---
category: literaturenote
citekey: liuforecastingtruckvmtgrowth2006
title: Forecasting truck VMT growth at the county and statewide levels
authors: "Liu, Feng; Kaiser, Robert G"
year: 2006
date: 2006-00-00 2006
zotero_key: DKDWR66U
zotero_storage: G9Z6Q5ME
collections: magistritöö / kohalikud teed
folder: 001_artiklid
firstAuthor: "Liu, Feng"
status: converted
---
**Forecasting Truck VMT Growth at the County and Statewide Levels**

Feng Liu, Ph.D. and Robert G. Kaiser

Michael Baker Jr., Inc., 1304 Concourse Drive, Suite 200, Linthicum, MD 21090

(410) 424-2210, FAX (410) 424-2300

Fliu@mbakercorp.com, BKaiser@mbakercorp.com

**ABSTRACT**

In this study, statistical models were developed to forecast truck VMT growth of four facility categories at the county and statewide levels. These models incorporate both socioeconomic and transportation system supply variables. Different model specifications were tested and evaluated in terms of statistical and forecasting validity. A selected set of models was used to forecast truck VMT for planning horizon years 2010, 2020, and 2030. The model results show that local socioeconomic variables alone explain a considerable amount of the truck VMT variance, particularly for urban interstate and non-interstate facilities. Adding external driving forces such as truck corridor or contributing state gross sate product variables increase the models' explanatory power, particularly for rural interstate facilities. Applicable to other states, this statistical modeling method offers a comprehensive approach that provides consistent results across multiple jurisdictions at a much lower cost than developing a statewide travel demand model.

# **TRUCK VMT FORECASTING METHODS**

Truck VMT growth forecasting is very rudimentary, and in most states, is often treated as part of total VMT growth forecasting. A variety of methods have been used to forecast statewide VMT growth. Based on the data used, VMT growth estimation and forecasting methods can be classified into three categories: traffic-count-based methods, socioeconomic-data-based methods, and travel demand forecasting models. Based on forecasting techniques, VMT growth forecasting can be grouped into four categories: trend/growth factors, time series, regressions, and alternative statistical methods. Each method has its strengths and weaknesses.

### **Based on the Type of Data Used**

Traffic-count based methodologies are the most common approaches used to forecast VMT growth. The United States Environmental Protection Agency (U.S. EPA) recommends use of Highway Performance Monitoring System (HPMS) procedures to estimate VMT. The HPMSbased procedures use traffic count data, which are routinely updated statewide and consistently reported for most data items and allow comparison among states. Truck volume and classification counts are collected from a sample of roadways, and truck VMT are estimated either as a product of truck average daily traffic and the roadway length on a roadway segment basis or as a product of total VMT and the average truck percentages (Benkohl and Girianna 2004) The HPMS-based procedures have the potential of providing a consistent framework at

the detailed level such as functional types and vehicle types. They are generally simple and easy to implement.

However, count-based methods can be biased because of sampling size, frequency, or representation, and the extrapolation from the sampled sites to system wide total. Because HPMS is particularly designed for statewide estimation of travel, it is often not statistically valid below the statewide level. Extrapolation of the sample data to the entire network is usually based on expansion factors accounting for variations among functional classes and area types. However, these expansion factors ignore factors that could affect VMT growth over time such as link attributes, land use and socioeconomic characteristics. Count-based methods rely heavily on the assumption that VMT growth will behave in the same or similar manner as in the past, regardless of demographic, land use and other factors.

Socioeconomic-data-based methods do not rely on the characteristics of the roadways but instead focus on factors that affect an individual's travel behavior in a region and use these as the basis of estimating and forecasting VMT growth. These methods attempt to estimate and forecast VMT growth at a more fundamental level than the growth factor method, using variables that can be projected into the future.

Travel surveys have been used to estimate VMT based on household travel characteristics and on licensed driver characteristics. The Indiana statewide VMT study tested three methods licensed driver-based, household-based, and fuel-tax-based (Fricker and Kumapley 2002). Each of these methods is based on socioeconomic data.

To forecast state tax revenues, a fuel-based approach to estimating and forecasting VMT was adopted in Oregon (Oregon DOT 2000). Total VMT is divided into three categories— Light vehicle VMT, Medium-Heavy Vehicle VMT, and Heavy Vehicle VMT. For the first two categories, Oregon DOT uses monthly fuel consumption data, fuel refund claims, and national miles-per-gallon estimates to calculate VMT. For heavy vehicles, VMT is estimated using actual reported mileage from weight-mile tax records and adjustment factors.

Commodity and truck travel data have been used to simulate freight movements. These data include both proprietary and public databases such as the Commodity Flow Survey (CFS), the Vehicle Inventory and Use Survey, and the International Fuel Tax Agreement (IFTA) truck mileage database. These data, however, are too aggregate in geographic resolution to be directly used for metropolitan planning purposes. County-level commodity flows are only available through combination of different sources and some modeling processes. Freight generation models have been developed at the county level, using socioeconomic variables (Black 1999; Guo and Aultman-Hall 2005). These databases have also been used to develop commodity flows at the county level, which are then converted to truck trip tables.

Socioeconomic-data-based methods account for major forces that drive personal and a major portion of commercial VMT growth. They can provide a consistent forecasting framework for a state. However, these methods also have limitations. Because the data sources employed were not designed specifically for estimating VMT, potentially significant biases can result from

extrapolation from a sample to system wide VMT. These methods do not generate VMT estimates by functional class.

Based on both traffic counts and socioeconomic data, travel demand forecasting models can be used to estimate and forecast growth in traffic volumes and VMT. These models are designed to simulate travel behaviors of trip makers and account for major forces that drive VMT growth. VMT by functional classes, area types, and jurisdictions can be estimated.

For statewide VMT forecasting, regional travel demand models also have their limitations. Generally, they do not cover the entire state and do not account for the local travel because most local and minor roads are not included in the model network. Many regional travel demand models have a rudimentary or even lack of treatment of truck travel, although a few agencies have recently made efforts to improve truck travel forecasting in their regional modeling framework. With even less coverage of lower level roadways, a statewide model is generally too sketchy for statewide VMT forecasting. This limitation is also true of a statewide truck travel demand model.

### **Based on Forecasting Techniques**

The growth factor method appears to be the most popular technique used to forecast VMT growth. Readily available and routinely updated, historical traffic count data are used to derive growth factors, which can be used to project future VMT at a detailed level such as functional

types and vehicle types. Count-based, it has the same strengths and weaknesses as the countbased method discussed above. The growth factor method is a quick response method for truck travel growth forecasting (FHWA 1999).

In time series models, past trend is the key to predict the future. The assumption is that the VMT changes will behave as in the past. Past trends are modeled as linear or curvilinear equations. Benjamin (1986) presents a procedure for forecasting average daily traffic using time series model. The time series technique produced results that were close to the observed traffic volume data for small, steady growth areas.

Growth factors are a special case of time series methods. Growth factor method's strengths and weaknesses are also true for time series models. Time series results are sensitive to the data quality. The historical data used to develop time series models are particularly critical to determine if the model is applicable to forecasting the future. If the historical data include only the rapidly growing stage of an urbanizing area, the estimated model may overestimate future VMT growth for a long time horizon. These limitations come from the fact that time series models do not simulate the processes that underlie the VMT growth.

Regressions are generally used to describe the relationship between a dependent variable and its explanatory variables. For forecasting VMT growth, explanatory variables may consist of demographic and economic variables.

Using regression to forecast Annual Average Daily Traffic (AADT) received early attention in the literature. Regression models were developed to forecast traffic in the rural state highway systems in New York (Neveu, 1982) and Indiana (Saha and Fricker 1989), on county roads in Indiana (Mohamad, et al. 1998), and in the state highway system in West Virginia (Iskander, et al. 1996). A variety of independent variables have been tested in these studies, including major demographic, economic, land use, highway supply, and accessibility variables. It was found that different variables were significant for different roadway functional classes. The most common variables that were found to be significant include population, households, employment, and roadway miles. Regression has also been used to estimate truck volume, and it was shown that the regression approach made better estimates than a statewide truck travel demand model in New Jersey (Mittal, et al 2005).

The relationship between VMT growth and its driving forces has been a great interest in recent research, particularly in the debate on the relationship between highway capacity expansion and VMT growth (Noland and Lem 2002). Hansen and Huang (1997) estimated regression models using time series data on VMT for state highways in California. These are fixed effects models using panel data, and dummy variables were introduced to allow the intercept term to vary over cross-sectional units and time. The panel data and dummy variables allow capturing the influence of variables unknown or unmeasured in the model.

Two-stage least square regressions with instrumental variables have been used to address the simultaneity and causality issues between road supply (lane miles) and demand (VMT). An instrumental variable is a linear combination of predetermined model variables. Noland and

Cowart (2000) used a two-stage least squares regression, testing several instruments including urbanized land area. Fulton et al. (2000) used a difference (or growth) model specification and lagged growth in lane miles as an instrument for current growth in lane miles. Cervero and Hansen (2001) tested a wide range of instrumental variables reflecting political, environmental, and demographic influences.

Focusing on hypothesis testing, the research on VMT growth has not been reportedly applied to a practical statewide VMT forecasting, but it offers some insights. Regression (econometric) methods usually account for major forces that drive VMT growth, including socioeconomic factors. They may encompass a state, providing a consistent forecasting framework. However, they do not simulate trip-making processes.

Alternative statistical methods have been used to address issues that are difficult to deal with through traditional regression models. Neural Networks Modeling was tested in the Kentucky study of traffic growth rates (Kentucky Transportation Center 2001).

As a summary, Table 1 compares what each forecasting method offers with what Pennsylvania Department of Transportation (PENNDOT) needs. Some of the forecasting methods reviewed do not serve the PENNDOT needs. For example, socioeconomic-data-based methods do not produce forecasts by functional class and area groups. Travel survey data currently used are secondary data sources from national surveys. Sampling can introduce a major bias unless a state has an add-on, because these surveys are designed to represent the national population. Fuelbased VMT forecasting has also major limitations in terms of data bias. The estimation and

forecasting of fuel economy present the most difficult problem for this method, and fuel consumption across state borders is another challenging issue. Travel demand forecasting models do not serve all PENNDOT needs because of their limited coverage. Although very popular, the growth factors method has a major drawback in that growth factors do not respond to changing socioeconomic conditions over time. As a result of method evaluation, regression methods (econometric models) were selected for the detailed study.

**Table 1. Comparing Different Forecasting Methods against PENNDOT Needs**

|                                                          | PENNDOT<br>Forecasting                     | Needs<br>for<br>a<br>Level<br>of<br>Detail | VMT<br>Growth                       | Forecasting<br>Forecasting | System<br>Variables<br>and<br>Data  |             |  |  |  |
|----------------------------------------------------------|--------------------------------------------|--------------------------------------------|-------------------------------------|----------------------------|-------------------------------------|-------------|--|--|--|
| Candidate<br>Methods                                     | Four<br>Area/<br>Functional<br>1<br>Groups | County<br>Level<br>(all<br>counties)       | Passenger<br>vs.<br>Truck<br>Travel | Socioeconomic<br>Variables | Traffic<br>Information<br>Variables | Land<br>Use |  |  |  |
| Methods—Based<br>on<br>the<br>Type<br>of<br>Data<br>Used |                                            |                                            |                                     |                            |                                     |             |  |  |  |
| Traffic<br>Count<br>Based<br>Forecasting                 | X                                          | X                                          | X                                   |                            | X                                   |             |  |  |  |
| Socioeconomic<br>Data<br>Based<br>Methods                |                                            | X                                          | X                                   | X                          |                                     |             |  |  |  |
| Travel<br>Demand<br>Forecasting<br>Models                | X                                          |                                            | X                                   | X                          | X                                   | X           |  |  |  |
|                                                          |                                            | Methods—Based                              | on<br>Forecasting                   | Techniques                 |                                     |             |  |  |  |
| Growth<br>Factors                                        | X                                          | X                                          | X                                   |                            | X                                   |             |  |  |  |
| Time<br>Series<br>Models                                 | X                                          | X                                          | X                                   |                            |                                     |             |  |  |  |
| Econometric<br>Modeling<br>(Regressions)                 | X                                          | X                                          | X                                   | X                          | X                                   | X           |  |  |  |

Note 1: Urban interstate, urban non-interstate, rural interstate, and rural non-interstate.

## **STATISTICAL MODELING OF TRUCK VMT GROWTH**

### **Data and Variables**

A number of data sources were used to develop the models in this study. The PENNDOT provided an extensive traffic database. This database includes the VMT, linear mile, and lane mile by functional classification, by county, by year, for all public roads for the years between 1994 and 2003. Truck VMT data are available for PENNDOT maintained roads for the years between 1993 and 2003. PENNDOT's Roadway Management System is recognized for its timely and thorough counts that augment the HPMS count program, including a historical database of hundreds of count locations and data by day, time of day and vehicle type.

The 2004 State Profile, developed by Woods & Poole Economics, is the major source for socioeconomic data in this study. It includes historical data and forecasts by year from 1969 through 2030 for every county in Pennsylvania. A variety of variables, different forms of these variables, and indices have been tested in the statistical modeling process. Major socioeconomic variables include:

- Number of households
- Population/population density
- Employment/employment density
- Employment by sectors
- Per capita income/Household income
- Population by Age, and

### • Retail Sales

Commodity Flow Survey data were used to identify major states that contribute to freight movements in Pennsylvania. New Jersey, New York, Maryland, West Virginia, and Ohio contributed 20% of truck tonnage of inbound/outbound shipment in 2002; In-state shipment contributed 59%. Gross State Product (GSP) data, developed by Bureau of Economic Analysis, were used to represent economic activities in these contributing states. Based on the PENNDOT traffic database and the FHWA's Freight Transportation Profile for Pennsylvania, major truck routes were identified, and they are primarily interstate highway corridors, including I80/I84, I76/I70, I81/I83, I79, and I95 (see Figure 1). For each corridor, GSP data from contributing states were aggregated as a proxy to represent aggregate external driving forces for freight movements in Pennsylvania. Counties along these truck routes were also identified, and each county was coded with two variables— corridor GSP and corridor dummy.

![](_page_10_Figure_2.jpeg)

Figure 1. Major Freight Movement Corridors in Pennsylvania

### **Growth Trend Analysis**

Historical traffic and socioeconomic growth patterns are crucial to understand the underlying causes of traffic growth and the relationships between traffic growth and socioeconomic variables. Socioeconomic growth trends will play a critical role in shaping traffic growth in the future. This descriptive analysis will lay a foundation for developing quantitative, statistical models in the next section.

VMT growth trends are analyzed from the long-term (1980 to 2003) and short-term (1994-2003) perspectives. As shown in Table 2, long-term growth trends between 1980 and 2003 include:

- Statewide total VMT grew by almost 50 percent, representing a compound annual growth rate of 1.7 percent.
- Pennsylvania's historical VMT growth is lower than the national average, which has averaged over 3 percent since 1970.
- Overall VMT growth appears to be moderating; 1.8 percent for the 1980-1989 period versus 1.5 percent for the 1994-2003 period.
- Interstate VMT increased at a higher rate (3.9 percent annually) than non-interstate VMT (1.2 percent annually).
- Urban interstate VMT grew more rapidly than rural interstate VMT, with annual growth rates of 5.2 and 2.6 percent, respectively.
- Urban interstate VMT growth appeared to be moderating, but rural interstate VMT grew at a faster pace over the recent past decade than in the 1980s.

Table 2. Long Term Historical VMT Annual Growth Rates

|                   | RURAL | URBAN<br>INTERSTATE INTERSTATE INTERSTATE |        | RURAL NON- URBAN NON-<br>INTERSTATE | TOTAL<br>STATEWIDE | TOTAL<br>US |
|-------------------|-------|-------------------------------------------|--------|-------------------------------------|--------------------|-------------|
| 1980-1989         | 2.60% | 5.70%                                     |        |                                     | 1.80%              | 3.60%       |
| 1994-2003         | 4.10% | 4.80%                                     | -0.80% | 1.90%                               | 1.50%              | 2.40%       |
| Total (1980-2003) | 2.60% | 5.20%                                     |        |                                     | 1.70%              | 2.80%       |

Tables 3 and 4 and Figure 2 show short-term growth trends for total VMT and truck VMT between 1994 and 2003:

- Statewide VMT increased at a lower rate in 2000 and after, with a rate of 1 percent compared with 2 percent for the years before 2000.
- Interstate VMT grew more rapidly than non-interstate VMT, averaging 4.8 and 0.8 percent annually for interstates and non-interstates, respectively.
- Reclassification in 2003 significantly affects lane miles and VMT distribution among the four categories—a significant shift from rural to urban categories.
- VMT growth rates, for most years, move in tandem with lane mile growth rates; this is particularly evident for the 2003/2002 and 1996/1995 growth rates.
- Truck VMT growth shows similar patterns as total VMT; while aggregate truck growth outpaced total VMT growth between 1994 and 1998, their growth rates were similar between 1998 and 2003.

Table 3. Short Term Statewide Total VMT Annual Growth Rates

|                      |     |      |     |     |      |      |     | 1994-95 1995-96 1996-97 1997-98 1998-99 1999-00 2000-01 2001-02 2002-03 |       |
|----------------------|-----|------|-----|-----|------|------|-----|-------------------------------------------------------------------------|-------|
| Rural Interstate     | 5.3 | 20.3 | 3.3 | 4.6 | 4.2  | 1.2  | 1.3 | 5.4                                                                     | -6.9  |
| Rural Non-Interstate | 2.1 | -0.9 | 2.8 | 1.9 | 3.7  | 0.0  | 0.1 | 0.1                                                                     | -16.0 |
| Urban Interstate     | 6.1 | 2.7  | 3.8 | 4.3 | 2.9  | 1.0  | 3.9 | 2.7                                                                     | 9.8   |
| Urban Non-Interstate | 0.6 | 0.3  | 0.4 | 0.6 | -0.1 | -0.9 | 0.8 | 0.1                                                                     | 14.7  |
| Total                | 2.4 | 2.0  | 2.0 | 2.1 | 2.1  | -0.1 | 1.1 | 1.1                                                                     | 1.2   |

Table 4. Short Term Statewide Truck VMT Annual Growth Rates

|                      |     |      |     | 1994-95 1995-96 1996-97 1997-98 1998-99 1999-00 2000-01 2001-02 2002-03 |      |      |      |      |       |
|----------------------|-----|------|-----|-------------------------------------------------------------------------|------|------|------|------|-------|
| Rural Interstate     | 6.6 | 11.8 | 6.1 | 4.4                                                                     | 3.7  | 3.1  | 1.4  | 3.5  | -5.0  |
| Rural Non-Interstate | 2.3 | 1.1  | 3.0 | 2.2                                                                     | 1.9  | 0.3  | -0.6 | -0.7 | -18.2 |
| Urban Interstate     | 3.5 | 0.7  | 2.9 | 5.8                                                                     | 2.7  | 1.6  | 6.1  | 3.2  | 11.6  |
| Urban Non-Interstate | 0.1 | 0.0  | 0.4 | 0.2                                                                     | -0.3 | -1.1 | 0.8  | -0.8 | 29.7  |
| Total                | 3.1 | 3.5  | 3.3 | 3.1                                                                     | 2.1  | 1.1  | 1.6  | 1.3  | 0.8   |

![](_page_13_Figure_2.jpeg)

Figure 2. Statewide Truck VMT Growth Rates between 1994 and 2003

Socioeconomic trends can also be seen from both long-term (1970-2000) and short- term (1994- 2003) perspectives. As shown in Table 5 and Figures 3 though 7, long-term growth trends between 1970 and 2000 include:

- Statewide population growth has been slow in the last three decades, with less than a 0.5 percent annual growth rate.
- Households grew at a faster rate than population.
- Employment increased at a rate of around 1 percent.
- Income growth rates were higher than population, households and employment.
- The state has been losing the young population and gaining the elderly population.

- The state has been aging, despite the elderly population increasing at a much lower rate in the 1990s than in the previous two decades.
- Statewide VMT growth has outpaced most socioeconomic variables between 1980 and 2003.
- Significant regional differences are shown in geographic patterns of growth— strong growth in the eastern and south-central regions and decline and stagnancy in the western and northern regions.
- Older urban areas have declined in population, while population has spread out to urban fringes and exurban areas.

Table 5 and Figure 3 show the following forecasted trends between 2000 and 2030:

- Population growth rates will increase, catch up and even surpass the declining household growth rates in the next twenty years.
- Employment will grow at a slightly lower rate than the past three decades.
- Income growth will be moderating but still much higher than population and household growth.
- The state will continue to age, more rapidly after 2010 as baby-boomers enter the senior ranks.
- Regional divide and urban sprawl are forecast to continue in the next 25 years unless strong government policies reverse the trends.

Table 5. Long Term Annual Growth Rates

|                      | 1970-80 | 1980-90 | 1990-00 | 2000-10 | 2010-20 | 2020-30 |
|----------------------|---------|---------|---------|---------|---------|---------|
| Population           | 0.05%   | 0.03%   | 0.32%   | 0.27%   | 0.36%   | 0.45%   |
| Households           | 1.25%   | 0.63%   | 0.60%   | 0.53%   | 0.42%   | 0.23%   |
| Employment           | 0.76%   | 1.19%   | 0.98%   | 0.75%   | 0.89%   | 0.97%   |
| Income<br>PerCapita  | 2.50%   | 1.92%   | 1.73%   | 1.20%   | 1.25%   | 1.27%   |
| Mean<br>HH<br>Income | 1.34%   | 1.24%   | 1.30%   | 0.90%   | 1.16%   | 1.41%   |
| Pop<br><17<br>yrs    | -2.16%  | -1.08%  | 0.04%   | -0.79%  | 0.09%   | 0.09%   |
| Pop<br>65+<br>yrs    | 1.87%   | 1.71%   | 0.13%   | -0.26%  | 1.82%   | 1.87%   |
| Retail<br>Sales      | 1.34%   | 1.46%   | 2.63%   | 1.38%   | 1.38%   | 1.50%   |

In the short term, growth trends between 1994 and 2003, as shown in Table 6, include:

- Population growth was low, while household growth was higher than population growth.
- Employment and income growth peaked in the late 1990s and has become weaker since 2000.
- The state lost young population, while the elderly's share of total population remained stagnant or declined slightly during the period.

Table 6. Short Term Annual Growth Rates

|                  |       |        |       |        |        |        |        | 1994-95 1995-96 1996-97 1997-98 1998-99 1999-00 2000-01 2001-02 2002-03 |        |
|------------------|-------|--------|-------|--------|--------|--------|--------|-------------------------------------------------------------------------|--------|
| Population       | 0.27% | 0.18%  | 0.06% | 0.15%  | 0.15%  | 0.18%  | 0.14%  | 0.26%                                                                   | 0.33%  |
| Households       | 0.87% | 0.98%  | 0.37% | 0.35%  | 0.26%  | 0.64%  | 0.37%  | 0.53%                                                                   | 0.64%  |
| Employment       | 1.61% | 0.90%  | 1.74% | 1.39%  | 1.51%  | 2.09%  | 0.16%  | 0.80%                                                                   | 0.83%  |
| Income PerCapita | 0.65% | 2.10%  | 2.60% | 3.74%  | 1.53%  | 3.67%  | 0.84%  | 1.36%                                                                   | 1.19%  |
| Mean HH Income   | 0.00% | 1.09%  | 2.10% | 3.35%  | 1.20%  | 3.14%  | 0.53%  | 1.04%                                                                   | 0.82%  |
| Pop <17 yrs      | 0.00% | -0.41% | 0.00% | -0.42% | -0.42% | -0.84% | -0.85% | -0.85%                                                                  | -0.43% |
| Pop 65+ yrs      | 0.64% | 0.00%  | 0.00% | 0.00%  | -0.63% | -0.64% | 0.00%  | -0.64%                                                                  | -0.65% |
| Retail Sales     | 1.81% | 3.02%  | 1.33% | 2.97%  | 6.22%  | 4.63%  | -0.14% | 3.68%                                                                   | 1.31%  |

![](_page_16_Figure_0.jpeg)

Figure 3. Socioeconomic variables trends between 1970 and 2030

![](_page_16_Figure_2.jpeg)

Figure 4. Comparison of VMT trend with Socioeconomic Variables between 1980 and 2003

Figure 5. Population Annual Growth Rates 1970-1990

![](_page_17_Figure_1.jpeg)

Figure 6. Population Annual Growth Rates 1990-2000

![](_page_17_Figure_3.jpeg)

Figure 7. Population Annual Growth Rates 2000-2030

![](_page_17_Figure_5.jpeg)

### **Methodology**

In this research, different types of regressions and model specifications were tested, including Ordinary Least Squares (OLS) and cross-sectional time series OLS. A regular regression model generally regresses dependent variables on independent variables, forcing units of analysis (in this case, county) to have the same constant. The cross-sectional time-series fixed effect models use cross-sectional and/or time intercepts for each unit of observation. These so-called dummy variables capture factors that are not measured or unknown in the models. The factors that contribute to VMT growth may include labor force participation, vehicle availability, and spatial patterns of development. The cross-sectional time-series fixed effect models can also reduce the bias associated with the correlations between independent variables and error terms.

The logarithmic specification of a cross-sectional time-series OLS regression is often used to minimize heteroskedasticity in the cross-sectional data. In this formulation, the estimated coefficient λ k can be interpreted as elasticity of VMT with respect to independent variables.

$$Ln(VMT_{ii}) = c + \alpha_i + \beta_t + \sum_k \lambda^k (LnX_{ii}^k) + \varepsilon_{ii}$$
(1)

Where *Ln (VMTit)* = the logarithmic form of the annual vehicle miles of travel for county *i* in year *t*;

*LnX k it* = the logarithmic form of the value of explanatory variable *k* for county *i* and year *t*; <sup>α</sup>*<sup>i</sup>* = the fixed effect for county *i*, estimated;

β*<sup>t</sup>* = the fixed effect for year *t*, estimated;

*c* = a constant term;

λ *k* = the coefficient of the *k*th explanatory variable;

<sup>ε</sup>*it* = random error term for county *i* in year *t*, assumed to be normally distributed with mean zero.

The major unit of analysis was at the county level. County grouping was also tested and modeled, and results were compared with those of county-level models at the aggregate state level. In addition, the focus of the forecasting system is on four functional classifications:

- urban interstate,
- urban non-interstate,
- rural interstate, and
- rural non-interstate.

During the modeling process, statistical diagnostic tests were conducted to identify violations of OLS assumptions. These statistical models were also evaluated against several criteria as well as against standard regression goodness-of-fit and error statistics. Measures included adjusted Rsquared, root mean squared error (RMSE), and mean absolute percentage error (MAPE).

### **Model Results**

This section presents a brief summary of the major modeling results from a selected group of models. Models using the logarithmic specification of a fixed effect OLS regression are preferred over other models for a number of reasons. A variety of statistical modeling tests have been conducted, and for the brevity purposes, many tests and their results are not reported here.

The correlation matrices of the variables were examined, and for urban facilities, lane miles had very high correlations with socioeconomic variables at the county level. Use of lane miles per capita reduces the correlations greatly. For rural facilities, lane miles have low correlations with socioeconomic variables at the county level. Total employment and employment by sectors are highly correlated with demographic variables such as population and households and thus dropped from the model testing process.

After variable transformation, correlations among independent variables are reduced to a level that poses no threat to the models as a whole. However, some correlations among socioeconomic variables are unavoidable. The magnitude and sign of the estimated coefficients represent interactions among independent variables, and some mixed results may reflect these interactions.

#### *Base Models*

County level OLS models are logarithmic formulations. Dependent variables are natural logs of truck VMT by four categories. Independent variables consist of both demand and supply variables—demographic and economic variables in natural logarithmic forms, as well as lane miles and lane miles per capita. Different forms of the OLS based model were specified and estimated, using different socioeconomic variables. Model POP has population and per capita income as independent variables, while Model HH has households and mean household income as independent variables. Retail sales are another socioeconomic variable tested with lane miles/lane miles per capita. Retail sale is highly correlated with employment by sector variables; retail sale and retail employment can do an equally good job in the models. These tests show results that are similar to Model HH or Model POP. Table 7 shows model results for Model HH,

and similar results from Model POP and the retail sales model were omitted for the brevity purpose.

Table 7. Fixed Effect Base Model Estimation Results

| Dependent Var=LN(VMT)      | Rural Interstate |        | Rural Non-Interstate |        | Urban Interstate |        | Urban Non-Interstate |        |
|----------------------------|------------------|--------|----------------------|--------|------------------|--------|----------------------|--------|
|                            | Coefficient      | T-stat | Coefficient          | T-stat | Coefficient      | T-stat | Coefficient          | T-stat |
| Constant                   | -12.59           | -4.87  | 4.842                | 2.19   | -8.972           | -3.46  | -7.52                | -2.76  |
| LN (Households)            | 1.2132           | 4.48   | -0.0534              | -0.26  | 1.6362           | 5.85   | 2.2468               | 7.66   |
| LN (Mean Household Income) | 1.3019           | 7.32   | 0.2561               | 2.21   | 1.1886           | 8.44   | -0.101               | -0.68  |
| LN (Lane Miles)            | 0.33936          | 7.08   | 1.3058               | 11.17  |                  |        |                      |        |
| LN (Lane Miles Per Capita) |                  |        |                      |        | 0.71537          | 11.82  | 0.10557              | 2.87   |
| N                          |                  | 367    | 658                  |        | 411              |        | 543                  |        |
| 2<br>Adjusted R            |                  | 0.977  | 0.973                |        | 0.995            |        | 0.991                |        |
| R-Squared: within          | 0.44             |        | 0.18                 |        | 0.6              |        | 0.18                 |        |
| between                    | 0.11             |        | 0.62                 |        | 0.77             |        | 0.86                 |        |
| overall                    |                  | 0.12   |                      | 0.61   | 0.82             |        | 0.85                 |        |

Note: County dummy coefficients are omitted for brevity.

As shown in Table 7, both demand and supply variables are significant and positive, with exceptions of two negative, insignificant coefficients. The magnitude of coefficients varies by facility types. Urban non-interstates have the largest coefficients for households, among four facility categories. Lane miles and lane miles per capita have a wide range of coefficients across the models. Rural non-interstates have the highest coefficients, and urban non-interstates have the lowest coefficients.

With logarithmic formulation, the coefficients can be interpreted as elasticities of VMT with respect to independent variables. However, it should be noted that the elasticity of VMT with respect to lane miles or lane miles per capita in this study, represent the combined effects of new supply and reclassifications, and cannot be interpreted simply as induced travel. In particular, the 2003 VMT re-classifications have shifted VMT among different categories. These VMT reclassifications were undertaken to account for changes in area types during the urbanization process. Urbanization is a gradual process, and VMT shifts among urban and rural categories

should also be a gradual process. However, re-classification is undertaken only at 10-year intervals. Re-classification does not affect the demand-supply relationship for the aggregate VMT, but may shift the relationships in *individual facility categories*.

It should also be noted that the R 2 values in a fixed effect OLS model can not be interpreted the same way as in a regular OLS model. The dummy variables, which are used to represent the unmeasured and unknown variables specific to individual counties, contribute to the overall R Excluding these dummy variables, socioeconomic and transportation supply variables together explain 49% of the variance for rural interstate facilities, 76% for rural non-interstate facilities, 82% for urban interstate facilities, and 93% for urban non-interstate facilities. "R-squared", a measure of goodness of fit similar to R , is also reported in the table to show the fixed-effects estimation results from the cross-sectional time-series models.

.

In addition to R values, Mean Absolute Percentage Error (MAPE) was used to evaluate the model errors. The MAPE measures how the fitted values are deviated from the observations. Overall, these models have low errors.

#### *Alternative Models*

In the base model formulation, socioeconomic variables represent internal driving forces for truck VMT growth, and county dummy variables are used to represent county-level factors that are not measured or unknown in the models. Each county has its own estimated values, which are usually different from county to county. One major unmeasured factor is economic activities in other states that contribute to freight movements in Pennsylvania. As described earlier, two

variables were created to represent these external driving forces for truck VMT growth. The first is corridor dummy, which represents the truck corridor where each county is located. The second is corridor GSP, which represents external economic activities that may contribute to the freight movement in a corridor. Use of these two variables assumes that those counties in the same corridor have the same effect from the external driving forces.

An alternative model formulation includes one of these two variables, instead of county dummies, for interstate facility models. The results, as shown in Table 8, indicate that these variables are positive and significant for urban interstate models. It is a mixed result for rural interstate facilities. While it is positive and significant for I-80 and I-81 corridors, it is negative and significant for the I-76 corridor and insignificant for the I-79 corridor. The models show improvement over the regular OLS model in terms of the goodness-of-fit, particularly for the rural interstate model. Adding truck corridor or contributing states' GSP variables increase the models' explanatory power by 20 percent points for rural interstate facilities and a few percent points for urban interstate facilities. However, there are no GSP forecasts readily available for future years from either BEA or private vendors like Woods and Poole.

Table 8. Alternative Model Estimation Results

| Dependent Var=LN(VMT)      | Rural Interstate |        | Urban Interstate |        |                | Rural Interstate |        | Urban Interstate |        |
|----------------------------|------------------|--------|------------------|--------|----------------|------------------|--------|------------------|--------|
|                            | Coefficient      | T-stat | Coefficient      | T-stat |                | Coefficient      | T-stat | Coefficient      | T-stat |
| Constant                   | -9.347           | -3.79  | -3.118           |        | -1.51 Constant | -9.396           | -3.82  | -3.16            | -1.53  |
| LN (Households)            | 0.03082          | 0.85   | 1.10468          |        | 20.74 LN (HH)  | 0.03062          | 0.84   | 1.10441          | 20.72  |
| LN (Mean Household Income) | 2.0271           | 8.61   | 0.9905           |        | 5.20 LN (MHI)  | 2.0318           | 8.64   | 0.9946           | 5.22   |
| LN (Lane Miles)            | 0.93386          | 21.23  |                  |        | LN (LM)        | 0.93407          | 21.24  |                  |        |
| LN (Lane Miles Per Capita) |                  |        | 0.47267          |        | 8.98 LN (LMPC) |                  |        | 0.47258          | 8.98   |
| LN_I80GSP                  | 0.033949         | 7.24   | 0.015528         |        | 3.00 LN_I80    | 0.47984          | 7.24   | 0.2193           | 3.00   |
| LN_I76GSP                  | -0.029387        | -5.82  | 0.014343         |        | 2.31 LN_I76    | -0.41684         | -5.84  | 0.20264          | 2.30   |
| LN_I81GSP                  | 0.031564         | 6.28   | 0.067441         |        | 10.38 LN_I81   | 0.4328           | 6.27   | 0.92597          | 10.37  |
| LN_I95GSP                  |                  |        | 0.02879          |        | 2.81 LN_I95    |                  |        | 0.4031           | 2.80   |
| LN_I79GSP                  | 0.005024         | 1.00   | 0.011199         |        | 1.90 LN_I79    | 0.06987          | 1.00   | 0.15537          | 1.89   |
| N                          |                  | 367    |                  | 411    |                |                  | 367    |                  | 411    |
| 2<br>Adjusted R            |                  | 0.68   |                  | 0.86   |                |                  | 0.679  |                  | 0.86   |

### *Forecasting*

Base models were used to forecast truck VMT for 2010, 2020, and 2030. Socioeconomic forecasts were taken from the Woods & Poole data. For lane miles by facility categories, three levels of annual growth were assumed--zero growth, half of the 1994-2003 growth, and same growth as 1994-2003. Again, it should be noted that the growth includes both new supply and reclassification. VMT growth rates were calculated for periods of 2003-2010, 2010-2020, and 2020-2030. Table 9 summarizes annual growth rates, in comparison with historical growth rates of 1994-2003.

Table 9. Truck VMT Annual Growth Rates--Historical and Forecasts Using Base Models

*a. Assuming Zero Growth for Lane Miles*

|                      | 1994-2003 | 2003-2010 | 2010-2020 | 2020-2030 | 2003-2030 |
|----------------------|-----------|-----------|-----------|-----------|-----------|
| Rural Interstate     | 3.86      | 2.30%     | 2.40%     | 2.45%     | 2.39%     |
| Rural Non-Interstate | -1.18     | 0.20%     | 0.26%     | 0.34%     | 0.27%     |
| Urban Interstate     | 4.19      | 1.83%     | 1.86%     | 1.80%     | 1.83%     |
| Urban Non-Interstate | 2.84      | 1.30%     | 1.08%     | 0.67%     | 0.98%     |
| Total                | 2.21      | 1.57%     | 1.66%     | 1.69%     | 1.65%     |

*b. Assuming Half Historical Growth (1994-2003) for Lane Miles*

|                      | 1994-2003 | 2003-2010 | 2010-2020 | 2020-2030 | 2003-2030 |
|----------------------|-----------|-----------|-----------|-----------|-----------|
| Rural Interstate     | 3.86      | 2.36%     | 2.46%     | 2.51%     | 2.45%     |
| Rural Non-Interstate | -1.18     | -0.04%    | 0.02%     | 0.09%     | 0.03%     |
| Urban Interstate     | 4.19      | 2.51%     | 2.54%     | 2.48%     | 2.51%     |
| Urban Non-Interstate | 2.84      | 1.45%     | 1.21%     | 0.78%     | 1.11%     |
| Total                | 2.21      | 1.70%     | 1.80%     | 1.84%     | 1.79%     |

### *c. Assuming Same Historical Growth (1994-2003) for Lane Miles*

|                      | 1994-2003 | 2003-2010 | 2010-2020 | 2020-2030 | 2003-2030 |
|----------------------|-----------|-----------|-----------|-----------|-----------|
| Rural Interstate     | 3.86      | 2.42%     | 2.52%     | 2.56%     | 2.51%     |
| Rural Non-Interstate | -1.18     | -0.28%    | -0.22%    | -0.15%    | -0.21%    |
| Urban Interstate     | 4.19      | 2.79%     | 3.22%     | 3.17%     | 3.09%     |
| Urban Non-Interstate | 2.84      | 3.43%     | 1.28%     | 0.85%     | 1.67%     |
| Total                | 2.21      | 2.07%     | 1.96%     | 2.05%     | 2.02%     |

As shown in the table, urban and rural interstate categories have the highest growth rates among the four facility categories. Rural non-interstate facilities have the lowest growth rates, even negative growth, largely thanks to re-classification. The model shows show a moderate degree of sensitivity to the lane mile assumption in the future. Forecast annual VMT growth rates differ by a moderate range from less than 0.2 percent points to 0.5 percent points, depending on lane mile growth assumptions. Overall, forecast statewide annual growth rates are generally lower between 2003 and 2030 than the average historical growth of 1994-2003. As shown in Table 4, aggregate statewide truck VMT growth rates were higher pre-1999 than post-1999. The forecast annual growth rates are in the magnitude between the two periods.

### **CONCLUSIONS**

In this study, statistical models were developed to forecast truck VMT growth of four facility categories at the county and statewide levels. These models incorporate both socioeconomic and transportation system supply variables. Different model specifications were tested and evaluated. A selected set of models was used to forecast truck VMT for planning horizon years 2010, 2020, and 2030. The model results show that local socioeconomic variables alone explain a considerable amount of the truck VMT variance, particularly for urban interstate and noninterstate facilities. Adding external driving forces such as truck corridor or contributing state gross sate product variables increase the models' explanatory power, particularly for rural interstate facilities.

This research offers some insights for other states and areas that are interested in developing truck VMT growth forecasts:

- The statistical modeling method offers a comprehensive approach that provides consistent results across multiple jurisdictions at a much lower cost than developing a statewide travel demand-forecasting model.
- Both demand (socioeconomics) and supply variables (lane miles) help us understand truck VMT growth. They should be included in the statistical model development, as they represent major driving forces for truck VMT growth and account for truck VMT reclassification due to urbanization.
- VMT reclassification is an important part of a longitudinal VMT database. Effects of VMT reclassification on models and forecasting results should be examined, and sensitivity tests should be conducted.
- This truck VMT forecasting methodology is applicable to other areas as the data needed are readily available.

# **ACKNOWLEDGEMENTS**

This study is in part supported by PENNDOT as part of the Statistical Evaluation of Projected Traffic Growth. The authors would like to thank the PENNDOT Bureau of Planning and Research and the project panel headed by Mike Bonini and Chris Allison for their guidance. Thanks are also extended to Michail Zekkos for data preparation. However, the authors are solely responsible for the content of this paper, and this paper does not necessarily represent the positions or endorsement of PENNDOT.

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