11 The elasticity of population density for the total road equation is negative and statistically significant, suggesting that holding total population equal, lower population density (or higher per capita--and national--land area) is associated with longer total road length. The total road network in a country usually expands to connect all population distributed across the country. Therefore, a larger area requires more extensive road network to serve. In contrast, there is a weak relationship between population density and the total length of paved roads. This is because roads are paved for facilitating high volume of motorized traffic, instead of improving connectivity to human settlements and economic activities. Empirical analyses by Canning (1998) also provided similar findings.

Road provision at the urban level differs greatly from that at the national level. The urban results shown in Table 3 are based on panel data from 36 cities in both developing and developed countries, and the elasticities take into account the strong negative correlation between per capita income and population density at the urban level. (The results are from equations using the historical spatial endowment index, Appendix tables 5 and 7.) As the results indicate, urban road length has a population elasticity of 0.8, suggesting a decreasing scale effect. The elasticity of urban road length with per capita income is non-constant (increasing with income), and its elasticity with population density (negative) is much stronger than at the national level. Another maj or difference with the urban results is the relatively large differences between the long run (cross section) and short run (first difference) elasticity estimates--particularly for the elasticity of road provision with respect to income. Urban road length increases over time very slowly with income. The first difference elasticities of population and population density are also smaller than the cross section estimates. The cross section data and equation estimates of the relation between road length and income are summarized in Figure 3.

The strong non-linear relationship between urban road length and per capita income reflects the non-linear relationship between per capita income and per capita land area shown in Figure 1. Much of this cross section non-linearity stems from the growth of high income cities during the automobile age, discussed earlier.

In addition, as incomes rise in urban areas, population densities often decline in built up areas as both employment and residences decentralize. Some urban population growth occurs through expansion of the urban perimeter by annexation of surrounding municipalities. Municipalities that are annexed are usually already developed and have road networks. Therefore, most of the increases in urban road length stem from annexation and not from constructing new roads in built-up areas (Ingram and Liu, 1997). In fact, relatively little new road length is being constructed in the existing urban areas, presumably because the cost of new rights of way is high in both economic and political terms. Urban growth often takes place in the periphery where land costs are lower, more open space can be found, and less-congested roads are available. The strong implication of urban territory annexations is that urban areas provide road capacity by spreading development over space and not by increasing the density of roads in existing built up areas. Even with annexation as a source of new road capacity, however, urban road length is increasing much more slowly than the number of urban vehicles.