FHWA Travel Analysis 

Framework 

Development of VMT Forecasting 

Models for Use by the Federal Highway 

Administration

May 12, 2014

John A. Volpe National Transportation Systems Center

Research and Innovative Technology Administration

Don Pickrell

David Pace

Jacob Wishart
2

Contents

Introduction ..................................................................................................................................................3

Economic Theory of Travel Demand.............................................................................................................5

Model Development Methodology ..............................................................................................................8

Data Considerations................................................................................................................................12

Autocorrelation...................................................................................................................................12

Unit Roots ...........................................................................................................................................12

Cointegration ......................................................................................................................................13

Forecast Data ..........................................................................................................................................14

IHS Forecasts.......................................................................................................................................14

EIA Forecasts.......................................................................................................................................14

Volpe Forecasts...................................................................................................................................15

National Aggregate Travel Forecasting Models..........................................................................................15

Light-Duty Vehicles .............................................................................................................................16

Single-Unit Trucks ...............................................................................................................................17

Combination Trucks............................................................................................................................18

Buses...................................................................................................................................................20

Functional Class VMT Models.....................................................................................................................21

Light-Duty Vehicles .................................................................................................................................21

Single-Unit Trucks...................................................................................................................................22

Combination Trucks................................................................................................................................23

State-Level VMT Forecasting Models .........................................................................................................24

Light-Duty Vehicles .................................................................................................................................25

Single-Unit Trucks...................................................................................................................................26

Combination Trucks................................................................................................................................27

Fleet Model.................................................................................................................................................28

Description of Forecasting Tool ..................................................................................................................30
3

Introduction

This document details the process that the Volpe National Transportation Systems Center (Volpe) used 

to develop travel forecasting models for the Federal Highway Administration (FHWA). The purpose of 

these models is to allow FHWA to forecast future changes in passenger and freight vehicle use (as 

measured by the number of vehicle-miles traveled, or VMT) that is likely to occur in response to

predicted demographic trends and changes in future economic conditions. These models also provide

estimates of the volumes of gasoline, diesel, and other fuels consumed by motor vehicles, which are 

derived from its projections of future vehicle travel and fuel economy.

1 Forecasts of VMT developed 

using this model will inform and support the development of future Federal transportation planning and 

policy.

The FHWA VMT forecasting models provide forecasts of VMT for the entire U.S., as well as for individual

states. These forecasts are disaggregated into four vehicle type categories, as defined by FHWA: lightduty passenger vehicles, including automobiles and light-duty trucks (FHWA Vehicle Classes 1, 2, and 3);

buses (FHWA Vehicle Class 4); single-unit trucks (FHWA Vehicle Classes 5, 6, and 7); and combination 

trucks (FHWA Vehicle Classes 8 through 13). At the national level, VMT is also decomposed by roadway

functional classification (interstate highways versus other highways and roadways) and location (urban 

and rural). State-level VMT forecasts are provided for three different vehicle classes: light duty vehicles, 

single-unit trucks, and combination trucks. 

In addition to the econometric approaches used to construct the aggregate national- and state-level

VMT models, the FHWA models include a methodology for forecasting national VMT from a vehicle fleet 

perspective. This component of the VMT models disaggregates nationwide total VMT by vehicle class,

model year or vintage, and vehicle age. The aggregate national-level VMT models for each vehicle type 

were estimated and used as control totals for lower-level (functional classification, fleet, and state-level) 

models; for example, VMT forecasts for the 50 individual states (plus the District of Columbia) are 

constrained so that their sum equals the forecast of nationwide total VMT produced by the national 

model. 

The FHWA VMT forecasting model was calibrated using widely-used statistical and econometric 

techniques to estimate the influence of underlying economic and demographic factors on passenger and 

commercial vehicle use. Forecasts of these underlying demographic trends and economic factors are 

used in conjunction with the model’s individual equations to develop forecasts of future travel demand

and VMT growth.

The sections that follow describe the model development process, including the specification and 

econometric estimation results of the equations that comprise the final set of VMT forecasting models. 

The first section discusses the economic theory of travel demand, which provided the theoretical basis 

for identifying and selecting appropriate economic and demographic variables—those likely to influence

the demand for vehicle trips—for testing and inclusion in the forecasting models.

The second section details the methodology employed in developing the forecasting equations and 

selecting the most reliable versions. It describes the statistical tests and criteria used to ensure the final 

selected equations combine historical explanatory power with accurate forecasting performance.

 1 FHWA’s projections of fuel consumption are not intended to replace the more detailed and comprehensive 

forecasts of transportation energy use produced by the U.S. Energy Information Administration and reported in its 

Annual Energy Outlook (see http://www.eia.gov/forecasts/aeo/index.cfm). 
4

Subsequent sections of the report provide details of the specific models themselves. These sections 

offer further insight into the key influences on VMT incorporated in each individual equation, while also 

providing a more detailed look at the mechanics of the fleet model. The national-level VMT forecasting

models are addressed first, followed by the functional class models. Following the functional class 

models is a discussion of the structure of the state-level VMT forecasting model. Lastly, the structure 

and mechanics of the fleet model is examined in detail.

Details of the baseline VMT forecasts and the accompanying model tool are available from FHWA by 

contacting:

Patrick Zhang

FHWA, Room E83-451

U.S. Department of Transportation

1200 New Jersey Avenue, SE.

Washington, DC 20590

202-366-1941
5

Economic Theory of Travel Demand

Vehicle travel is often described as a derived demand, meaning that a trip taken in either a passenger or 

commercial vehicle is typically a means to transport passengers or freight from their original location to 

a desired geographic destination. Generating predictions of how the amount of travel will change in the 

future thus requires an understanding of the factors that motivate passenger travel and freight 

shipments, as well as expectations about how these explanatory factors will change going forward. 

In the case of passenger VMT, economic theory suggests several factors that exert strong influence on

household ownership and use of motor vehicles. The primary determinants of personal motor vehicle 

travel are household demographics—including the total number of households and their distribution by 

size, composition, and geographic location—and their economic circumstances, particularly their 

employment status and income levels. These factors collectively affect household members’ 

participation in activities outside of the home – working, shopping, conducting personal business, 

recreation, etc. – which is the underlying source of their demand to travel. In turn, household members 

choose among non-motorized forms of travel (such as walking and cycling), public or school-provided 

transportation services, and travel in personal motor vehicles to satisfy their demands for travel. 

The primary determinant of truck travel is likely to be the overall level of business or economic activity, 

particularly in manufacturing industries (as distinct from service industries), since goods production and 

distribution involves extensive movement of both raw materials and finished goods. Because some 

specific categories of economic activity such as construction and international trade generate 

particularly large volumes of freight movement, the composition of overall economic activity can also be 

an important determinant of total truck use. 

The price of motor vehicle travel is also a major influence on the demand for travel. In the case of 

personal vehicles, the price of vehicle use includes the value of the driver’s and any other occupants’ 

travel time, mileage-related depreciation of the vehicle itself, the cost of fuel consumed, prices for other 

operating and maintenance inputs, and any charges levied for roadway use or parking at trip 

destinations or stop-over points. For freight-carrying trucks, the price of travel includes the driver’s 

wage rate, use-related vehicle depreciation, fuel and other vehicle operating costs, vehicle maintenance, 

and the inventory value of freight or cargo being carried. In addition, the geographic distribution of 

households, employment opportunities, production and warehousing facilities, and shopping and 

recreational destinations are likely to influence the use of both passenger vehicles and freight trucks.

Recent research examining the economic and demographic influences on travel demand indicates that 

the contributions of these factors to total VMT growth have been changing over time.2 An example of 

this is growth in the number of licensed drivers, which has slowed as the fraction of the age-eligible 

population holding drivers’ licenses approaches the saturation point (Figure 1). Growth in licensed 

drivers was once a key component of increasing passenger VMT: between 1950 and 1960, nearly half of 

 2 For example, see David A. Hensher, Nariida C. Smith, Frank W. Milthorpe, "The Demand for Vehicle Use in the 

Urban Household Sector, Theory and Empirical Evidence," Journal of Transport Economics and Policy (1990); Don 

H. Pickrell, "Description of VMT Forecasting Procedure for "Car Talk" Baseline Forecasts," Volpe Center, U.S. 

Department of Transportation (1995); and Steven E. Polzin, "The Case for Moderate Growth in Vehicle Miles of 

Travel, A Critical Juncture in U.S. Travel Behavior Trends," Center for Urban Transportation Research, University of 

South Florida, report to U.S. Department of Transportation (2006).
6

the growth in passenger vehicle use was associated with an increase in the number of licensed drivers.3

By the 1980s, however, the contribution of increases in the number of licensed drivers to growth in 

vehicle travel diminished sharply as the fraction of those already licensed moved toward saturation, and 

the more recent decline in VMT has accompanied a slight decline in the fraction of the eligible 

population holding drivers’ licenses. Over this same time, factors such as personal income, labor force 

participation – particularly among women – and the costs of owning and operating personal vehicles

also varied in ways that influenced growth in the use of personal vehicles.

Figure 1: Licensed Drivers as a Percent of Driving Age-Population

(Source: FHWA Highway Statistics, U.S. Census Bureau)

Changes in the price of gasoline have historically had a pronounced effect on the demand for vehicle 

travel: for example, the sharp oil price spikes of the mid-1970s and early 1980s, together with the 

accompanying economic recessions, exerted strong downward pressure on VMT growth. However, a 

subsequent sharp drop in petroleum prices during the mid-1980s was partly responsible for the 

resumption of growth in vehicle use. Other factors whose effect on VMT growth has varied widely over 

time include changes in the distribution and density of the U.S. population, including major shifts in 

population between regions of the country, between urban and rural locations, and within many major 

metropolitan areas. 

Since the mid-1970s there has been a gradual downward trend in the rate of VMT growth, and year-toyear variation in travel growth rates has become less pronounced over time (Figure 2). Within this longterm trend, however, there have been shorter periods during which VMT growth advanced strongly; this 

was particularly evident during the mid-1980s, when the U.S. economy’s emergence from recession 

combined with the sharp decline in petroleum prices from their early-decade highs to produce a surge in 

VMT growth. The 1990s, a period of sustained economic growth and low oil prices, also showed short 

periods of strong VMT growth. 

 3 More specifically, if the annual VMT per licensed driver had remained at its 1950 level, growth in the number of 

licensed drivers would have resulted in half of the growth in total annual VMT that actually occurred between 

1950 and 1960. 
7

More recently, the sharp increase in gasoline prices beginning in 2008 combined with the subsequent 

deep recession and other developments to produce a prolonged period of declining vehicle use. Unlike 

the pattern observed after previous post-war recessions, vehicle use still remains below its mid-2000s 

peak, prompting extensive speculation about the causes of its prolonged decline and prospects for a 

resumption of growth in travel. 

Figure 2: Light Duty Vehicle Miles Traveled (Annual Percent Change 1967 – 2012)

(Source: FHWA Highway Statistics)

Although this discussion has focused primarily on passenger vehicle travel, developing approaches to 

modeling truck VMT is also important. While truck use represented only about 10% of total VMT in 2012 

(Figure 3), freight traffic is a central component of the nation’s transportation activity. Truck use is also 

an important consideration for infrastructure investment policy, since trucks are responsible for a large 

portion of highway wear and tear, and may contribute disproportionately to congestion and road safety 

conditions. Trucks also play an important role in the national economy; in 2002 trucks moved 58% and 

64% of all commercial freight, as measured by weight and value, respectively. More recently, rapid 

growth in the international trade in goods has relied largely upon trucks to move imports and exports 

between U.S. coastal ports and inland distribution centers. 

-4%

-2%

0%

2%

4%

6%

8%

67 72 77 82 87 92 97 02 07 12
8

Figure 3: Truck VMT as a Percent of Total VMT

(Source: FHWA Highway Statistics)

Because of the importance of freight transportation, careful consideration was given to distinguishing 

the factors likely to influence truck travel from those more likely to affect the use of passenger vehicles.

In particular, since the demand for truck use is largely derived from raw materials shipments to supply 

manufacturing and distribution of finished goods, particular attention was paid to including various 

measures of manufacturing activity and goods production and delivery. These include the fraction of 

total economic activity accounted for by goods production, the volume of international trade, and the 

value of mail-order and internet sales, which substitute increased truck use for home delivery for 

shoppers’ travel to and from retail stores.

Model Development Methodology

A major challenge in developing VMT forecasting models arises in when comparing and selecting the 

best specification from among multiple alternative possibilities (ranging into the hundreds). To meet this 

challenge, this effort employed a comprehensive and systematic approach to model development,

evaluation, and selection. 

The first step in the model development process was identifying the factors likely to influence vehicle 

use. Guided by the economic theory of travel demand, these factors were selected separately for each 

vehicle category: light-duty vehicles, single-unit trucks, combination trucks, and buses. Within each 

broad category of underlying influences on vehicle use, alternative measures were identified for 

potential inclusion in varying model formulations; for example, household income levels could 

alternatively be measured by total or per capita GDP, total or per capita disposable personal income, 

median household income, and other measures. Table 1 summarizes the broad categories of 

explanatory variables and the alternative measures that were used to represent each category. 

Historical data are drawn from a range of sources, most of which are publicly available. These include 

FHWA (notably, its annual Highway Statistics publication), the Energy Information Administration, R.L. 

Polk, the U.S. Bureau of the Census, and the U.S. Department of Labor. The historical range over which 

the national-level models are estimated spans 47 continuous years for light-duty vehicles, and 43 years 

6%

7%

8%

9%

10%

11%

12%

66 71 76 81 86 91 96 01 06 11
9

for trucks and buses; these data series begin in 1966 and 1970, respectively. Data used in the state-level 

models were collected from 1993 onward. 

An important category of variables that was explored comprises data representing land use; that is, 

measures capturing the geographic distribution of the population—particularly, its density within and 

dispersion around central cities, and its distribution between urban and suburban regions of 

metropolitan areas. At the nationwide level, however, no suitable measure of the influence of land use 

on motor vehicle travel could be identified. Candidate measures either did not display sufficient 

variation over time to identify their influence on vehicle use, or were inadequately or inconsistently 

defined at the national level throughout the historical period used to develop the models. At the state 

level, however, one land-use measure was included in the final model specification: the percent of each 

state’s population living within the boundaries of its metropolitan statistical areas (MSAs). 

The economic and demographic variables selected as candidates for testing were then entered into a 

model specification matrix. Within this matrix, alternative model specifications were carefully designed 

to test and compare how effectively each variable captured the underlying influences it was intended to 

measure, both individually and in conjunction with other important determinants of VMT. This allowed 

for examination of the stability and robustness of each individual variable in its relationship to vehicle 

use, particularly when combined with other explanatory influences, and also enabled easy tracking of 

the many specifications that were tested. At the national level, approximately 300 different model 

specifications were examined for each vehicle class as part of this process.
10

Table 1: Alternative Variables Tested in Modeling Procedures

Variable Type Light-Duty Single-Unit Trucks Combination Trucks

Dependent 

Variable Total Annual VMT*† Total Annual VMT Total Annual VMT

Demographic 

Characteristics

Total Population

Percent of Population Aged 20-65 Yrs.

Number of Households

Average Persons per Household

Percent of Households that are Families

Percent of Families with Children < 18 Yrs.

Percent of Population in Urban Areas

Regional Population Variables

[no variables] [no variables]

Economic 

Activity/Income 

Measures 

Total GDP*†

Disposable Personal Income*†

Median Household Income

Consumer Confidence Index

Total GDP

Real Value of Durable Nondurable Goods

Real Retail Sales

Real Retail Sales (% of GDP)

Electronic and Mail-Order Sales (as % of 

Retail Sales)

Real Value of Service Sector (% of GDP)

Real Consumer Spending

Real Private Fixed Residential Investment

Total GDP*

Value of Durable plus Nondurable Goods

Value of Durable plus Nondurable Goods (% 

of GDP )

Imports plus Exports of Goods (% of GDP )

US Industrial Production

Diesel Price per gallon

Cost of Driving 

Gasoline Price per Gallon

Fuel Economy (MPG)

Fuel Cost per Mile Driven

Diesel Price per Gallon

Single Unit Truck MPG

Fuel Cost per Mile

Driver Wages

Diesel Price per Gallon

Fuel Cost per Mile

Driver Wages

Combination Truck MPG

Vehicle Price

New Vehicle Price Index

Used Vehicle Price Index

Vehicle Parts and Price Index

New Vehicle Price Index/Consumer Price 

Index

New Vehicle Real Sales Price

Producer Price Index (Transportation 

Equipment)

New Vehicle Price Index 

Producer Price Index (Transportation 

Equipment)

New Vehicle Price Index

Road Supply Total Road-Miles*†

Road-Miles per Vehicle

Total Highway-Miles

Total Highway-Miles per All Vehicles

Highway-Miles in Urban Areas

Percent of Population in Urban Areas

Total Highway Miles per All Vehicles

Total Highway-Miles

Total Public Road-Miles

Employment 

Total Employment

Labor Force Participation Rate (%)

Employed Persons per Household

[no variables] [no variables]

Transit Service

Vehicle-Miles of Bus and Rail Transit 

Service*

Vehicle-Miles of Rail Transit Service*

Number of Cities with Rail Transit Service

[no variables] [no variables]

Entries marked with “*” were examined in per capita terms

Entries marked with “†” were examined in per household terms

The strength of each model specification was judged based upon several statistical criteria, including:

• Plausibility of the arithmetic signs and magnitudes of the estimated coefficients on each 

explanatory variable included in the specification
11

• Precision and statistical significance of estimated coefficients 

• Tests for serial correlation in model residuals or error terms

• Adjusted R-squared value and other measures of goodness of fit of the overall model

• Mean absolute percent error and other indicators of accuracy for within-sample and out-ofsample forecasts generated using each specification

The primary aim of this model-building procedure was to develop a model that forecasts accurately—in 

other words, to minimize total forecasting error. The error in the forecasts produced using a given 

model can be separated into two components. First, future values of the model’s explanatory (or input)

variables are unknown and must themselves be forecast; “input error” refers to the component of error 

in the model’s forecast that can be attributed to imperfect predictions of its input variables. Minimizing

such input error will tend to favor the development of parsimonious models: the smaller the number of 

input variables a model includes, the lower the combined uncertainty of the predictions of these 

variables. 

“Specification error,” on the other hand, is the component of error inherent in the design and 

calibration of a particular model. This error reflects how well the variables it includes (and the 

relationships expressed by their estimated coefficients) capture the “true” determinants of the 

dependent variable. If a model is poorly designed— for example, if it excludes important variables,

includes variables that do not belong, or its functional form causes it to understate or exaggerate the 

contributions of certain explanatory variables— the forecasts it produces will exhibit high specification 

error, even when they are generated with perfect foresight about the model’s input variables. 

Minimizing specification error would generally lead the model developer to include more, rather than 

fewer, explanatory variables, so as not to omit any important influences from the model. Thus, attempts 

to reduce each type of error will frequently entail conflicting recommendations for the model-building 

procedure. 

The emphasis during the testing process was placed on models exhibiting the lowest level of 

specification error. In isolating the magnitude of specification error from that of input error, the mean 

average percentage error (MAPE) statistic is a particularly useful tool. The relative extent of the two 

error components for a given model can be examined by comparing the MAPEs calculated from out-ofsample and in-sample forecasting tests. Specifically, the accuracy of a model’s in-sample “forecasts,” 

which are constructed using the actual historical values of its explanatory variables, provides a measure 

of its specification error. This form of error was also examined by using the models to generate out-ofsample forecasts, which are constructed using the known values of the explanatory variables to forecast 

VMT for part of the historical period over which the model was calibrated. The model’s accuracy can 

then be examined by comparing its forecasts of vehicle use against their actual values for this part of the 

period.

4 The final model selection process aimed to ensure high forecasting accuracy, while also insuring 

the structural integrity of the model by including all theoretically influential and significant factors. 

 4 As an illustration, the most promising alternative model specifications were re-estimated over a period ending in 

2005, and then used in conjunction with the actual values of their explanatory variables to produce VMT 

“forecasts” for 2007-12. The forecasting accuracy of the models in this test – particularly their ability to predict the 

downturn in total VMT beginning in 2007 and its sustained sluggishness – is a particularly useful test of their likely 

future forecasting performance. 
12

Data Considerations

During the model development process, particular attention was paid to issues that commonly arise due 

to the time series nature of economic data. One particular concern is the presence of autocorrelation in 

the residuals of an econometric equation, which occurs when the unexplained residual or error terms in 

successive time periods tend to be correlated. Another concern is the potential existence of strong 

underlying time trends or unit roots in the individual variables used to estimate model parameters, and

the potential for accompanying cointegration between the model’s dependent variable and its 

explanatory variables. In the presence of such cointegration, relying on standard statistical estimation 

and diagnostic methods may lead to the development of models that appear reliable, but embody 

spurious associations rather than stable behavioral relationships. 

Autocorrelation

If autocorrelation is present, regression coefficients will be inefficiently estimated (although their 

estimates remain unbiased), normal significance tests are not valid, and the performance of the forecast

from the equation is not as good as it could be. Autocorrelation can occur if the model’s specification 

does not accurately reproduce fluctuations in the growth of its dependent variable over time, or 

conversely, if the model predicts more variation in the growth of its dependent variable than has 

actually occurred over time. This problem can also arise if the explanatory variables in an equation are 

themselves autocorrelated, which is often the case with economic time series data (i.e., the current 

value is correlated with the previous value). Indeed, the fact that many economic time series increase 

over time (i.e., the mean of the series does not remain constant) often leads to problems with 

autocorrelation, as well as to the related problems of unit roots and cointegration.

Remedies for autocorrelation, which were examined and used during the model building process, 

include introducing a lagged dependent variable into the equation, adding an auto regressive term or 

estimating the equation in differences to make the time series data stationary. 

Unit Roots

The presence or absence of a unit root is one way to characterize the underlying temporal structure of a 

data series. The absence of a unit root essentially means that the data series lacks a trend, and instead 

varies around a stable mean; such a variable is referred to as stationary. Its average may be positive, 

negative, or zero–as long as it remains approximately constant. Conversely, the presence of a unit root 

implies that the variable is non-stationary–its mean is either rising or declining consistently over time, in 

which case the change in its value between two successive time periods tends to be approximately 

constant. The existence of unit roots is often discussed in terms of whether the series is “integrated;” a 

series is integrated of order one when the first difference of the variable is stationary, or the difference 

between successive values is roughly constant. 

Many of the economic variables included in the models have unit roots (or are integrated of order one); 

in practical terms, these series typically show a steady upward trend over time.5 A similar pattern can be 

seen in the dependent variable (vehicle use, as measured by VMT) as well. In the presence of unit roots, 

the standard errors estimated via the models may be inaccurate, leading to improper inference about 

the significance of the model coefficients. More important, estimated relationships that fit the data well 

and appear to reflect causal association may in fact be spurious if their variables have unit roots.

 5 Similarly, a variable is integrated of higher orders when the variable must be differenced more than once to 

produce a stationary series. However, series that are integrated of more than order one are uncommon in 

econometric analysis.
13

Cointegration

Cointegration is a concern related to the unit root issue; while the presence of a unit root is a 

characteristic of an individual variable, cointegration is a property of multiple variables. In practical 

terms, two variables that have unit roots and share a common underlying trend are cointegrated, in the 

sense that they tend to increase (or decline) over time in a consistent pattern.6 Thus growth in one of 

two cointegrated variables can appear to cause the other to grow, when in fact they simply happen to 

share similar underlying trends and their apparent relationship is spurious.

7

Nevertheless, cointegration can provide useful information regarding the long-run equilibrium 

relationship between two variables. The fact that they share underlying trends means that the value of 

one variable may be useful in producing a more reliable prediction of the value of the other, although 

the resulting prediction is of course still prone to random variation. Estimating and utilizing 

cointegrating relationships offers an alternative to differencing time series as a means of resolving the 

problems that unit roots introduce. That is, if cointegrating relationships are detected among the 

variables included in a proposed model specification, they can sometimes be exploited to estimate its 

coefficients more reliably, and thus to improve its forecasting performance.

8

During the model development process, every variable was first tested for the presence of a unit root. 

Extensive testing was then conducted to identify the existence of cointegration between pairs of 

variables displaying unit roots, focusing particularly on cointegration between the VMT measures to be 

used as dependent variables in the models and the candidate explanatory variables listed previously in 

Table 1.

9 These tests indicated the presence of unit roots in some variables, as well as some degree of 

cointegration among the variables included in many of the proposed model specifications.

Accordingly, alternative econometric estimation procedures were tested for their effectiveness in using 

cointegrating relationships to improve these specifications and develop models that produced more 

reliable forecasts. These alternative approaches included estimating single-equation error correction 

models in cases where tests showed only limited cointegration between a model’s dependent variable 

and its candidate explanatory variables. Where potential simultaneity among a model’s variables was 

suspected and tests detected more pervasive cointegration among them, multi-equation vector 

autoregression (VAR) models that included error correction terms (often referred to as vector error 

 6

Technically, two non-stationary variables are cointegrated if there exists a linear combination of the variables that 

is stationary. For example, if two series x and y are integrated of order one, but a third variable z can be created as 

some linear combination of x and y (say, the difference between x and y) and has no unit root itself, then x and y 

are cointegrated.

7

 Engle, Robert F., Granger, Clive W. J. (1987) "Co-integration and error correction: Representation, estimation and 

testing", Econometrica, 55(2), 251-276. 8 The usual procedure for doing this is to use the residual terms from estimated cointegrating relationships, which 

provide a measure of the extent to which the values of two cointegrated variables during a specific time period 

diverge from their common underlying trends, as additional explanatory variables in a model relating changes in 

the same two variables to each other. Because cointegrating relationships in theory capture useful information 

about long-term equilibrium relationships between variables, exploiting these relationships in constructing models 

is often preferable to simply differencing the individual series and using their differenced values to estimate the 

relationship between their period-to-period changes. 9 The augmented Dickey-Fuller test was used to check for the presence of unit roots in individual variables. The 

Engle-Granger test was relied on to detect cointegration between individual pairs of variables, while the more 

complex Johansen test was used to analyze the presence of multiple cointegrating relationships 
14

correction models) were tested for their ability to improve econometric results and produce more 

reliable forecasting models. 

Despite extensive experimentation with both approaches, neither single equation nor vector error 

correction approaches proved successful in using information from estimated relationships between 

cointegrated variables to improve the econometric performance or predictive reliability of the VMT 

forecasting models. That is, neither approach yielded econometric results that appeared to improve the 

models. Using single-equation error correction specifications produced models that were very similar to 

the analogous versions of the same equations estimated using ordinary least squares (OLS) regression, 

while vector error correction models consistently showed little statistical significance or explanatory 

power. These result suggested that standard ordinary least squares (OLS) regression produced 

acceptably accurate representations of the relationships being modeled, and the OLS-estimated versions 

of the VMT models would provide reasonably reliable forecasts.

Forecast Data

Forecasts of the input variables come from three sources: IHS Incorporated (IHS), the Energy 

Information Administration (EIA), and the Volpe Center. IHS provides the majority of the variables used 

in forecasting for the national, state, and fleet models. Forecasts of the changing distribution of total 

fuel consumption by specific type of fuel are drawn from the U.S. Energy Information Administration’s 

Annual Energy Outlook. The Volpe Center developed independent forecasts of road supply and truck 

fuel efficiency; Volpe’s forecasts employed growth rates of light-duty fuel efficiency that were previously 

developed for NHTSA as part of its analysis of future Corporate Average Fuel Economy (CAFE) standards. 

Both IHS and EIA provide scenario-based forecasts (i.e., a baseline and high and low growth outlooks). 

The Volpe-produced forecasts are not constructed around the same scenarios, but can be modified to 

produce alternative future outlooks.

IHS Forecasts

IHS provides forecasts for three potential macroeconomic outlooks, referred to as the baseline, 

optimistic, and pessimistic scenarios. The optimistic and pessimistic scenarios are to be considered 

relative to the baseline. The optimistic scenario has relatively high U.S. economic growth and low world 

oil prices, while the pessimistic scenario combines relatively low domestic economic growth with high 

world oil prices. Table 2 shows the forecast growth rates of several important aggregate economic 

indicators for each scenario, to illustrate the differences among the alternatives.

10

Table 2: 30-Year Annual Growth Rates for Selected Economic Indicators

Baseline 

Scenario

Optimistic 

Scenario

Pessimistic

Scenario

GDP 2.5% 2.9% 1.9%

Employment 0.8% 1.0% 0.6%

Goods Production 3.1% 3.6% 2.1%

U.S. Population 0.7% 0.8% 0.6%

Gasoline Prices -0.4% -0.6% -0.4%

EIA Forecasts

Forecasts of the fractions of total energy use by light-duty vehicles and trucks represented by different 

fuel types were obtained from the most recent edition of the U.S. Energy Information Administration’s 

 10 These data are from the IHS April 2014 U.S. Macro long-term forecast
15

Annual Energy Outlook.

11 These were aggregated to produce estimated shares of total fuel energy 

consumption represented by gasoline, diesel, other liquid fuels (including ethanol and liquid petroleum 

gas), gaseous fuels (natural gas and hydrogen), and electricity. 

Volpe Forecasts

The data series forecast by Volpe were those that were not available from external sources, and thus

they are not tied to specific future scenarios. Future fuel economy of the light-duty vehicle fleet will be 

heavily dependent upon the corporate average fuel economy (CAFE) standards. The baseline forecast of 

average fleet-wide fuel economy was based on Volpe’s analysis of fuel economy trends for NHTSA, 

which accounts for expected future increases in CAFE standards and fuel efficiency standards for 

medium- and heavy-duty trucks.12

Road-supply variables appear in both the national- and state-level models. In most cases the Volpe 

forecasts simply extrapolate historical trends in total road mileage, while also considering whether 

historical growths rates might reasonably be expected to moderate over the future. For example, 

construction of the U.S. Interstate Highway System is now largely complete, meaning that future growth 

in Interstate Highway mileage is likely to be close to zero. Volpe’s forecasts of road supply growth in 

urbanized and rural areas account for differences in their historical rates of road construction activity, as 

well as for the effect of gradual reclassification of rural territory at the boundaries of growing 

metropolitan areas to urbanized status. 

A similar approach was applied to produce the state-level road-supply forecasts. Specifically, each 

state’s historical growth rate in total roadway mileage over the last 16 years was applied annually each 

year in the forecast period. In some specific instances, however (such as where data were unavailable or 

were determined to be inaccurate, or where historical growth rates were judged to be unsustainable), a 

state’s future growth rate was further constrained to prevent unrealistic forecasts.

National Aggregate Travel Forecasting Models

The FHWA travel forecasting system includes separate models to forecast nationwide total vehicle-miles 

traveled by four separate vehicle classes: light-duty vehicles (automobiles plus light trucks used primarily 

as passenger vehicles), single-unit trucks, combination trucks, and buses. The four national-level models 

are similar in structure and in the types of explanatory variables they include. This is particularly the case 

with regards to the light-duty, single-unit, and combination truck models; although the bus travel 

forecasting model has a similar economic structure, due to the difficult nature of forecasting bus VMT, 

it includes slightly different categories of variables.13

In general, each model includes one or more measures of the level and composition of the specific 

components of economic activity that affect demand for personal travel or freight shipping. For 

example, truck usage is influenced by the level of real GDP, as well as the fraction of GDP accounted for 

by specific economic sectors such as manufacturing, construction, and international trade. Similarly, 

 11 U.S. Department of Energy, Energy Information Administration, Annual Energy Outlook 2014, 

http://www.eia.gov/forecasts/aeo/index.cfm. 12 See NHTSA, Environmental Impact Statement for the Joint Rulemaking to Establish CAFE and GHG Emissions 

Standards, MY 2012-2016 (2010). Available from http://www.nhtsa.gov/fuel-economy. 13 The difficulty of forecasting nationwide bus VMT arises from the fact that buses serve several distinct markets, 

each with different influences on demand: urban public transit, intercity coach travel, charter and commuter 

service, and school travel.
16

light-duty vehicle use is partly a product of real personal disposable income, since this variable 

influences household members’ opportunities to participate in activities that require travel away from 

home. Household characteristics such as average size, number of children, age distribution of members, 

metropolitan location, and distribution by geographic region were also expected to affect the volume of 

light-duty vehicle travel, but their effects generally proved difficult to identify. 

Each model also includes a measure of fuel cost per mile driven, which is equal to fuel price per gallon 

divided by average fuel economy in miles per gallon for the relevant vehicle class. This variable is 

intended to capture the fuel-related cost of driving, which is typically the largest component of the total 

cost of operating each type of vehicle. Although there are several alternative measures of fuel-related 

costs, fuel price divided by fuel efficiency was preferred because it accurately reflects the independent 

influences of both variables on vehicle operating costs.14 The effects of vehicle purchase prices and 

ownership costs on aggregate vehicle use were also tested in the VMT forecasting models for each 

vehicle class, but the influence of these variables on vehicle use was difficult to detect. 

Measures of aggregate highway mileage or average highway miles per registered vehicle were also 

included in the national-level VMT forecasting models for single-unit and combination trucks. These 

variables were intended to capture the effect of road capacity and the intensity with which it is utilized 

on travel speeds, which in turn are expected to influence demands for personal travel and freight 

shipping. Measures of the supply and prices of competing travel modes – public transit service levels 

and fares, as well as rail shipping rates – were also tested for their influence on aggregate light-duty 

vehicle and truck use, but no such effects could be detected. 

Light-Duty Vehicles

As Table 3 shows, the national light-duty vehicle forecasting model includes personal disposable income 

per capita, average fuel cost per mile, and a measure of consumer confidence in the economic outlook. 

Personal disposable income per capita enters the equation in both linear form, and with a squared term; 

the estimated coefficient on the linear term is positive, while that on the quadratic term is negative. This 

implies that personal disposable income per capita has a positive impact on VMT (that is, as household 

income levels rise, vehicle use per person increases), but that the magnitude of this effect declines as 

income rises. 

Table 3: Explanatory Variables Included in Light-Duty VMT Forecasting Model*

Variable Coefficient Functional Form

Lagged dependent 

variable 0.6274 Log

Personal disposable 

income per capita 1.7217 Log

 14 This specification implies that the effects of variation in fuel prices and average fuel economy on the demand for 

vehicle use that are equal in magnitude but opposite in direction. While some research suggests that fuel prices 

and fuel efficiency may have different effects on vehicle use, when these variables were entered separately the 

estimated magnitudes of their effects did not differ significantly from each other for any of the four vehicle classes. 
17

Personal disposable 

income per capita 

squared

-0.2304 Log

Fuel cost per mile -0.0292 Log

Consumer confidence 

index 0.0565 Log

* Dependent variable is log of annual light-duty VMT per Capita.

The negative sign on the squared disposable income variable presumably captures the increasing 

opportunity cost of driving: at high levels of income, household members’ time becomes so valuable 

that they choose to spend less of it travelling. Throughout the forecast period, the linear term 

dominates, and the effect of an increase in personal disposable income continues to produce an 

increase in VMT. However, by about the year 2025, the model predicts that the opportunity cost of 

driving will have increased to the point where it causes the growth rate in VMT to slow noticeably. 

Fuel cost per mile appears with a negative coefficient, indicating that as the cost of driving increases, 

households choose to travel less. As expected, higher consumer confidence in the future of the

economy is associated with an increase in the number of vehicle-miles driven per person. 

As Table 3 also indicates, the light-duty VMT forecasting equation also includes the previous period’s 

value of the dependent variable. The significance of this variable implies that aggregate light-duty 

vehicle use adjusts gradually to changes in disposable income, fuel costs, and prices for new vehicles. 

Specifically, the magnitude of its estimated coefficient suggests that the effects of changes in these 

factors on VMT are only partly felt in the year when they occur, and require almost three years to be felt 

completely. This presumably reflects the existence of structural inertia in households’ decisions affecting 

travel demand and vehicle use, such as where their residences or workplaces are located and the 

number of vehicles they own. As a consequence, the longer-term effects of changes in income levels, 

fuel costs, and vehicle prices are nearly three times as large as their immediate effects, but require

approximately three years to be realized fully. 

Single-Unit Trucks

The national single-unit truck VMT forecast is a function of consumer spending, residential construction 

activity, and fuel cost per mile. Table 4 shows that the estimated coefficients on each of these three 

variables are positive, which is the expected result for consumer spending and residential construction, 

but opposite of that anticipated for fuel cost per mile.15 The “jackknife” specification of this equation 

allows the effects of each of these variables to increase after 1994, with the effects of residential 

 15 The coefficients on fuel cost per mile variables are statistically insignificant and indistinguishable from 0. 

Nevertheless, despite the suggestion from this result that fuel cost per mile is not a significant determinant of VMT 

at an aggregate national level, which possibly could be the case if fuel is not a completely transparent component 

of final invoice cost in this market, these variables were left in the equation to maintain theoretical completeness 

of model specification. While its’ forecasting performance is satisfactory, the specification of the single unit truck 

equation remains under investigation and with the inclusion of more data will likely be updated prior to the next 

forecast release in May 2015. 
18

investment increasing after that date, while that of consumer spending becomes significantly less 

pronounced. 

Table 4: Explanatory Variables Included in Single-Unit Truck VMT Forecasting Model*

Variable Coefficient Functional Form

Lagged dependent 

variable 0.6286 Log

Consumer spending 0.2507 Log

Private residential 

investment 0.0694 Log

Fuel cost per mile 0.0023 Log

Consumer spending X 

Jackknife -0.1875 Log

Private residential 

investment X 

Jackknife

0.0642 Log

Fuel cost per mile X 

Jackknife 0.0697 Log

Jackknife 1.4443 Level

*Dependent variable is log of annual single-unit truck VMT.

As with the light-duty VMT forecasting equation, the past period’s level of single-unit truck VMT is an 

important predictor of VMT in the current period, as indicated by the inclusion of the lagged value of the 

equation’s dependent variable. Again, the magnitude of its effect indicates that the response of singleunit truck use to changes in consumer spending and residential construction activity require nearly three 

years to be felt completely. The time lag required for use of single-unit trucks to adjust to changes in 

economic activity of may reflect factors such as the prevalence of long-term contracts for transportation 

services, difficulties in adjusting service frequency or routing decisions for goods delivery and 

distribution services, and rigidities in the market for drivers’ services. 

Combination Trucks

As Table 5 shows, the national aggregate forecasting model for combination truck VMT includes real 

GDP, fuel cost per mile, and the extent of the U.S. Interstate Highway system (measured as center-line

miles rather than lane-miles). As expected, the coefficient on real GDP is positive, implying that growth 

in overall economic activity increases demand for the longer-distance shipping services typically 
19

provided using combination trucks. Fuel cost per mile appears with a negative sign, again as expected, 

which suggests that declining retail fuel prices or improvements in combination-truck fuel economy will 

also increase shipping activity using combination trucks. Not surprisingly, combination truck use is 

closely related to the extent of the U.S. Interstate Highway System, since its nationwide geographic 

coverage, connectivity, and generally higher travel speeds are ideally suited to combination truck 

operations. 

Table 5: Explanatory Variables Included in Combination Truck VMT Forecasting Model*

Variable Coefficient Functional Form

AR(1) 0.6962 Log

AR(2) 0.2251 Log

Real GDP 0.5580 Log

Fuel cost per mile -0.0750 Log

Interstate center-line 

miles 0.6174 Log

Real GDP X Jackknife 1.1496 Log

Fuel cost per mile X 

Jackknife 0.0662 Log

Jackknife -10.0536 Level

*Dependent variable is log of annual combination truck VMT.

Like the forecasting equation for single-unit trucks, the specification of the VMT forecasting model for 

combination trucks allows the effects of its explanatory variables to change during the estimation 

period. In the case of the combination truck model, the effect of GDP becomes significantly less 

pronounced after 1980, while that of fuel costs becomes much more important after that year. This 

probably reflects the effect of deregulation of interstate trucking services beginning about that year, 

which allowed carriers to exercise much more flexibility in pricing truck services to reflect variation in 

their costs by shipment distance, origin and destination, and time. 

Unlike the light-duty and single-unit truck equations, however, the combination truck model does not 

include a lagged dependent variable, although it does employ terms intended to correct for the effects 

of autocorrelation in the model’s error terms. This specification suggests that freight shipping activity 

using combination trucks adjusts relatively rapidly to changes in aggregate economic activity, fuel costs,

and historical expansion of Interstate Highway mileage. This may be due to the highly competitive 
20

nature of shipping services that operate combination trucks and the high ratio of variable to total costs 

characterizing long-distance trucking. In such an environment, truck operators must be capable of 

adjusting supply and shipping rates dynamically in response to changing levels of freight-generating 

economic activity, or fluctuating prices for fuel and other operating inputs. 

Buses

The national-level bus VMT measure includes activity in four distinct sub-markets: school transportation, 

urban transit service, intercity bus service, and charter and tour operations. Although it was not possible 

to separate VMT for these categories, it is likely that school bus VMT accounts for the largest portion, 

probably followed by urban transit service. Due to the heterogeneous nature of the factors influencing 

these four distinct sources of travel demand and the inability to examine them separately, forecasting 

aggregate bus VMT presents a difficult challenge. In an attempt to capture the varying influences on 

these distinct markets in a single equation, the bus VMT forecasting model includes the size of the 

school-age population, real personal disposable income per capita, and consumer spending on fuel as a 

fraction of total consumer spending (a measure of the burden fuel prices impose on household 

budgets). 

Table 6: Variables Included in Bus VMT Forecasting Model*

Variable Coefficient Functional Form

AR(1) 0.9693 Log

AR(2) -0.4574 Log

Population between 

ages 5-21 1.0091 Log

Personal disposable 

income per capita 0.3243 Log

Consumer spending 

on fuel as a percent 

of total consumer 

spending

0.0559 Log

Jackknife -0.0359 Level

*Dependent variable is log of annual bus-miles.

As Table 6 shows, the population measure appears with a strong positive sign, indicating that bus VMT is 

highly sensitive to the number of school-age children: as this subset of the population has grown

historically, school bus service has increased as well. While the model implies that a change in schoolage population produces a proportional change in bus VMT, this probably captures related 

developments such as the effect of urban decentralization on school bus route lengths, and more 

frequent busing of school children to extracurricular activities such as sports or vocational training.

Growth in disposable income and the fuel price burden on household budgets both appear to be 
21

associated with increased bus VMT, although their effects are far smaller than that of the school-age 

population. The bus VMT equation also includes terms intended to remove the effect of serial 

correlation in its error terms. 

Functional Class VMT Models

The functional class models break down the forecasts of nationwide aggregate VMT for each vehicle 

type into separate forecasts for each roadway type. To ensure robust forecasts for low-volume roadway 

types, certain components of FHWA’s nine roadway functional classifications were aggregated to 

produce larger categories. Five roadway classes were ultimately used: urban interstate highways, urban 

other roadways (including all other roadway functional classes in urbanized areas), rural interstate

highways, rural arterials, and rural other roadways (including all other functional classes outside 

urbanized areas). In combination with the three vehicle types (light-duty vehicles, single-unit trucks, 

and combination trucks), these five roadway classes required the development of fifteen separate 

forecasting models. For each vehicle type, forecasts of VMT for the five separate functional classes are 

constrained to sum to the forecast of national aggregate VMT for that vehicle type. 

The national aggregate VMT forecasting models previously developed for each vehicle models were 

used as the starting point to guide development of forecasting models at the roadway functional class 

level. In most cases, the road supply measures included as explanatory variables in the national 

aggregate models were redefined to correspond to the VMT measure used as the dependent variable in 

each functional class VMT model. For example, the road supply measure included in the light-duty VMT 

forecasting models for each roadway class included only mileage for that particular category of facilities 

(Interstate Highways, Arterials, or Other Roadways) and location (urban or rural). Limitations on the 

availability of geographically-specific measures of economic activity prevented similar “tailoring” of the 

economic activity and fuel cost variables used in the models for individual roadway classes, so identical 

values were generally used in the VMT forecasting models for different roadway classes. As an 

illustration, both real U.S. GDP and nationwide average fuel cost per mile for single-unit trucks appear in 

the models for single-unit truck VMT on each of the five roadway classes. 

Light-Duty Vehicles

Table 7 summarizes the explanatory variables included in the light-duty VMT forecasting models for

individual roadway classes. As it shows, disposable personal income per Capita appears in each of the 

models, although the squared value of this variable is used only in those for the two categories of urban 

roadways. The arithmetic signs on both variables match those on the same variables in the nationwide 

aggregate forecasting equation for light-duty VMT (positive for the linear income term, and negative for 

its squared term), indicating the expected positive influence of income on personal vehicle travel, 

although the strength of this influence declines at higher income levels for travel on both categories of 

urban roadways. The nationwide average value of fuel cost per mile for light-duty vehicles also appears 

in each model with the expected negative sign, and has similar effects on light-duty vehicle travel using 

each of the five roadway classes. 
22

Table 7: Explanatory Variables Included in Light-Duty VMT Forecasting Models for Individual 

Roadway Classes

Variable 

Category 

Roadway Functional Class

Urban 

Interstate Urban Other Rural Interstate Rural Arterial Rural Other

Economic 

Activity Measure

Real Personal 

Disposable 

Income per 

capita*

Real Personal 

Disposable 

Income per 

capita*

Real Personal 

Disposable 

Income per 

capita

Real Personal 

Disposable 

Income per 

capita

Real Personal 

Disposable 

Income per 

capita

Operating Cost 

Measure

Fuel cost per 

mile

Fuel cost per 

mile

Fuel cost per 

mile

Fuel cost per 

mile

Fuel cost per 

mile

Demographic 

Variable

Average 

persons per 

household

Average 

persons per 

household

None None None

Road Supply

Measure

Fraction of 

centerline 

miles that are 

urban

Fraction of 

centerline 

miles that are 

urban

Fraction of 

centerline miles 

that are rural

Fraction of 

centerline 

miles that are 

rural

Fraction of 

centerline 

miles that are 

rural

Additional 

Variables

Lagged 

Dependent 

Variable

Lagged 

Dependent 

Variable

Lagged 

Dependent 

Variable

Lagged 

Dependent 

Variable

Lagged 

Dependent 

Variable

* Indicates that variable was also included in both linear and squared forms.

The two models for light-duty VMT on urban roadway classes include a measure of average household 

size; because smaller households tend to generate more commuting and shopping trips per household 

member, the historical decline in this measure has been associated with rising light-duty VMT per 

person. Each model also incorporates the fraction of nationwide road mileage that is located in urban 

or rural areas, depending on whether its dependent variable represents VMT for an urban or rural 

roadway category. 

Not surprisingly, the rising fraction of roadway mileage located in urban areas over time has been 

associated with a shift of light-duty VMT from rural roadway categories to urban roadways; part of this 

effect may simply reflect the reclassification of some rural areas as urban over the time period analyzed. 

Finally, each model also includes the previous period’s value of its dependent variable, reflecting the 

previous finding that more than a single year is required for light-duty VMT to respond fully to changes 

in any of the influences on vehicle use that are captured by the model’s other explanatory variables. 

Single-Unit Trucks

Table 8 summarizes the structure of the forecasting equations for single-unit truck VMT occurring on the

different roadway classes. As it shows, real GDP is uses as a measure of economic activity in the VMT 

models for individual roadway types, and has the expected positive influence on single-unit truck travel 

on each category of roadways. Fuel cost per mile for single-unit trucks is also included in each model; 

higher fuel costs reduce VMT on each roadway class, and this effect tends to be similar in magnitude to 

across roadway classes. 
23

Table 8: Explanatory Variables Included in VMT Forecasting Models for Single-Unit Trucks by 

functional class

Variable 

Category

Roadway Functional Class

Urban 

Interstate Urban Other Rural Interstate Rural Arterial Rural Other

Economic 

Activity 

Measure

Real GDP Real GDP Real GDP Real GDP Real GDP

Operating Cost 

Measure

Fuel cost per 

mile

Fuel cost per 

mile

Fuel cost per 

mile

Fuel cost per 

mile

Fuel cost per 

mile

Road Supply

Measure

Fraction of 

centerline 

miles that are 

urban 

interstate

Fraction of 

centerline 

miles that are 

urban other

Fraction of 

centerline miles 

that are rural

interstate

None None

Additional 

Variables

Lagged 

Dependent 

Variable

Lagged 

Dependent 

Variable

Lagged 

Dependent 

Variable

AR(1) term 

(autocorrelation 

correction)

Lagged 

Dependent 

Variable

As Table 8 also shows, the equations for single-unit truck VMT on urban interstate, urban other, and 

rural interstate roadways include the fraction of nationwide total road mileage in that functional class, 

and increases in this fraction have the expected effect of increasing VMT in each functional class. With 

one exception, these models also incorporate the previous period’s value of single-unit truck VMT on 

the relevant functional class. The significance of this variable indicates that as at the national aggregate 

level, demand for the services provided by single-unit trucks requires 2-3 years to adjust completely to 

variation in overall economic activity, changes in fuel prices or fuel economy, and expansion of road 

supply. 

Combination Trucks

Table 9 shows details of VMT forecasting equations for combination truck use of the five roadway 

functional classes. Most of these utilize real GDP, the same measure of economic activity found to 

influence nationwide combination truck VMT, although the equation for urban interstate VMT uses the 

real value of goods production instead. As expected, increasing economic activity has a positive 

influence on combination truck travel using each category of roadways. Fuel cost per mile for 

combination trucks is also employed in each equation, and the estimated coefficients on this measure 

show that higher fuel costs reduce combination trucks’ use of all roadway classes. The magnitude of this 

effect varies slightly among roadway classes, but is generally similar to that observed at the national 

aggregate level.
24

Table 9: Explanatory Variables Included in Forecasting Models for Combination Truck VMT by 

Roadway Functional Class

Variable 

Category

Roadway Functional Class

Urban 

Interstate Urban Other Rural Interstate Rural Arterial Rural Other

Economic 

Activity 

measure

Real Goods

Production Real GDP Real GDP Real GDP Real GDP

Operating Cost 

Measure

Fuel cost per 

mile

Fuel cost per 

mile

Fuel cost per 

mile

Fuel cost per 

mile

Fuel cost per 

mile

Road Supply

Measure None

Fraction of 

centerline 

miles that are 

urban

None None None

Additional 

Variables

Lagged 

Dependent 

Variable

Lagged 

Dependent 

Variable

AR(1) term 

(autocorrelation 

correction)

Lagged 

Dependent 

Variable

Lagged 

Dependent 

Variable

For combination trucks, only the equation for combination truck VMT on urban other roadways includes 

a road supply measure. Not surprisingly, historical growth in the fraction of total road mileage in urban 

areas, which has resulted from both new investments and incorporation of some rural area into 

urbanized areas, has been associated with increasing use of combination trucks on roads in that 

functional class. 

Again with a single exception, the models for combination truck VMT on different roadway functional 

classes also incorporate the previous period’s value of VMT, reflecting the result that (unlike at the 

national aggregate level) the use of combination trucks on most classes of roadways appears to require 

more than one year to respond fully to changes in economic activity or fuel costs. This result may 

suggest that the origin-destination pattern of the long-distance freight shipments usually carried by 

combination trucks shifts more slowly than aggregate shipping activity, or that combination truck 

routings over different types of roadway classes require some time to adjust to changes in shipping 

patterns. 

State-Level VMT Forecasting Models

The national-level and functional class VMT forecasting models utilize aggregate time-series data for the 

nation as a whole, so that only a single measure of each variable is available during each time period 

(year). In contrast, the state-level VMT models have an additional data dimension, since both their 

dependent variable (VMT) and most explanatory variables have 51 separate observations available for 

each time period (one for each of the 50 states as well as Washington, DC). In this context, the states 

represent a “cross-section,” and a continuous annual sequence of these cross-sections is available. 

Data with this structure (i.e., containing both time-series and cross-sectional information) is often 

referred to as a panel, and using it to estimate a model offers two advantages over relying on timeseries data alone. First, the finer granularity of this information means that VMT can be forecast for 

each individual state simultaneously; the same model is equipped to make 51 separate predictions, 
25

rather than a single one, for a given future year. This may lead to more stable and reliable forecasts, as 

errors in forecasting VMT for individual states partially offset one another. 

Second, certain variables that have theoretically important influences on travel behavior but display 

insufficient historical variation at the national level to identify their contributions to VMT growth (such 

as the concentration of population in metropolitan areas or the average number of persons in a 

household) may vary widely across states, even within a single year. While aggregating state-level data 

to national totals can mask the underlying cross-sectional variation in such measures, using a 

combination of cross-sectional and time-series variation in their values can allow their effects to be 

more successfully incorporated into state-level forecasting models. 

Annual data on VMT by vehicle type and many of the variables hypothesized to influence light-duty 

vehicle travel and truck shipping activity were collected for each individual state over the period from 

1993 through 2008. As with development of the functional class VMT forecasting models described 

previously, the initial specifications of the state-level models was guided by the final variable selection in 

the national aggregate VMT models developed for each vehicle class. One important distinction, of 

course, was that most of the variables included in the initial specifications of the state VMT models were 

the state-specific analogs of those utilized at the national level. For example, state-level estimates of

GDP were included as explanatory variables, rather than national aggregate GDP. 

Light-Duty Vehicles

Table 10 summarizes the structure of the state-level light-duty VMT forecasting model. As it indicates, 

light-duty vehicle travel per capita in each state was found to be a function of the average number of 

persons per household in that state, its level of disposable personal income per capita, the percent of 

the state’s population living in metropolitan statistical areas (MSAs), the fraction of each state’s 

population under 19 years of age, fuel cost per mile for that state16, and state-level highway lane-miles 

per capita. The equation also contains a lagged dependent variable, as well as “fixed effect” coefficients

for each state, which are intended to capture differences among states’ VMT that are not fully 

attributable to other explanatory variables included in the model.

The household size measure appears with a negative coefficient, reflecting the fact that as the size of 

the average household has declined over time, light-duty vehicle travel per person has increased. This 

result is consistent with the hypothesis that at least some decisions involving travel-generating activities 

are made at the household rather than the individual level, and that if a given total population is 

organized into fewer households, the total number of vehicle trips made for some purposes (such as 

shopping, recreation, and perhaps commuting) can be reduced. Personal disposable income per capita 

shows the same positive impact on driving as was evident in the forecasting model for aggregate 

nationwide light-duty VMT. 

 16 Recall that fuel cost per mile is equal to retail fuel price per gallon divided by average miles per gallon achieved 

by each type of vehicle. Retail fuel prices vary among states for two reasons: delivered wholesale (or pre-tax) 

prices for gasoline and diesel vary geographically, primarily due to refinery locations and transportation costs, and 

state-level fuel taxes vary widely. Although average fuel economy probably does differ among states, no measures 

of its variation are readily available, so its annual value for each state was assumed to be identical to its nationwide 

average during that year. Thus the measure of fuel cost per mile used in the models varies over time as well as 

among states during any single year, but the latter source of variation reflects only interstate differences in retail 

fuel prices. 
26

The fraction of a state’s population living in MSAs also appears with a negative sign, which appears to 

reflect the effect of higher population density in urban areas on trip distances, as well as perhaps on the 

fraction of trips using private vehicles. Thus as more of a state’s population resides in urbanized areas,

which can occur as population density in rural areas at the periphery of its metropolitan regions 

increases, personal vehicle trips will tend to be shorter and fewer. As the magnitude of the coefficient 

estimate indicates, however, this effect appears to be quite small. 

Table 10: Explanatory Variables Included in State-Level Forecasting Model for Light-Duty VMT

Variable Coefficient Functional Form

Lagged dependent 

variable 0.7416 Log

Average persons per 

household -0.4951 Log

Disposable personal 

income per capita 0.0690 Log

Percent of 

population in MSAs -0.0002 Level

Percent of 

population under 19 0.6650 Level

Fuel cost per mile -0.0387 Log

Lane Miles per capita 0.0349 Log

The final demographic variable, the fraction of a state’s population under 19, enters with a positive sign

and its influence is quite strong, indicating that when children represent a larger fraction of its total 

population, light-duty vehicle use increases. This presumably reflects “chauffeuring” of children to and 

from destinations such as school and recreation activities, which increases per capita VMT by household 

vehicles. Fuel cost per mile appears with the expected negative sign, but appears to have a larger effect 

on VMT at the state level than was evident at the national level, particularly after the adjustment to 

higher fuel prices is complete. Finally, the number of roadway lane-miles per capita shows a positive 

influence on light-duty VMT, again presumably reflecting the effect of additional highway capacity on 

travel speeds and thus on the time component of the inclusive cost of personal travel. 

Single-Unit Trucks

As Table 11 shows, the state-level forecasting equation for single-unit truck travel is a function of state 

GDP, fuel cost per mile for that state, and lane-miles of urban roadways in that state. The equation also 

includes the one-period lagged value of its dependent variable and cross-sectional fixed effects, which 
27

again are used to capture interstate differences in single-unit truck use that are not accounted for by the 

economic and road supply variables included in the model. State GDP appears with a positive sign, 

illustrating the positive effect of overall economic activity on demand for transportation services 

provided using single-unit trucks. Fuel cost per mile again has the expected negative impact on singleunit truck VMT, while an increase in the extent of a state’s urban roadway network has a positive impact 

on single-unit truck activity. The magnitude of the coefficient on the lagged value of VMT reveals that 

changes in these variables require about three years for their impacts on single-unit truck travel to be 

felt completely, but their effects are considerably larger when that adjustment is complete.

Table 11: Explanatory Variables Included in State-Level Forecasting Model

for VMT by Single-Unit Trucks

Variable Coefficient Functional Form

Lagged dependent 

variable 0.6628 Log

State GDP per capita 0.2571 Log

Fuel cost per mile -0.0561 Log

Urban lane miles 0.1829 Log

Combination Trucks

The state-level forecasts of combination truck VMT are produced using a model that includes state GDP, 

the value of U.S. exports and imports expressed as a fraction of GDP, fuel cost per mile for each state, 

and the density of rural roadways per square mile of each state’s land area. However, the variable 

measuring the importance of the U.S. trading sector, U.S. imports plus exports as a fraction of total U.S. 

GDP, can only be measured at the national aggregate level. Thus it varies over time, but takes the same 

value for all states during any specific year, while each of the other variables the model uses varies both 

year-by-year and among individual states. Fixed effect terms for each state are also included in the 

equation, again to control for the influence of factors other than the variables included in the equation.

As Table 12 reports, state GDP exercises the usual positive influence on VMT, meaning that higher 

economic activity within a state is associated with more of the large-volume and long-haul freight 

shipments that are typically carried by combination trucks. The variable measuring the contribution of 

international trade to U.S. GDP, imports plus exports as a fraction of GDP, also has a positive impact on 

combination truck use. This measure appears to capture the effect of national trends in the use of 

combination trucks for transporting goods over long distances to and from U.S. coastal ports, which 

often causes truck shipments to be routed through multiple states. Other measures of international 

trading activity, such as container movements at U.S. coastal ports, were also examined, but did not 

perform as well in the combination truck VMT model. 
28

Table 12: Explanatory Variables Included in State-Level Forecasting Model

for VMT by Combination Trucks

Variable Coefficient Functional Form

State GDP 0.3793 Log

Imports and exports 

as a percent of GDP 

(national)

1.4759 Log

Fuel cost per mile -0.1036 Log

Rural lane miles per 

square mile 0.3576 Log

Fuel cost per mile shows the expected negative impact on VMT, indicating that increases in retail diesel 

prices – which raise costs for shipping via combination truck – reduce the demand for freight 

movements by truck (or increase utilization of combination trucks’ carrying capacity), while increases in 

combination truck fuel economy have the opposite effect. The variable measuring rural roadway lanemiles per square mile is intended to capture the coverage or “connectivity” that each state’s highway 

network provides among its metropolitan areas, as well as to those in neighboring states. As expected, 

higher values of this measure have a positive effect on combination truck use, since highway networks 

providing more complete coverage of a state’s land area or greater connectivity among freight origins 

and destinations have the effect of reducing costs for shipping by combination truck. In turn, this would 

be expected to raise the volume of freight that is shipped to and from (or even within) a state using 

combination trucks. 

Fleet Model

The vehicle fleet models represent a different approach to forecasting VMT than do the econometric 

equations discussed above. The previous models directly estimate and predict total light-duty and truck 

VMT for a specific geographic region (the U.S. as a whole or individual states) or a particular category of 

roadways (urban interstate highways, rural arterials, etc.). In contrast, the fleet models build up 

estimates of light-duty or truck VMT by first decomposing the relevant vehicle fleet by model year or 

vintage during each calendar year, and then using well-defined relationships between vehicle age and 

average utilization – measured by average annual miles driven per vehicle during a year – to develop 

annual estimates of total travel by each vehicle class for the current and future years.

Three distinct steps are involved in developing each fleet VMT models: (1) estimating the number of 

vehicles of each age that will be in service during a given calendar year, (2) estimating average annual 

VMT per vehicle for vehicles of each age, and (3) multiplying the number of vehicles of each age that are 

in use during a calendar year by average annual VMT for vehicles of that age. The results of these 

calculations can then be summed to yield an estimate of national-level VMT for each calendar year. 
29

The resulting estimates of total VMT for each future year are unlikely to agree exactly with the forecasts 

produced by the national aggregate VMT forecasting models for each vehicle class described previously. 

In order to insure that they do, the results of step 3 are used to predict the fraction of total annual VMT 

that will be produced by the vehicles of each age during each future calendar year. These shares are 

subsequently applied to the forecasts of total VMT during each calendar year produced by the nationallevel econometric forecasting equations to estimate the number of VMT accounted for by vehicles of 

each age. 

The fleet profile for each calendar year, which consists of the number of vehicles produced during each 

model year that are expected to be in service during each future calendar year, was constructed using 

vehicle registration data obtained from R. L. Polk and forecasts of future new vehicle sales developed by 

IHS. The process outlined below is similar for each of the four vehicle types used in the fleet model 

(automobiles, light-duty trucks, single-unit trucks, and combination trucks), although the discussion 

highlights some minor differences among the vehicle classes.

Constructing the fleet profile begins by obtaining counts of the number of vehicles produced during 

each model year that were registered for use during a sequence of calendar years ending with the most 

recent year for which these data are available. A vehicle’s age during any calendar year is defined as the 

difference between that calendar year and the model year when it was produced; for example, vehicles 

produced in model year 2000 are defined as 10 years old in calendar year 2010 (2010 – 2000 = 10).17

These data are then used to calculate the survival rates for vehicles of each age in each calendar year 

prior to the most recent. As an illustration, dividing the number of model-year 2000 vehicles registered 

during calendar year 2006 (when they are defined to be 6 years of age) by the number registered during 

2005, when those same vehicles were 5 years of age, yields the (conditional) survival rate for 5-year old 

vehicles in calendar year 2005. Where no strong trend in the survival rates for vehicles of a specific age 

is evident over time, their values for recent calendar years can be averaged to develop an estimate of 

survival rates for future model years as they reach each age. Where survival rates for vehicles of the 

same age have exhibited a clear trend during recent calendar years, these trends can be extrapolated to 

develop estimated survival rates for vehicles that will reach that age during future calendar years.

These projected survival rates are then applied to the registration data for the most recent calendar 

year available (say, 2012) to estimate the number of vehicles of each model year and age that will 

remain in service during the following calendar year (2013). Forecast sales of new vehicles during that 

year (2013) are then added to the fleet, virtually all of which are predicted to survive and remain in 

service as age 1 vehicles during the following calendar year (2014 in this example).18 This process is 

 17 This convention ignores the fact that vehicle model years do not correspond exactly to calendar years. Because 

vehicles produced during a model year may be sold as early as the preceding calendar year (for example, most 

model year 2010 cars and light trucks were first offered for sale during calendar year 2009) or as late as the 

following calendar year, not all vehicles of the same model year will have been in use equally long during any 

future calendar year. Nevertheless, they are assumed to be of the same age for purposes of this analysis. This 

problem is most acute for light-duty vehicles (cars and light trucks), and much less serious for heavy trucks. 

18 Again, distinctions between model year and calendar year are ignored; for example, all new vehicles projected 

to be sold during calendar year 2011 are assumed to be produced during model year 2011. For light trucks and 

automobiles, the assumption may create some distortion, since, for example, a significant number of model year 

2012 vehicles will be sold during 2011, for instance. However, in the long term, any resulting distortions to 

estimates of VMT and the aggregate number of vehicles in service are likely to be minor.
30

repeated to produce estimates of the number of vehicles of each model year (and thus age) that will be 

in use during each subsequent calendar year through the forecast horizon. 

Average yearly VMT by vehicle age was estimated separately for four vehicle classes: combination 

trucks, single-unit trucks, automobiles, and light trucks; the latter two classes were then combined to 

produce estimates of average annual VMT by age for all light-duty vehicles. For each of these vehicle 

classes, regression analysis was used to develop a function relating average annual VMT to vehicle age. 

After extensive experimentation, a quadratic structure was chosen for each vehicle type, in which 

average annual VMT per vehicle depends on both vehicle age and its squared value. Data on vehicle age 

and annual use for single-unit and combination trucks were obtained from the 2002 Vehicle Inventory 

and Use Survey (VIUS), while information on age and estimated annual use for automobiles and light 

trucks was drawn from the 2009 National Household Transportation Survey (NHTS). Average annual 

VMT by vehicles of each type and age was projected to grow over the future at rates derived from 

analyses of differences in historical growth rates of total VMT and the number of vehicles in use. 

Finally, the number of vehicles of each model year and age projected to be in use during each future 

calendar year was multiplied by the estimate of average annual miles driven for vehicles of that age to 

calculate the contribution by vehicles of that age to total VMT during each future year. These 

contributions can then be summed to develop forecasts of fleet-wide aggregate VMT during future 

calendar years, and this entire process is repeated for each class of vehicles. 

As indicated previously, however, the resulting estimates of total VMT for future calendar years differ 

slightly from the annual forecasts produced by the aggregate VMT models for the three vehicle classes. 

Thus to ensure that they correspond, the estimated contributions by vehicles of each model year and 

age to total VMT for that vehicle class are expressed as proportions, and these proportions are then 

applied to the forecast of total annual VMT for that class. This produces revised estimates of VMT by 

vehicles of each model year and age during future calendar years that are consistent with the forecast of 

total VMT for that vehicle class and year.

Description of Forecasting Tool

The forecasting tool is separated into two distinct parts, both of which are Microsoft Excel 2007 files. A 

first spreadsheet file contains the national-level models (nationwide aggregate, roadway functional 

classification, and fleet forecasts), while a second contains the state-level forecasts. Although the

forecasts are separated for ease of use, the general capabilities of each of the spreadsheet tools are the 

same. 

Each of the spreadsheet tools allows the user to modify and customize various forecasting parameters, 

reflecting assumptions about economic and demographic conditions, as well as policy decisions that

affect projected future growth in vehicle use. Macroeconomic and demographic conditions such as 

growth in population, gross domestic product, personal income, imports and exports, and fuel prices 

tend to be closely linked to one another. In the case of these factors, the user may select one of three 

possible scenarios—baseline, optimistic, or pessimistic, which correspond to the alternative IHS outlooks 

for economic growth. In each scenario, all of these related variables are forecast as a single “package,” 

in order to preserve their expected relationships.

Two other factors that were found to have important effects of VMT in many of the models, fleet-wide 

fuel efficiency and the cost of driving, are partially exogenously determined; that is, future changes in 
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these two variables may be independent of domestic economic and demographic conditions. The 

primary exogenous effects on these two factors would come directly from federal regulation. Changes in 

fleet-wide fuel efficiency come about as a result of both technological advancement and consumers’

purchase decisions regarding new vehicles. Both of which may be directly affected by government 

mandates, such as the CAFE standards. 

Further, the federal government may directly alter current tax rates on fuel, which constitute a 

significant component of retail fuel prices, and thus affect the cost of driving. Although not a policy that 

has been previously adopted, the federal government could also influence the cost of driving through 

non-fuel-related policy regulations, such as by imposing VMT fees. Such a policy has been discussed 

extensively in recent months, and advocated by one Congressional Commission created to study 

alternatives for financing future investments in transportation infrastructure.

Expectations regarding both of these exogenous parameters may be controlled by the spreadsheet user. 

In the case of fleet fuel efficiency, changes are made relative to a baseline forecast for each vehicle type

by applying a multiplicative factor to the baseline forecast growth. The user may input expected changes 

in the fuel-related cost of driving in several manners. Changes in federal fuel taxes may be made subject 

to several possible future scenarios (for example, by modifying the federal fuel tax in one or many 

isolated future years, or by linking the growth of the gas and/or diesel taxes to the expected rate of 

inflation). Future changes in the cost of driving may also be simulated by introducing per-mile VMT fees. 

Detailed tables and graphs illustrate the effect of the predictions made for the explanatory variables, by 

way of comparison to historical growth and baseline forecasts. The resulting VMT forecasts are 

displayed by vehicle type, as well as by roadway functional class or state, in both graphical and 

numerical form, and growth rates in VMT over various time horizons are computed and displayed. The 

composition of the vehicle stock may also be examined in detail for any selected future year using the 

output from the fleet models. Energy consumption estimates are also generated for five fuel types, 

based on projected vehicle use, fuel shares, and future trends in fuel efficiency.