Railroad Investment in Track Infrastructure

Abstract

A model of investment in basic track components is estimated from 1985-2008 data for Class I railroads. Network size is measured in miles of road (MOR), while traffic is measured in revenue gross ton-miles (RGTM). In addition to MOR and RGTM, the model includes railroad indicator and time variables. The purpose of the railroad variables is to capture fixed effects (e.g., effects other than traffic and network size) that are specific to particular railroads, but which do not change over time. The time variable, on the other hand, accounts for industry-wide trends and changes that occur during the period. The study shows that when miles of road are held constant (a realistic scenario), a 100% increase in RGTM results in a 50% increase in track investment. However, it is important to consider the interpretative context described in the paper. Several data anomalies were discovered and handled statistically. The parameter estimates vary somewhat with the index used to convert nominal dollars to constant dollars.

Full text

Railroad Investment in
Track Infrastructure
MPC 18-365 | D. Tolliver, P. Lu and D. Benson
Colorado State University
North Dakota State University
South Dakota State University
University of Colorado Denver
University of Denver
University of Utah
Utah State University
University of Wyoming
A University Transportation Center sponsored by the U.S. Department of Transportation serving the
Mountain-Plains Region. Consortium members:

Railroad Investment in Track Infrastructure
Prepared By
Dr. Denver Tolliver
Director
Denver.Tolliver@ndsu.edu
Dr. Pan Lu
Associate Professor/ Associate Research Fellow
Pan.lu@ndsu.edu
Doug Benson
Associate Research Fellow
Doug.Benson@ndsu.edu
Department of Transportation and Logistics/College of Business
Mountain-Plains Consortium/Upper Great Plains Transportation Institute
North Dakota State University
September 2018

Acknowledgements
This research was made possible with funding supported by the U.S. Department of Transportation
though the Mountain-Plains Consortium (MPC) Transportation Center. The authors express their deep
gratitude to U.S. DOT and MPC.
Disclaimer
The contents of this report reflect the views of the authors, who are responsible for the facts and the
accuracy of the information presented. This document is disseminated under the sponsorship of the
Department of Transportation, University Transportation Centers Program, in the interest of information
exchange. The U.S. Government assumes no liability for the contents or use thereof.
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EXECUTIVE SUMMARY
A model of investment in basic track components is estimated from 1985-2008 data for Class I railroads.
Network size is measured in miles of road (MOR), while traffic is measured in revenue gross ton-miles
(RGTM). In addition to MOR and RGTM, the model includes railroad indicator and time variables. The
purpose of the railroad variables is to capture fixed effects (e.g., effects other than traffic and network
size) that are specific to particular railroads, but which do not change over time. The time variable, on the
other hand, accounts for industry-wide trends and changes that occur during the period. The study shows
that when miles of road are held constant (a realistic scenario), a 100% increase in RGTM results in a
50% increase in track investment. However, it is important to consider the interpretative context described
in the paper. Several data anomalies were discovered and handled statistically. The parameter estimates
vary somewhat with the index used to convert nominal dollars to constant dollars.

TABLE OF CONTENTS
1. OVERVIEW ............................................................................................................................ 1
2. TRACK INVESTMENT MODEL ........................................................................................ 3
2.1 Traffic Measures .............................................................................................................................. 3
2.2 Network Size .................................................................................................................................... 4
2.3 Main Effects ..................................................................................................................................... 4
2.4 Treatment of Other Effects .............................................................................................................. 5
2.5 Statistical Model .............................................................................................................................. 6
2.5.1 Functional Form ..................................................................................................................... 6
2.5.2 Initial Model ........................................................................................................................... 9
2.5.3 Autoregression Model .......................................................................................................... 10
2.5.4 Data Issues ........................................................................................................................... 12
2.6 Model Interpretations ..................................................................................................................... 13
2.6.1 Defining Predictive Equations ............................................................................................. 13
2.6.2 Implications of Constant Elasticity ...................................................................................... 13
2.6.3 Economies of Density .......................................................................................................... 14
2.6.4 Magnitudes of Parameter Estimates ..................................................................................... 14
2.7 Sensitivity of Estimates to Cost Indexes ........................................................................................ 15
3. INTERPRETIVE CONTEXT ............................................................................................. 17
3.2 Delayed Capital Expenditures ........................................................................................................ 17
3.3 Regulated Versus Market Investments .......................................................................................... 18
3.4 Accounting Interpretations ............................................................................................................. 18
3.5 Economies of Traffic Density ........................................................................................................ 18
3.6 Forecasting with the Model ........................................................................................................... 18
3.7 Relative Contributions of Traffic and Network Size ..................................................................... 18
3.8 Other Statistical Issues ................................................................................................................... 19
3.8.1 Multicollinearity ................................................................................................................... 19
3.8.2 Impacts of Other Activity Variables .................................................................................... 20
4. RESEARCH TO EXPAND THE ANALYSIS ................................................................... 21
4.1 Other Roadway Investment Models ............................................................................................... 21
4.2 Individual Component Models ...................................................................................................... 21
4.3 Density Class Models .................................................................................................................... 21
4.4 Axle Load Effects .......................................................................................................................... 21

APPENDIX A: STATISTICAL MODELING PROCEDURES............................................. 23
A.1 OLS Model: The Starting Point ..................................................................................................... 23
A.2 Autocorrelated Errors..................................................................................................................... 24
A.2.1 Equation of Autocorrelated Error Term ............................................................................... 24
A.2.2 Error Variance and Correlation ............................................................................................ 24
A.2.3 Transformations to Achieve Desired Error Properties ......................................................... 25
A.3 Autocorrelation Modeling Process ................................................................................................ 25
A.3.1 Model Specification ............................................................................................................. 26
A.3.2 Illustrative Manual Process .................................................................................................. 27
A.3.3 Generalized Least Squares ................................................................................................... 28
A.3.4 Iterated Yule-Walker Method .............................................................................................. 28
A.4 Test for Autocorrelation ................................................................................................................. 29
APPENDIX B: DATA................................................................................................................. 30

LIST OF TABLES
Table 1.1 Class I Railroad Track Investment Per Route Mile (Nominal 2008 Dollars) ............................ 1
Table 2.1 Density Categories used in Uniform System of Accounts ........................................................ 3
Table 2.2 Parameter Estimates from Logarithmic Model of Track Investment ........................................ 9
Table 2.3 Main Parameter Estimates from Linear Regression Model of Track Investment ................... 10
Table 2.4 Mean Square Error and F-Value for Log Model of Track Investment .................................... 10
Table 2.5 R-Square and Coefficient of Variation for Log Model of Track Investment .......................... 10
Table 2.6 Results of Test for Serial Correlation in Log Model of Track Investment .............................. 10
Table 2.7 Results of Autoregression Model of Track Investment ........................................................... 11
Table 2.8 Durbin-Watson Test for First Order Autocorrelation .............................................................. 12
Table 2.9 Data for Illinois Central Gulf (ICG) Railroad ......................................................................... 12
Table 2.10 Data for Conrail, CSX, and Norfolk Southern Before and After Acquisition ......................... 12
Table 3.1 Estimated Elasticities of Track Investment with Respect to Miles of Road, Gross
Ton-Miles, and Time Under Different Assumptions............................................................... 17
Table 3.2 Results of Track Investment Model with Train-Miles Added ................................................. 20
Figure A.1 Autocorrelations in Track Investment Model .......................................................................... 26
Table A.2 Parameter Estimates from Autoregression Model Using Maximum Likelihood Method ....... 29
Table B.1 Values of Variables Used in Study .......................................................................................... 30
LIST OF FIGURES
Figure 2.1 Trends in Miles of Road and Revenue Gross Ton-Miles .......................................................... 5
Figure 2.2 Plot of Track Investment against Miles of Road ....................................................................... 7
Figure 2.3 Plot of Log of Track Investment against Log of Miles of Road ................................................ 7
Figure 2.4 Plot of Track Investment against Revenue Gross Ton-Miles .................................................... 8
Figure 2.5 Plot of Log of Track Investment against Log of RGTM ........................................................... 8
Figure 2.6 Variations in Predicted Track Investment from Log Model Holding Miles of Road
Constant at Mean Value .......................................................................................................... 14
Figure 3.1 Comparison of RCRI, RCAF, and CWCC Indexes ................................................................ 17

1
1. OVERVIEW
Class I railroads in the United States have invested over $67 billion in basic track components:1 rails, ties,
ballast, other track materials (such as tie plates, spikes, bolts, and anchors), and grading. These
investments grew by 223% between 1985 and 2008, in nominal dollars, and by 137% in real dollars.2 As
shown in Table 1.1, rails and other track materials comprise the largest investment component (43%),
followed by crossties (26%), ballast (16%), and grading (15%), which includes expenditures for the initial
construction (and subsequent reconstruction) of the roadbed. Collectively, these investments average
$563,000 per route mile. However, the replacement cost of these assets is much greater than their nominal
value.
Table 1.1 Class I Railroad Track Investment Per Route Mile (Nominal 2008 Dollars)
Track Component
Investment per Mile
Percent of Total
Rail and Other Track Material
$243,439
43%
Ties
$144,027
26%
Ballast
$90,575
16%
Grading
$84,898
15%
Total: Basic Track Components
$562,939
100%
Investments in basic track components are necessary to (1) provide safe transportation of passengers and
goods, (2) maintain infrastructure in a state of good repair, (3) add capacity, (4) reduce congestion, and
(5) increase the overall efficiency of operations. Track investments are important from a regulatory
perspective, as railroad revenues must recoup operating expenses and allow companies to earn an
adequate return on invested capital.
In many areas of regulation, the Surface Transportation Board (STB) utilizes the Uniform Railroad
Costing System (URCS) to provide information about railroad costs. A return of 50% on roadway
investment is reflected in the URCS variable cost.3 This long-standing assumption (that half of road
capital investments are fixed) is based on traffic patterns and practices prior to 1955.4 Since then there
have been many changes, including the following:
1. Deregulation has allowed railroads greater decision-making authority and the capability to
expeditiously abandon unprofitable lines.
2. Changes in regulatory policies (e.g., the interpretation of the Public Convenience and Necessity
clause) have made it easier to propose new rail lines or extensions.
3. Car weights have dramatically increased.
1 This value is estimated from data reported to the U.S. Surface Transportation Board in Schedule 416 of the R-1
Report.
2 These percentages are estimated from data reported to the U. S. Surface Transportation Board in Schedule 416 of
the R-1 Report. The real percentage increase is computed using the Rail Cost Adjustment Factor
3 Surface Transportation Board. “Report to Congress Regarding the Uniform Rail Costing System.” May 27, 2010.
4 See: Interstate Commerce Commission (Bureau of Accounts). Explanation of Rail Cost Finding Procedures and
Principles Relating to the Use of Costs, Statement No. 7-63, Washington, D.C., November 1963. In developing the
50% variability estimate, the ICC used data from 1939 through 1951, including traffic and investment data for the
World War II period. The analysis includes “road-to-road comparisons” for 1944, 1946, and 1951. In synthesizing
the results of several studies, wartime and prewar traffic densities were adjusted to 1951 levels. Based on these
studies, the ICC found “operating expenses to be between 80 and 90 percent variable and plant investment to be
upwards of 50 percent variable” [page 86]. In reaching its conclusion, the ICC noted: “The use of a figure of 50
percent variable for road property and 100 percent variable for equipment is approximately equivalent to the use of
an overall figure for road and equipment of 60 percent” [page 86].

2
4. A much greater proportion of traffic moves in unit trains.
5. Improvements in materials, metallurgy, and manufacturing techniques have resulted in improved
track durability and response.
For these (and many other reasons), a current analysis of railroad investment practices is needed. The
objectives of this study are to describe patterns of track investment in the United States and show how
track investments vary with network size, traffic, and other factors.
It is important to note that the previously mentioned 50% variability ratio, which was developed by the
Interstate Commerce Commission (ICC), applies to all road investments, not just basic track components.
It is not clear if the ICC intended this ratio to apply specifically to track. This paper does not intend to
assess the process by which the factor was originally developed or interpret the ICC’s original intent.
Instead, the variability ratio is used in a general sense as a “null hypothesis.” An assessment will be made
at this paper’s conclusion to determine if sufficient evidence exists to conclude that it is not applicable to
basic track components.

3
2. TRACK INVESTMENT MODEL
This study is based on R-1 reports submitted to the STB from 1985 through 2008. Elements of the R-1
database include miles of road and track (derived from Schedule 700), gross ton-miles (derived from
Schedule 755), and investments in basic track components from Schedule 416. All investment data have
been restated in constant dollars. The increment to investment in each year is computed by subtracting the
gross investment in year t + 1 from the investment in year t. Each yearly increment is restated in 1985
dollars and the recomputed increments are added back to the 1985 base to compute an adjusted value for
each year.
The track investment model reflects the sum of investments in density classes I and II (Table 2.1) from
Column L of Schedule 416 and includes capital expenditures for rails, ties, ballast, other track materials,
and grading. The latter category includes the preparation and reconstruction of roadbed. Collectively,
these elements are referred to as basic track components. The hypothesized model is =(,,,),
where I denotes capital expenditures for track. K represents network size or scope. Q is a measure of
traffic activity. F symbolizes firm (railroad-related) effects. And T stands for time.
Table 2.2 Density Categories used in Uniform System of Accounts
Class
Description
I
Lines carrying at least 20 million gross ton-miles per mile on an annual basis and not
designated as belonging to Density Class III
II
Lines carrying less than 20 million gross ton-miles per mile on an annual basis and not
designated as belonging to Density Class III
III
Lines identified as potentially subject to abandonment pursuant to Section 10904 of the
Interstate Commerce Act
IV
Yard and way switching tracks
V
Electronic yards
Capital expenditures for basic track components include installation costs. For example, the costs of new
rails reflect their placement in the track. In addition to the cost of materials, capital expenditures reflect
labor, logistics, equipment, and other costs incurred in moving and installing components. However, the
cost of maintaining and preserving the track is treated as an annual expense. Capital expenditures include
replacements, additions, improvements, and rebuilding activities—when those activities extend the
service lives of components. Repairs are classified as maintenance.
When track components are replaced, they are considered to be “retired” and are no longer reflected in the
investment base. The same track segment may experience capitalized expenditures and retirements
several times over its life, as older light rails are replaced with new heavier ones; grades and/or curves are
reconstructed to improve alignments; and passing tracks, side tracks, switches, and turnouts are added.
2.1 Traffic Measures
There are several potential traffic measures, including revenue ton-miles and gross ton-miles. A ton-mile
represents the movement of one ton in one mile. It is a composite measure of weight and distance. The
ton can be transported (i.e., hauled) or travel under its own power, as in the case of locomotives. Revenue
ton-miles are computed by multiplying the cargo weight by the distance traveled. Gross ton-miles include
the weights of locomotives, freight cars, containers, trailers, cargo, and other equipment, as well as the
distance traveled. A subset of gross ton-miles (train or revenue gross ton-miles) excludes work-related
and track equipment, but includes locomotive, car, container/trailer, and cargo ton-miles.

4
RGTM is the most appropriate measure for this study for the following reasons: (1) Cargo ton-miles alone
do not describe the type of track structure that is needed. A track must be designed to support gross
vehicle weights. (2) Revenue gross-ton-miles exclude non-revenue activities (e.g., work train miles).
2.2 Network Size
There are several potential measures of network size, including miles of road (MOR) and miles of
running track (MRT). Both measures have been used in previous studies. MOR (or route miles) represent
a railroad’s base network. Most rail lines were originally built as single-track lines to connect points or
nodes within a network. As defined by the STB, MOR reflect only the first main track. In addition to the
main track, a rail line may include second, third, and fourth main tracks and/or side tracks. For example, a
10-mile segment between two junctions may consist of two main tracks and two miles of crossover or
passing track. Altogether, this segment comprises 22 miles of running track, which includes 10 miles of
road and 12 miles of “other running track.”
As traffic grows, railroads may add capacity by adding second or third main tracks and/or passing and
side tracks, i.e., other running tracks. Similarly, if traffic declines, other running tracks may be
disassembled and the assets liquidated or used elsewhere in the network. However, the first main track
can only be abandoned if local traffic disappears and through traffic moving over the line can be rerouted.
Even then, the railroad must petition the STB for authority to abandon the line. In the short to
intermediate run, miles of road are relatively fixed. Miles of other running track can be more easily
adjusted.
2.3 Main Effects
A certain level of investment in the base network is necessary regardless of the level or composition of
traffic. Initially, lines may be built with lighter rails and thinner ballast sections suitable for traditional
(e.g., carload) traffic at lower volumes. Capacity may be provided by a single main track with periodic
sidings or passing tracks. However, when unit trains and heavy axle load cars are added to a network and
faster speeds are desired, the quality of the track infrastructure must be improved through investments in
heavier (more durable) rails, heavier tie plates, more ballast, and, in some cases, concrete ties.
Base investment is strongly correlated with miles of road and may not change substantially with modest
increases in traffic. However, incremental investments—those designed to handle unit trains and heavier
railcars—are a function of traffic. As traffic grows, other running tracks (such as passing and side track)
may be added to increase capacity. Eventually, some lines may be doubled-tracked. Changes in miles of
other running track are a function of traffic. If MRT is used to represent network size (instead of MOR)
these investments will be attributed to the network, not to traffic.
Conceptually, MOR and RGTM are correlated. However, in practice, they are independent, at least over
the analysis period. This fact is illustrated in Figure 2.1, which shows distinctly different trend lines for
the two variables. Miles of road have declined since 1985, but at a decreasing rate. In comparison,
revenue gross ton-miles have increased. The decline in miles of road owned by Class I carriers is largely a
function of line sales to local and regional railroads and line abandonments. However, MOR has remained
relatively constant since 1998. The recent drop in RGTM reflects a downturn in the global economy.

5
Figure 2.1 Trends in Miles of Road and Revenue Gross Ton-Miles
2.4 Treatment of Other Effects
A density variable is not included in the model because miles of road and gross ton-miles implicitly
capture density effects. Increasing revenue gross ton-miles (while holding miles of road constant) results
in higher traffic densities. Alternatively, increasing miles of road (while holding RGTM constant) reduces
traffic density.
Most variations in basic track components result from the scope and quality of the base network and
traffic. Nevertheless, investments may be made over time for other reasons. Throughout much of the
analysis period, Class I railroads were making incremental track investments to effectively handle
286,000-lb. and 315,000-lb. railcars. While RGTM is the best traffic measure available, it does not
explicitly account for axle weights. Two groups of traffic may generate the same RGTM, but have
different effects on track because of differences in axle loads. Heavier axle loads require higher-quality
track. However, the use of heavier railcars may result in fewer car-miles (thus, fewer tare ton-miles) and
fewer locomotive-miles to move the same quantity. Because of these trade-offs, the effects of heavier
railcars on gross ton-miles are mixed.
Axle loads are not reported in the R-1 data and cannot be computed directly from public sources. Given
the mixed relationship between axle weights and RGTM, the effects of increasing axle loads may be
subsumed in the time trend variable rather than being reflected in RGTM, which is expected to be
positive. The time variable may reflect other changes in investment patterns over time that are not
associated with traffic, network size, or specific railroads. As described later, the effects of mergers and
consolidations are explicitly accounted for.
0
500
1000
1500
2000
2500
3000
3500
4000
1980 1985 1990 1995 2000 2005 2010
MOR (Hundreds) RGTM (Billions)

6
2.5 Statistical Model
The theoretical model is transformed into a statistical model in Equation 1. The subscript “i” denotes an
observation for a particular railroad, while the subscript “t” indicates a particular year of the data series.
Using this notation and letting epsilon () represent the error term, the regression equation may be written
as:
(1)  =+ ++ ++
The model includes two main explanatory variables (traffic and network size), time (T), and an array of
railroad indicator variables (Fi). The purpose of the railroad variables is to capture fixed effects that are
specific to particular railroads but do not change over time. T, on the other hand, accounts for industry-
wide trends and changes that occur over time. Even when all of these variables are considered (21
altogether, including the indicator variables), a great many factors are not accounted for in the model and
are subsumed in the error term (epsilon).
Fi can assume values of 0 or 1. Fi is equal to 1 when the observation comes from a particular railroad.
Once i is specified (i.e., the observation is determined to come from a particular railroad), the effect of β4
is to shift the intercept (β0) for that railroad.5 T is an integer that measures the elapsed time in years since
1984. For example, t assumes a value of 1 in 1985, 5 in 1989, 10 in 1994, and so forth. Once t is specified
(i.e., the observation is determined to belong to a particular year), the contribution of time is computed as
β3 × t. Once computed in this manner, the contribution of time becomes a constant that shifts the intercept
for a particular year. The slope of the regression is determined by MOR and RGTM.
2.5.1 Functional Form
The choice of functional form is based on data and statistical issues. A plot of track investment against
miles of road is shown in Figure 2.2. In addition to revealing non-constant variance, the graph highlights
the vast differences in scale between smaller Class I railroads (e.g., the Kansas City Southern and Soo
Line) and the largest carriers (e.g., BNSF and UP).
While the apparent heteroscedasticity can be accounted for, the differences in scale are problematic. A
linear model results in a negative intercept for MOR in a simple regression equation and a negative
(counterintuitive) sign in a multiple regression model.
For comparative purposes, a plot of the natural log of track investment against the natural log of miles of
road is shown in Figure 2.3. A graph of track investment and RGTM is presented in Figure 2.4, while
Figure 2.5 depicts the logarithmic relationship between these two variables. Comparisons of Figures 2.2
and 2.3 and 2.4 and 2.5 suggest that the variances of the log relationships are relatively constant—more so
than the linear ones.
5For purposes of simplification, β4 is used in a collective sense in this description. In actuality, each railroad
indicator variable has its own beta coefficient in the model (e.g., β4–β21).

7
Figure 2.2 Plot of Track Investment against Miles of Road
Figure 2.3 Plot of Log of Track Investment against Log of Miles of Road
-2E+09
0
2E+09
4E+09
6E+09
8E+09
1E+10
1.2E+10
1.4E+10
1.6E+10
- 5,000 10,000 15,000 20,000 25,000 30,000 35,000 40,000
Investment$
Miles of Road
17
18
19
20
21
22
23
24
6 7 8 9 10 11
ln(Investment)
ln(MOR)

8
Figure 2.4 Plot of Track Investment against Revenue Gross Ton-Miles
Figure 2.5 Plot of Log of Track Investment against Log of RGTM
0
2E+09
4E+09
6E+09
8E+09
1E+10
1.2E+10
1.4E+10
1.6E+10
0 5E+11 1E+12
Investment$
RGTM
17
18
19
20
21
22
23
24
22 23 24 25 26 27 28 29
ln(Investment)
ln(RGTM)

9
2.5.2 Initial Model
The parameter estimates and standard errors from a logarithmic regression model are shown in Table 2.2.
The dependent variable is the natural log of track investment, where investments are expressed in constant
1985 dollars using the Rail Cost Adjustment Factor (RCAF). The primary explanatory variables are the
logs of MOR and RGTM. However, each Class I railroad that existed during the 1985-2008 period is
represented by an indicator variable, e.g., KCS. When the observation is for the Kansas City Southern
Railway, KCS equals 1. Otherwise, KCS equals zero. Additional indicator variables are defined for
mergers. For example, the UP system includes three railroads that appear in the database: Union Pacific
(UP), Southern Pacific (SP), and Chicago and North Western (CNW). CNW was acquired by UP in 1995.
UP merged with SP in 1997. In the analysis, UP-CNW assumes a value of 1 in 1995, and each year
thereafter, but is zero otherwise. Similarly, the variable UP-SP assumes a value of 1 in 1996, and each
year thereafter, but is zero otherwise.
Table 2.3 Parameter Estimates from Logarithmic Model of Track Investment
Variable
Parameter Estimate
Standard Error
t Value
Pr > |t|
Intercept
-3.9008
1.93940
-2.01
0.0456
ln(MOR)
0.34868
0.06448
5.41
<.0001
ln(RGTM)
0.83199
0.08085
10.29
<.0001
ln(T)
0.08896
0.02067
4.30
<.0001
ATSF
0.40643
0.08134
5.00
<.0001
BNSF
-0.41320
0.13223
-3.12
0.0020
BN
0.14038
0.05686
2.47
0.0144
UPSP
-0.53416
0.13430
-3.98
<.0001
UPCNW
-0.31632
0.19125
-1.65
0.0996
SP
0.53123
0.06809
7.80
<.0001
CNW
0.38754
0.14885
2.60
0.0099
SOO
0.42883
0.17406
2.46
0.0146
ICG
0.68665
0.18027
3.81
0.0002
ICG89
-0.14949
0.13323
-1.12
0.2631
GTW
0.65526
0.25117
2.61
0.0097
GTC
-0.17770
0.32128
-0.55
0.5808
KCS
0.94761
0.19579
4.84
<.0001
CR
0.79455
0.07507
10.58
<.0001
CSX
0.42085
0.05668
7.43
<.0001
CSXCR
-0.78369
0.10486
-7.47
<.0001
NSCR
-0.93980
0.11257
-8.35
<.0001
NS
0.56670
0.06820
8.31
<.0001
Analogous variables are defined for other mergers or acquisitions. For example, Burlington Northern
merged with Atchison, Topeka, and Santa Fe (ATSF) in 1996 to form the Burlington Northern-Santa Fe
(BNSF). CSX and Norfolk Southern (NS) acquired parts of Conrail in 1999. In 2002, the Canadian
National Railway consolidated the Illinois Central Gulf (ICG), Grand Trunk Western (GTW), and other
rail lines into the Grand Trunk Corporation (GTC). In the Grand Trunk system, GTC is 1 if the year is
2002 or later; however, GTC is zero otherwise. The ICG indicator variable assumes a value of 1 when
GTC is 1, or when the observation is for the old ICG prior to 2002. The GTW variable works in a similar

10
manner. The sign and estimate of each railroad indicator variable is relative to the variable omitted from
the equation, which is the unmerged UP railroad. The meaning of the variable ICG89 is discussed later.
The results of a linear model, which includes the same fixed (railroad) and time variables as the log
model, are shown in Table 2.3. In the linear model, MOR has a negative sign and weaker statistical
relationship than in the log model. For statistical reasons, subsequent analyses are based on the
logarithmic model.
Table 2.4 Main Parameter Estimates from Linear Regression Model of Track Investment
Variable
Parameter Estimate
Standard Error
t Value
Prob. > |t|
Intercept
-688008058
994797992
-0.69
0.4899
MOR
-35083
38001
-0.92
0.3570
RGTM
0.01187
0.00086289
13.75
<.0001
As shown in Tables 2.4 and 2.5, the logarithmic model has excellent statistical properties, including an R-
Square of 0.99 and a coefficient of variation of less than 1%. The model explains nearly all of the
variation in the log of investment and provides a very precise fit. The low coefficient of variation (0.6%)
suggests that the model could be an excellent predictor within the range of observed values. However, the
Durbin-Watson test (Table 2.6) indicates autocorrelation, i.e., the errors are correlated over time. This
leads to the formulation of an autoregressive model.
Table 2.5 Mean Square Error and F-Value for Log Model of Track Investment
Source
Degrees
of Freedom
Sum of
Squares
Mean
Square
F Value
Prob. > F
Model
21
367.48915
17.49948
1051.34
<.0001
Error
210
3.49544
0.01664
Corrected Total
231
370.98459
Table 2.6 R-Square and Coefficient of Variation for Log Model of Track Investment
Root Mean Square Error
0.12902
R-Square
0.99
Coefficient of Variation (%)
0.60547
Adjusted R-Square
0.99
Table 2.7 Results of Test for Serial Correlation in Log Model of Track Investment
Durbin-Watson Statistic
0.725
Prob. < DW
<.0001
Prob. > DW
1.0000
1st Order Autocorrelation Coefficient
0.638
2.5.3 Autoregression Model
In regression analysis, each t is assumed to be normally and independently distributed with a mean of zero
and a variance of  (i.e., ~(0, ). Violation of this assumption may affect statistical tests and
parameter estimates. In the revised model, the original regression equation is augmented with an
autoregressive sub-model of the error term. This process is described in Appendix A.
As shown in Table2.7, the parameter estimates of the structural variables have changed. The coefficient of
the log of MOR indicates that track investment increases by roughly 0.59% when miles of road increase
by 1%. The estimate for the log of RGTM indicates that track investment increases by roughly 0.50%

11
when gross ton-miles increase by 1%. As expected, the time-related variable is positive and highly
significant, indicating that track investment has been increasing over time for other reasons.6 Many of the
railroad and merger variables are highly significant, capturing differences among railroads attributable to
economic, managerial, and locational factors and post-merger synthesis and rationalization.
Table 2.8 Results of Autoregression Model of Track Investment
Variable
Parameter Estimate
Standard Error
t Value
Approx. Pr. > |t|
Intercept
2.2451
2.0308
1.11
0.2703
ln(MOR)
0.5902
0.0650
9.08
<.0001
ln(RGTM)
0.5026
0.0877
5.73
<.0001
ln(T)
0.1780
0.0196
9.07
<.0001
ATSF
0.5035
0.0834
6.04
<.0001
BNSF
-0.3110
0.1222
-2.54
0.0118
BN
0.1699
0.0554
3.07
0.0025
UPSP
-0.5807
0.1124
-5.17
<.0001
UPCNW
0.0592
0.1770
0.33
0.7383
SP
0.6215
0.0743
8.37
<.0001
CNW
0.2117
0.1420
1.49
0.1375
SOO
0.1372
0.1716
0.80
0.4250
ICG
0.5070
0.1771
2.86
0.0047
ICG89
-0.2709
0.0657
-4.12
<.0001
GTW
0.5299
0.2371
2.24
0.0266
GTC
-0.0843
0.3025
-0.28
0.7809
KCS
0.6806
0.1912
3.56
0.0005
CR
0.7689
0.0709
10.84
<.0001
CSX
0.4392
0.0497
8.83
<.0001
CSXCR
-0.7520
0.0926
-8.12
<.0001
NSCR
-0.9769
0.0982
-9.95
<.0001
NS
0.5558
0.0578
9.62
<.0001
The Durbin-Watson statistic for first order autocorrelation in the revised model is essentially 2.0. The
probability values shown in Table 2.8 indicate that the null hypothesis (independence of errors) should
not be rejected. Because the transformed model is estimated via generalized least squares, the error
variances are homoscedastic. The regression R-square is essentially unchanged. The error sum of squares
is 1.4145 and the mean square error is 0.00756.
6 In this study, the model is estimated from a population of observations, not a sample. The relationships between
the parameter estimates and standard errors are important in assessing the fit and precision of the regression.
Technically, the probability or p-values based on sampling theory are not applicable to the interpretation of results.
Nevertheless, the population of Class I railroads may be thought of as a sample consisting of railroads that were
classified as Class I carriers during a given year (based on the revenue definitions established by the Surface
Transportation Board) from a larger population of railroads. In this way, the familiar interpretations of p-values can
be applied. It is also instructive to note that the null hypothesis for a t-test is that the slope of a parameter estimate is
zero. The t-ratios and p-values are instructive in this regard, indicating the likelihood of observing a larger value of
the parameter estimate when the null hypothesis is true, its value is actually zero.

12
Table 2.9 Durbin-Watson Test for First Order Autocorrelation
DW
Prob. < DW
Prob. > DW
1.9981
0.2128
0.7872
2.5.4 Data Issues
Most of the data series are consistent throughout the period. However, data for the Illinois Central Gulf
(ICG) stand out (Table 2.9). Line investment suddenly drops by 46% between 1988 and 1989. Distinct
trends exist before and after 1989. The sudden drop is captured by the indicator variable ICG89, which
assumes a value of 1 if the railroad is ICG and the year is 1989. Otherwise, ICG89 is zero.
Table 2.10 Data for Illinois Central Gulf (ICG) Railroad
Year
Miles of Road
Nominal Line Investment (millions)
1988
2,900
$691
1989
2,887
$396
1990
2,773
$398
1991
2,766
$405
As shown in Table 2.7, ICG89 is highly significant and negative, suggesting that the indicator variable is
capturing the sudden drop in investment without a corresponding drop in miles of road. The actual reason
for the sudden decrease in reported investments is unknown. Without a detailed inquiry, it must be
assumed that the data are correct but anomalous. Irrespective of the reason for the sudden drop, the
parameter estimates are largely unaffected when the indicator variable is included in the model.
Table 2.10 indicates a second anomaly in the data. Conrail was acquired by Norfolk Southern and CSX in
1999. Conrail appears in the data series for the last time in 1998. In 1999, the miles of road reported by
CSX and NS collectively increased by 38%, reflecting the integration of Conrail into the two networks.
Similarly, the collective RGTM of CSX and Norfolk Southern increased by 37% between 1998 and 1999.
However, the reported investments in basic track components increased by only 4%.
Table 2.11 Data for Conrail, CSX, and Norfolk Southern Before and After Acquisition
Year
Railroad
Miles of Road
RGTM (millions)
Nominal Line Investment
(Thousands)
1998
CR
10,797
209,069
$3,169,190
CSX
18,181
337,311
$5,742,229
NS
14,423
249,840
$4,633,736
1999
CSX
23,357
440,836
$6,024,295
NS
21,788
364,826
$4,728,444
2000
CSX
23,320
461,935
$6,467,962
NS
21,759
376,550
$4,751,575
There could be many reasons for this inconsistency. As shown in Table 2.7, all five indicator variables
associated with these railroads (CR, CSX, CSXCR, NSCR, and NS) are highly significant. The two
indicator variables associated with the post-acquisition railroads (CSXCR and NSCR) are highly
significant and negative, suggesting that these variables are capturing the anomaly, where MOR and
RGTM jump while line investment remains largely unchanged. The indicator variables may be capturing
other effects as well.

13
2.6 Model Interpretations
2.6.1 Defining Predictive Equations
The model can be used to predict the log of investment for individual railroads. The intercept and all
applicable indicator variables are used in these predictions. For example, the mean-value formula for
BNSF (Equation 2) uses the average values of MOR and RGTM for the 1996-2008 period.
(2) ()
=+ln(







)+ln(








)+ln()+ + +
Where:
()
= Predicted log of investment for BNSF
ln(







)= Log of mean value of miles of road for BNSF
ln(








)=Log of mean value of RGTM for BNSF
ln()= Log of T, where T* represents the midpoint of the period
Similar equations can be developed for other railroads using different indicator variables. The predictions
for Norfolk Southern utilize the variables CR, NS, and NSCR. Predictions for CSX utilize CR, CSX, and
CSXCR. When the appropriate indicator variables are selected, the model yields a series of predictive
equations for individual railroads.
2.6.2 Implications of Constant Elasticity
The log model is a constant elasticity model, e.g., the percentage change in track investment resulting
from a 1% change in RGTM is the same for all output levels. However, this does not mean that the
increase in investment is the same at all levels. A 1% increase starting from an investment base of $1
billion is much greater than a 1% increase starting from a base of $500 million. The slope of the log
model reflects the same (relative) rate of change in investment over the range of observations. In
comparison, the slope of a linear model represents a constant (absolute) rate of change.
Even though the elasticity of the log model is constant, the effects are nonlinear. This is illustrated in
Figure 2.6, which shows how the predicted values of investment for a particular railway (BNSF) derived
from Equation 2 change when RGTM is varied, while holding miles of road constant at its mean value:
(







). The graph is juxtaposed against a linear trend line to illustrate economies of density.

14
Figure 2.6 Variations in Predicted Track Investment from Log Model Holding Miles of Road Constant
at Mean Value
2.6.3 Economies of Density
RGTM and miles of road are the numerator and denominator, respectively, of traffic density as measured
in revenue gross ton-miles per route mile. As Equation 3 suggests, density can be increased by scaling
(reducing) the size of the network in relation to traffic or increasing traffic for a given size of network.
(3)  =

As shown in Figure 1, MOR decreased throughout much of the period. The elasticity of MOR suggests
that track investments decrease when miles of road decrease, but at a less-than-proportionate rate. If
RGTM is held constant, a 1% MOR reduction results in a 0.59% decrease in track investment. Similarly,
the elasticity of RGTM indicates that track investments increase with traffic, but at a less-than-
proportionate rate. If miles of road are held constant while RGTM increases, capital expenditures for
basic track components will rise by approximately 0.50% for each 1% increase in RGTM. Output will
increase at a greater rate than input cost, implying economies of density.
2.6.4 Magnitudes of Parameter Estimates
Several obvious questions stem from the results.
• Why is the elasticity of track investment with respect to MOR substantially less than 1.0? Should
not a 1% reduction in MOR result in a proportional decrease in track investment? If the
investment in each mile of road was the same (e.g., a constant $500,000 per mile) the expected
elasticity would be 1.0 (ceteris paribus). However, the average investment in rail lines sold or
abandoned by Class I railroads (and thus disappear from the investment base) may be less than
the average investment in retained lines (which tend to be mainlines). Moreover, when miles of
road are decreased while revenue gross ton-miles are held constant, the same level of traffic is
concentrated on fewer route miles. While this leads to economies of density, the additional traffic
may require incremental investments elsewhere in the system, i.e., on those lines that now have
0
2
4
6
8
10
12
14
16
18
0 500 1000 1500 2000
Investment ($billion)
RGTM(billions)

15
higher traffic levels. If this occurs, the overall reduction in track investment resulting from a 1%
reduction in MOR will be less than 1%.
• Why is the elasticity of track investment with respect to revenue gross ton-miles less than 1.0?
(1) Economies of Utilization: In many cases, significant traffic volumes can be added to lines with
low traffic levels before any incremental investments are needed. When investments are needed,
adding passing tracks to an existing line to accommodate traffic growth costs less than the
construction of the main track. (2) Economies of Design: In some cases, the strength of materials
increases in a nonlinear manner with size or weight. For example, a rail’s moment of inertia is an
indication of its tendency to resist rotational and bending forces. Moment of inertia increases with
both the cross-sectional area of the rail and its weight. Upgrading a track from 115-lb. to 136-lb.
rail increases the weight of the rail by only 18%, but the moment of inertia increases by 45%. As
described below, incremental capital investments made to existing track and roadbed realize
foundational economies.
• Why is the elasticity of track investment with respect to revenue gross ton-miles less than the
elasticity with respect to MOR? Economies of design and utilization are two key factors. Some
base level of investment in roadbed, ties, ballast, rails, and other track materials is necessary to
initially build and operate a line, regardless of the expected traffic level. In the model, base
investment is a function of MOR. However, once a line is built, further improvements (which are
a function of traffic) comprise incremental capital investments, such as replacing lighter rails with
heavier ones. Incremental investments such as these may not require re-grading or roadbed
reconstruction. Because of foundational investments, capital projects that utilize existing
roadbeds and tracks may be less expensive than initial construction, which reflects extensive
grading and roadbed preparation costs. While the parameter estimates of MOR and RGTM are
different, they are not divergent or inconsistent.
2.7 Sensitivity of Estimates to Cost Indexes
In the results presented thus far, track investments have been restated in constant 1985 dollars using the
RCAF. The Railroad Cost Recovery Index (RCRI) is an alternative series. However, neither index is
perfect for this study. Both are heavily influenced by increases in fuel costs. The mix of labor, materials,
fuel, and other inputs for track construction is unique. While fuel is a significant construction cost, other
railroad activities, such as train and yard operations, are more fuel-intensive than construction projects.
The disadvantage of using an aggregate index is that it reflects cost increases for the railroad as a whole,
not for a specific category such as track investment.
For comparison purposes, the Civil Works Construction Cost (CWCC) Index for roads, railroads, and
bridges, published by the U.S. Army Corps of Engineers, is shown in Figure 7.7 This index is specific to
construction, but reflects highways and bridges as well as track. As the graph shows, the RCAF and the
CWCC are closely aligned until 2008. All things considered, the RCAF may be the best index.
The sensitivities of the parameter estimates to the two indexes are illustrated in Table 2.10, where
elasticities for miles of road, gross ton-miles, and time are shown using the RCRI and the RCAF. These
values are compared with parameter estimates derived from a model that uses nominal investments,
unadjusted by either index. The elasticities based on nominal dollars reflect the true underlying mix of
labor, materials, fuel, and other inputs used in track construction each year. However, the coefficients
7 U.S. Army Corps of Engineers, Department of the Army. Civil Works Construction Cost Index System, March 31,
2011.

16
may be misleading because the dollars are not constantly valued. All things considered, the elasticities
based on the RACF may be the most relevant ones.

17
3. INTERPRETIVE CONTEXT
In addition to the uncertainties posed by cost indexes, other factors should be considered when
interpreting the results of this study.
Figure 3.7 Comparison of RCRI, RCAF, and CWCC Indexes
Table 3.12 Estimated Elasticities of Track Investment with Respect to Miles of Road, Gross Ton-Miles,
and Time Under Different Assumptions
Nominal Dollars
Constant Dollars Based on
Rail Cost Adjustment
Factor
Railroad Cost
Recovery Index
Miles of Road
0.6623
0.5902
0.5831
Gross Ton-Miles
0.6088
0.5026
0.4791
Time
0.2136
0.1780
0.1721
3.2 Delayed Capital Expenditures
The full cost of owning and operating a rail line includes both capital and maintenance expenditures. If
capital expenditures are delayed or deferred, maintenance costs may rise. On the other hand, timely
capital investments may reduce maintenance costs.
In an earlier era, railroads may have delayed capital expenditures because of low returns on investment.
However, Class I industry returns improved from 1.7% in 1970 to more than 10% in 2006 and exceeded
5% for most years since 1985. Given this trend, there is a greater likelihood that capital investments were
made when needed during the analysis period.
1.00
1.20
1.40
1.60
1.80
2.00
2.20
2.40
2.60
2.80
1985 1990 1995 2000 2005 2010
RCRI RCAF CWCC

18
3.3 Regulated Versus Market Investments
Some investment (and disinvestment) decisions are regulated, while others are not. For example,
decisions to abandon a main track, extend a line, or construct a new rail line must be approved by the
STB. In contrast, decisions to upgrade an existing line or add tracks within the existing right-of-way are
often independent decisions under control of the railway. Nevertheless, investment levels must provide
for safe operations, as rail lines are subject to inspection by the Federal Railroad Administration. In many
respects, railroad investment decisions are mixed choices, reflecting purely private objectives as well as
societal goals.
3.4 Accounting Interpretations
For the most part, the data series appear to be consistent. However, the distinction between capital and
maintenance expenditures can be subjective. If expenditures are to be capitalized, the cost of a rebuilding
a line should be “material” in relation to the cost of replacing it. But, what is material? Projects to
improve track alignment without roadbed reconstruction pose interpretative dilemmas. Nevertheless, it is
likely that these decisions are made similarly across railroads. If this is not the case, the railroad indicator
variables should capture the differences.
This study utilizes gross (original) investment instead of net investment. The latter is computed by
subtracting accumulated depreciation from gross investment. Depreciation is an accounting concept,
based on the typical lives of assets. However, depreciation may reflect tax guidelines or incentives and
include “accelerated depreciation.” In some years, negative accumulated depreciation is reported in the R-
1. Issues such as these would need to be addressed before net investment could be used as the dependent
variable in a model. These issues do not affect gross investment, which is a reflection of the railroad’s
reactions to traffic and profit potential, as well as to general economic indicators.
3.5 Economies of Traffic Density
While the data and model suggest that economies of traffic density exist with respect to investments in
basic track components, this conclusion cannot be generalized to track maintenance and line operating
costs. Overall economies of density may be different when line operating and maintenance expenses are
considered. The model is not offered as a comprehensive cost function. Rather, the study is an empirical
one, in which patterns of investment are observed over time.
3.6 Forecasting with the Model
MOR have been relatively constant for the last decade. Given this stability, forecasting investments into
the future based on variations in RGTM may yield valid results. Nevertheless, railway investment
decisions are influenced by a variety of business and regulatory factors. Using the model for forecasting
purposes assumes that these unobserved and uncontrollable factors, which were present between 1985 and
2008, will remain the same in the future. Predicting beyond the range of RGTM poses additional risks,
given the nonlinear nature of the model.
3.7 Relative Contributions of Traffic and Network Size
The relative contributions of MOR and gross ton-miles to track investment are of interest from a
regulatory perspective. When MOR are held constant (a very realistic scenario), the increase in track
investment is roughly 50%; i.e., for a 100% increase in RGTM, track investment is expected to increase
by 50%. However, this is not a completely satisfactory answer. As shown in Table 2.7, the elasticity of

19
investment with respect to time is 18%. T could, at least in part, reflect the upgrading of tracks to handle
heavier axle loads.
Investments to handle heavier cars do not represent fixed investments. It is unclear whether these effects
should be attributed, wholly or in part, to “traffic.” Perhaps the best conclusion that can be drawn from
this study is that there is no compelling evidence to suggest that the traditional assumption (i.e., half of a
railroad’s investment in road varies with traffic) is no longer applicable to investments in basic track
components. However, this conclusion cannot be extended to other areas of roadway investment.
Note that in the long run, track investments are primarily a function of traffic. The investment function
estimated in this study is a short- to intermediate-run one. In the long run, miles of road are theoretically a
function of traffic, even though MOR and RGTM are independent in the short run. A challenge for this
and similar studies is that it is impossible to observe track investments measured on a consistent basis
over a truly long-run period. If the same model was estimated from 75 years of consistent investment
data, the parameter estimates could change.
3.8 Other Statistical Issues
3.8.1 Multicollinearity
The railroad indicator variables provide valuable information in the model and absorb data anomalies.
However, the indicator variables are strongly correlated with MOR and RGTM. While multicollinearity is
often a concern in multiple regression analysis, it poses no real problems for the track investment model,
with the possible exception that some of the hypothesis tests for the indicator variables may be affected.
The null hypothesis for an indicator variable is that it does not significantly shift the intercept; i.e., its
effect is nil. As shown in Table 2.7, only four of the indicator variables have p-values > 0.05, meaning
that they are not statistically significant. It is possible that the standard errors of these variables are so
inflated by multicollinearity that the hypothesis tests are misleading and that these four indicator variables
are actually statistically significant. Even if this were true, it would have no real impact on the primary
interpretations of the study.
However, multicollinearity has a more general effect. The parameter estimates are conditional on the
indicator variables being included in the model. If the indicator variables are removed, the parameter
estimates of MOR and RGTM will change. Since there are strong theoretical and practical justifications
for the indicator variables being included in the model, they should not be removed. Moreover, the
statistical significance of the indicator variables must be appraised collectively. Dropping the indicator
variables with high p-values, while keeping the other indicator variables in the model, would not be
appropriate.8
8 The significance of the indicator variables as a group can be assessed through a partial F-test. The error sum of
squares from a reduced model excluding the railroad indicator variables is 3.6592. In comparison, the error sum of
squares from the full model (including the railroad indicator variables) is 1.4145. The difference in the error sum of
squares attributable to the railroad indicator variables is 2.2448. This calculated value (which is reflected in the
numerator of the F-statistic) has 21 minus 18, or 3 degrees of freedom. The error sum of squares from the full model
(which is reflected in the denominator of the F-statistic) has 232 – 21 – 1, or 210 degrees of freedom. The computed
F-value of 111 is far greater than the critical F-value of 2.65 for an alpha of .05. This test formally confirms what is
apparent from Table 2.7. Collectively, the railroad indicator variables significantly improve the model. Therefore, all
18 indicator variables should stay in the model.

20
3.8.2 Impacts of Other Activity Variables
Introducing another highly correlated activity variable into the model will change the parameter estimates.
For example, it could be argued that changes in other running track miles are linked to train-miles, more
so than to revenue gross ton-miles. However, the R-square from a regression of the log of train-miles
(TM) against the log of RGTM is 0.99.
As shown in Table 3.2, the log of TM is not statistically significant when it is included in a model with
the log of RGTM and the log of MOR. Its p-value is 0.07. However, this is not a binding statistical
conclusion, given the possible effects of multicollinearity on hypothesis tests. The primary justification
for including TM would be if they contribute a unique and independent effect that RGTM does not. This
is a difficult argument to make, given that the R-square from a regression of the log of TM against the log
of RGTM is 0.99.
Table 3.13 Results of Track Investment Model with Train-Miles Added
Variable
Estimate
Standard Error
t Value
Approx. Prob. > |t|
ln(MOR)
0.5591
0.0664
8.42
<.0001
ln(RGTM)
0.3385
0.1354
2.50
0.0133
ln(TM)
0.2398
0.1306
1.84
0.0680
ln(T)
0.1766
0.0195
9.07
<.0001
For purposes of brevity, only the main variables from a model that also includes 18 indicator variables
are shown.
The primary effect of TM (when it is included in the model) is to reduce the parameter estimates of the
other variables. However, the combined partial effects of TM and RGTM are only marginally greater than
the effect of RGTM in the previous model. The general conclusion regarding the elasticity of track
investment with respect to “traffic” does not change substantially when TM is added to the model.
The decision in this case is not to add TM, for all of the reasons noted above. However, this is a
judgmental decision as there may be differing points of view.

21
4. RESEARCH TO EXPAND THE ANALYSIS
The model presented in this paper includes only a subset of roadway investment costs, e.g., the basic track
accounts. Therefore, it only partially addresses the gap in knowledge. No definitive statements can be
made regarding the efficacy of the STB’s overall assumption that roadway investment costs are 50%
variable with traffic. Roadway investment includes many other cost elements. Thus, other models of
roadway investment are possible.
4.1 Other Roadway Investment Models
A model of traffic control and communication infrastructure could be estimated using investments in
communication systems, signals and interlockers, power transmission systems, and grade crossings.
These investments may be more closely related to TM than to RGTM. Traffic control and communication
investments are affected more by the number of trains per day than by train weight.
Investments in structures, such as tunnels, bridges, and trestles, and miscellaneous facilities could
comprise additional clusters. Gross ton-miles may be the most logical traffic variable for a structure’s
sub-model, while investments in other facilities, including station and office buildings, may be more
appropriately modeled as a function of revenue gross ton-miles or revenue tons. Investments in
specialized facilities, such as COFC/TOFC terminals, could be modeled as a function of related activities
(e.g., container and trailer units loaded and unloaded).
A moderate level of effort is involved in developing these models. The R-1 database developed for this
project includes all of the variables. However, programs must be written to create the input datasets in
proper format for the models. These data elements have not been examined for consistency or statistical
issues.
4.2 Individual Component Models
It is also possible to develop models for individual track components, such as rails and other track
materials, ballast, ties, and roadbed. However, a sub-modeling approach may impose restrictions on the
regression functions. For example, railroads may trade off better ballast and ties against heavier rails in
some cases. The track is an integrated structure. The results of individual component models must be
interpreted accordingly.
4.3 Density Class Models
Using data from Schedule 720, it may be possible to develop separate regression models for density
classes I and II. The consistency of Schedule 720 data has not been examined. Moreover, programming
changes are needed to create a database for use with density class models. However, the time and
resource costs to develop these databases are moderate. The practical applications of the models with
respect to URCS are unclear.
4.4 Axle Load Effects
In theory, track impacts are a function of axle loads and speed, which determine the dynamic impacts and
deflections of the track. Car axle loads cannot be effectively computed from R-1 data. In order to add this
variable, a weighted average would have to be computed from the waybill sample for each railroad, for
each year. The axle weights in the sample could be weighted by the car-miles of travel.

22
An aggregate measure of speed can be computed from R-1 data by dividing train-miles by train-hours.
However, this calculated value is a broad system performance measure that includes many factors, such
as train delays. It is of little use in analyzing the dynamic effects of axle loads. A more promising
approach is to estimate the weighted-average speed limit from Schedule 720. This variable could serve as
a proxy for the weighted dynamic effect on each railroad’s system, based on the carrier’s line
classifications and speed limits.
The resource cost of adding these variables is moderate. However, the probability of success is unknown.

23
APPENDIX A: STATISTICAL MODELING PROCEDURES
In this study, the SAS REG and AUTOREG procedures are used in conjunction with the underlying data
illustrated in Appendix B. Because the initial results indicate serial correlation, the regression model is
transformed. To illustrate the issues associated with autocorrelation and potential solutions, the structure
and assumptions of the ordinary least squares (OLS) model (the results of which are shown in Table 3)
are briefly introduced.
A.1 OLS Model: The Starting Point
If the track investment model was not affected by serial correlation, the OLS procedures inherent in
PROC REG could be used. Using matrix notation, the OLS model can be depicted as:
(A. 1) = +
 represents an (n × 1) vector of observations on the dependent variable, e.g., a 232 × 1 vector of track
investment data for Class I railroads over time.  is an augmented (n × (k + 1)) matrix of observations of
explanatory variables. In this case,  is a (232 × [21 + 1]) matrix, in which the first column is a vector of
ones corresponding to the implied coefficient of the intercept term.  is a (k + 1) × 1 vector of parameters
to be estimated (including the intercept). The expected value of  (E[]) is . The variance of  is
equal to the assumed-to-be-constant variance () times an identity matrix (i.e., []=). The
covariance of the errors (e) is assumed to be zero, i.e., (,)= 0, which is equivalent to saying
that the (,)= 0. The objective is to minimize the sum of the squared errors (SSE or 󰆒). Since
=, SSE may be expressed as:
(A. 2) SSE =(  )󰆒(  )
A.2 is minimized by taking the partial derivative with respect to , setting the derivative equal to zero,
solving for , and verifying that the second derivative is nonnegative.
(A. 3) 
SSE =
(󰆒  2󰆒 +󰆒󰆒)
Expand the expression
(A. 4) 
SSE =
(2󰆒+ 2󰆒)
Take the first derivative
(A. 5) 2󰆒+ 2󰆒 = 0
Set it to zero
(A. 6) 󰆒 =󰆒
Rearrange the expression
(A. 7) =(󰆒)󰆒
Solve for 
(A. 8) 
SSE =󰆒
Evaluate the second derivative
An assumption in OLS regression is that the errors (i.e., the residuals of the regression) are uncorrelated,
i.e., their covariance is zero. If this is not true, the OLS parameter estimates may no longer be the
minimum variance estimators, in which case an autocorrelation model offers improvements.

24
In the following paragraphs, a transformation and autoregression modeling process is illustrated for the
simple case of first-order autocorrelation. This process—referred to as AR(1)—serves to illustrate a more
complex process with higher orders of autocorrelation.
A.2 Autocorrelated Errors
An autocorrelated error term may be envisioned as consisting of two components: (1) an inertial error that
is carried forward from the previous time period, and (2) an error that is specific to the current period.9
The inertial error reflects perceptions of railroad managers about factors outside the model. These
unobserved and uncontrolled influences may include perceptions of government policies, regulations, and
programs; modal competition; the cost of capital and projected ROI; and a variety of risks. Such
perceptions tend to change slowly.
In addition to inertial perceptions, new factors may affect decision making in any given year. Changes in
tax policies, stimulus spending, new or revised loan programs and other financial changes not reflected in
the model may introduce error disturbances. Changes in the competitive milieu (such as changes in
highway funding and truck size and weight regulations) may have similar effects.
A.2.1 Equation of Autocorrelated Error Term
The previous theory of unobserved influences is reflected in Equation A.9, where  represents the
inertial error carried forward from the previous time period and  represents the uncorrelated disturbance
in the current year.
(A. 9) = +
Rho (ρ) is the autocorrelation coefficient. In a stationary process, it can assume values < |1.0|. The inertial
error carried forward () must be less than the error in the previous period. This restriction has a
practical benefit of preventing the error from increasing without bound.
A.2.2 Error Variance and Correlation
Letting 
 denote the variance of  (the inertial component) and 
 represent the variance of , it can be
shown that:
(A. 10) 
=

1 
Moreover, it can be shown that the error covariance [(,)] is equal to 
 and that ρ is the
correlation coefficient that describes the strength of the relationship between  and . If ρ > 0
successive errors are positively correlated. If ρ < 0 successive errors are negatively correlated. The
covariance between errors more than one period apart (i.e., k periods apart) is equal to 
, while  is
the correlation coefficient of errors separated by more than one time period. The errors in the
autocorrelation model are homoscedastic because the variance of  is equal to 
 (1 ), which is the
same for all observations.
9 Griffiths, W., Hill, R. and Judge, G.: Learning and Practicing Econometrics, John Wiley and Sons, 1993

25
A.2.3 Transformations to Achieve Desired Error Properties
The objective of the transformation process is to derive a new equation in which the error term is 
instead of . De-emphasizing the indicator variables that affect only the intercept, the regression equation
for any observation (except the first one) can be represented as:
(A. 11) ln()=+ln()+ln()++ +
The equation for the previous observation (in period t−1) can be denoted as:
(A. 12) ln()=+ln()+ln()++
Solving Equation A.12 for , multiplying both sides of the solved equation by ρ (which results in
 on the left-hand side), substituting the solved equation for  into Equation A.11, and
simplifying the results yields a transformed equation in which the modified terms are:
(A. 13) ln(
)= ln() ln()
(A. 14) ln(
)= ln() ln()
(A. 15) ln(
)= ln() ln()
(A. 16) 
= 1  

 is the transformed intercept. After transformation, the error term has the following properties:
~(0, 
). However, the transformation results in only n−1 new observations, leaving the first
observation unchanged. Since, the error of the first observation is not linked to previous ones, the
equation for the first observation may be written as:
(A. 17) ln()=+ln()+ln()++
It can be shown that multiplying A.17 by (1 ) results in a variance of:
(A. 18) (
)=(1 )()=(1 )

1 =

With this transformation, the errors for all observations have the same desired properties.
A.3 Autocorrelation Modeling Process
The primary steps in the process are:
1. Run the regression
2. Output the residuals (errors) to file
3. Use the outputted errors in a new regression model to estimate the autocorrelation coefficient (ρ)
4. Estimate the transformed regression equation using the estimated value of ρ from the regression in
step 3 and the transformed variables shown in Equations A.13–A.16
5. Output the residuals of the regression using the transformed equation to file
6. Return to step 3 and use the outputted residuals from step 5 to estimate a revised value of rho
7. Repeat steps 4–6 until the value of rho from the previous iteration is essentially unchanged

26
To illustrate step 3, let  represent the residuals outputted in step 2. The new regression model can be
depicted as =
󰆹 +, where 
󰆹 is an OLS estimate of the autocorrelation coefficient () and 
is an estimate of the uncorrelated component of the error term.
The process described above is broadly referred to as generalized least squares (GLS). SAS
AUTOREG uses a matrix algebra procedure to simultaneously estimate a vector of autoregressive
parameters that includes many lag variables, not just a single variable corresponding to the first lag
period.
A.3.1 Model Specification
In many cases, the form of autocorrelation can be hypothesized from theory or observation. In addition to
the AR(1) model, second- and third-order autocorrelation models are frequently hypothesized. In each
case, the error process is well understood. In this case, it is not.
In the long run, investment in basic track components is a regular process. However, it can be quite
irregular and periodic in the short run. Rails have long lives. When a line is rebuilt with new rail, it may
be some time before significant capital investments are made in the line again. Perceptions related to ROI
and risks may lag several periods. Reactions to changes in government policies may be cautious and
unfold over many years. Inertial forces may extend over several periods, complicated by the scale and
cyclical nature of capital investments.
First-order autocorrelation is very likely to be found in the track investment model. However, higher
orders of autocorrelation may exist. Given the complex structure of the error covariances, an empirical
approach is used. The R-1 database includes 24 years of observations for most railroads. Therefore, 23 lag
periods are analyzed. The estimated values of rho () are graphed in Figure A.1, which shows
autocorrelation throughout much of the period, including significant autocorrelations in lag years 11
through 15.
Figure A.14 Autocorrelations in Track Investment Model
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 5 10 15 20 25
Autocorrelation coefficient
Lag Period (Years)

27
A.3.2 Illustrative Manual Process
An iterative solution procedure for an AR(1) process can be derived using PROC REG. The SAS
statements used in the first iteration of the process are shown below.
proc reg data=track ;
model LnI=LnMOR LnRGTM LnT;
output out=gls1(keep=ehat)
r=ehat /* residuals */;
data gls2;
set gls1;
* compute lagged value of residual;
lage=lag(ehat);
proc reg data=gls2
outest=rho1
(keep=lage rename=(lage=rhohat));
model ehat=lage;
data gls4;
if _n_=1 then set rho1;
set track;
* create lag variables;
ylag = lag(LnI);
x1lag = lag(LnMor);
x2lag = lag(LnRGTM);
x3lag = lag(LnT);
* transform variables, including intercept;
if _n_ = 1 then do; /* first obs. */
y = sqrt(1- rhohat**2)*LnI;
x1 = sqrt(1- rhohat**2)*LnMOR;
x2 = sqrt(1- rhohat**2)*LnRGTM;
x3 = sqrt(1- rhohat**2)*LnT;
int = sqrt(1- rhohat**2);
end;
else do;
y = LnI - rhohat*ylag;
x1 = LnMOR - rhohat*x1lag;
x2 = LnRGTM - rhohat*x2lag;
x3 = LnT - rhohat*x3lag;
int= 1 - rhohat;
end;
proc reg data=gls4;
model y=int x1 x2 x3/noint;
This process could be repeated several times by outputting the residuals from the last data step (gls4) and
returning to step 3 (gls2), until the estimated value of ρ (rhohat) does not change significantly from the
previous iteration. While this process could be automated with an SAS macro, it is inefficient and
becomes quite cumbersome when several lag periods are considered. Instead of the manual process,
PROC AUTOREG is used. The essential SAS statements are shown below.

28
proc autoreg data=track;
model LnI=LnMOR LnRGTM LnT ATSF BNSF BN UPSP UPCNW SP CNW SOO ICG ICG89
GTW GTC KCS CR CSX CSXCR NSCR NS / nlag=23 iter;
Before describing how the estimation procedures in PROC AUTOREG work, the generalized least
squares (GLS) process is highlighted.
A.3.3 Generalized Least Squares
When the errors of a regression model are correlated, the calculation of the variance as  is no longer
valid. The covariance matrix can no longer be represented as the product of a common (scalar) variance
times an identity matrix, which has ones on the diagonal and zeros elsewhere. The off-diagonal elements
of the matrix, which represent the covariances among the errors from different time periods,
e.g.,[(,)], may not be zero. Instead, the variance-covariance matrix resembles A.19, in the case
of first-order autocorrelation.
(A. 19) 





1  
1  
1 
    
   1





=
In this situation, the error covariances have a general, but not a specific, form. The variance is equal to
 (as shown above) rather than . Letting =, the objective of GLS is to minimize the
generalized sum of squares, as shown in A.20.
(A. 20) =(  )󰆒(  )
Equation A.21 depicts the normal GLS equation, derived in the same manner as before, which can
subsequently be solved for .
(A. 21) (󰆒)=󰆒
With this background, the estimation procedures used in SAS AUTOREG are described.
A.3.4 Iterated Yule-Walker Method
AUTOREG uses what is called the iterated Yule-Walker method, a GLS process in which the OLS
residuals are used to estimate the error covariances. Since the autocorrelation coefficient (ρ) is unknown
and must be estimated from the residuals, the method may be referred to as estimated generalized least
squares (EGLS), a process in which the estimators have desirable large sample or asymptotic properties
only. In some publications, the Yule-Walker method has been referred to as the two-step full transform
method. For an AR(1) process, Yule-Walker estimates are consistent with Prais-Winsten estimates.
In the Yule-Walker method, the initial (structural) model is augmented with a vector of autoregressive
terms. By simultaneously estimating the regression coefficients and the autoregressive terms of the error
model, the parameter estimates can be corrected for autocorrelation. In this process, the variance matrix 
is formed from the autoregressive parameters (as illustrated in A.19). Afterward,  is computed as 
and efficient parameters estimates are derived via generalized least squares. The estimation of  using
GLS is alternated with the estimation of  (a vector of autocorrelation coefficients), in much the same

29
manner as the manual process described earlier. The method starts by generating the OLS estimates of .
Next,  is estimated from the OLS residuals.  is estimated from the estimate of  and  is estimated
from  and the OLS estimate of the common variance σ2. The estimates of the regression parameters 
(corrected for autocorrelation) are computed via GLS, using the estimated  matrix. The only difference
is that in the iterated method, the steps are repeated until the estimates of  are essentially stable. A
convergence criterion of 0.001 is used.
Other estimation methods can be used with AUTOREG, including unconditional least squares (also
referred to as nonlinear least squares) and maximum likelihood. The maximum likelihood method is
recommended in cases where there are many missing values in the data series, which does not apply in
this case.
The Yule-Walker estimates were shown earlier in Table 2.7. As shown in Table A.2, the maximum
likelihood method yields somewhat different estimates. Nevertheless, the selection of methods does not
affect the conclusions of the study.
Table A.15 Parameter Estimates from Autoregression Model Using Maximum Likelihood Method
Variable
Parameter Estimate
Standard Error
t Value
Approx. Pr > |t|
ln(MOR)
0.5886
0.0636
9.26
<.0001
ln(RGTM)
0.5415
0.0869
6.23
<.0001
ln(T)
0.1749
0.0197
8.87
<.0001
A.4 Test for Autocorrelation
The Durbin-Watson test was referred to several times in the paper. The calculation of the Durbin-Watson
statistic (D) is illustrated in Equation A.22.
(A. 22) =( )





Where =  is the residual for observation “i” from the regression.
A more technically correct statistic for panel datasets has been proposed by Bhargava, et al. (1982).10 In
this approach, the D statistic shown in Equation A.223 is estimated within each cross-sectional class, e.g.,
each railroad.
(A. 23)  =  , ,



   ,




Both statistics have been calculated in this study. Because the time period is 24 years, the two approaches
produce essentially the same results. Therefore, the Durbin-Watson statistic generated by the SAS
software is reported in this study. Before a regression analysis is run, the data are sorted by railroad and
year—a prerequisite for the calculation of either statistic and the running of PROC AUTOREG.
10 Bhargava, A., Franzini, L., and W. Narendranathan. “Serial Correlation and the Fixed Effects Model.” Review of
Economic Studies (1982), XLIX, pp. 533-549.

30
APPENDIX B: DATA
Table B.16 Values of Variables Used in Study
Year
Railroad
Nominal
Investment
(Millions)
Real
Investment
Based on RCRI
(Millions)
Miles
of
Road
Rev. Gross Ton-
Miles (Millions)
1985
ATSF
$1,699.49
$1,699.49
11,869
157,684
1986
ATSF
$1,799.32
$1,798.55
11,661
151,567
1987
ATSF
$1,906.36
$1,901.53
11,709
162,949
1988
ATSF
$1,964.07
$1,954.27
11,652
176,361
1989
ATSF
$1,999.36
$1,985.16
11,266
184,985
1990
ATSF
$1,984.65
$1,972.90
10,650
174,188
1991
ATSF
$1,990.52
$1,977.58
9,639
183,349
1992
ATSF
$1,997.78
$1,983.24
8,750
191,942
1993
ATSF
$2,129.92
$2,085.27
8,536
204,541
1994
ATSF
$2,300.21
$2,214.80
8,352
219,414
1995
ATSF
$3,971.82
$3,429.94
9,126
231,333
1985
BN
$3,903.63
$3,903.63
26,780
372,141
1986
BN
$4,000.85
$4,000.10
25,539
379,314
1987
BN
$3,955.10
$3,956.09
23,476
405,198
1988
BN
$3,849.95
$3,860.00
23,391
418,197
1989
BN
$4,140.81
$4,114.62
23,356
430,129
1990
BN
$4,379.87
$4,313.86
23,212
444,586
1991
BN
$4,404.02
$4,333.15
23,088
434,152
1992
BN
$4,572.68
$4,464.43
22,786
432,203
1993
BN
$4,740.11
$4,593.72
22,316
441,711
1994
BN
$4,937.18
$4,743.61
22,189
477,845
1995
BN
$5,155.14
$4,902.05
22,200
529,042
1996
BNSF
$9,758.43
$8,119.94
35,208
732,330
1997
BNSF
$10,118.87
$8,368.03
33,757
838,302
1998
BNSF
$11,192.65
$9,096.80
33,353
921,062
1999
BNSF
$11,371.33
$9,218.35
33,264
949,469
2000
BNSF
$11,910.07
$9,554.09
33,386
958,576
2001
BNSF
$12,429.78
$9,869.05
33,063
981,469
2002
BNSF
$13,429.25
$10,470.39
32,525
955,477
2003
BNSF
$14,117.32
$10,869.94
32,266
991,230
2004
BNSF
$14,820.72
$11,256.99
32,150
1,106,373
2005
BNSF
$15,711.84
$11,691.92
32,154
1,158,305

31
Year
Railroad
Nominal
Investment
(Millions)
Real
Investment
Based on RCRI
(Millions)
Miles
of
Road
Rev. Gross Ton-
Miles (Millions)
2006
BNSF
$17,558.73
$12,547.49
31,910
1,223,757
2007
BNSF
$18,472.58
$12,951.87
32,205
1,227,033
2008
BNSF
$19,542.32
$13,368.06
32,166
1,224,930
1985
CNW
$619.41
$619.41
7,301
53,455
1986
CNW
$640.60
$640.43
6,305
56,303
1987
CNW
$665.22
$664.12
6,214
56,446
1988
CNW
$664.63
$663.58
5,794
61,037
1989
CNW
$552.68
$565.58
5,650
57,719
1990
CNW
$584.67
$592.25
5,624
56,911
1991
CNW
$618.93
$619.61
5,573
57,540
1992
CNW
$673.47
$662.06
5,419
59,830
1993
CNW
$724.44
$701.42
5,337
65,651
1994
CNW
$756.69
$725.95
5,211
71,018
1985
CR
$3,014.27
$3,014.27
14,025
174,647
1986
CR
$3,322.99
$3,320.62
13,739
175,305
1987
CR
$3,539.05
$3,528.49
13,341
188,585
1988
CR
$3,794.03
$3,761.48
13,111
198,112
1989
CR
$3,991.19
$3,934.07
13,068
191,552
1990
CR
$4,115.38
$4,037.57
12,828
193,964
1991
CR
$3,765.09
$3,757.82
12,454
187,539
1992
CR
$4,055.61
$3,983.96
11,895
193,025
1993
CR
$3,310.39
$3,408.51
11,831
200,936
1994
CR
$3,369.21
$3,453.25
11,349
217,930
1995
CR
$3,171.24
$3,309.34
10,701
211,182
1996
CR
$3,034.50
$3,213.75
10,543
215,110
1997
CR
$3,114.26
$3,268.65
10,801
220,096
1998
CR
$3,169.19
$3,305.93
10,797
226,994
1985
CSX
$3,110.62
$3,110.62
23,945
299,388
1986
CSX
$3,534.61
$3,531.36
22,887
288,572
1987
CSX
$3,628.41
$3,621.60
21,494
310,651
1988
CSX
$3,743.39
$3,726.67
20,376
315,604
1989
CSX
$3,830.15
$3,802.62
19,565
293,003
1990
CSX
$4,152.94
$4,071.65
18,943
318,267
1991
CSX
$4,470.51
$4,325.27
18,854
295,766
1992
CSX
$4,418.19
$4,284.55
18,905
309,593

32
Year
Railroad
Nominal
Investment
(Millions)
Real
Investment
Based on RCRI
(Millions)
Miles
of
Road
Rev. Gross Ton-
Miles (Millions)
1993
CSX
$4,771.31
$4,557.22
18,779
317,469
1994
CSX
$4,926.64
$4,675.36
18,759
333,507
1995
CSX
$5,049.52
$4,764.69
18,645
343,071
1996
CSX
$5,394.76
$5,006.03
18,504
345,489
1997
CSX
$5,494.33
$5,074.56
18,285
356,293
1998
CSX
$5,742.23
$5,242.81
18,181
363,024
1999
CSX
$6,024.30
$5,434.69
23,357
474,249
2000
CSX
$6,467.96
$5,711.18
23,320
497,518
2001
CSX
$6,598.98
$5,790.59
23,297
489,717
2002
CSX
$6,817.81
$5,922.24
23,160
467,258
2003
CSX
$7,194.58
$6,141.02
22,841
485,501
2004
CSX
$10,272.84
$7,834.87
22,153
507,184
2005
CSX
$10,390.04
$7,892.07
21,357
501,575
2006
CSX
$10,811.76
$8,087.43
21,114
510,137
2007
CSX
$11,273.38
$8,291.70
21,166
493,041
2008
CSX
$11,745.58
$8,475.41
21,204
483,792
2002
GTC
$3,721.43
$2,306.01
6,390
104,014
2003
GTC
$3,701.34
$2,294.34
6,493
105,363
2004
GTC
$4,013.63
$2,466.18
6,822
109,589
2005
GTC
$4,176.46
$2,545.66
6,736
109,498
2006
GTC
$4,314.97
$2,609.82
6,737
111,835
2007
GTC
$4,353.93
$2,627.06
6,738
110,833
2008
GTC
$4,538.17
$2,698.74
6,738
108,413
1985
GTW
$138.46
$138.46
1,310
14,201
1986
GTW
$139.81
$139.79
1,311
14,021
1987
GTW
$124.17
$124.76
943
13,380
1988
GTW
$120.89
$121.76
931
13,905
1989
GTW
$128.91
$128.78
959
14,436
1990
GTW
$137.82
$136.20
927
14,096
1991
GTW
$144.02
$141.15
925
13,277
1992
GTW
$156.14
$150.59
925
14,008
1993
GTW
$173.99
$164.37
925
15,998
1994
GTW
$186.51
$173.89
925
16,715
1995
GTW
$189.31
$175.93
916
16,265
1996
GTW
$201.00
$184.10
918
23,514

33
Year
Railroad
Nominal
Investment
(Millions)
Real
Investment
Based on RCRI
(Millions)
Miles
of
Road
Rev. Gross Ton-
Miles (Millions)
1997
GTW
$189.78
$176.38
659
25,165
1998
GTW
$211.04
$190.81
646
23,877
1999
GTW
$239.52
$210.18
628
24,829
2000
GTW
$278.93
$234.74
627
26,645
2001
GTW
$298.19
$246.42
627
28,015
1985
ICG
$843.26
$843.26
4,772
54,016
1986
ICG
$780.42
$780.90
3,788
42,052
1987
ICG
$705.10
$708.44
3,205
36,262
1988
ICG
$686.17
$691.14
2,900
36,652
1989
ICG
$349.26
$396.22
2,887
36,086
1990
ICG
$351.10
$397.75
2,773
35,137
1991
ICG
$363.76
$405.46
2,766
37,037
1992
ICG
$376.43
$417.66
2,732
35,207
1993
ICG
$393.16
$430.58
2,717
37,690
1994
ICG
$407.82
$441.73
2,665
39,290
1995
ICG
$430.47
$458.20
2,642
45,337
1996
ICG
$448.65
$470.90
2,623
41,905
1997
ICG
$483.49
$494.89
2,598
42,128
1998
ICG
$511.64
$514.00
2,593
44,463
1999
ICG
$543.75
$535.84
2,591
46,451
2000
ICG
$577.39
$556.80
2,544
50,168
2001
ICG
$609.09
$576.01
2,544
50,094
1985
KCS
$263.88
$263.88
1,661
24,101
1986
KCS
$272.05
$271.99
1,666
22,999
1987
KCS
$292.09
$291.27
1,665
23,095
1988
KCS
$301.02
$299.43
1,681
22,878
1989
KCS
$366.14
$356.43
1,681
23,056
1990
KCS
$391.16
$377.28
1,681
23,669
1991
KCS
$389.98
$376.34
1,682
23,678
1992
KCS
$411.18
$392.84
1,680
25,459
1993
KCS
$433.71
$410.24
1,712
26,313
1994
KCS
$700.50
$613.16
2,880
33,412
1995
KCS
$753.51
$651.69
2,931
37,697
1996
KCS
$769.70
$663.01
2,954
36,916
1997
KCS
$769.26
$662.71
2,845
38,335

34
Year
Railroad
Nominal
Investment
(Millions)
Real
Investment
Based on RCRI
(Millions)
Miles
of
Road
Rev. Gross Ton-
Miles (Millions)
1998
KCS
$784.21
$672.86
2,756
41,956
1999
KCS
$803.69
$686.11
2,756
42,986
2000
KCS
$812.23
$691.43
2,701
38,434
2001
KCS
$887.89
$737.28
3,102
39,271
2002
KCS
$931.52
$763.53
3,084
37,494
2003
KCS
$950.62
$774.63
3,084
41,104
2004
KCS
$1,009.75
$807.16
3,072
43,630
2005
KCS
$1,094.60
$848.57
3,197
53,943
2006
KCS
$1,118.58
$859.68
3,176
55,721
2007
KCS
$1,290.98
$935.97
3,151
54,431
2008
KCS
$1,506.99
$1,020.01
3,165
53,501
1985
NS
$2,638.60
$2,638.60
17,620
202,461
1986
NS
$2,733.98
$2,733.25
17,520
200,234
1987
NS
$2,707.71
$2,707.98
17,254
203,048
1988
NS
$2,877.33
$2,862.98
17,006
208,730
1989
NS
$3,026.94
$2,993.94
15,955
209,196
1990
NS
$3,417.24
$3,319.24
14,842
218,678
1991
NS
$3,458.20
$3,351.95
14,721
211,409
1992
NS
$3,637.36
$3,491.40
14,703
221,153
1993
NS
$3,755.77
$3,582.83
14,589
228,558
1994
NS
$4,036.88
$3,796.65
14,652
246,101
1995
NS
$4,228.76
$3,936.13
14,407
255,330
1996
NS
$4,505.18
$4,129.36
14,282
261,810
1997
NS
$4,628.21
$4,214.04
14,415
270,247
1998
NS
$4,633.74
$4,217.79
14,423
272,617
1999
NS
$4,728.44
$4,282.22
21,788
396,548
2000
NS
$4,751.58
$4,296.64
21,759
408,243
2001
NS
$4,833.75
$4,346.44
21,569
377,468
2002
NS
$5,077.69
$4,493.20
21,558
372,260
2003
NS
$5,221.11
$4,576.48
21,520
378,836
2004
NS
$9,302.68
$6,822.41
21,336
406,904
2005
NS
$9,613.29
$6,974.01
21,184
415,827
2006
NS
$9,781.08
$7,051.74
21,141
417,423
2007
NS
$10,156.48
$7,217.85
20,890
398,857
2008
NS
$10,665.95
$7,416.07
20,831
391,457

35
Year
Railroad
Nominal
Investment
(Millions)
Real
Investment
Based on RCRI
(Millions)
Miles
of
Road
Rev. Gross Ton-
Miles (Millions)
1985
SOO
$535.27
$535.27
7,975
39,346
1986
SOO
$539.12
$539.09
7,747
42,956
1987
SOO
$396.23
$401.63
5,809
43,689
1988
SOO
$414.77
$418.57
5,807
39,856
1989
SOO
$420.99
$424.01
5,770
39,235
1990
SOO
$501.96
$491.49
5,293
43,707
1991
SOO
$502.27
$491.74
5,045
43,600
1992
SOO
$549.52
$528.52
5,033
43,556
1993
SOO
$573.62
$547.13
5,062
43,730
1994
SOO
$597.25
$565.11
5,139
40,327
1995
SOO
$351.66
$386.57
5,130
48,893
1996
SOO
$390.15
$413.48
4,980
48,547
1997
SOO
$453.06
$456.79
3,364
41,566
1998
SOO
$500.93
$489.27
3,358
40,282
1999
SOO
$520.57
$502.63
3,261
40,639
2000
SOO
$481.61
$478.35
3,225
43,329
2001
SOO
$505.98
$493.12
3,225
45,281
2002
SOO
$547.28
$517.97
3,225
45,427
2003
SOO
$562.96
$527.08
3,258
48,191
2004
SOO
$602.56
$548.86
3,251
49,945
2005
SOO
$631.23
$562.86
3,511
47,713
2006
SOO
$670.52
$581.06
3,267
48,323
2007
SOO
$697.59
$593.04
3,267
48,670
2008
SOO
$735.55
$607.81
3,267
46,122
1985
SP
$2,491.11
$2,491.11
15,624
200,706
1986
SP
$2,651.37
$2,650.14
15,194
194,792
1987
SP
$2,712.88
$2,709.32
15,046
203,470
1988
SP
$3,062.36
$3,028.67
15,023
210,530
1989
SP
$3,332.37
$3,265.03
15,023
220,390
1990
SP
$3,498.59
$3,403.57
14,846
215,851
1991
SP
$3,554.38
$3,448.12
14,389
214,183
1992
SP
$3,721.61
$3,578.29
14,389
233,049
1993
SP
$3,819.43
$3,653.82
14,099
246,077
1994
SP
$3,620.63
$3,502.62
13,715
268,935
1995
SP
$3,668.91
$3,537.72
15,388
288,759

36
Year
Railroad
Nominal
Investment
(Millions)
Real
Investment
Based on RCRI
(Millions)
Miles
of
Road
Rev. Gross Ton-
Miles (Millions)
1996
SP
$3,907.74
$3,704.67
14,404
306,641
1985
UP
$1,566.95
$1,566.95
24,259
297,972
1986
UP
$2,967.25
$2,956.52
24,793
304,890
1987
UP
$2,999.35
$2,987.41
24,074
359,644
1988
UP
$3,379.96
$3,335.20
22,653
388,379
1989
UP
$3,508.62
$3,447.83
21,882
389,286
1990
UP
$3,778.91
$3,673.10
21,128
404,333
1991
UP
$3,838.58
$3,720.76
20,261
419,745
1992
UP
$4,044.66
$3,881.17
19,020
436,341
1993
UP
$4,279.23
$4,062.29
17,835
460,359
1994
UP
$4,517.95
$4,243.87
17,499
492,756
1995
UP
$6,668.97
$5,807.51
22,785
626,250
1996
UP
$6,812.47
$5,907.83
22,266
658,322
1997
UP
$9,656.12
$7,865.15
34,946
939,906
1998
UP
$10,588.35
$8,497.84
33,706
905,103
1999
UP
$11,282.92
$8,970.35
33,341
987,482
2000
UP
$12,026.13
$9,433.51
33,035
1,020,951
2001
UP
$12,610.23
$9,787.49
33,586
1,046,395
2002
UP
$13,369.19
$10,244.12
33,141
1,080,195
2003
UP
$14,021.04
$10,622.64
32,831
1,105,236
2004
UP
$14,762.22
$11,030.48
32,616
1,123,480
2005
UP
$15,609.93
$11,444.22
32,426
1,134,716
2006
UP
$16,479.55
$11,847.07
32,339
1,169,215
2007
UP
$17,319.48
$12,218.75
32,205
1,148,521
2008
UP
$18,470.82
$12,666.68
32,012
1,111,650