2.0 FREIGHT MOVEMENT BY HIGHWAY

2.1 Introduction

This chapter presents a discussion of the methodology used for preparing the provisional estimates of FAF origin-destination-commodity-tonnage-value freight flow matrix for highway mode of transportation. It covers both domestic and transborder highway freight transportation. The provisional estimates are for 2005 and 2006. The estimation methods are formulated based on the FAF²'s 2002 benchmark estimates, and the latest publicly available and reliable information from different data sources.

2.2 Principal Data Sources

The following are the main data sources used in developing the estimates for freight movement by highways, both domestic and international by land border crossings.

Monthly Trucking Tonnage Report – Published by the American Trucking Association (ATA) and provides up-to-date information on the trends of for-hire trucking activities. This monthly trucking tonnage index is based on an ongoing ATA survey of monthly tonnage by Class I and II general freight carriers. It includes both large and small truckload carriers, along with less-than-truckload carriers. The data are released with five weeks of time lag.

County Business Pattern Database – Published by the U.S. Census Bureau on an annual basis and provides national, state, and county level data on payroll, employment, and number of establishments by detailed NAICS industries. The series provides subnational economic data by industry and excludes data on self-employed individuals, employees of private households, railroad employees, agricultural production employees, and most government employees. The report is released with a two-year time lag. It can be accessed at http://www.census.gov/epcd/cbp/view/cbpview.html.

Gross State Product – Prepared by the Bureau of Economic Analysis (BEA) of the U.S. Department of Commerce and provides data on gross state product including components of gross state product like compensation of employees, operating surplus, taxes, etc. Gross domestic product (GDP) by state is the state counterpart of the nation's GDP and is derived as the sum of the GDP originating in all the industries in the state. The data are published with a one-year time lag. It can be accessed at http://www.bea.gov/regional/.

State Personal Income – Published by BEA of the U.S. Department of Commerce on a quarterly basis. Data on state personal income, employment, and compensation for NAICS industries are available from this source. Personal income is the income received by all persons from all sources. It is measured before the deduction of personal income taxes and other personal taxes and is reported in current dollars (no adjustment is made for price changes). Data are published with a three-month time lag. It can be accessed at http://www.bea.gov/regional/.

Monthly Manufacturers' Shipments, Inventories, and Orders (M3) Survey – Conducted by the Census Bureau, it provides broad-based monthly statistical data on the economic conditions in the domestic manufacturing sector. It measures current industrial activity and provides an indication of future production commitments. The value of shipments measures the value of goods delivered during the month by domestic manufacturers. The data are released with a two-month time lag. The survey results can be accessed at http://www.census.gov/indicator/www/m3/ as of January 2006.

Monthly Wholesale Trade Survey – The Census Bureau provides monthly estimates of sales and inventories of wholesale trade industries. This provides statistics on sales, and inventory/sales ratios along with standard errors. Data are both seasonally adjusted and unadjusted. The data are released six weeks after the close of the reference month. It can be accessed at http://www.census.gov/mwts/www/mwts.html.

Surface Transborder Freight Database – Published by the Bureau of Transportation Statistics (BTS) and contains data on North American merchandise trade by commodity, surface mode (rail, truck, pipeline, mail, and other), and by port of entry and geographic detail for the U.S. trade to and from Canada and Mexico. This source provides the dollar value of both imports and exports, and tonnage of imports. The data are published with a three-month time lag. It can be accessed at http://www.bts.gov/programs/international/transborder/.

Producer Price Index – Measures the average change over time in the prices received by domestic producers of goods and services. This measures price changes from the point of view of the producer. The data are reported by detailed industry and detailed type of commodities. The Bureau of Labor Statistics (BLS) publishes these data on a monthly basis with a time lag of one-month.

2.3 Methodology for Domestic Freight

The method used for preparing annual provisional origin-destination (O-D) freight flow metrics for domestic highway freight transportation involves the following steps:

1. Determine annual growth of highway freight tonnage and value at the national level.
2. Estimate growth factors for each O-D pairs at the FAF region level.
3. Estimate annual growths of each O-D pairs by applying the respective O-D regional growth factors to the national annual growth.
4. Determine the provisional freight level (in terms of tonnage and value) of each O-D pairs for 2005 and 2006 by adding the growths to the freight level of the corresponding O-D pairs in the FAF² benchmark year or the provisional estimate of the previous year.

This approach can be characterized as an 'updating approach.' In comparison to producing provisional commodity O-D estimates entirely from updated input data, this approach, which produces provisional estimates by adding estimated growths (or changes) to the corresponding estimates in the benchmark year, has the following advantages:

• It fully utilizes all relevant new information including the most recent data, which become available after the benchmark year, to allow the provisional estimates to capture any changes that occurred after the benchmark year.
• It takes full advantage of the knowledge and detailed information embodied in the estimates of the benchmark year, but not available for the provisional estimates.

2.3.1 Determine Annual Growth of Highway Freight at the National Level

The following four definitions are important for the discussions presented in this document.

Estimates of highway freight – indicates the level of or volume of highway freight in a year with units of short ton and dollar. “Estimates of highway freight” and “highway freight” are used interchangeably in this report.

Growth – is defined as the change in highway freight either in terms of tons or dollar value between two years. Unless otherwise specified, it is calculated as the difference between highway freight for the current year and highway freight for the previous year. Its units are tons and dollars.

Rate of growth – indicates the relative magnitude of growth when growth is compared to the level of the base year. Rate of growth is expressed in percent. “Rate of growth” and “growth rate” are used interchangeably in this report.

Current year – refers to the years for which provisional estimates are prepared, i.e., 2005 and 2006.

2.3.1.1 Freight Tonnage

The monthly trucking tonnage index published by the American Trucking Association (ATA) in the Monthly Truck Tonnage Report and highway tonnage reported in the FAF benchmark year are used in preparing the provisional domestic freight tonnage carried by trucks on the highway. The formula for deriving the provisional tonnage estimate at the national level is given by the following equation.

Where
T_t= National tonnage by truck for year t (t = 2005 and 2006)
T₀ = Truck tonnage for FAF benchmark year, i.e., 2002
I_t = Trucking tonnage index for year t
I₂₀₀₂ = Trucking tonnage index for 2002

This estimate provides the national aggregate tons of freight shipment by truck. The freight tonnage by two-digit SCTG commodity is derived by using the following procedure:

1. First, the current year (i.e., 2005 and 2006) output of commodities is multiplied by the corresponding ton-per-output ratios for the FAF benchmark year to derive tonnages by type of commodities. The information on output by type of commodity is obtained from the Census Bureau's Monthly Manufacturers' Shipments, Inventories, and Orders (M3) Survey. The type of commodities from these data source is established based on each industry's primary product.
2. Second, commodity shares are calculated based on the commodity distribution of the above tonnage estimates.
3. Third, these shares are used to break down the growth in national highway freight tonnage, estimated with ATA data, into growth in tonnage by two-digit SCTG commodity.
4. Finally, the national aggregate tonnage growth by type of commodity is added to the FAF benchmark estimates to provide the national aggregate tonnage by type of commodity for the provisional years.

In this method, both highway freight weight/value ratio by commodity and highway shipment tonnage to output-value ratio by commodity in the current year are assumed to remain the same as in the FAF benchmark year. The advantage of this method is that it utilizes the latest available indicator on the growth of highway freight tonnage.

2.3.1.2 Freight Value

Freight value is determined not only by its tonnage but also by its weight/value ratio. Weight/value ratio, in turn, changes over time due to changes in the commodity components of freight and changes in their prices. The freight value is estimated using data from the 2002 FAF benchmark database, and the value of output by industry from the Census Bureau's Monthly Manufacturers' Shipments, Inventories, and Orders (M3) Survey.

1. First, the current year (i.e., 2005 and 2006) output of commodities is multiplied by the corresponding ton-per-output ratios for the FAF benchmark year to derive freight tonnage by type of commodities. Data on output by type of commodity are obtained from the Census Bureau's Monthly Manufacturers' Shipments, Inventories, and Orders (M3) Survey. The type of commodities from this data source is determined based on each industry's primary product.
2. Second, commodity shares are calculated based on the tonnage estimates above.
3. Third, these shares are used to disaggregate the growth in national highway freight tonnage, estimated with ATA data, into growth in tonnage by two-digit SCTG commodity.
4. Fourth, multiplying the growths in tonnage at two-digit SCTG commodity level with the their corresponding value/weight ratios obtained from the FAF benchmark year yields the growth in value of highway freight by commodity. The value/weight ratios of the FAF benchmark year are adjusted for inflation on the basis of changes in the producer prices at two-digit SCTG levels. The producer price indexes are obtained from Bureau of Labor Statistics (BLS).
5. Finally, adding the growth in freight value by type of commodity to the corresponding FAF benchmark year freight value provides the current year freight value by type of commodity. Note that the FAF benchmark year freight value by commodity are also adjusted for inflation.

This method assumes that highway shipment tonnage to output value ratio by commodity are assumed to remain the same in the current year as in the FAF benchmark year. The approach takes advantage of the available current information on the growth of highway freight tonnage, as well as the changes in prices.

2.3.2 Estimate Growth Factors for Each O-D Pairs of FAF Regions

The purpose of preparing growth factors is to enable the annual provisional commodity O-D estimates to capture the impacts of differences in regional growths on freight shipments. A State-County-FAF Region approach was used in estimating the regional growth factors. There are three reasons for using this approach. First, all the necessary economic data for estimating regional growth factors are timely available at the state level, not at the FAF regional level. Second, most of the economic data that can be used for estimating regional growth factors are available at the county level, are not readily available in a timely fashion for the provisional estimate purpose. These kinds of data are usually released with a time lag of more than one year, and hence could not be used as primary inputs for our purpose. Third, counties are sub-regions to both states and FAF regions, and hence they provide a bridge for the crosswalk between states and FAF regions.

The approach for estimating growth factors for each O-D pairs involves the following steps:

1^st Determine annual state growth rates
2^nd Estimate county share of state growth
3^rd Estimate annual FAF regional growth
4^th Estimate annual growth factors for each O-D pairs at the FAF region level

2.3.2.1 1st Determine Annual State Growth

The best indicator of the size and growth of a state's economy is its Gross State Product (GSP). Similar to Gross Domestic Product (GDP) at the national level, GSP measures the annual net output of a state's economy. Given the positive link between freight and output, freight grows as the economy grows, and hence GSP can serve as a reasonable indicator of freight growth.

GSP by state are published by the Bureau of Economic Analysis (BEA) and can be used to directly calculate the annual growth rate of sates. However, the GSP data are only available with a lag of one year. Currently, 2005 is the latest year for which GSP data are readily available. This creates a timeliness problem for FAF annual provisional commodity O-D estimates, whose annual updates for a year are scheduled to be completed at the end of the same year. In order to overcome this problem, the State Quarterly Personal Income statistics from BEA is used to calculate state annual growth rates for the current year.¹ Currently, the state quarterly personal income estimates are available with a lag of about three months, which implies that three quarters data are available for estimating the current year annual growth rates of GSP.² Using the quarterly personal income statistics, the current year growth of GSP by state is estimated by the following relationship:

ΔGSPs = SG_s * GSP_s,t-1

Where:
ΔGSP_s = Current year growth of GSP for state s ($)
SG_s = Current year GSP growth rate (approximated by the growth of personal income) for state s (%)
GSP_s,t-1= State GSP for previous year for state s ($)

2.3.2.2 2nd Estimate County Share of State Growth

In order to calculate the FAF regional growth, state growth factors are allocated among counties of that state, estimate the county's share of the state growth, and then sum county growths up to FAF regional growth.³ Current year growths of counties are estimated using the following formula:

ΔCG_k,s = GSP_s*CS_k,s

Where:
ΔCG_k,s = Current year growth of county k in state s ($)
ΔGSP_s = Current year growth of GSP for state s (%)
CS_k,s= Share of county k in the GSP of state s ($)

The county shares in state GSP is estimated with the most recent data on total payroll of a county, which is obtained from the Census Bureau's County Business Patterns. These data are released with a lag of two years.

2.3.2.3 3rd Estimate FAF Regional Growth

Current year FAF regional growths are calculated by summing up current year growths of counties within a given FAF region.

RG_j = ΣΔCG_k,j

Where:
ΔRG_j = Growth for region j
ΣCG_k,j = Current year growth of county k in region j

2.3.2.4 4th Estimate Annual Growth Factors for Each O-D Pairs of FAF Regions

Estimates of current year growths for all FAF regions provide the basic input information necessary for estimating annual growth factors of FAF O-D pairs. Instead of attempting to estimate the economic-spatial relationship between each pair of FAF regions using geo-spatial interaction models, such as various gravity models, the approach uses an interregional flow modifier method, which was developed by MacroSys in its multi-regional Input-Output modeling research, for deriving growth factors of FAF O-D pairs. The method involves the following basic steps.

1. Converting economic growth into pseudo-growth in highway freight

The conversion of economic growth into pseudo-growth in highway freight tonnage is given by the following relationship:

Where:
ΔPGT_i,j = Pseudo-growth in highway freight tonnage between two regions (region i and region j)
ΔCEG_i,j = Combined economic growth of the two regions for the current year , (i.e., region i and region j)
CGSP_i,jt-1 = Combined economic size of the two regions (i.e., region i and region j) for previous year or t-1
T_i,j,t-1 = Highway freight tonnage between region i and region j for previous year.

The combined economic growth and the combined economic size of region i and j in the above formula are established based on the real dollar state GSP of region i and j.

Similarly, the conversion of economic growth into pseudo-growth in highway freight value is accomplished using the following formulation:

Where:
ΔPGV_i,j = Pseudo-growth in highway freight value between two regions (region i and region j)
ΔCEG_i,j = Combined economic growth of the two regions for the current year , (i.e., region i and region j)
ΔCGSP_i,j,t-1 = Combined economic size of the two regions (i.e., region i and region j) for previous year or t-1
V_i,j,t-1 = Highway freight value between region i and region j
for previous year

The freight value is estimated using current dollar values of the combined economic growth and the combined economic size of region i and j. The combined economic size and growth of the regions are estimated using state GSP statistics.

2. Estimating annual growth factor for each FAF O-D pair

Let ΔTPGT be the sum of all pseudo-growths of all FAF O-D pairs in highway freight tonnage (= ΣΔPGT_i,j),ΔPGT_i,j be pseudo-growth in highway freight tonnage of each O-D pair. Then the annual freight tonnage growth factor for each FAF O-D pair, GFT_i,j, is given by:

Let ΔTPGV be the sum of all pseudo-growths of all FAF O-D pairs in highway freight value (= ΣΔPGV_i,j), and ΔPGV_i,j be the pseudo-growth in freight value of each O-D pairs, then the annual freight value growth factors for each FAF O-D pairs, GFV_i,j is given by:

The separation between tonnage growth factors and value growth factors recognizes the differences in commodity components and their prices among FAF O-D pairs. The main advantage of the interregional flow modifier method is that it captures the special economic-spatial relationships developed over time among FAF regions and at the same time recognizes recent changes in these relationships.

2.3.3 Estimate Growth of Highway Freight for Each FAF O-D Pair

Once the annual growth factors are established, the estimation of growth in highway freight for each FAF O-D pairs is straight-forward and is obtained through the following formula.

1. Let ΔGT be the annual growth of national highway freight tonnage,⁴ GFT_i,j be the annual freight tonnage growth factor of FAF O-D pair between region i and region j, the annual growth for the FAF O-D pair in highway freight tonnage, G_i,j, is given by the formula:
   
   ΔG_i,j = ΔGT*GFT_i,j
2. Let ΔGV be the annual growth of national highway freight value, GFV_i,j be the annual freight value growth factor of FAF O-D pair between region i and region j, the annual growth for the FAF O-D pair in highway freight value, ΔG_i,j, is given by the formula:
   
   ΔG_i,j = ΔGV*GFV_i,j

2.3.4 Determine the Provisional Freight Flow Estimates for Each FAF O-D Pairs

The provisional estimate of highway freight tonnage of a FAF O-D pair for the current year is calculated by adding its estimated annual tonnage growth to its freight tonnage in the 2002 FAF benchmark year (or the provisional estimate of the previous year if the current year is two or more years away from the benchmark year).

FT_i,j,t = FT_i,j,t-1 + ΔGT_i,j,t

Where:
FT_i,j,t = Highway freight tonnage for O-D pair i and j for year t
FT_i,j,t-1 = Highway freight tonnage for O-D pair i and j for year t-1.
ΔGT_i,j,t = Estimated annual tonnage growth for O-D pair i and
j for year t

Similarly, the provisional estimate of highway freight value of a FAF O-D pair are calculated in the updating year by adding its estimated annual growth of freight value to its freight value in the FAF² benchmark year (or the provisional estimate of the previous year if the updating year is two or more years away from the benchmark year).

FV_i,j,t = FV_i,j,t-1 + ΔGV_i,j,t

Where:
FV_i,j,t = Highway freight value for O-D pair i and j for year t
FV_i,j,t-1 = Highway freight value for O-D pair i and j for year t-1
ΔGV_i,j,t = Estimated annual growth of value for O-D pair i and j for year t

2.4 Methodology for International Freight

The U.S. international freight shipments by highway are channeled to or coming from Canada and Mexico. Our general approach to estimating highway freight between U.S. and Canada, and between U.S. and Mexico follows the following steps:

1. Determine state transborder highway freight to and from Canada and Mexico by type of commodity, and port of exit and entry.
2. Disaggregate state level imports and exports into FAF regions based on information from BTS's Surface Transborder database, Census Bureau's County Business Patterns database, and 2002 FAF benchmark estimates.

2.4.1 Determine State Transborder Highway Freight to and from Canada and Mexico by Port of Exit and Entry

Statistics on the value of exports to Canada and Mexico, and tons and value of imports from Canada and Mexico by surface modes (highway, rail, and pipeline) are available from the Bureau of Transportation Statistics (BTS)'s North American Transborder Freight database. The data are reported by origin state (for exports) and destination state (for imports) using the Harmonized Schedule (HS) commodity classification method, and by port of exit (for exports) and port of entry (for imports). The data were converted into SCTG commodity classification using BTS's working cross-walk between HS and SCTG. The port of exit or entry in the North American Transborder Freight database and the port of exit and entry in FAF database are different. The data were converted from Transborder Freight database port of exit or entry into FAF port of exit or entry.

No data on the tonnage of U.S. exports to Canada and Mexico are available from this or any other data sources. Therefore an imports weight/value ratio approach was used to produce tonnage estimates of highway freight of U.S. exports to Canada and Mexico. Two sets of weight/value ratios at two-digit SCTG commodity level of detail are used for this purpose. One set of weight/value ratio are calculated based on imports statistics from Canada and the other set of ratios are computed using imports from Mexico. The ratios are country specific and therefore recognize the differences in trade between United States and Canada and trade between United States and Mexico. To reduce the impacts of variations in imports weight/value ratios over time and extreme weight/value ratios, it was necessary to smooth the import weight/value ratios by commodity using simple moving average (SMA) method. Multiplying the export values by the weight/value ratios of imports provide the tonnage of exports. This method assumes that the respective weight/value ratios of U.S. exports to Canada and Mexico are the same as the weight/value ratios of U.S. imports from Canada and Mexico at the 2-digit SCTG commodity level.

Currently, data from the Transborder Freight database are available up to November, 2006. Data for December, 2006 was not released at the time of developing these estimates. As such, the trade volume for the month of December was estimated based on the trade volume of the early months of the year and trade volumes of previous years.

2.4.2 Disaggregate State Level Imports and Exports into FAF Regions

Two separate sets of data are obtained from the Transborder Freight database, namely, (1) state exports and imports by type of commodity, and (2) state exports by port of exit and state imports by port of entry. However, no data is available on imports and exports by type of commodity, port of exit or entry, and origin or destination state. A procedure was developed to fill in this data gap. The procedure keeps the original aggregate state level data by type of commodity, and by port of exit and entry unchanged. This means that when aggregating the detailed estimates into state level exports and imports by type of commodity, and state level exports by port of exit or imports by port of entry, the results would consistent with the actual data from the Transborder Freight database.

2.4.2.1 Imports

1^st stage – at this stage, the statistics on imports by type of commodity for each state are distributed into FAF port of entry and destination region using shares from the 2002 FAF benchmark estimates. Country specific shares were used, which means that the shares used for Canada are different from those used for Mexico. This effort provides detailed data by type of commodity, country of origin, destination region, and port of entry.

Let M_i,c,s = imports of commodity i from country c to state s, S_i,c,s,j,p = share of imports of commodity i imported from country c to state s and region j through port of entry p,⁵ then imports of commodity i from country c to state s and region j via port of entry p, M_i,c,s,j,p, is given by the following formula:

M_i,c,s,j,p = M_i,c,s * S_i,c,s,j,p

Where: ΣS_i,c,s = 1

There are some commodities (i.e., some of M_i,c,s) imported by states that do not have corresponding shares in the 2002 FAF benchmark estimates, because these commodities were not imported by the states in 2002. For these commodities, first, calculate state level average port of entry and FAF region shares from the 2002 FAF database, and then apply these shares to disaggregate the commodities into port of entry, and destination region. Let M_i,c,s = imports of commodity i from country c to state s that do not have corresponding shares in the 2002 FAF database, P_c,s,j,p = shares of port p in the total imports from country c to state s and region j, then imports of commodity i from country c to state s and region j via port of entry p, M_i,c,s,j,p, is calculated using the following relationship:

M_i,c,s,j,p = M_i,c,s * P_c,s,j,p

At this stage of the estimation process, imports of the state by type of commodity, when aggregated from the detailed estimates (or from M_i,c,s,j,p), would be the same as the actual data obtained from the Transborder Freight database. However, imports of the state by port of entry may not be consistent with the data from the Transborder Freight database anymore.

2^nd stage, at this stage of the process, adjustments are made to the detailed estimates (i.e., to M_i,c,s,j,p) computed in the 1^st stage to make it the same as the actual data when aggregated by port of entry, without affecting the actual commodity composition as reported in the Transborder database.

Let M_c,s,p = imports from country c to state s through port p from the Transborder database, and µ_c,s,p = estimated imports from country c to state s through port p compiled from the detailed estimates (i.e., from M_i,c,s,j,p), and let µ_c,s,p — M_c,s,p = ΔM_c,s,p. Clearly, ΔM_c,s,p could be greater/less than or equal to zero. Note that Σ(ΔM_c,s,p >0) = Σ(ΔM_c,s,p<0). The objective is to adjust M_i,c,s,j,p so that it is comparable to the actual data from the Transborder database when aggregated by port of entry or type of commodity at the state level. The adjustment process involves the following steps:

1. Whenever ΔM_c,s,p >0, adjust M_i,c,s,j,p downward by multiplying it by 1-(ΔM_c,s,p/µ_c,s,p).
2. ΔM_c,s,p could be negative because M_c,s,p is greater than µ_c,s,p or due to the fact that there are no corresponding estimates (µ_c,s,p) during the first stage of the estimation process.
   
   If ΔM_c,s,p is negative because M_c,s,p is greater than µ_c,s,p, then ΔM_c,s,p is added to the M_i,c,s,j,p. Since ΔM_c,s,p is not as detailed as M_i,c,s,j,p, the former was disaggregated so that it is possible to add it to the later. First, ΔM_c,s,p is broken down by type of commodity on the basis of the commodity distribution in the ΔM_c,s,p >0. ΔM_c,s,p>0 is equivalent
   
   to (M_i,c,s,j,p*(ΔM_c,s,p/µ_c,s,p)). Let M_i,c,s,j,p*(ΔM_c,s,p/µ_c,s,p) = ΔM_i,c,s,j,p >0, then commodity
   
   shares for each state (Z_i,c,s) from ΔM_i,c,s,j,p are calculated as ΔM_i,c,s,j,p /
   
   ΔM_i,c,s,j,p. These shares are applied to the ΔM_c,s,p<0 to provide ΔM_i,c,s,p<0.
   
   ΔM_i,c,s,p<0 is not yet additive to M_i,c,s,j,p. Second, ΔM_i,c,s,p<0 is further disaggregated by destination FAF region. For this purpose, the latest available county level indicator from County Business Pattern database was used. Currently, 2004 is the latest year for which data are available from this data source. The shares of FAF regions in their respective total state payroll were calculated and applied to M_i,c,s,p<0 to disaggregate it into FAF region level of detail (i.e., ΔM_i,c,s,j,p<0).
   
   Whenever ΔM_c,s,p is negative due to unavailability of corresponding µ_c,s,p, then include it as new record with the M_i,c,s,j,p. However, the ΔM_c,s,p is required to be disaggregated by type of commodity and destination FAF region before included as new records. First, use the commodity shares (Z_i,c,s), which are estimated above from ΔM_i,c,s,j,p >0 to disaggregate ΔM_c,s,p<0 by type of commodity. Second, distribute the ΔM_i,c,s,p<0 into destination FAF regions based on their shares in the total state payroll estimated from the County Business pattern database. These shares are multiplied by the ΔM_i,c,s,p<0 to provide the data at FAF region level of detail (i.e., ΔM_i,c,s,j,p).
3. No adjustments are required if ΔM_c,s,p=0.

2.4.2.2 Exports

The procedure used for preparing disaggregated exports freight statistics are exactly the same as that used for imports.

1^st stage – the statistics on exports by type of commodity for each state are disaggregated into FAF origin region and port of exit using shares from the 2002 FAF benchmark estimates. Country specific shares were applied for this purpose. This effort provides detailed data by type of commodity, country of destination, origin region, and port of exit.

Let X_i,c,s = exports of commodity i to country c from state s, S_i,c,s,j,p = share of exports of commodity i exported to country c from state s and region j through port of exit p, then exports of commodity i to country c from state s and region j via port of exit p, X_i,c,s,j,p, is given by:

X_i,c,s,j,p = X_i,c,s * S_i,c,s,j,p

Where: ΣS_i,c,s = 1

Not all exported commodities have corresponding shares in the 2002 FAF benchmark estimates. For these commodities, port and origin region shares were established from the 2002 FAF database. State level exports by type of commodity multiplied by these shares provide state exports by type of commodity, origin region, and port of exit. Let X_i,c,s = exports of commodity i to country c from state s that do not have corresponding shares in the 2002 FAF database, P_c,s,j,p = shares of port p in the total exports of state s and region j to country c, then exports of commodity i to country c from state s and region j via port of exit p, X_i,c,s,j,p, is calculated using the following relationship:

X_i,c,s,j,p = X_i,c,s * P_c,s,j,p

At the end of this stage, exports of states by type of commodity, when aggregated from the detailed estimates (or from X_i,s,j,p), would be the same as the actual data obtained from the Transborder Freight database. However, exports of states by port of exit may not be consistent with the actual data.

2^nd stage, at this stage, adjustments are made to the detailed estimates (i.e., X_i,c,s,j,p) to make it equal to the actual data from the Transborder database, when aggregated by port of exit, or by type of commodity.

Let X_c,s,p = exports to country c from state s through port p from the Transborder database, and µ_c,s,p = estimated exports to country c from state s via port p by aggregating the detailed estimates (X_i,c,s,j,p), and let µ_c,s,p – X_c,s,p = ΔX_c,s,p. Clearly, ΔX_c,s,p could be greater/less than or equal to zero. Note that Σ(ΔX_c,s,p>0) = Σ(ΔX_c,s,p<0). The objective is to adjust X_i,c,s,j,p so that its aggregation will be comparable to the actual data from the Transborder Freight database by port of exit or by type of commodity. The adjustment process involves the following steps:

1. If ΔX_c,s,p >0, adjust X_i,c,s,j,p downward by multiplying it by 1-( ΔX_c,s,p/µ_c,s,p).
2. ΔX_c,s,p could be negative because X_c,s,p is greater than µ_c,s,p or due to the fact that there are no corresponding estimates (µ_c,s,p) in the first stage of the estimation process.
   
   If ΔX_c,s,p is negative because X_c,s,p is greater than µ_c,s,p, then X_c,s,p is added to the X_i,c,s,j,p. Since ΔX_c,s,p is not as detailed as X_i,c,s,j,p, the former is disaggregated so that it is possible to add it to the later. First, ΔX_c,s,p is broken down by type of commodity on the basis of the commodity distribution in the ΔX_c,s,p >0. ΔX_c,s,p>0 is equivalent
   
   to (X_i,c,s,j,p)*(ΔX_c,s,p/µ_c,s,p)). Let X_i,c,s,j,p*(ΔX_c,s,p/µ_c,s,p) = ΔX_i,c,s,j,p >0, then commodity shares for each state (Y_i,c,s) are calculated as ΔX_i,c,s,j,p / ΔX_i,c,s,j,p. These shares are applied to the ΔX_c,s,p<0 to provide ΔX_i,c,s,p<0. Second, ΔX_i,c,s,p<0 is further disaggregated by destination FAF region. Similar to imports, county level payroll statistics from County Business Pattern database was used to calculate shares of FAF regions in their respective state payroll. These shares are applied to ΔX_i,c,s,p<0 to distribute it into FAF regions (i.e., ΔX_i,c,s,j,p<0).
   
   Whenever ΔX_c,s,p is negative due to unavailability of corresponding µ_c,s,p, then include tit as new record in the X_i,c,s,j,p. However, the data need to be disaggregated by type of commodity and origin FAF region before they are included as new records. First, use the commodity shares (Υ_i,c,s) as estimated above to disaggregate ΔX_c,s,p<0 by type of commodity, (i.e, Υ_i,c,s * (ΔX_c,s,p<0) = ΔX_i,c,s,p<0). Then, disaggregate the ΔX_i,c,s,p<0 into FAF regions using shares of FAF regions estimated based on payroll information from the County Business Pattern database.
3. No adjustments are required if ΔX_c,s,p=0.