15 The estimated linear and non-linear relations between the vehicle-road ratio and income are illustrated in Figures 4a and 4b for the purpose of comparison. As Figure 4b shows, the ratio of vehicles to total roads is an increasing function of income (though at a decreasing rate) across the wide range of country income levels. This is consistent with our argument that the vehicle-road ratio should increase with income on the national total road network. The non-linear equation for the ratio of vehicles to paved roads suggests that across countries the ratio increases with country per capita income up to about US$5,000 (in 1987 US dollars) and then declines. This income level is close to the benchmark (US$5,500) that separates countries into low-income and high-income groups. Caution should apply to the non-linear relation for the ratio on paved roads, however, because we do not know how many vehicle trips are actually made on the paved roads and on the unpaved roads. That the ratio of vehicles to paved roads is independent of income should not be ruled out, as the analysis with the constant elasticity specification indicates that both the motor vehicle fleet and paved road length expand roughly at the same rate as income.

At the urban level, because of the linearity in vehicle ownership and the nonlinearity in road provision (see Tables 2 and 3), it is not surprising that the vehicle-road ratio exhibits a strong non-linear relation with income. As per capita income grows, the vehicle-road ratio first increases up to an income level of about US$2,000 (in 1987 US dollars), then decreases.

This non-linear relation can be explained by the presence of road congestion in urban areas. Although the vehicle-road ratio is an imperfect indicator of the level of road congestion, it is nonetheless a reasonably good proxy. As the statistics shown in Table A-I of Annex A indicate, on average the number of motor vehicles per kilometer of total roads at the urban level is more than ten times higher than at the national level for developing countries, and five times higher for high-income countries. Moreover, the data for 29 world cities shown in Figure 5 indicate that the vehicle-road ratio at the urban level is highly correlated with average road speeds. The figure reveals a clear negative relationship between the vehicle-road ratio and average road speed, which is generally similar to the empirical relationship between speed and the volume-capacity ratio commonly used in urban transport planning. As a proxy for the traffic level on the road network, the vehicleroad ratio is expected to increase with the relative prices of vehicles to roads at low vehicle-road ratios (such as on national total road networks). Most of the national road networks have fewer than 50 motor vehicles per kilometer of road length, so congestion on national roads is not a common problem even in high income countries. But when congestion occurs in urban areas, speeds fall and travel time cost increases, thus economically justifying more roads.

The peak and decline of the vehicle-road ratio for national paved roads is likely to be related to an increasing demand for higher quality roads, and possibly for vehicle speed, as incomes increase. Paving roads is an obvious means of improving road quality, which reduces vehicle operating costs. Speeds are typically higher on paved roads than on unpaved roads, and the demand for speed (lower travel times) increases with income and the value of time.