1

# **1.** Introduction

A previous paper used panel data from 50 countries and 35 urban areas to summarize trends in motorization and the provision of roads, and to examine the ratio of motor vehicles to roads in a production function framework at both the national and urban levels (Ingram and Liu, 1997). The countries and urban areas, which covered a wide range of income levels, exhibited strong regularities in cross section regressions across country and city characteristics. In particular, income was a strong determinant of both the level of vehicle ownership and road provision. Road provision was buoyant at the national level but not at the urban level, where congestion stimulated decentralized growth and urban road length increased mainly from the annexation of surrounding areas.

The current paper presents additional empirical results obtained using essentially the same national and urban data sets.' These new empirical analyses explore alternate specifications of the underlying relations between three dependent variables--vehicle ownership, road length, and the vehicle-road length ratio--and various independent variables. In particular, they investigate (i) whether income elasticities of motor vehicle ownership and road length vary or are essentially constant across a wide range of income, and (ii) how vehicle ownership and road provision respond to changes in income over time.

An income elasticity measures how responsive demand for a good or service is to a change in income, and income elasticities may vary across income levels. However, most empirical studies of motorization (including our previous paper) have estimated only constant income elasticities. Constant elasticities are usually estimated from regressions with a restricted functional form (typically a log-linear specification). One major weakness of a constant income elasticity is its limited predictive power for forecasting beyond the observed income range when the true elasticities vary with income. While constant elasticity estimates are often statistically very robust, their usefulness in forecasting depends on whether they are at least as robust as variable elasticity estimates. This paper reports estimates of variable elasticities and compares them with constant elasticities.

Our previous paper suggested differences between the cross-section and time series relations in the panel data, particularly in the urban data. Cross-section variation often results from long-run behavior, and time series variation from short-run behavior. Specifically, long-run income elasticities capture the change in demand when consumers are able to make an unconstrained behavioral adjustment in response to a change in income, and short-run income elasticities measure the demand change in a constrained situation. Empirically, long-run income elasticities can be estimated using cross-section data that cover a wide range of income levels, while short run elasticities require time series data. The empirical results presented in Ingram and Liu (1997) are essentially longrun estimates because they are obtained from cross-section analyses. While these long-run estimates provide a broad picture of growth patterns of motorization and road provision, in this paper we also compare them with short-run income elasticities.

I Based on additional data sources, we made minor corrections on the national data set and added two new observations to the urban data set. See Annex A for details and Appendix Tables 10 to 12 for the national data.