Explanation of Elasticity. Elasticity is a measure of the responsiveness of one (dependent) variable to changes in another (independent) variable. Elasticity is a popular method of looking at these interdependent variable changes since the elasticity is measured in percentage terms, thus negating the need to compare items in the same units of measure (dollars per ton or trips per land use density, for example). In transportation the most often used elasticities are demand elasticities1. This describes how the demand for travel changes as the price of travel changes. However, researchers have calculated the elasticity for many variables. While some transportation researchers champion the use of elasticities to evaluate the potential for changes in trip making that result from changes in urban form, others believe that elasticity variables are surrogates for unknown relationships between urban form and transportation.
Elasticity is readily calculated as:
Elasticity = (∆Y/∆X) * X/Y
Note that the presence of both the change in variables (∆Y and ∆X) as well as the absolute value of the variables themselves are being considered simultaneously in this equation. Hence, the elasticity can, and usually does, change as the value of X and Y change. In other words, the elasticity can change at different points on the curve representing the supply or demand of an item. Where there are two goods that are complements to each other, the elasticity will be negative, such as the relationship between price of fuel and gas-guzzling cars. When the price of fuel goes up, the demand for cars with low fuel efficiencies goes down. For items that are substitutes for one another, the elasticity relationship is positive. This is the case for margarine and butter, wool and cotton, and so forth.
Values of elasticity greater than 1.0 are called relatively elastic, meaning that small percentage changes in the independent variable cause larger percent changes in the dependent variable. Conversely, values of elasticity less than one are called relatively inelastic. That is, percentage changes in the independent variable cause relatively smaller changes in the value of the dependent variable. In those rare instances where a change in one variable exactly equals the change in another variable (elasticity of 1.0), the relationship is called unit elasticity. Those familiar with elasticity will notice that transportation-related elasticities are typically relatively inelastic: a one percent change in the independent variable causes less than a one percent change in the dependent variable.
While some researchers find elasticities useful others argue that elasticities do not represent meaningful relationships. The thrust of the argument is that land use density is confounded with other key variables such as sidewalks, local design factors, accessibility, or land use mix. These researchers argue that there are threshold values that must be attained before accessibility, density, design factors, or diversity cause measurable changes. This makes the elasticity relationship non-smooth, with sudden rises according to synergistic effects of multiple variables.
Using Elasticity. Elasticity measures can provide useful insights into the likely travel-related responses to changes in land use patterns. However, their best use may be in broadly assessing the direction and possible magnitude of changes. The explanatory power of elasticity as it relates to changes in travel is fairly weak with most values being less than -0.1 (that is, a 10% change in the degree of diversity in an area, for example, produces a 1% change in trip-making behavior). The analyst should consider the following general guidance when using elasticity to measure effects.
Consider the interaction between categories that either reinforce or dampen the elasticity relationship.
Accessibility has the strongest effect in most of the research dealing with the subject and should always be considered.
The three D's (Density, Diversity, and Design) have relatively small effects individually, particularly if there is little support for alternative modes of travel.
Unless density is above 7-10 dwelling units per acre it is unlikely that the other D's will have any effect, even in combination.
Selecting Elasticity. The tables on the following pages summarize the elasticities associated with four categories: regional accessibility, local density, local design, and local diversity. Most of these values are summarized from Ewing and Cervero's "Transportation and the Built Environment - Synthesis". The top row of each table shows a typical elasticity for vehicle trips and vehicle miles of travel. While the typical elasticity shown for each category is probably a good beginning point, the user should carefully consider whether or not the proposed changes are in a range of the independent variable that shows sensitivity. For example, doubling the housing density from two to four units per acre is unlikely to cause a measurable change in transit use. However, above seven dwelling units per acre there is a measurable change in transit use as density increases.
It is also important to reemphasize that the broad categories in the tables below are interrelated, and as such changes in one of the categories may not be effective without concurrent changes in another of the broad categories. For example, adding sidewalks without changing land use mix will not necessarily create more walking trips.
Regional Accessibility Measures. Regional accessibility is typically a measure of the number of jobs available within a certain distance or time. If time is the measure it is often set at the average or median amount of time required for people within a study area to reach their jobs from home. Measuring outward from the study area in travel time increments can define a commuteshed, which is an area or buffer describing a travel time isochrones.
Network connectivity measures are also included in this category. More highly connected networks tend to offer more route choice and greater accessibility. There is some evidence that highly connected networks, as measured by the percentage of four-way intersections, reduce the total amount of congested travel although possibly not the total amount of travel. The mechanism for this effect seems to be the creation of more, and better direct, connections between origin and destination.
|Typical Value||Trips N/A||VMT -0.20|
|Regional Accessibility||VMT -0.34|
|VMT (non-work) -0.35|
|Regional Accessibility to Jobs||Vehicle Trips 0.13; -0.36|
|VMT -0.29; -0.31|
|Fraction of 4-way intersections||VMT -0.09|
|Employment Accessibility by Transit||VMT -0.06|
|Jobs within 5 km||VMT -0.05|
|Intersections /road-km||VMT -0.04|
Local Density Measures. Local density is one of the more common measures used to assess the number of trips, vehicle trips, transit trips, and vehicle miles of travel associated with an area. Researchers have speculated on whether density alone accounts for changes in trip making as density increases, or whether density is simply the most readily observable component of a group of features that vehicle travel albeit inducing more total trips . Regardless density is one of the easier urban form variables to observe, understand, and explain and so is commonly used as the explanatory variable.
The threshold value at which density seems to have a meaningful effect upon VMT, or trips, is somewhere probably between 6,000 and 7,000 persons per square mile (7-10 dwelling units per acre). At that point the doubling of land use/development density seems to reduce new VMT by as much as 40 percent.
Local Design Measures. The term local design measures accounts for those local scale design features such as sidewalks or building orientation that can subtly influence a person's desire to walk or bicycle. Local design features affect the way people perceive walking, bicycling, and transit as travel choice. Local design features can work one of two ways. A person may choose to walk to a closer location or may choose to make a walking trip that would not otherwise occur. A note of caution, sidewalks alone do not create a viable pedestrian environment. Jamboree Road in Irvine, California is a six-lane arterial street with ten-foot sidewalks on both sides and little pedestrian traffic. Notably there are few desirable destinations connecting directly to the sidewalks as most of the adjacent properties belong to gated communities. Conversely, the streets on nearby Balboa Island teem with pedestrian, bicycle, and automobile traffic. Without higher density (over four dwelling units per acre) and diverse land use it is unlikely that local design measures have much effect on travel patterns and behaviors.
|Typical Value||Trips -0.05||VMT -0.05|
|Net Density||Vehicle Trips -0.07|
|Overall Density||Vehicle Trips -0.03|
|Employment Density||Vehicle Trips -0.002|
|Vehicle Trips(work) -0.04|
|Vehicle Trips (non-work) -0.04|
|VMT -0.03; -0.09|
|Population Density||Vehicle Trips(work) -0.05|
|Vehicle Trips (non-work) -0.11|
|Vehicle Trips -0.05; -0.14; -0.013|
|VMT -0.16; -0.09; -0.07|
|Business Density||Vehicle Trips (non-work) -0.03|
|Zonal Density||VMT -0.06|
|Typical Value||Trips -0.03||VMT -0.03|
|Presence of Sidewalks||VMT -0.14|
|Pedestrian Environment Factor||VMT -0.19|
|% Buildings Built before 1951||VMT -0.06|
Local Diversity Measures. Diversity measures are measures of the variability of land uses within a given area. As land use becomes more diverse (i.e., more different types of land use closer together) trips by vehicle will tend to decrease as will VMT. Essentially these measures try to assess how closely jobs, or retail, and housing balance within a local area.
Entropy measures deserve additional explanation because entropy is not a commonly used, or understood. Entropy is a measure of the homogeneity of an area. The entropy variable is an index ranging from 0 (homogeneity) to 1 (maximal heterogeneity) that is sometimes used to define "degree of land use mix". A high degree of uniformity (0) describes single use settings while maximum entropy (1) a high level of uniformity (equality among land use categories) denotes high mix.
|Typical Value||Trips -0.03||VMT -0.05|
|Non-Residential within 300'||Vehicle trips(work) -0.005
VMT - 0.032
|Fraction of retail within 1/4-mile||Vehicle trips -0.08|
|Fraction of vertical mixed use||VMT -0.07|
|Jobs/Population Balance||VMT -0.09|
|Land Use Mix (entropy measure)||Vehicle Trips (work) -0.12|
|Land Use Balance (entropy measure)||VMT -0.10; -0.11|
|Land Use Balance (dissimilarity measure)||VMT -0.10|
|Proximity to Grocery||VMT -0.09|
Other Useful Elasticities. The elasticities presented in the previous tables describe possible relationships between land use and travel characteristics. Historically, most work on the elasticity of travel has been related either directly or indirectly to the cost of travel. For example, the elasticity of transit use with respect to fares or the elasticity of vehicle miles of travel with respect to lane miles. The following table presents some elasticity results for vehicle miles of travel and transit ridership as compared to capacity and demand variables. While not to be interpreted as additive, these relationships may enhance or dampen the effects of land use variables.
|Vehicle Miles of Travel and Lane Miles||0.2 - 0.62
0.5 - 0.93
|Vehicle Miles of Travel and Travel Time4||-0.3 - -0.5|
|Transit Ridership and Transit Service5||0.5 - 1.1|
|Transit Ridership and Regional Employment6||~0.25|
|Transit Ridership and Vehicle Miles of Service7||~0.71|
2 Lewis M. Fulton, Robert b. Noland, Daniel J. Meszler, John v. Thomas, "A Statistical Analysis of Induced Travel Effects in the U.S. Mid-Atlantic Region. 79th Annual Meeting of the Transportation Research Board, Washington, DC, January 2000.
3Norman L. Marshall, Resource Systems Group Incorporated., "The Need to Account for the Effects of Induced Demand to Support Reliable Travel Demand and VMT Estimates for Metropolitan Planning, Project Need and Alternatives Analysis and Conformity." September 2000
5 Victoria Transportation Policy Institute, Online TDM Encyclopedia - Transportation Elasticities, Accessed August 17, 2004.