Analysis and prediction of private car ownership and use in Denmark: Part of the ELISA Project

This report presents the main findings from econometric analyses of car ownership and use levels for Denmark using historical macro data for the period 1976-2018. We model car ownership and use levels as a function of other economic variables including GDP and official indices for car purchase prices and vehicle operating costs.

The models are estimated using dynamic time series methods to obtain estimates of long run cointegration relations and coefficients reflecting short-run dynamics. The car ownership model is estimated using an Error Correction Model (ECM), a model that assumes the existence of an equilibrium relationship that determines both short and long run relationships.

It is formulated as the 2004 ART model (Fosgerau, Holmblad & Pilegaard, 2004), keeping the ratio between long run and short run elasticities equal for all explanatory variables. The validity of this restriction was tested statistically, and the restriction was accepted as an appropriate description of the data.

With the restriction, we obtained a higher precision of the estimated elasticities compared to the case without the restriction. The estimated long run elasticities of GDP and purchase price from this model are 0.83 and -0.57, respectively. The implied long run elasticity of operating cost is -0.34, but it is not significant at the conventional 5% level (its p-value is 0.29).

Forecasts based on this model show that car ownership is predicted to increase from 0.49 cars per capita in 2018 to 0.62-0.71 in 2040 depending on alternative assumptions about the growth rate of purchase prices. Compared to estimates from the 2004 ART model (Fosgerau, Holmblad & Pilegaard, 2004), we now find higher long run income and purchase price elasticities while the operating cost elasticity is lower.

For the car use model, we considered two different measures – mileage per car and mileage per capita. Mileage per car is the measure used in the original 2004 ART model, but this choice had to be reconsidered due to a change in the trend of mileage per car during the sample period. Mileage per car has shown an increasing trend until the early 1990s, after which it declined.

This change could be explained by the general increase in the car fleet and especially the increase in the share of households with two or more cars. With other explanatory variables showing an overall upward or downward trend, it proved difficult to identify the effect of individual factors on this measure of car use.

We therefore chose the model formulation with mileage per capita, which has a positive trend. We model mileage per capita in terms of its lagged values and contemporaneous and lagged values of GDP, purchase price and operating costs, using an Error Correction Model. Our analysis shows a significant and negative long run effect of operating costs and purchase price on the extent of car use.

In particular, a percentage increase in operating costs (resp. purchase price) is associated with a decline in mileage per capita by 0.61% (resp. 0.64%) in the long run. GDP has a positive and significant long run effect on car use - the estimated long run elasticity is 0.80. Our analysis shows that mileage per capita is predicted to increase from 7,500km in 2018 to 9,900km - 11,600km in 2040 depending on the alternative assumptions regarding the growth rate of purchase price in this period.