Updated March 2022

Bureau of Transportation Statistics (BTS)
U.S. Department of Transportation

Introduction

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. 

The Bureau of Transportation Statistics (BTS) supported this research through a research grant on "Leading Economic Indicators for the Transportation Industry."   The research lead to the development of a set of indexes that reflected passenger, freight, and total transportation services output.   The researchers designed these indexes to serve as coincident measures of the transportation sector of the economy and recognized as valuable measures that BTS should produce and provide to the public.

The indexes developed by the researchers became the Transportation Services Index (TSI). The 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 (carloads and intermodal units,
• Inland waterway traffic,
• Pipeline movements (petroleum 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 for-hire:

• 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.

BTS selected these services to cover the services provided by the for-hire transportation industry, subject to current limitations on the availability of monthly data. This document provides insight into the calculation of the TSI, starting with the raw data, seasonal adjustment, indexing, weighting, aggregation and chaining, and final production of the indexes. 

Data

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’ for truck, rail freight (carloads and intermodals), water, air freight and pipeline (petroleum and natural gas) 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 when such monthly data do not exist, BTS uses proxies. 

BTS uses annual data for weights in the index calculation.  BTS uses annual GDP value-added figures by mode and supplements the data with annual revenue data for air (passenger and freight) and rail (passenger and freight). 

Details regarding both the monthly and annual data follow.

Monthly Data

FREIGHT: Truck Tonnage

Name of Series	American Trucking Associations (ATA) Monthly Truck Tonnage Index (NSA)
Explanation	Represents the freight volumes (tonnage) that motor carriers actually reported to ATA and is absent of any adjustment for recurring seasonal factors
Source	ATA Monthly Truck Tonnage Report (subscription service) – BTS receives a hardcopy of the report every month. ATA also publishes the latest month in their press release online: https://www.trucking.org/news-insights
Contact	econdept@trucking.org (link sends e-mail) (703) 838-1700
Data format	Index number, monthly, seasonally unadjusted
Publication date	3rd of every month for the data 2 months earlier
Revisions	The current monthly data are preliminary, and the data for the previous month are revised.  All other data are final.
Comments	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.

Notes on 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. Each month, ATA asks its membership the amount of tonnage each carrier hauled, including all types of freight. ATA calculates the indexes based on those responses.

ATA assembles the NSA index by adding up all the monthly tonnage data reported by the survey participants for the two latest months. ATA calculates the monthly percent change and then applies the change to the index number for the n-1 month (that is, for a 5 percent increase in tonnage between March and April, ATA increases the March level by 5 percent to obtain the April index value).

To protect participants, ATA does not publicize the sample size and keeps the sample confidential. However, ATA says the sample contains a representative number of carriers for each segment of the industry, including LTL and TL (specialized, refrigerated, flatbed, dry van, and bulk/tank.).

Data Entry 

BTS copies (entered by keyboard) the current monthly values from the monthly press releases ATA publishes on their website: https://www.trucking.org/news-insights. The data also are available in ATA’s Monthly Truck Tonnage Report – a subscription service.

FREIGHT: Railroad Monthly Carloads and Intermodals

Name of Series	Rail monthly carloads and intermodal
Explanation	Two series – carloads and intermodals from Association of American Railroads (AAR).
Source	AAR: http://www.aar.org/ (link is external)
Contact	Policy and Economics Department Association of American Railroads Email: policy@aar.org
Data format	Weekly data
Publication date	There is a 1-week lag after the end of the period for the weekly data.
Revisions	One year after latest week
Comments	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.

Data Entry

BTS receives weekly rail freight data directly from AAR. AAR sends BTS a file containing US originated total rail carloads and intermodal units for the current and past year by week.

BTS converts the weekly data to monthly data using the ‘PROC EXPAND” procedure in SAS. This procedure calculates an average daily number from the weekly data and then multiples that number by the number of days of that week that occur in a particular month. The monthly numbers calculated by BTS are different from the monthly numbers published by AAR. AAR assigns each week to a particular month. AAR assigns weeks completely within a particular month to that month and assigns weeks that bridge two months to the month in which more of their days fall. AAR then sums the weekly values assigned to the month. The assignation results in some months having 4 weeks and some having 5 weeks. To create a series of comparable monthly values comparable, AAR additionally averages weekly values for each month.

FREIGHT: Waterborne Trade

Name of Series	Monthly Tonnage Indicator for Internal U.S. Waterways
Explanation	Internal waterway tonnage of coal, petroleum and chemicals, food and farm products, estimated from 11 key locks on 9 rivers
Source	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: https://publibrary.planusace.us/#/series/Commodity%20Monthly%20Indicators
Contact	Contact: U.S. Army Corps of Engineers, Waterborne Statistics Commerce Center Email: ceiwr-ndcwcsc.webmaster@usace.army.mil
Data format	Millions of short tons, monthly
Publication date	The middle of each month for the data 1 month earlier
Revisions	The latest 12 months are preliminary
Comments	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

BTS obtains inland waterborne data from the US Army Corps of Engineers Waterborne Statistics Commerce Center: https://www.iwr.usace.army.mil/About/Technical-Centers/WCSC-Waterborne-Commerce-Statistics-Center-2/. BTS collects data from the waterborne commerce monthly indicator dataset – the all commodity series: https://publibrary.planusace.us/#/series/Commodity%20Monthly%20Indicators

FREIGHT: Air Revenue Ton Miles

Name of Series	Air Revenue Ton Miles of Freight and Mail (RTMFM)
Explanation	Ton miles of freight and mail transported by the air industry
Source	U.S. Department of Transportation, Bureau of Transportation Statistics, Office of Airline Information: T1 dataset used to produce the monthly Air Carrier Traffic Statistics Monthly
Contact	Contact: U.S. Department of Transportation, Bureau of Transportation Statistics https://www.bts.gov/learn-about-bts-and-our-work/contact-us
Data format	Unit:  Thousand RTMFM (1 ton = 2000 pounds)
Publication date	Data for two months earlier published at the end of every month
Revisions
Comments	The data currently include system (domestic + non-domestic) for large certificated carriers (majors + nationals + large and medium regionals) providing both scheduled and non-scheduled services

Data Entry

BTS extracts the data monthly from the internal database maintained by BTS' Office of Airline Information. 

FREIGHT: Pipeline Movement

Name of Series	Pipeline Movement
Explanation	Movement between Petroleum Administration for Defense Districts (PADDs) by pipelines and Alaska field consumption
Source	Energy Information Administration (EIA), Petroleum Supply Monthly, EIA’s Movements of Crude Oil and Petroleum Products by Pipeline between PAD Districts (table 58) and Production of Crude Oil by PAD District and State (table 26): http://www.eia.gov/petroleum/supply/monthly//
Contact	Contact: U.S. Energy Information Administration https://www.eia.gov/about/contact/
Data format	Thousands of barrels
Publication date	Estimates released one month after
Revisions	Not specified.
Comments

Data Entry

BTS collects the data from two tables in the Energy Information Administration’s Petroleum Supply Monthly: EIA’s Movements of Crude Oil and Petroleum Products by Pipeline between PAD Districts (table 58) and Production of Crude Oil by PAD District and State (table 26).

FREIGHT: Natural Gas Consumption

Name of Series	Natural Gas Consumption
Explanation	Consumption of natural gas
Source	Energy Information Administration (EIA), U.S. Natural Gas Consumption: http://www.eia.gov/dnav/ng/hist/n9140us2m.htm EIA Short-term Energy Outlook, Natural Gas Supply, Consumption, and Inventories: https://www.eia.gov/outlooks/steo
Contact	Contact: U.S. Energy Information Administration https://www.eia.gov/about/contact/
Data format	Measure Unit: BCF - Billion Cubic Feet
Publication date	Actual through end of month one month back from the last month in the series used in BTS' TSI; forecast provides estimate for the last month in the series used in BTS' TSI
Revisions	Forecast replaced with actual when it becomes available the following month
Comments	EIA estimates gross withdrawals and marketed production for the lower-48 States from submissions by well operators on the monthly Form EIA-914, “Monthly Natural Gas Production Report.”  EIA collects production volumes specifically for Texas, Louisiana, Oklahoma, Wyoming, New Mexico, the Federal Offshore Gulf of Mexico, and the sum of all other States (except Alaska).  EIA obtains gross withdrawals for Alaska from summary reports posted by the State of Alaska, Oil and Gas Conservation Commission. EIA estimates marketed production from gross withdrawals using historical relationships between the two, while taking into consideration recent disturbances to those relationships.

Data Entry

BTS pulls the data from EIA’s website:

http://www.eia.gov/dnav/ng/hist/n9140us2m.htm

BTS collects an additional month of data - one step ahead from the final month in the above series - from EIA’s Short-term Energy Outlook for Natural Gas Supply, Consumption, and Inventories:  https://www.eia.gov/outlooks/steo/

PASSENGER: Aviation Revenue Passenger Miles

Name of Series	Air Revenue Passenger Miles
Explanation	One revenue passenger transported one mile
Source	U.S. Department of Transportation, Bureau of Transportation Statistics, Office of Airline Information: T1 dataset used to produce the monthly Air Carrier Traffic Statistics Monthly
Contact	Contact: U.S. Department of Transportation, Bureau of Transportation Statistics  https://www.bts.gov/learn-about-bts-and-our-work/contact-us
Data format	Unit:  Thousand RPM
Publication date	Data for two months earlier published the end of every month
Revisions
Comments	The data currently include system (domestic + non-domestic) for large certificated carriers (majors + nationals + large and medium regionals) providing both scheduled and non-scheduled services

Data Entry

BTS extracts the data monthly from the internal database maintained by BTS' Office of Airline Information.

PASSENGER: National Transit Ridership

Name of Series	Estimated unlinked passenger trips
Explanation	Unlinked passenger trips are the number of passengers who board public transportation vehicles
Source	Data for years prior to 2010: Public Transportation Association (APTA) (private nonprofit organization): https://www.apta.com/research-technical-resources/transit-statistics/ridership-report/ Data for years 2010 to present: FTA (Federal Transit Administration)’s NTD (National Transit Database): https://www.transit.dot.gov/ntd.
Contact	Contact (APTA): Matthew Dickens email: mdickens@apta.com Contact (NTD): Federal Transit Administration ntdhelp@dot.gov
Data format	Thousands of trips
Publication date	30 days elapse from the end of the month until transit agencies submit data. Three months elapse before data released to the public.
Revisions	NTD: Transit agencies may revise their data at any time during the calendar year reporting cycle
Comments	Data include ridership on commuter rail, heavy rail, light rail and others (e.g.: motor bus, van pools, etc.).

Data Entry

BTS collected data for years prior to 2010 from the Public Transportation Association (APTA): https://www.apta.com/research-technical-resources/transit-statistics/ridership-report/

For data years 2010 and after, BTS collects data from the Federal Transit Administration's National Transit Database (NTD): https://www.transit.dot.gov/ntd/data-product/monthly-module-adjusted-data-release. BTS selected 2010 as the first year to use the NTD, because 2010 corresponds to the year when collection for the NTD stabilized.

PASSENGER: Rail Revenue Passenger Miles

Name of Series	AMTRAK and Alaska Railroad Corporation Passenger Miles
Explanation	BTS gathers only the passenger miles from AMTRAK and the Alaska Railroad Corporation because the transit data covers the other passenger railroads
Source	Federal Railroad Administration (FRA), Office of Safety website, Table 1.02 Operational Data Tables http://safetydata.fra.dot.gov/OfficeofSafety/
Contact	Contact: Federal Railroad Administration RsisHelpdesk@dot.gov
Data format	Passenger mile: the movement of a passenger for a distance of one mile
Publication date	Beginning of month for two months back
Revisions	The latest 12 months of data are preliminary
Comments	BTS collects only AMTRAK and Alaska, as they are the largest passenger rail systems and other passenger rail systems are part of the transit dataset

Data Entry

BTS pulls the current monthly data for the two railroads from the Operational Data table 1.02: http://safetydata.fra.dot.gov/OfficeofSafety/publicsite/Query/rrstab.aspx published by FRA’s Office of Safety Analysis

Seasonal Adjustment

The principal purpose of the index is to show monthly shifts in transportation services output and analyze short-term trends. To highlight 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.

BTS seasonally adjusts the data underlying the TSI using X12-ARIMA: https://data.bts.gov/Research-and-Statistics/Transportation-Services-Index-and-Seasonally-Adjus/bw6n-ddqk. X12-ARIMA adjusts, when specified, for the effects of trading days, 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, X12-ARIMA isolates and removes the seasonal effects from the original data series. In applying this methodology to the transportation services time-series data, BTS 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 trading days and moving holidays affects some but not all series. A brief description of trading-days, moving holidays, 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

Trading-Day

The weekday composition of the month frequently affects monthly time series that are totals of daily economic activities. 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.

Holiday

Holidays affect certain kinds of transportation services, such as aviation (passenger and freight). 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 and thereby captured without any additional specification in the seasonal adjustment model. Moving holiday effects are effects associated with holidays  occurring on a different date each year, such as Labor Day, Thanksgiving, and Easter. These types of holidays can affect the month prior to the holiday, the month of the holiday, and the month after the holiday differently each year, depending on when the holiday occurs. For this reason, moving holidays must be included as an additional parameter in the seasonal adjustment model. Not all moving holidays may affect a particular data series.

Seasonal 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 adjusting for trading days and moving holidays. Because seasonal effects can disguise important features of a data series, such as direction, turning points, and consistency between other economic indicators, seasonal adjustment also can 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 less useful 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, the TSI begins at January 2000, although data from January 1979 are available.

BTS publishes the details of the models used to seasonally adjust the TSI in this Excel workbook. BTS selected a multiplicative decomposition, instead of an additive decomposition, when the magnitude of the seasonal variation fluctuated with the level of the series. BTS included trading-day and holiday effects in the seasonal adjustment model, when present with statistical significance, and thereby removed these effects from the original data series. The seasonal adjustment model removed the remaining seasonal component of the data series 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

https://data.bts.gov/api/views/bw6n-ddqk/files/b336c34b-84de-4881-aa3f-0f168d90bc19?download=true&filename=SeasonalAdjustmentModels_Documentation.xls

Merging energy data

BTS merged the pipeline petroleum and natural gas data series after seasonally adjusting each. Because the two series are in different units, BTS applied the following energy conversion and then added the two series together.

Energy Conversion:

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

Natural gas
1 cubic foot = 1023 btu

combined:
1 million Btu = .025 ton

Indexing

Index numbers characterize the magnitude of change over time.  They describe trends of these changes with respect to a base period.  BTS calculates the average of the 12 months in 2000 for each of the deseasonalized series and uses it as the base.  Using 12 months means any change in the index is with respect to the 2000 annual average.

After indexing, BTS combines the two rail freight series (carloads and intermodals). AAR provides annual percentage splits in revenues between carloads and intermodals from 2000 to 2011. BTS averages the 11 years of data to obtain weights for combining the two rail freight series. Intermodals account for, on average, 19 percent of rail revenue and carloads account for, on average, 81 percent.

Weighting

In the final step, BTS combines the individual mode indexes into the three summary indexes: the freight TSI, the passenger TSI, and the overall, or total, TSI. To combine the series, BTS uses weights 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, BTS recognizes these differences. Additionally, in using economic weights, the resultant indexes potentially may be used as economic indicators.

The weights used in the TSI creation come from two sources – annual  value added data by industry, published by BEA on their website, and the annual average of the deseasonalized indexed modal data.  Value added is an industry's gross output (sales or receipts and other operating income, commodity taxes and inventory change) minus its intermediate inputs (consumption of goods and services purchased from other industries or imported). For transportation industries, it reflects the volume of physical transportation as well as the value of that volume.  The sum of the value added by transportation and non-transportation industries equals gross domestic product (GDP) – a measure of all output in the economy. BTS uses value added so that modes contributing more to the economy receive a higher weight in the index. This enables comparison of the index to other economic indicators that reflect economic activity, such as industry production. By using value added, rather than gross revenues for each sector, BTS additionally avoids double counting inputs (i.e., diesel fuel) to the transportation sector.

The following describes how BTS split value added data to match the modes included in the TSI.

Splitting GDP into modal categories

BEA publishes the value added by each of the following transportation industries:

• 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 modes in the TSI, air and rail need to be split into passenger and freight values.  BTS splits the air and rail value added data by using annual passenger and freight revenues for that mode. BTS uses these revenues to estimate the percent attributed to freight and passenger and then applies these percentages to the total value added by the mode.

For rail, passenger rail revenue consists of AMTRAK and Alaska Railroad.  BTS pulls the annual revenue from annual reports published on the website of each company:

https://www.amtrak.com/reports-documents
https://www.alaskarailroad.com/corporate/leadership/reports

BTS publishes the data for AMTRAK in the National Transportation Statistics, table 3-22 (Total Operating Revenues)

For air, BTS pulls annual revenue for passenger and cargo airlines from air carrier financial reports collected by BTS’ Office of Airline Information. Large U.S. certificated air carriers, small certificated air carriers, and commuter air carriers must complete Form 41 Financial and Traffic Reporting Requirements and provide the data to BTS. BTS includes revenue from the following account types:

Passenger Account Codes	Freight Account Codes
39010 – Transport Revenue Passenger	39061 – Property Freight
39071 – Charter Passenger	39072 – Charter Property
39062 – Property Excess Passenger Baggage	39050 – Mail

Unit value added calculation

BTS next converts the value added data to unit value added.  BTS divides the modal value added number by the average of the seasonally-adjusted monthly indexed values for the same mode.  BTS uses these ‘adjusted’ value added figures to remove the  effect of changes in output level captured in total value added (changes in value added are a function of changes in price and changes in output).  If BTS used value added directly, changes in output will be “double” counted – counted by changes in indexed values and counted by changes in value added.

This approach is not unique to the TSI.  The Federal Reserve Board follows a similar procedure in calculating their Industrial Production (IP) Index. For the 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, http://www.federalreserve.gov/pubs/bulletin/1997/0297lead.pdf (link is external)

Extending the unit value added

The annual value added data have two drawbacks: first, they are annual, and the TSI is monthly; and second, the annual data are about one year behind the current values needed for the TSI.  BTS explored several possible procedures for extending the value added data:

• NO CHANGE: Repeat the most recent values for the next year.
• PPI CHANGE: Use the annual percentage changes in the producer production index to estimate the most recent value added numbers.
• 10 YEAR CHANGE IN GDP:  Use the average annual change in the GDP value for the last 10 years to estimate the most recent value added numbers.

To determine the best approach, BTS forecasted value added using historical data and compared the estimated value added to the actual.  First, BTS established a cut-off in the historical data  and selected the most recent stable years to estimate.  BTS avoided estimating years during the 2007 to 2009 recession and additionally 2001 (the September 2001 terrorist act  impacted transportation data).  BTS selected data through 2002 and estimated 2003 and 2004. BTS forecasted the value for 2003 and 2004 based on the three proposed methods, compared to the actual, and calculated the Mean Absolute Percent Error (MAPE) for each mode to determine the best fit.

The ‘no change’ technique was best for four of the modes and never worst.  Therefore, BTS selected the ‘no change’ technique of extending the last two years of the GDP values. 

Up to this point in the calculation, the weights for the TSI index are annual. The next step involves converting these annual values into monthly weights.  BTS follows the same procedure as the Federal Reserve Board for their industrial production index (p. 137 in Carrado, C. “Industrial Production and Capacity Utilization: The 2000 Annual revision.” Federal Reserve Board Bulletin, March 2001, p. 132-148, http://www.federalreserve.gov/pubs/bulletin/2001/0301scnd.pdf (link is external) and linearly interpolates the annual unit value-added measures.

BTS uses SAS to perform the linear interpolation, through the JOIN method in Proc EXPAND.

The output of the procedure are monthly weights.

Aggregation and Chaining

Following the procedure employed by other federal agencies, BTS utilizes 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, https://apps.bea.gov/scb/account_articles/national/0597od/maintext.htm

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 [industrial production] 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”  (p. 137 in Carrado, C. “Industrial Production and Capacity Utilization: The 2000 Annual revision.” Federal Reserve Board Bulletin, March 2001, p. 132-148, http://www.federalreserve.gov/pubs/bulletin/2001/0301scnd.pdf (link is external)

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:

 

for all freight modes for Freight TSI, all passenger modes for Passenger TSI and all modes for Total TSI.  BTS calculated Fisher changes:

   

for each month of each index (with the exception of the first month – January 2000 – which is set to 1) – based on Fisher Ideal index.  BTS then multiplies (or ‘chains’) these ‘Fisher changes’ down through time, so that (for example) the 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.  BTS then rebases the index to 2000 by taking the average of the 12 months of that chained Index and dividing it into the monthly chained values, multiplied by 100, and rounds to 4 decimal places. 

The freight TSI combines the following modes: trucking, rail ton miles, water tonnage, air ton-miles and combined pipeline.  The passenger TSI combines air revenue passenger miles, transit, and rail passenger miles.  The combined or total TSI combines all modes.  

For a PDF with more detailed documentation, please feel free to contact Ken Notis (202-366-3576 or ken.notis@dot.gov).

 

References

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 http://www.catherinechhood.net/WhySeasAdj.pdf.

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 https://www.census.gov/content/dam/Census/library/working-papers/1998/adrm/jbes98.pdf.

Hood, C. 2009. Seasonal Adjustment and Time Series FAQ. Nashville, TN: Catherine Hood Consulting. Available online at http://www.catherinechhood.net/safaqmain.html.

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

Footnotes

X-12-ARIMA was created by the U.S. Department of Commerce, U.S. Census Bureau. (For details on X-12 ARIMA, see: https://www.census.gov/data/software/x13as.html