadian transit agencies.  The report includes quarterly and year-to-date estimated unlinked transit passenger trips for the current and previous year by transit mode.  In addition, agency specific ridership is provided for participating transit agencies.  Reports are published approximately 60-75 days after the end of the quarter.


The data in this report pertain to public transportation agency services operating directly operated (DO) and/or purchased transportation (PT) modes. There are four data items which are reported by public transportation agency participants — average weekday for the current calendar year, monthly totals for the current and past two calendar years. The data items are reported as the number of unlinked passenger trips. Unlinked passenger trips are defined as the number of passengers who board public transportation vehicles. Passengers are counted each time they board vehicles no matter how many vehicles they use to travel from their origin to their destination. Details for each system are only shown if there is data for some or all months in the current year (up to and including the current quarter) and the previous year.

For the rail systems (heavy rail, light rail, commuter rail and trolleybus) that do not report data for the current quarter, it is assumed that the percentage growth for a missing agency or agencies is equal to the percentage growth for the entire category. The national percentage increase for the category is applied to stored data values for any missing agencies in that category and the total estimated count is reflected in the “Projected Total” line on each category page. Responding rail agencies represent 99.9% of ridership in those categories.

Bus agencies are sorted into population groups based on the population of the urbanized area (UZA) that they serve. The ridership numbers for the quarter for these population groups are calculated by taking ridership data from the National Transit Database (NTD) and extrapolating it for the entire population group using the percentage change in ridership experienced by agencies in the population group that reported data to APTA as a base.

Data Entry

The data are pulled from APTA’s PUBLIC TRANSPORTATION RIDERSHIP REPORT, which can be obtained at the following webpage:

By clicking on the link to the summary page of the most recent ridership report, the transit ridership report is obtained.  The total monthly data for the United States are pulled from this report.

PASSENGER: Rail Revenue Passenger Miles

Name of Series

AMTRAK and Alaska RR Corp Passenger Miles


Only the passenger miles from AMTRAK and the Alaska RR Corp are gathered – since the APTA data covers the other passenger railroads


FRA, Office of Safety website, Table 1.02 Operational Data Tables


Mary Beth Butts  202-493-6296

Data format

Passenger mile: the movement of a passenger for a distance of one mile

Publication date

Beginning of month for two months back


The latest 12 months of data are preliminary


Only AMTRAK and Alaska are tracked since they are the largest passenger rail systems; do note that some of  Alaska is included in the APTA numbers.

Data Entry

The link:
takes you to the operational data tables of the Office of Safety Analysis for the Federal Railroad Administration.  The current monthly data for the two railroads are pulled from the Operational Data table 1.02.  From this page, AMTRAK and Alaska RR can be selected (along with the appropriate months):

Seasonal Adjustment

Because the principal purpose of the index is to reflect monthly shifts in transportation services output and analyze short-term trends, the variation introduced by normal seasonal changes must be removed from the data. Transportation is highly seasonal, and without adjustment, the index would not give an accurate picture of underlying changes in transportation output.

The data underlying the TSI are seasonally adjusted using X12-ARIMA, Release 0.21. X12-ARIMA adjusts, when specified, for the effects of trading day, moving holidays, and data outliers and then decomposes the time series into three components: trend (including cyclic phenomena), seasonal, and irregular. By a series of iterative steps, the seasonal effects are isolated and removed from the original data series. In applying this methodology to the transportation services time-series data, we found that each element of the TSI—rail (passenger and freight), pipeline (petroleum and natural gas), transit, waterborne, trucking, and aviation (passenger and freight)—displays strong seasonal patterns and some but not all are affected by trading days and moving holidays. A brief description of trading-day, holiday, and seasonal effects follows along with a description of the models used to seasonally adjust the TSI data series.

Trading-Day, Holiday, and Seasonal Effects


Monthly time series that are totals of daily economic activities are frequently influenced by the weekday composition of the month. Trading-day effects reflect the number of days in the month and the number of times each day of the week occurs in the month, which can affect the monthly totals of output services. Recurring effects associated with weekday composition in monthly (or quarterly) economic time series are called trading-day effects.


Certain kinds of transportation services and their associated time series, such as aviation (passenger and freight), are affected significantly by holidays. Effects from holidays, such as Christmas, that always occur on the same date of a month each year are seasonal components of a time series. Effects associated with holidays that are not always on the same date of a month, such as Labor Day, Thanksgiving, and Easter, are called moving holiday effects.


The seasonal effect in a time series is any effect that is reasonably stable in terms of annual timing, direction, and magnitude. Seasonal adjustment is the process of estimating and removing the seasonal effects from a time series after adjustments have been made for trading days and moving holidays. Because the seasonal effects can disguise important features of economic series such as direction, turning points, and consistency between other economic indicators, seasonal adjustment can also be thought of as focused noise reduction.

Model Specification

The time series data used to create the TSI have varying amounts of historical data. Earlier data are useful for historical purposes, but are of little help in seasonally adjusting data in recent years. Data in the most recent years carry the most weight in seasonal adjustment; data from the beginning of the series have only a marginal impact. For this reason, all time series used in the current (2013) TSI begin at January 2000. This is more than sufficient time to obtain a good seasonal adjustment.

The models for the seasonal adjustment of the TSI inputs are specified in the table below. A multiplicative decomposition was selected, instead of an additive decomposition, when the magnitude of the seasonal variation fluctuated with the level of the series. Trading-day and holiday effects were included in the decomposition, when present with statistical significance, and removed from the original data series. The remaining seasonal component of the data series was removed through the use of an appropriate Autoregressive Integrated Moving Average (ARIMA) model. The ARIMA model describes the relationship between the data points in the time series by decomposing the data into the trend, seasonal, and irregular component.

Models for seasonal adjustment of TSI data inputs

Mode Data points forecasted Model1 Trading days2 and holidays3 Outliers4 ARIMA
Passenger 1 A No TD; Easter[7], Labor Day, Thanksgiving_7 No significant outliers (0,1,1)(0,1,1)
Rail Freight          
Carloads None A No TD; Leap year LS DEC2008; LS APR2009; LS JUL2009; (0,1,1)(0,1,1)
Intermodals None M No TD; Leap year; Easter[7], Memorial Day, Thanksgiving_8, Christmas AO OCT2002; LS MAR2008; LS DEC2008; LS FEB2009  
Trucking None A TD; No holidays LS MAR2000 (2,1,1)(0,1,1)
Waterborne None A No TD; No holidays A JAN2000; AO MAY2011 (0,1,2)(0,1,1)
Transit 3 A TD; No holidays AO MAY2007; LS NOV2008 (0,1,1)(0,1,1)
Freight 1 M TD; Easter[2], Memorial Day, Thanksgiving_8 AO SEP2001; TC OCT2002; LS FEB2004; LS NOV2008; (0,1,2)(0,1,1)
Passenger 1 A No TD; Easter, Labor Day, Thanksgiving_8 AO SEP2001; LS OCT2001; LS DEC2001; AO DEC2002; LS SEP2008 (0,1,1)(0,1,1)
Natural gas None M No TD; Leap year; No holidays AO DEC2000; AO JAN2006; AO FEB2007 (0,1,2)(0,1,1)
Petroleum 1 A No TD; Leap year; No holidays AO SEP2008; AO AUG2009; AO OCT2009 (0,1,2)(0,1,1)

1 M = Multiplicative; A = Additive
2 TD = Trading Days
3 Moving Holidays/Calendar Effects = Easter, Memorial Day, Labor Day, Thanksgiving, and Christmas.
Easter[n] = number of days n before Easter
Easter = Thursday before to Tuesday after (6 days).
Memorial Day = Friday before to the Tuesday after (5 days).
Labor Day = Friday before to Tuesday after (5 days).
Thanksgiving_7 = Tuesday before to Sunday after (7 days)
Thanksgiving_8 = Tuesday before to Monday after (8 days).
If Christmas falls on a Monday = Friday before through Tuesday after (12 days).
If Christmas falls on a Friday = Wednesday through Sunday after (12 days).
If Christmas falls on a Saturday = Wednesday through Sunday after (12 days).
If Christmas falls on a Sunday = Thursday through Monday after (12 days).
4 LS = Level Shift; AO = Automatic Outlier; TC = Temporary Change


For a good overview of the X-11 method, see D. Ladiray and B. Quenneville. Seasonal Adjustment with the X-11 Method. 2001. New York: Springer-Verlag.Ashley, J. D. 2001. Why Seasonal Adjustment – Draft. Washington, D.C.: Bureau of the Census. Available online at

Findley, D. F., Monsell, B. C., Bell, W. R., Otto, M. C., and Chen, B. 1998. New Capabilities and Methods of the X-12-ARIMA Seasonal-Adjustment Program. Washington, D.C.: Bureau of the Census.  Available online at

Hood, C. 2009. Seasonal Adjustment and Time Series FAQ. Nashville, TN: Catherine Hood Consulting. Available online at

Ladiray, D., and Quenneville, B. 2001. Seasonal Adjustment with the X-11 Method. New York: Springer.

Merging energy data

An additional change following the seasonal adjustment calculation (and prior to the indexing step) is the combining of the two energy data series:

Energy Conversion

pipeline (petroleum)
1 barrel (bbl) = 5800000 btu

Natural gas
1 cubic foot = 1023 btu

1 million Btu = .025 ton

Using the conversion factors from EIA’s website, the natural gas and petroleum data are converted into the same units, and then added (after seasonal adjustment), thereby providing the final set of seasonally adjusted series.


Index  Method:

While physical measures are gathered for each mode, ultimately for combination and analysis, the data from the different modes must be converted into an index.  Index numbers characterize the magnitude of change over time.  They describe trends of these changes – and, to do so, index numbers are calculated with respect to a base period.  At this stage of analysis, the seasonally adjusted data are indexed to the base year of 2000 (which are simply the average of the 12 months of 2000 for each of the deseasonalized modal data series).  While the base year of 2000 is many years past, these average annual values for the modal data will shift slightly from month to month due to minor changes in the seasonally adjusted data from month to month.

At this stage of analysis, the rail freight numbers will be combined after the two individual series (carloads and intermodals) have been indexed. AAR has provided annual percentage splits in revenues between carloads and intermodals. By averaging the last 11 years (back to 2000, the beginning of the published TSI), a fixed percent of 19% for intermodals (81% for carloads) was established, by which the two series were combined. 


The final step in the creation of the index numbers is the combining of the individual mode indexes into the three summary indexes: the freight TSI, the passenger TSI, and the overall, or total, TSI. The weighting is based on the relative economic value added of each mode. Not all ton-miles are equivalent in their economic importance, nor are all passenger-miles. For example, the average price paid per ton-mile for freight moved by rail is less than the average price paid per ton-mile for freight shipped by truck due to differences in factors such as haul length, shipment volumes, and resultant economies of scale. By using an economic measure for weighting, we recognize these differences and make the index more valuable as a transportation measure that can be used together with other economic measures, such as GDP.

The weights currently used in the TSI creation come from two sources – the annual GDP value added data, provided by BEA every November in their Survey of Current Business publication, and the annual average of the deseasonalized indexed modal data.  Valued added reflects the volume of physical transportation as well as the value of that volume.  Value added is used for consistency with other indicators that are used in relation to GDP, for example industrial production. By using value added, rather than gross revenues for each sector, we avoid double counting inputs (i.e., diesel fuel) to the transportation sector.

First – let us look at how the value added GDP data are split to match our modal categories.

Splitting GDP into modal categories

The current categories of the value added GDP figures for transportation are:

  • Air transportation
  • Rail transportation
  • Water transportation
  • Truck transportation
  • Transit and ground passenger transportation
  • Pipeline transportation

Whereas the water, truck, pipeline and transit GDP values match categories presently in the TSI, air and rail need to be split into passenger and freight values.  The method to split the air and rail GDP data is to employ the annual passenger and freight revenues for that mode, and to then use these revenues to create percentages to be applied to the value added GDP data. 

For rail, annual operating revenues for rail freight are drawn from the Association of American Railroads, "Railroad Facts," annual editions, "Condensed Income Statement" table.  These freight revenues are also tabulated in the National Transportation Statistics tables, Table 3-22: Total Operating Revenues, for class 1 rail revenues:

The passenger rail is comprised of two rail companies: AMTRAK and Alaska Railroad.  The annual revenues are pulled from the respective company website (in their annual reports):

Another source for the AMTRAK revenues is on the National Transportation Statistics tables, Table 3-22: Total Operating Revenues, for intercity/AMTRAK revenues.  Note that we also include Alaska Rail as a passenger rail – but Alaska Railroad revenues are not captured in the NTS report. 

The aviation revenue split between passenger and freight is calculated by extracting the annual revenue for passenger and cargo airlines through Sybase “TranStats.”

Unit value added GDP calculation

The GDP values are next corrected for ‘double-counting’ by converting to unit value added GDP.  These adjusted value added figures are derived by dividing the modal value added GDP values by an annual value of the modal quantity index.  The reason to create these ‘adjusted’ value added figures,  rather than value added, as the proxy for “price” is because  the unit value added allows the TSI to get rid of the “double counting” effect of the changes in output level that is embodied in the value added of the industry.  In other words, changes in the value added of an industry are a function of changes in price and changes in output.  If value added is directly used as weight for changes in output, changes in output will be “double” counted.

This approach is not unique to the TSI procedure.  The Federal Reserve Board follows a similar procedure in calculating their Industrial Production (IP) Index:

“The ‘price’ weights used in the new IP formulation are annual unit value added, that is, value added (an annual series in dollars) divided by an IP index for the year, Py=vy/Iy.” (taken from: Carrodo, C., C. Gilbert and R. Raddock. “Industrial Production and Capacity Utilization: Historical Revision and recent Developments.” Federal Reserve Board Bulletin, Feb. 1997, p. 67-92,  

The unit value added GDP is simply calculated by dividing the annual GDP numbers by the ‘average annual quantity index,’ which is a 12-month average of the deseasonalized indexed monthly modal values.  These annual values of the modal indexes are then divided into the value added GDP (as calculated in the previous section) to derive the unit value added GDP.

Extending the unit value added GDP

The annual GDP data provide the best values of ‘price’ to create the TSI quantity index – but the annual data have two drawbacks: first, they are annual, and the TSI is monthly; and second, the annual data are about two years behind the current values needed for the TSI.  As can be seen in the above table of GDP values, the annual figures do not extend into the most current year.  Since the TSI is a monthly series, which holds data that contains data that are only two months old, there is a need for more current annual values. 

Several possible procedures for extending these GDP values were explored:

NO CHANGE: Repeat the most recent values for the next two years

PPI CHANGE: Use the annual percent changes in the corresponding values of the producer production index to grow the most recent value of the GDP (The PPI numbers were used in a previous version of the TSI)

10 YEAR CHANGE IN GDP:  Use the average annual change in the GDP value for the last 10 years to grow the most recent value of GDP.

To determine the best fitting approach, a simple forecast experiment was devised.  First, a cut-off in the historical data had to be determined – primarily to establish the most stable period of recent time.  This meant that the years around the most recent recession needed to be avoided, and cutoff should be beyond the 2001 terrorist act (which might have an impact on transportation data).  So the historical values of GDP were terminated at 2002, and a hold-out sample of years 2003 and 2004 was created.  Projections for 2003 and 2004 for each mode were calculated based on the three proposed methods. These projections were then compared to the actuals, and the Mean Absolute Percent Error (MAPE) for each mode was calculated to determine the best fit:

For the ‘No change’ forecasts, the technique was best for 4 of the modes - and never worst.  Therefore the technique of extending the last two years of the GDP values by simply repeating the most recent value was selected as the most appropriate procedure. 

An additional favorable characteristic of employing the same value for the last two years will be evident when theses annual GDP values are interpolated to monthly weights, which is the next section of this documentation.


Up to this point in the calculation, the weights for the TSI index are annual – so the next step in the process is to convert these annual values into monthly weights.  Following the same procedure as the Federal Reserve Board for their IP index (p. 137 in Carrado, C. “Industrial Production and Capacity Utilization: The 2000 Annual revision.” Federal Reserve Board Bulletin, March 2001, p. 132-148,, the annual unit value-added measures are linearly interpolated. 

SAS is employed to perform the linear interpolation, through the JOIN method in Proc EXPAND:

“The JOIN method fits a continuous curve to the data by connecting successive straight line segments. For point-in-time data, the JOIN method connects successive nonmissing input values with straight lines. For interval total or average data, interval midpoints are used as the break points, and ordinates are chosen so that the integrals of the piecewise linear curve agree with the input totals.

For point-in-time output series, the JOIN function is evaluated at the appropriate points. For interval total or average output series, the JOIN function is integrated over the output intervals.” (

The monthly weights for the TSI have now been finalized.  The next step in the documentation is aggregation and chaining.

Aggregation and Chaining

Following the procedure employed by other federal agencies, we utilize the Fisher Ideal Index (also called the Chained Fisher Index) to aggregate and chain the TSI data.   BEA first introduced the chain-type Fisher index into its measures of real output and prices:

“This index, developed by Irving Fisher, is a geometric mean of the conventional fixed-weight Laspeyres index (which uses weights of the first period in a two-period example) and a Paasche index (which uses the weights  of the second period).  Changes in this measure are calculated using the weights of adjacent years.  These annual changes are ‘chained’ (multiplied) together to form a time series that allows for the effects of changes in relative prices and the composition of output over time.” (p. 59-60 in Landefeld, J.S. and R.P. Parker, BEA’s Chain Indexes, Time Series, and Measures of Long-Term Economic Growth. SURVEY OF CURRENT BUSINESS, May 1997, p. 58-68,

The Federal Reserve Board also uses the Fisher Ideal Index in their calculation of the Industrial Production Index:

“As with the earlier formulation, the percentage change in IP can be considered as the value-added weighted sum of the percentage changes in its components…..Specifically, the change in IP for a month is the geometric mean of the change in the aggregate industrial output computed using weights for the previous month; the formula for a monthly IP aggregate is given by

uppercase i uppercase p lowercase m divided by uppercase i uppercase p lowercase m minus 1 is equal to the square root of summation uppercase i lowercase m uppercase p lowercase m minus 1 divided by summation uppercase i lowercase m minus 1 uppercase p minus 1 multiplied by summation uppercase i lowercase m upper case p lowercase m divided by summation uppercase i lowercase m minus 1 uppercase p lowercase m

where pm denotes the monthly unit value added for month m.” (p. 137 in Carrado, C. “Industrial Production and Capacity Utilization: The 2000 Annual revision.” Federal Reserve Board Bulletin, March 2001, p. 132-148,

The following describes the application of the Fisher Ideal Index calculation to the TSI data.

Let p(t) be the monthly unit GDP value added for that mode at time t.  Let p(t-1) be the monthly unit GDP value added for that mode at time t-1.  Let i(t) be the index level at time t.  I(t)*P(t) would  be equal to:

(Ʃ (i(t)*p(t)))/ Ʃp(t),

for all freight modes for Freight TSI, all passenger modes for Passenger TSI and all modes for Total TSI.  Calculate (for Total TSI, Freight TSI and Passenger TSI): Fisher changes:

the square root of upper case i (lowercase t) multiplied by upper case p (lowercase t minus 1) divided by uppercase i (lowercase t-1) multiplied by upper case i (lowercase t) multiplied by uppercase p (lowercase t) dived by uppercase i (lowercase t minus 1) multiplied by uppercase p (lowercase t)

for each month of each index (with the exception of the first month – in our case, January 2000, which is set to 1) – based on Fisher Ideal index.  Then , multiply (or ‘chain’) these ‘Fisher changes’ down through time, so that (for example) February 2000 chained value is the Fisher change for February 2000 times the chained value for January 2000 (which, in this case, is 1).  The March 2000 chained value is the Fisher change for March 2000 times the chained value for February 2000, and so on.  Once the chained values for an Index have been calculated, then that index is rebased to 2000 (taking the average of the 12 months of that chained Index and dividing it into the monthly chained values).  The final index is multiplied by 100 and then rounded to 4 decimals.

For the freight TSI, the following modes are combined: Trucking, Rail Ton Miles, Water tonnage, air ton-miles and combined pipeline.  For the passenger TSI, Air RPM, transit and rail PM are combined.  All modes are combined for the total TSI.  The following provides a graph of all three indexes.

Final Transportation Services Indexes

Aggregating the data as specified in the previous results in three time series: Freight TSI, Passenger TSI and Total TSI.  The following graph illustrates the final work:

Freight Passenger and Total TSI

For a PDF with more detailed documentation, please feel free to contact Dr. Peg Young (202-366-2483 or or Ken Notis (202-366-3576 or ).


X-12-ARIMA was created by the U.S. Department of Commerce, U.S. Census Bureau. (For details on X-12 ARIMA, see: