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The 2007 TSI Bi-annual Revision

The 2007 TSI Bi-annual Revision

The 2007 Annual Revision is performed in order to incorporate changes in methodology, revisions to the raw data (including changes in data sources), and changes in estimated weights and seasonal adjustment parameters. The Transportation Services Index (TSI) revision policy was adopted in November 2004 to balance the goals of providing the most accurate and up-to-date measure and month-to-month stability. Prior to November 2004, all data points were revised with each monthly release- in a process characterized by small but frequent changes to previously published values of the indexes. The new policy achieves greater stability by limiting changes in each data point between Annual Revisions to one revision in the fourth month after its initial release. The Annual Revision allows for the latest methodological research and improvements in source data to be incorporated in a systematic way and also ensures that historical data reflects recent revisions to both the raw data and to the estimated weights and seasonal adjustment parameters. This document identifies the methodological changes that have occurred since the 2005 Annual Revision, serves as a reference for those changes, and conducts a detailed analysis of the effects on the TSIs of changes in the raw data, seasonal adjustment factors and weights. Although the original plan was to systematically revise the TSI once a year, there was no revision performed in 2006, so this years Annual Revision includes changes that have occurred since the 2005 Annual Revision.

METHODOLOGICAL CHANGES

The 2007 Annual Revision includes three methodological changes and one change in the source data. The major methodological change is the advancement by one month of the most recent index data published with each release. The second methodological change is the modification of the models used to seasonally adjust individual modal series (largely the addition of Trading Day effects to several series.) The other changes involve the weights used to combine modes into the aggregated TSI. The first change to the weights involves a modification of the formula used to convert annual value-added weights from the Bureau of Economic Analysis (BEA) into monthly weights. The new formula provides a smoother change in the weights between one year and the next and is specified in the documentation on aggregating the TSI and in the appendix to this document. The change in the source data is a switch in the Producer Price Index (PPI) used to estimate weights for months subsequent to those for which BEA value-added data is available. The change is from the PPI for natural gas distribution, primary products (series id. PCU221210221210P) to the PPI for natural gas distribution, delivered to ultimate consumers for the account of others (transportation only) (series id. PCU22121022121012). The change was made to better reflect the transportation component of natural gas and reduce the variability of the series. The only previous methodological change to the TSI was to change the base year from 1996 to 2000. The base year was changed in order to provide a more meaningful reference to the most recent data since the most recent data is of greatest concern to analysts.

Methodological or Source Data Changes to the TSI

Excel | CSV

Year of implementation Change
2007 Seasonal adjustment models:
(i.e., models specified in
http://www.bts.gov/programs/economics_and_finance/transportation_services_index/methodology/)
Rail Freight Intermodal: added Trading Days
Waterborne: added Labor Day effects
Transit: added Trading Days.
Aviation Passenger: added Trading Days.
2007 Formula for conversion of BEA value-added annual values to monthly values.
2007 Change BLS PPI for natural gas
from PCU221210221210P
to PCU22121022121012
2006, March release of January 2006 data. Advancement by one month of most recent index data published with each release.
2005 Changed base year to 2000 from 1996.

DETAILED ANALYSIS OF CHANGES IN THE TSIs DUE TO THE ANNUAL REVISION

Overview

The analysis of the effects of the Annual Revision decomposes changes in each TSI index (Freight, Passenger, and Combined) into changes in the source data, changes in seasonal adjustment factors, and changes in weighting factors/methodology. The reference points used for the analysis are the TSI numbers that were revised 4 months after their initial release, but a summary of changes to the TSIs between the initial release and the 4-month revision is provided in the appendix. In what follows, we use final to refer to the latest data, seasonal factors, and methodology as of the Annual Revision and original to refer to these components as of the 4-month revision for each TSI release. For example, the preliminary TSIs for December 2006 were initially released in February 2007 and were revised with the June 2007 release of the TSI (Original) and then were revised again with the July 2007 annual revision (Final). The analysis in this section with respect to the December 2006 TSIs refers to changes to the December 2006 TSIs from the June 2007 release.

The basic model for analysis is given below:

Let t = 1,.., 204 index the months between January, 1990 and December 2006.

Let uppercase t superscirpt{0} subscript{lowercase t} be the TSI index published in June 2007, without the Annual Revision.

Let uppercase t superscript {uppercase a uppercase r} subscript {lowercase t} be the TSI index following the Annual Revision. (Note that changes in the source data after the 4-month revision will not be reflected in uppercase t superscirpt{0} subscript{lowercase t}in the monthly releases following the 4-month but before the annual revision.)

Let uppercase t superscript {uppercase f uppercase s uppercase d} subscript {lowercase t}be the TSI index compiled using the final source data, but the same seasonal factors and weights/methodology as in uppercase t superscirpt{0} subscript{lowercase t}.

Let uppercase t superscript {uppercase f uppercase s  uppercase f} subscript {lowercase t}be the TSI index compiled using both the final source data and the final seasonal factors, but the weights/methodology as in uppercase t superscirpt{0} subscript{lowercase t}.

Then the following measures decompose the proportional changes in the TSI due to changes in the source data, seasonal adjustment factors, and weighting factors:

δt(delta) measure data changes,

ψt(psi) measure seasonal adjustment factor changes,

ωt(omega) measure weighting factor changes.

Where the following relations hold:

lowercase delta subscript {lowercase t} is equal to uppercase t superscript {uppercase f uppercase s uppercase d} subscript {lowercase t} over uppercase t superscript {0} subscript {lowercase t}

lowercase psi subscript {lowercase t} is equal to uppercase t superscript {uppercase f uppercase s uppercase f} subscript {lowercase t} over uppercase t superscript {uppercase f uppercase s uppercase d} subscript {lowercase t}

lowercase omega subscript {lowercase t} is equal to uppercase t superscript {uppercase a uppercase r} subscript {lowercase t} over uppercase t superscript {uppercase f uppercase s uppercase f} subscript {lowercase t}

uppercase t superscript {uppercase a uppercase r} subscript {lowercase t} is equal to lowercase delta subscript {lowercase t} dot lowercase psi subscript {lowercase t} dot lowercase omega subscript {lowercase t} dot uppercase t superscript {0} subscript {lowercase t}

The impact of Source Data Revisions on the TSIs

Data revisions received during the calendar year for each TSI component change the individual index numbers as well as the overall index. First, these revisions change the index numbers of the individual months for which source data were revised. Second, the source data revisions change index numbers for other months through their effects on the estimation of the seasonal adjustment factors, which potentially affects all numbers in the index. Third, revisions to the source data also affect the weights due to the influence on adjusted value-added. In this section we look at the effects of the first of these changes.

Table 1 shows the impact of data source revisions before seasonal adjustment. Revisions in the source data generally have a greater impact on the TSI for recent years. The largest upward revisions in the TSI indexes were: 1.48 percent for Freight in May 2006, 1.18 percent for Passenger in November 2000, and 0.77 percent for the combined TSI in May 2006. The largest downward revisions were: 0.73 percent for Freight in December 1994, 1.25 percent for Passenger in July 2005, and 0.63 percent for the Combined TSI in March 2005. The large downward revisions that occurred in the earlier years are an exception to the general pattern as two of the modal data sources conducted historical updates. Averages over the last two years for percentage changes due to source data revision were; an upward revision of 0.48 percent for Freight, a downward revision of 0.47 percent for Passenger, and an upward revision of 0.16 percent for the Combined TSI.

Table 1. Percentage Changes in the TSIs due to Revisions in the Source Data

Excel | CSV

Date Freight Passenger Combined
Dec-06 1.33 −0.68 0.67
Nov-06 1.33 −0.51 0.72
Oct-06 1.30 −0.63 0.67
Sep-06 1.32 −0.64 0.68
Aug-06 1.34 −0.59 0.71
Jul-06 1.29 −0.84 0.48
Jun-06 1.46 −0.30 0.75
May-06 1.48 −0.29 0.77
Apr-06 1.02 −0.55 0.39
Mar-06 0.61 0.54 0.56
Feb-06 0.38 0.53 0.41
Jan-06 0.00 0.71 0.24
Dec-05 0.24 −0.40 0.05
Nov-05 0.20 −0.13 0.10
Oct-05 0.24 −1.16 −0.15
Sep-05 0.05 −0.35 −0.07
Aug-05 0.32 −0.24 0.15
Jul-05 −0.23 −1.25 −0.52
Jun-05 −0.27 −0.46 −0.33
May-05 −0.52 −0.49 −0.51
Apr-05 −0.41 −0.53 −0.45
Mar-05 −0.50 −0.92 −0.63
Feb-05 −0.31 −0.87 −0.48
Jan-05 −0.06 −1.13 −0.37
Summary January 2005-December 2006      
Average 0.48 −0.47 0.16
Minimum −0.52 −1.25 −0.63
Date of Min May-05 Jul-05 Mar-05
Maximum 1.48 0.71 0.77
Date of Max May-06 Jan-06 May-06
Summary of Prior Years:      
January 2002-December 2004      
Average −0.10 −0.15 −0.12
Minimum −0.63 −0.74 −0.49
Date of Min Sep-04 Apr-02 Sep-04
Maximum 0.01 0.89 0.20
Date of Max Aug-04 Sep-02 Sep-02
January 1990-December 2001      
Average −0.01 −0.13 −0.04
Minimum −0.73 −1.17 −0.62
Date of Min Mar-91 Apr-00 Mar-91
Maximum 0.11 1.18 0.38
Date of Max Mar-01 Nov-00 Nov-00

Source: Bureau of Transportation Statistics

Impact of Revisions to Weights and Methodology on the TSIs

The weights for the TSI are used to combine the output indexes of the nine component transportation services into aggregated indexes, namely the Freight TSI, the Passenger TSI and the Combined TSI. The weights for each service are based on the adjusted value-added 1 for the service and determine the relative importance of the individual modes that comprise each TSI. The relative importance of the individual modal freight services for the most recent year, from highest to lowest, was: Trucking, Rail, Inland Water, Aviation, Pipeline-Petroleum, and Pipeline-Liquefied Natural Gas. The relative importance of individual modal passenger services for the most recent year, also from highest to lowest, was: Aviation, Public Transit, and Rail. Freight comprises about three-fourths of the combined TSI, or about three times the weight of Passenger. The primary data sources for the TSI weights are the estimates of Gross Domestic Product (GDP) by industry produced by the Bureau of Economic Analysis (BEA). Weights are also estimated for splits of modal GDP among different services for aviation, rail, and pipelines (in particular, aviation freight service versus passenger service, railroad carload service versus intermodal service, and petroleum products versus natural gas). Revisions in weights are due to updates and revisions to the BEA and modal source data. Holding constant the component services, the TSI will tend to increase when the estimated weight of a faster-growing service increases, and vice versa.

In addition to changes in the source data for the weights, there was also a change in methodology for the interpolation of the weights from annual to monthly values, and in the producer-price index used to extrapolate weights for months after the latest value-added data is available. The change in methodology is given in detail in the appendix, but the basic purpose of the change is to remove the potential addition of seasonal variability to the index due to the weights and to reduce the December-January effect inherited from the changes in the annual value-added data from BEA.

Table 2 shows changes in the weights/methodology did not affect the TSI with a particular time pattern, but instead had some impact over the entire span of the index. Percentage upward revisions in the Freight and Passenger TSIs were greatest in the earlier years with averages of 0.71 and 0.18 percent over the 1990-2001 period. In contrast, for the Combined TSI, the greatest impact due to changes in weights/methodology was for the latest two years, with an average 0.64 percent downward revision. Revisions to the BEA value-added data were only for the most recent years, so changes for the earlier years can be attributed to methodological changes. It is also worthy of note that half of the extreme changes in the TSI for the three subperiods occur for the months of December and January because one objective of the methodological change was to smooth the impact of the introduction of new value-added data on the TSIs for December and January.

Table 2. Percentage Changes in the TSIs due to Changes in Weights/Methodology

Excel | CSV

Date Freight Passenger Combined
Dec-06 −0.52 0.10 −0.81
Nov-06 −0.55 0.09 −0.83
Oct-06 −0.58 0.09 −0.86
Sep-06 −0.85 0.06 −1.08
Aug-06 −0.54 0.05 −0.85
Jul-06 −0.45 0.06 −0.68
Jun-06 −0.47 0.04 −0.53
May-06 −0.55 −0.01 −0.71
Apr-06 −0.53 −0.02 −0.94
Mar-06 −0.58 0.02 −0.89
Feb-06 −0.51 0.04 −0.74
Jan-06 −0.23 0.14 −0.41
Dec-05 −0.60 −0.08 −0.63
Nov-05 −0.37 0.02 −0.40
Oct-05 −0.40 0.03 −0.47
Sep-05 −0.32 0.03 −0.45
Aug-05 −0.50 0.02 −0.53
Jul-05 −0.59 0.01 −0.63
Jun-05 −0.53 −0.01 −0.57
May-05 −0.50 −0.06 −0.55
Apr-05 −0.47 0.05 −0.47
Mar-05 −0.46 −0.01 −0.47
Feb-05 −0.43 0.04 −0.42
Jan-05 −0.48 0.07 −0.40
Summary January 2005-December 2006      
Average −0.50 0.03 −0.64
Minimum −0.85 −0.08 −1.08
Date of Min Sep-06 Dec-05 Sep-06
Maximum −0.23 0.14 −0.40
Date of Max Jan-06 Jan-06 Nov-05
Summary of Prior Years:      
January 2002-December 2004      
Average −0.16 0.15 −0.19
Minimum −0.47 −0.04 −0.44
Date of Min Dec-04 Jan-02 Oct-04
Maximum 0.11 0.24 −0.02
Date of Max Sep-02 Dec-02 Sep-02
January 1990-December 2001      
Average 0.71 0.18 0.03
Minimum −0.27 −0.35 −0.65
Date of Min Jan-98 Sep-01 Dec-94
Maximum 2.84 0.62 1.12
Date of Max May-90 Mar-91 Jan-90

Source: Bureau of Transportation Statistics

Impact of Changes in Seasonal Adjustment Factors on the TSIs

The 2007 Annual Revision incorporates changes in both the methodology for estimating seasonal adjustment factors and the effects on estimated seasonal factors due to revisions in the source data 2.

The impact of changes in the estimated factors is presented in Table 3. The greatest upward revisions due to changes in the estimated seasonal factors were: 0.15 percent for Freight in February, 0.59 percent for Passenger in April, and 0.20 percent for the Combined TSI in February. The greatest downward revisions were: 0.17 percent for Freight in August, 0.21 percent for Passenger in November, and 0.08 percent for the Combined TSI in August.

Table 3. Average Percentage Change in TSI due to Changes in Seasonal Factors by Month (1990-2006)

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Month Freight Passenger Combined
January −0.01 0.53 0.13
February 0.15 0.36 0.20
March 0.07 −0.06 0.03
April −0.05 0.59 0.13
May −0.08 0.09 −0.03
June −0.07 0.02 −0.05
July −0.05 0.07 −0.02
August −0.17 0.15 −0.08
September −0.02 −0.07 −0.04
October 0.02 0.06 0.04
November 0.08 −0.21 −0.01
December 0.06 0.34 0.14

Source: Bureau of Transportation Statistics

Impact of Changes in Source Data, Seasonal Adjustment Factors, and Weights/Methodology by Type of Service on the TSI.

The previous three tables are organized by the components of change while this section gives the components of change by type of transportation service. The organization in this section highlights the relative contributions of each component of change. The pattern is broadly similar across the three indexes with changes due to source data revisions having the greatest relative impact for the latest years while changes due to revisions to the weights/methodology have the greatest relative impact in the earliest years. There is also a consistent inverse relation between changes due to source data revisions and changes due to revisions in the estimated seasonal factors. The inverse relation is expected as increases (decreases) in the source data for a given month will require greater adjustment in the opposite direction to smooth changes across months.

Table 4. Freight TSI - Percentage Changes Due to:

Excel | CSV

Date Changes
in Source Data
Changes
in Seasonal
Factors
Changes
in Weights/
Methodology
All Charges
Dec-06 1.33 −0.01 −0.52 0.79
Nov-06 1.33 −0.01 −0.55 0.76
Oct-06 1.30 0.05 −0.58 0.76
Sep-06 1.32 0.04 −0.85 0.51
Aug-06 1.34 −0.06 −0.54 0.73
Jul-06 1.29 −0.18 −0.45 0.66
Jun-06 1.46 −0.23 −0.47 0.74
May-06 1.48 −0.21 −0.55 0.70
Apr-06 1.02 −0.11 −0.53 0.38
Mar-06 0.61 −0.26 −0.58 −0.23
Feb-06 0.38 0.32 −0.51 0.20
Jan-06 0.00 0.60 −0.23 0.37
Dec-05 0.24 0.35 −0.60 −0.02
Nov-05 0.20 0.78 −0.37 0.61
Oct-05 0.24 −0.01 −0.40 −0.16
Sep-05 0.05 −0.09 −0.32 −0.36
Aug-05 0.32 −0.31 −0.50 −0.49
Jul-05 −0.23 −0.39 −0.59 −1.21
Jun-05 −0.27 −0.42 −0.53 −1.21
May-05 −0.52 −0.29 −0.50 −1.31
Apr-05 −0.41 −0.20 −0.47 −1.08
Mar-05 −0.50 0.10 −0.46 −0.85
Feb-05 −0.31 0.82 −0.43 0.08
Jan-05 −0.06 0.26 −0.48 −0.28
January 2005-December 2006        
Average 0.48 0.02 −0.50 0.00
Minimum −0.52 −0.42 −0.85 −1.31
Date of Min May-05 Jun-05 Sep-06 May-05
Maximum 1.48 0.82 −0.23 0.79
Date of Max May-06 Feb-05 Jan-06 Dec-06
Prior Years:        
January 2002-December 2004        
Average −0.10 −0.01 −0.16 −0.27
Minimum −0.63 −0.46 −0.47 −1.11
Date of Min Sep-04 Aug-03 Dec-04 Jun-04
Maximum 0.01 0.50 0.11 0.20
Date of Max Aug-04 Feb-04 Sep-02 Jan-02
January 1990-December 2001        
Average −0.01 −0.01 0.71 0.69
Minimum −0.73 −0.40 −0.27 −0.43
Date of Min Mar-91 Aug-01 Jan-98 Oct-97
Maximum 0.11 0.26 2.84 3.01
Date of Max Mar-01 Mar-94 May-90 May-90

Source: Bureau of Transportation Statistics

Table 5. Passenger TSI - Percentage Changes Due to:

Excel | CSV

Date Changes
in Source Data
Changes
in Seasonal Factors
Changes
in Weights/
Methodology
All Changes
Dec-06 −0.68 0.12 0.10 −0.46
Nov-06 −0.51 −0.05 0.09 −0.47
Oct-06 −0.63 0.22 0.09 −0.32
Sep-06 −0.64 0.10 0.06 −0.48
Aug-06 −0.59 0.18 0.05 −0.36
Jul-06 −0.84 0.47 0.06 −0.32
Jun-06 −0.30 −0.23 0.04 −0.48
May-06 −0.29 0.44 −0.01 0.14
Apr-06 −0.55 0.64 −0.02 0.07
Mar-06 0.54 −0.29 0.02 0.27
Feb-06 0.53 0.82 0.04 1.39
Jan-06 0.71 −0.19 0.14 0.66
Dec-05 −0.40 −0.07 −0.08 −0.54
Nov-05 −0.13 0.05 0.02 −0.05
Oct-05 −1.16 0.74 0.03 −0.39
Sep-05 −0.35 −0.05 0.03 −0.37
Aug-05 −0.24 0.83 0.02 0.61
Jul-05 −1.25 0.32 0.01 −0.92
Jun-05 −0.46 0.36 −0.01 −0.12
May-05 −0.49 −0.17 −0.06 −0.72
Apr-05 −0.53 −0.27 0.05 −0.75
Mar-05 −0.92 0.11 −0.01 −0.82
Feb-05 −0.87 2.41 0.04 1.56
Jan-05 −1.13 0.66 0.07 −0.40
January 2005-December 2006        
Average −0.47 0.30 0.03 −0.14
Minimum −1.25 −0.29 −0.08 −0.92
Date of Min Jul-05 Mar-06 Dec-05 Jul-05
Maximum 0.71 2.41 0.14 1.56
Date of Max Jan-06 Feb-05 Jan-06 Feb-05
Prior Years:        
January 2002-December 2004        
Average −0.15 0.13 0.15 0.12
Minimum −0.74 −1.05 −0.04 −1.42
Date of Min Apr-02 Feb-04 Jan-02 Feb-04
Maximum 0.89 1.68 0.24 1.45
Date of Max Sep-02 Feb-03 Dec-02 Feb-03
January 1990-December 2001        
Average −0.13 0.14 0.18 0.19
Minimum −1.17 −2.74 −0.35 −2.88
Date of Min Apr-00 Feb-96 Sep-01 Feb-96
Maximum 1.18 1.29 0.62 1.84
Date of Max Nov-00 Feb-90 Mar-91 Dec-01

Source: Bureau of Transportation Statistics

Table 6. Combined TSI - Percentage Changes Due to:

Excel | CSV

Date Changes
in Source Data
Changes
in Seasonal Factors
Changes
in Weights/
Methodology
All Changes
Dec-06 0.67 0.18 −0.81 0.04
Nov-06 0.72 0.14 −0.83 0.02
Oct-06 0.67 0.25 −0.86 0.05
Sep-06 0.68 0.22 −1.08 −0.19
Aug-06 0.71 0.16 −0.85 0.01
Jul-06 0.48 0.15 −0.68 −0.06
Jun-06 0.75 −0.13 −0.53 0.09
May-06 0.77 0.13 −0.71 0.19
Apr-06 0.39 0.28 −0.94 −0.28
Mar-06 0.56 −0.18 −0.89 −0.51
Feb-06 0.41 0.61 −0.74 0.27
Jan-06 0.24 0.40 −0.41 0.23
Dec-05 0.05 0.27 −0.63 −0.31
Nov-05 0.10 0.62 −0.40 0.32
Oct-05 −0.15 0.23 −0.47 −0.40
Sep-05 −0.07 −0.05 −0.45 −0.57
Aug-05 0.15 0.02 −0.53 −0.36
Jul-05 −0.52 −0.17 −0.63 −1.32
Jun-05 −0.33 −0.18 −0.57 −1.08
May-05 −0.51 −0.24 −0.55 −1.30
Apr-05 −0.45 −0.20 −0.47 −1.12
Mar-05 −0.63 0.12 −0.47 −0.98
Feb-05 −0.48 1.29 −0.42 0.39
Jan-05 −0.37 0.39 −0.40 −0.38
January 2005-December 2006        
Average 0.16 0.18 −0.64 −0.30
Minimum −0.63 −0.24 −1.08 −1.32
Date of Min Mar-05 May-05 Sep-06 Jul-05
Maximum 0.77 1.29 −0.40 0.39
Date of Max May-06 Feb-05 Nov-05 Feb-05
Prior Years:        
January 2002-December 2004        
Average −0.12 0.04 −0.19 −0.27
Minimum −0.49 −0.33 −0.44 −0.93
Date of Min Sep-04 Jul-04 Oct-04 Jun-04
Maximum 0.20 0.72 −0.02 0.37
Date of Max Sep-02 Feb-03 Sep-02 Feb-03
January 1990-December 2001        
Average −0.04 0.01 0.03 0.00
Minimum −0.62 −0.85 −0.65 −1.19
Date of Min Mar-91 Feb-96 Dec-94 Feb-96
Maximum 0.38 0.46 1.12 1.24
Date of Max Nov-00 Dec-01 Jan-90 Feb-90

Source: Bureau of Transportation Statistics

Appendix

Summary of Changes to the TSIs Between the Initial Release and the Four-Month Revision.

The changes in the TSIs that occur with the 4-month revision are identified in the monthly TSI press release and are summarized here. In addition to the percentage change in the index numbers, the revision to the percentage growth rates are also given. Growth rates give the relative increases or decreases, which are the most used feature of index numbers. While in general the revisions to the growth rates are lower than the revisions to the index numbers, as indicated by the average revision, this need not be the case when the index is revised in opposite directions in consecutive months.

Table 7. Percentage Changes between Initial Release and the Four-Month Revision, 1/2005-12/2006

Excel | CSV

Date Freight TSI Passenger TSI Combined TSI
% Revision to Index Revision to % Growth Rate % Revision to Index Revision to % Growth Rate % Revision to Index Revision to % Growth Rate
Jan-05 −1.34 −0.48 0.77 −0.14 −0.69 −0.38
Feb-05 −1.52 −0.18 −0.23 −0.98 −1.10 −0.41
Mar-05 −1.05 0.48 −0.33 −0.10 −0.81 0.30
Apr-05 0.23 1.28 −0.30 0.03 0.07 0.87
May-05 −0.31 −0.55 −1.05 −0.77 −0.53 −0.61
Jun-05 −0.36 −0.04 −0.75 0.30 −0.48 0.06
Jul-05 −0.21 0.15 −0.38 0.37 −0.29 0.19
Aug-05 −0.30 −0.10 −0.14 0.24 −0.24 0.05
Sep-05 −1.06 −0.76 0.59 0.74 −0.65 −0.42
Oct-05 −1.23 −0.17 −0.20 −0.78 −0.98 −0.33
Nov-05 −0.95 0.29 0.34 0.54 −0.63 0.35
Dec-05 −0.77 0.17 −0.47 −0.81 −0.72 −0.09
Jan-06 −1.05 −0.28 1.39 1.84 −0.32 0.40
Feb-06 −1.56 −0.51 1.22 −0.16 −0.70 −0.38
Mar-06 −0.89 0.68 1.62 0.40 −0.13 0.58
Apr-06 −1.28 −0.39 0.99 −0.63 −0.61 −0.48
May-06 −1.13 0.16 1.80 0.80 −0.21 0.41
Jun-06 −0.84 0.28 1.57 −0.22 −0.12 0.09
Jul-06 −0.85 −0.01 1.74 0.16 −0.12 0.00
Aug-06 −0.28 0.56 2.94 1.17 0.30 0.41
Sep-06 −0.80 −0.53 2.28 −0.66 −0.31 −0.61
Oct-06 −0.54 0.26 2.00 −0.27 −0.30 0.01
Nov-06 −0.47 0.07 2.24 0.23 −0.30 0.00
Dec-06 −0.69 −0.22 2.07 −0.17 −0.50 −0.21
Summary            
Average −0.80 0.01 0.82 0.05 −0.43 −0.01
Minimum −1.56 −0.76 −1.05 −0.98 −1.10 −0.61
Date of Min Feb-06 Sep-05 May-05 Feb-05 Feb-05 May-05
Maximum 0.23 1.28 2.94 1.84 0.30 0.87
Date of Max Apr-05 Apr-05 Aug-06 Jan-06 Aug-06 Apr-05

Source: Bureau of Transportation Statistics

Converting the Annual Adjusted Value-Added Weights to Monthly Values

Ideal weights for aggregating across modes for the monthly TSI would consist of relative prices for modal services exclusive of both the cost of inputs from other sectors and seasonal effects. Although monthly price indexes are available from the Bureau of Labor Statistics (BLS), these monthly indexes generally include both the cost of inputs from other sectors and seasonal effects. The approach used here is to convert the annual adjusted value-added weights for each mode into monthly weights such that three desirable properties hold: 1) the weights for any year depend only on BEAs published value-added data for that year and earlier, and 2) changes in the weights will be smooth across months and 3) the December value will be consistently defined across years as a function of the current and previous years value-added. The first criterion implies that values from subsequent years cannot be used to weight the TSI for any historical year. The second is desirable to avoid large changes in the weights that can occur between December and January 3. The third is desirable for consistency and to avoid current weights depending on the distant past. The chosen conversion method uses a geometric average of the growth rates in value added for the current and previous year to determine the transition between months 4.

For simplicity, modal subscripts are suppressed below.

Let Vy be value-added for year y as published by BEA for y=1990 ..

Let Iy be the average of the quantity indexes for calendar year y.

Let uppercase y subscript {lowercase y, lowercase m} be the interpolated value for adjusted value-added, [ uppercase v subscript {lowercase y} over uppercase i subscript {lowercase y} ], for month m=1,,12 and year y.

Let lowercase pi subscript {lowercase y} is equal to ( uppercase u subscript {lowercase y} over uppercase u subscript {lowercase y minus 1) superscript {1 over 12}, the monthly average (gross) growth rate in adjusted value-added.

Let the initial condition be such that that December value-added is consistently defined over the years and depends only on Uy and Uy-1.

The following monthly conversion satisfies these properties:

Let the monthly transition be given by: uppercase u subscript {lowercase y, lowercase m} is equal to uppercase u subscript {lowercase y, lowercase m minus 1} cross ( lowercase pi superscript {12 minus lowercase m} subscript {lowercase y minus 1} dot lowercase pi superscript {lowercase m} subscript {lowercase y} ) superscript {1 over 12}.

Let the initial December value be given by: uppercase u subscript {1989,12} is equal to 1 over 12 dot uppercase u superscript {11 over 24} subscript {1988} dot uppercase u superscript {13 over 24} subscript {1989}, then in general the December value for each year is given by uppercase u subscript {lowercase y, 12} is equal to 1 over 12 dot uppercase u superscript {11 over 24} subscript {lowercase y minus 1} dot uppercase u superscript {13 over 24} subscript {lowercase y}.

Then the monthly conversions values can be rewritten in terms of the TSI quantity indexes and value-added as provided by BEA5:

First define the powers, leaving factors of 12 to simplify evaluation for December. For m=1,2,..,12 , we have

lowercase a is equal to 1 over (2 dot 12 superscript {2}) [ 11 dot 12 minus 2 dot 12 dot lowercase m plus lowercase m (lowercase m plus 1)],

lowercase b is equal to 1 over (2 dot 12 superscript {2}) [ 13 dot 12 plus 2 dot 12 dot lowercase m minus 2 dot lowercase m (lowercase m plus 1)],

lowercase c is equal to 1 over (2 dot 12 superscript {2}) [ lowercase m (lowercase m plus 1)].

Resulting in: uppercase u subscript {lowercase y, lowercase m} is equal to (uppercase v subscript {lowercase y minus 2} over uppercase i subscript {lowercase y minus 2}) superscript {lowercase a} dot (uppercase v subscript {lowercase y minus 1} over uppercase i subscript {lowercase y minus 1}) superscript {lowercase b} dot (uppercase v subscript {lowercase y} over uppercase i subscript {lowercase y}) superscript {lowercase c}

Using BLS Price Indexes to Estimate the Most Recent Value-Added Weights

The BEA value added numbers for year y are first published in the fall of year y+1 so the most recent weights for the TSI quantity data available are estimated using modal price indexes from BLS. The weights for the most recent months are estimated in a manner consistent with the conversion of value-added to monthly values specified above, which avoids introducing potential seasonal effects from the BLS series. The modal representation of the BLS price indexes matches that for the value-added weights after processing in the BLS update workbook so no additional manipulation is necessary and the modal subscript is suppressed below for simplicity.

Let uppercase p superscript {uppercase b} subscript {lowercase y}be the average BLS price index for the full calendar year y.

Let uppercase p superscipt {uppercase b} subscript {lowercase y lowercase t lowercase d}be the average BLS price index for the year-to-date through the month of the most recent TSI quantity data for calendar year ytd.

Let lowercase pi superscript {uppercase b} subscript {lowercase y} is equal to [ uppercase p superscript {uppercase b} subscript {lowercase y} over uppercase p superscript {uppercase b} subscript {lowercase y minus 1} ] superscript {1 over 12}and lowercase pi superscript {uppercase b} subscript {lowercase y lowercase t lowercase d} is equal to [ uppercase p superscript {uppercase b} subscript {lowercase y lowercase t lowercase d} over uppercase p superscript {uppercase b} subscript {lowercase y lowercase t lowercase d minus 1} ] superscript {1 over 12}.

Let TV represent the last time period for with value added is available from BLS.

Then the estimate of adjusted valued added for time periods subsequent to TV is given by sequential application of the following formula, starting with January of year TV+1:

When there is only TSI quantity data for year TV+1:

uppercase u subscript {lowercase y, lowercase m} is equal to uppercase u subscript {lowercase y, lowercase m minus 1 cross ( [lowercase pi subscript {lowercase y minus 1}] superscript {12 minus lowercase m} dot [lowercase pi superscript {uppercase b} subscript {lowercase y lowercase t lowercase d}] superscript {lowercase m} ) superscript {1 over 12}.

When there is TSI quantity data for both years TV+1 and TV+2:

uppercase u subscript {lowercase y, lowercase m} is equal to uppercase u subscript {lowercase y, lowercase m minus 1 cross ( [lowercase pi {uppercase b} subscript {lowercase y minus 1}] superscript {12 minus lowercase m} dot [lowercase pi superscript {uppercase b} subscript {lowercase y lowercase t lowercase d}] superscript {lowercase m} ) superscript {1 over 12}.

1 Adjusted value-added for each service is calculated for each year by dividing nominal value-added by the average of the TSI quantity index for the year.

2 Note that when the source data is held constant, there will be an inverse relationship between changes in the estimated seasonal patterns and the impact on the TSIs because seasonal adjustment reduces (increases) actual output the most for months that are estimated to be the most (least) important for annual output.

3 Interpolation from annual to monthly values using only historical values will always include transition points at which new information is introduced. The procedure used here smooths, but does not eliminate the change at the December-January transition points.

4 The current version was implemented with the 2007 Annual Revision. The previous version was based on the growth rate for value-added, lowercase g subscript {lowercase y} is equal to uppercase v subscript {y} over uppercase v subscript {lowercase y minus 1}, and used the formula uppercase v subscript {lowercase y, lowercase m} is equal to (uppercase v subscript {lowercase y minus 1 over 12) cross [lowercase g superscript {lowercase m plus 5} subscript {lowercase y} plus lowercase g superscript {lowercase m plus 6} subscript {lowercase y} over 2] over 2. The growth rate in the value-added weights for this formula make a discrete change between December and January.

5 To solve for the monthly transition, first substitute the definition of monthly growth into the monthly transition equation and transform into logarithms:

log {uppercase u subscript {lowercase y, lowercase m}} minus log {uppercase u subscript {lowercase y, lowercase m minus 1}} is equal to 1 over 12 superscript {2} [ (12 minus lowercase m) (log {uppercase u subscript {lowercase y minus 1}} minus log {uppercase u subscript {lowercase y minus 2}}) plus lowercase m dot (log {uppercase u subscript {lowercase y}} minus log {uppercase u subscript {lowercase y}} ].

Use the above equation to solve forward from Uy,1 using the general form of the initial condition for Uy-1,12 and the rule summation of lowercase j with lowercase j equals to 1 to lowercase m is equal to lowercase m (lowercase m plus 1) over 2

log {uppercase u subscript {lowercase y, lowercase m}} is equal to [11 over 24 log {uppercase u subscript {lowercase y minus 2}} plus 13 over 24 log {uppercase u subscript {lowercase y minus 1}}] plus 1 over 12 superscript {2} [ summation of {(12 minus lowercase j) (log{uppercase u subscript {lowercase y minus 1}} minus log {uppercase u subscript {lowercase y minus 2}} with lowercase j equals to 1 to lowercase m} plus summation of {lowercase j dot (log {uppercase u subscript {lowercase y}} minus log {uppercase u subscript {lowercase y}}} with lowercase j equals to 1 to lowercase m ] is equal to [11 over 24 minus 1 over 12 superscript {2} (12 lowercase m minus lowercsae m (lowercase m plus 1) over 2)] log {uppercase u subscript {lowercase y minus 2}} plus [13 over 24 plus 1 over 12 superscript {2} (12 lowercase m minus lowercase m (lowercase m plus 1))] log {uppercase subscript {lowercase y minus 1}} plus 1 over 12 superscript {2} lowercase m (lowercase m plus 1) over 2 log {uppercase u subscript {lowercase y}}