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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.

NDSU does not discriminate in its programs and activ ities on the basis of age, color, gender expression/identity, genetic information, marital status, national origin, participation in lawfu l

off-campus activity, physical or mental disa bility, pregnancy, public assistance status, race, religion, sex, sexual orienta tion, spousal relationship to current employee, or veteran status, as

applicable. Direct inquiries to Vice Provost, Title IX/ADA Coordinator, Old Main 201, 7 01-231-7708, ndsu.eoaa@nds u.edu.

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