More connected urban roads reduce US GHG emissions

Ideally, we would directly estimate the elasticity of vehicle distance traveled with respect to differences or changes in road network connectivity. This relationship across US states is shown in the top row of figure 3 for total urban annual per capita vehicle distance traveled. The distribution of state values suggests that states with higher-connectivity roads, as measured by $\bar{D}$ (left) and D⁴⁺ (right), exhibit lower vehicle travel per capita⁵. However, these data [34] are available only at the state level, and include commercial and freight vehicles in addition to household travel.

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Because we are interested in the local-scale impact of street connectivity, our estimates use block group level data. Comprehensive data on household urban vehicle travel are not available for such small geographic areas. Instead, our candidate proxies for vehicle travel are household vehicle ownership and commute mode share, both available from the American Community Survey. We consider the vehicle ownership variable to be the most natural proxy for household urban vehicle travel, not least because most household vehicle use is for trips other than commuting. Thus, of the measures available from the American Community Survey, the total number of cars chosen by households has a better theoretical link with overall car use than the measures which focus only on commuting.

Empirically, both vehicle ownership and commute mode share are highly correlated with vehicle travel. Using data from the National Household Travel Survey [12], we find that the log of vehicle miles traveled has a correlation of 0.28 with the share of commutes by driving, and 0.35 with the number of vehicles per household (and 0.42 with the same variable in log form). These correlations are at the household level, using the provided survey weights. Below it will be important only to assume that the relationship between the number of vehicles per household and mean distance traveled is roughly linear. Figure 4 shows that this is, as a correlational claim, an excellent assumption. The great majority of households have fewer than five vehicles, and for these households, the number of vehicles is nearly perfectly correlated with the mean vehicle distance traveled. While there are undoubtedly a host of factors which codetermine vehicle ownership and vehicle travel, we hereafter focus our causal identification on the link between urban form and vehicle ownership, and based on figure 4, assume similar fractional changes in vehicle ownership.

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The lower panels in Figure 3 show distributions of mean degree $\bar{D}$ and D⁴⁺ at the scale of block groups, plotted against the average number of vehicles per household, taken from the 2007–2011 American Community Survey. There is a clear linear relationship between higher connectivity streets and fewer vehicles per household. The supplementary information contains further tables (A2 and A3) stacks.iop.org/ERL/12/044008/mmedia listing the means, standard deviations, and bivariate correlations for our key variables.

The relationships shown in figure 3 are descriptive only, because they reflect numerous sources of variation, for instance at the state or county levels where demographics, other policies and geographical features may vary somewhat independently of the average local road connectivity. Moreover, we wish to isolate the causal pathway (link 3 in figure 2) from other factors which might simultaneously affect both car ownership and the street network. To do this, we use two statistical techniques in our estimates. The first is to control for arbitrary (unmeasured) fixed effects at the scale of counties or states. The second, simultaneous, improvement on previous work is to estimate an instrumental variables model, in which a first-stage projection captures an exogenous component of the variation in road network connectivity.

In order to capture this variation, we employ topography as an 'instrument' for street-network sprawl. This allows us to estimate the underlying effect of street networks on car ownership at the local scale. The instrumental variables (IV) approach, which avoids the endogeneity biases with ordinary least squares regression discussed above, depends on two main assumptions.

The first assumption is the existence of a relationship between topography and street-network sprawl. Steeper or uneven terrain is somewhat less easily paved with a gridded road network than flat terrain, although other influences remain and the relationship is by no means deterministic, as the gridded hills in San Francisco testify.

We calculate slope using gridded elevation data at ⅓ arc second (∼10 m) resolution from the National Elevation Dataset [35]. We report two measures: average slope within a geographic unit such as a county, and the fraction of grid cells with slope >10°. Figure 5 shows the simple bivariate relationships between these two measures of terrain slope and our two measures of road network connectivity. Nonparametric estimates are shown for each of three spatial scales—block groups, counties, and states—as are scatter plots for the larger two scales. The trends are robustly negative. When we estimate linear models of these same relationships, and account for street-network connectivity using both measures of terrain steepness at once, we find that all of the explanatory power comes from the second measure, the fraction of grid cells with slope >10°.

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In particular, we find at the block group scale that 9% and 6%, respectively, of the variation in nodal degree $\bar{D}$ and fraction of 4⁺ intersections D⁴⁺ can be accounted for by this measure of slope. Given that street-network sprawl is also strongly influenced by socio-economic and other variables such as local development policies and regulations at the time of planning and construction, 6% to 9% is a remarkably high share of the variation⁶. In fact, even after controlling for state or county level fixed effects, our slope measure accounts for a further 4% to 5% of variation in our two measures of street-network connectivity.

The second assumption is that topography is exogenous and has a one-way influence on travel that operates only through the channel of urban form⁷. Invariably in any instrumental variables estimate, this second assumption is hard to empirically verify, but the diagnostic tests reported below support our contention of exogeneity.

We proceed by first predicting the explanatory variable (e.g. fraction of 4⁺ nodes) as a function of the fraction of grid cells with mean slope >10° and a complete set of fixed effects that control for unmeasured properties of counties or states. Formally, this projection of the endogenous variable onto the instrument and geographic indicators is shown in the first-stage equation (1), below. These predicted values of the explanatory variable are then used along with the state or county indicators, but without the measure of slope, in the second-stage equation (2) that estimates car ownership [2, 36]. Formally,

$$\begin{equation} X_0 = \theta \cdot {\bf Z} + \delta \cdot {\bf X}_{\rm 1} + \varepsilon \end{equation} \tag{ 1 }$$

$$\begin{equation} A = \beta _0 \hat{X}_0 + \beta _1 \cdot {\bf X}_{1} + \mu \end{equation} \tag{ 2 }$$

where X₀ is the local measure of street connectivity for a given block group; $\circ{X}_0$ is its predicted value from equation (1); Z is a vector of slope variables (but we use only one in our preferred specification); A is the dependent variable measuring automobility (vehicles per household); X₁ is a vector of other covariates (state or county fixed effects); μ and ε are error terms with mean zero; θ is a coefficient that indicates the strength of our first-stage estimates; and β₀ is an estimated coefficient that indicates the causal impact of street connectivity on vehicle ownership. Since Z and A enter in log form, β₀ can be interpreted as the elasticity. In an ordinary least squares (OLS) approach, X₀ is used directly in equation (2) without need for equation (1).

The indicators in X₁ control for all unobserved heterogeneity across states or across all ∼2400 counties. Using a complete set of geographic controls at the county and state scales is appropriate because policy environments relevant to urban form and transportation are most likely to vary at these scales. In addition, an individual's daily travel is likely to be within a county or across only one county line, but to span a distance similar to the scale of an urban county.

Estimates of our IV model were carried out using the generalized method of moments (GMM) implemented in ivreg2 in Stata [2], with the slope > 10° measure as an instrument. Our estimates of standard errors are robust to heteroskedasticity and allow for clustering at the county level.

Vehicle travel increased steadily through the 20th Century (green and blue lines, figure 6), in line with rising incomes, expansion of roadway infrastructure, and urban development trends such as lower densities and less connected streets. This growth, however, leveled off shortly after the turn of the century. Much research suggests that demand for travel may have saturated, at least in per-capita terms, with changes in mobility and residential preferences among young people, new information and communications technologies, and diminishing marginal returns to mobility cited as some potential explanations for 'peak travel' [15, 19, 20].

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Growth in vehicle travel through most of the last century was accompanied by an increase in street-network sprawl (i.e. declining $\bar{D}$), until a turnaround occurred in the mid-1990s for newly constructed streets (thin purple line in figure 6). Because new streets in a particular year account for a small fraction of the total, the stock of all streets (thick purple line) was slower to respond, but also reached a turning point in 2012 [1].

The extent to which changes in street-network sprawl are responsible for past travel growth and for the 'peak travel' phenomenon is unclear, and many different factors likely contributed. However, a continued trend of declining sprawl will almost certainly affect travel behavior, given the well-established relationships discussed above. The Energy Information Administration (EIA) projects that steady growth in vehicle travel will resume, while CO₂ emissions from gasoline will fall as a result of improved fuel economy (figure 6, dashed lines). While recent EIA analysis acknowledges shifts in travel behavior, such as travel growth beginning to decouple from economic growth [7], its projections do not yet explicitly model the impact of changing urban form. Here, we analyze the magnitude of the impact of different trends in street-network sprawl on vehicle travel and emissions under three scenarios for the future connectivity of the street network.

Each scenario is defined in terms of the fraction of 4⁺ nodes $d_{t}^{4+}$ in newly constructed streets in each year t = 1995, 1996,..., 2100 (figure 7, dashed lines)⁸. Scenario 1: 1994 plateau illustrates what would have happened in the absence of the recent turnaround in street-network sprawl. Under this scenario, d⁴⁺ remains at the low of ∼0.14 achieved in 1994. Scenario 2: continued trend represents an extrapolation of the recent decline in street-network sprawl into the future. d⁴⁺ follows its observed trajectory from 1995–2012, and continues to grow at the same annual average rate (∼1.6%) until it reaches a ceiling of 0.65, which approximates the connectivity of large New Urbanist developments such as Stapleton in Denver, Colorado [1]. Formally, $d_{t}^{4+} = {\rm min}\;(1.016\;d_{t-1}^{4+},0.65)$ for t > 2012. Scenario 3: connectivity policy illustrates a more rapid increase in street-network connectivity, such as might be produced by widespread anti-sprawl policies. For example, Virginia enacted statewide standards in 2009 that strongly discourage cul-de-sacs, and many similar policies exist at the city or county level [1, 14]. Under Scenario 3, d⁴⁺ follows Scenario 2 (the observed trajectory or continued trend) from 1995–2015. The annual average rate of change then increases to ∼12.8%, so that the ceiling of 0.65 is reached ten years later in 2025. This would mean that the majority of intersections in new developments would be 4⁺.

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While the scenarios are defined in terms of the connectivity of new streets, it is the connectivity of the entire stock of streets that affects travel behavior. Thus, the impact of the trends in d⁴⁺ will depend on how they affect the fraction of 4⁺ degree nodes in the stock, denoted D⁴⁺, which in turn depends on the assumed rate of urban growth.

We use growth in the housing stock to estimate the growth of the street-network stock. We assume that the growth rate of nodes, γ_N, is linearly proportional to the annual growth rate γ_H of the housing stock, so that γ_N = νγ_H, where ν (dimensionless) denotes the nodes-to-housing growth ratio. We derive γ_H from the housing growth forecasts in Zeng et al [37], with the starting value adjusted to match the 2013 retrospective revision from the US Census Bureau. Alternative projections for housing growth provide similar estimates (figure 8).

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We extrapolate the trends beyond 2050 by assuming a constant rate of new units added (∼1.25 million year⁻¹), based on the 2040–2050 average. The same procedure is used to separately extrapolate each bound of the uncertainty envelope. These data points give us a central estimate for γ_H of 1.1% in 2014, declining to 0.5% by 2100. Importantly, the housing growth figures refer to net new units rather than total new construction; the latter is ∼42% greater than the former according to [22].

We estimate the nodes-to-housing growth ratio ν at ∼1.4 using our historical street-network data, which we describe in full in [1]. A value of ν of greater than one indicates that the street network grows at a faster rate than the net housing stock. This could be partly driven by more rapid growth in non-residential development, and partly by the replacement of housing units in a different geographic location (e.g. abandoned housing in Detroit or New Orleans being replaced by units in Phoenix). The relationship between ν and sprawl is unclear a priori. Less sprawl might lead to a lower value of ν if new housing units take the form of tall apartment buildings, or a higher value of ν if less sprawl is accompanied by smaller blocks. Therefore, we assume that ν is constant rather than a function of the level of sprawl.

Given estimates for γ_H and ν, we proceed to estimate the impact of trends in d⁴⁺, the fraction of 4⁺ nodes in new construction, on the fraction D⁴⁺ in the stock. The growth rate in the stock N of nodes, i.e. the number of intersections, evolves as:

$$\begin{equation} N_t = N_{t - 1} (1 + \gamma _N ) = N_{t - 1} (1 + v\gamma _H ) \end{equation} \tag{ 3 }$$

The connectivity of the stock (shown in figure 7, solid lines) then evolves as:

$$\begin{equation} \begin{array}{*{20}l} {D_t^{4 + } } & = & {\frac{{N_{t - 1} D_{t - 1}^{4 + } + d_t^{4 + } v\gamma _H N_{t - 1} }}{{N_{t - 1} (1 - v\gamma _H )}}} \\ {} & = & {\frac{{D_{t - 1}^{4 + } + d_t^{4 + } v\gamma _H }}{{(1 + v\gamma _H )}}} \\ \end{array} \end{equation} \tag{ 4 }$$

Finally, we use our projections of D⁴⁺ to estimate changes in vehicle travel, energy use and CO₂ emissions, using two estimates for the elasticity of vehicle travel with respect to D⁴⁺. Assuming that fleet fuel efficiency and fuel carbon content are not affected by D⁴⁺, the elasticity of vehicle travel will be identical to those for household vehicle energy consumption and CO₂ emissions. The analysis in section 2 provides the first elasticity estimate, −0.15. The second estimate, −0.12, is taken from the meta-analysis in Ewing and Cervero [10]. Based on an elasticity $\epsilon \in \{-0.15, -0.12\}$, the one-year fractional change in vehicle distance and hence emissions δE is as follows:

$$\begin{equation} \delta E_t \equiv \frac{{\Delta E_t }}{{E_{t - 1} }} \approx \varepsilon \frac{{D_t^{4 + } - D_{t - 1}^{4 + } }}{{D_{t - 1}^{4 + } }} \end{equation} \tag{ 5 }$$

As with any application of elasticities, equation (5) is only valid for small changes in D⁴⁺. Under the assumption of constant elasticity (see section 5.2), the accumulated changes in emissions from the 2015 baseline can be calculated as:

$$\begin{equation} \delta E_t = \frac{{E_t - E_{2015} }}{{E_{2015} }} = \left( {\frac{{D_t^{4 + } }}{{D_{2015}^{4 + } }}} \right)^\varepsilon - 1 \end{equation} \tag{ 6 }$$

The two elasticity estimates combined with the three housing growth estimates (the central projection and bounds in figure 8) generate six values for each scenario. Our central estimate uses the central estimate for housing growth combined with our preferred elasticity (−0.15). The shaded envelope represents the highest and lowest of the six values.

We assume that the level of sprawl does not affect the fuel efficiency of vehicles nor the carbon content of fuels, and thus δE is the same as the fractional change in private vehicle travel. This assumption is also used in [32]. Because we ultimately compare fractional changes across scenarios, this does not imply constant fuel economy or carbon content over the 2015–2100 period, but rather that any changes over time are identical across our three scenarios. Vehicles are likely to become more efficient and shift to electricity and other fuels over this time frame, and autonomous vehicles may become widespread. These changes will affect the absolute emissions impacts, but provided that the factors are independent, we provide valid estimates of the proportional emissions impacts of trends in street-network sprawl.