Substitution between cars within the household

https://doi.org/10.1016/j.tra.2016.01.007Get rights and content

Highlights

  • We estimate a general model for the demand for kilometres in multiple car households.

  • We find substantial differences with formulations that neglect the possibility of substitution.

  • We find that car efficiency and substitution are strongly correlated.

Abstract

In this paper we study the demand for car kilometres in two-car households, focusing on the substitution between cars of different fuel efficiency in response to fuel price changes. We use a large sample of detailed Danish data on two-car households to estimate – for each car owned by the household – own and cross-price effects of increases in fuel costs per kilometre. The empirical results show that failure to capture substitution between cars within the household can result in substantial misspecification biases. Ignoring substitution, the basic model yielded fuel price elasticities of −0.98 and −1.41 for the primary and secondary cars, respectively. Accounting for substitution effects, these figures reduce to, respectively, −0.32 and −0.45. Consistent with substitution behaviour, we find that the fuel price elasticity of fuel demand exceeds the elasticity of kilometre demands with respect to the fuel price; the difference strongly increases at the highest deciles of the distribution of kilometre demand. Extending the model to account for driver heterogeneity and the role of car characteristics confirmed the relevance of substitution between cars within the household. We found strong evidence of substitution from the secondary to the primary car, especially if the latter is a more recent car with more horsepower. In general, the results of this paper emphasise the importance of behavioural differences related to the position of the most fuel efficient car in the household, suggesting that households’ fuel efficiency choices are related to their price sensitivity.

Introduction

Increasing environmental awareness in transport policy-making, concerns of energy security and increasing fuel prices have generated a recent revival of interest in the economic implications of fuel prices on car use (see, among many others, West, 2004, Gillingham, 2012, Linn, 2013). In this paper, we focus on a very specific behavioural implication of changes in fuel prices: the fact that higher fuel prices may induce households that own multiple cars to substitute between cars of different fuel efficiency. This phenomenon is well known, and it has been studied several decades ago (see, among others, Mannering, 1983, Greene and Hu, 2005). Moreover, although they were not the main focus of these studies, substitution possibilities have been allowed for in several recent papers dealing with car ownership, vehicle choice and the demand for mileage (see, e.g., Feng et al., 2005, Bento et al., 2009 and Spiller (2011)).

The purpose of this paper is to reconsider the question of how households owning several cars of different fuel efficiency respond to changes in fuel prices. These price changes affect the relative per-kilometre cost of using the different cars and, hence, they may induce substitution towards the more fuel efficient car in the household. Based on a simple theoretical framework that imposes very few restrictions on substitution possibilities, we develop and estimate an econometric model in first differences and investigate whether, and to what extent, such substitution takes place. Note that our focus is on the issue of substitution within households, not on estimating the overall price elasticity of the demand for vehicle kilometres.

The analysis is based on a unique Danish data set that allows us to observe, based on exact odometer readings, the number of kilometres driven by the different cars in different periods of time. In Denmark cars and car fuels are relatively expensive, which implies a relatively small share of two-car households (see the data section below). However, since we have access to all register data, we are still able to use a large sample of almost 23,000 of such households to estimate own and cross-price effects of increases in fuel prices. The empirical results point at important substitution effects, so that models that estimate responses to fuel prices on the implicit or explicit assumption of one car per household, or multiple cars that are treated independently, may imply biased results for the individual vehicle elasticities.

To see how this paper relates to the existing literature, first note that there is a large theoretical and empirical discrete choice literature that deals with households’ choice of the number and type of cars to own, and the associated demand for car kilometres. Among many others, Mannering and Winston, 1985, Train, 1986, Berkowitz et al., 1990, De Jong, 1990, De Jong, 1991, Goldberg, 1998, West, 2004 developed detailed empirical analyses of car ownership and car use in both single and multiple vehicle households. More recently, Fullerton and Gan, 2005, Feng et al., 2005 analyse empirical models that allow simultaneous estimation of decisions related to car ownership, car type and kilometre demand, and they use the models to study the relative efficiency of different emission reduction policies (an emission tax, a fuel tax, annual registration fees, etc.). Fang, 2008, Brownstone and Fang, 2014 study the impact of the residential location on car ownership and utilisation. Although several of the studies mentioned implicitly allowed for some substitution within the household, analysing such substitution was not their main focus.1

Second, a substantial literature specifically focuses on the economic effects of changes in gasoline prices, but few of these papers account for possible substitution within the household. Some studies have focused on the implications of gasoline prices for the car market itself, others emphasised the impact on car use. For example, with respect to the former, Busse et al. (2013) study the equilibrium market adjustments in response to changes in fuel prices and other usage cost. They find that in the new car market, the adjustment is primarily in market shares, while in the used car market the adjustment is primarily in prices. Klier and Linn (2010) also find large demand responses of higher gas prices on the car market, arguing that nearly half of the decline in market share of U.S. manufacturers from 2002 to 2007 was due to the increase in the price of gasoline. Increases in the gasoline tax were found to have remarkably modest effects on average fuel economy of new cars.

A few recent studies have focused on the implications of fuel price changes on the demand for car use. Gillingham (2012) argues that household choices of vehicle and utilisation of the vehicle are closely linked: vehicle choice is affected by how much consumers anticipate using it, and the characteristics of the good such as fuel efficiency in turn influences subsequent usage. He estimates an empirical model based on these premises and explores the implications of ignoring the “selection on anticipated usage”. Using a dataset of new personal vehicle registrations and odometer readings in California, he estimates a medium-run gasoline price elasticity of driving of −0.15 and of fuel economy of 0.09. He emphasises that ignoring the selection issue leads to an over-estimate of the gasoline price responsiveness. He further finds (see Gillingham (2014)) considerable heterogeneity in elasticities across buyer types, demographics, and geography. Vehicle-level responsiveness is found to increase with income. Interestingly (given the topic of the current paper), the author argues that this finding may be due to within-household switching of vehicles.

In the literature discussed so far, substitution possibilities between cars within a household are not the main focus, and they play no major role. Of course, as mentioned above, such substitution has been studied before. In an early study, Mannering (1983) developed an econometric analysis of car use in households with multiple vehicles, and he found important substitution effects. Greene and Hu (2005) estimated a bundle model to capture multiple household cars, specifically focusing on the effect of the gasoline price on the use of the different cars. However, as they only distinguished between small cars, large cars and trucks, they find that price elasticities are not strongly affected by substitution between vehicles. Later models developed by Golob and McNally, 1997, Golob et al., 1996 have also emphasised the importance of travel interactions within households. Most recently, Spiller (2011) develops a model of households simultaneously choosing car types and vehicle miles, allowing miles to be the result of optimal allocation of total mileage over the bundle of cars owned. By doing so she allows for substitution in response to changes in gasoline prices. Taking into account a very wide range of car types in households’ choice sets, she finds larger substitution possibilities than earlier studies.

While some of the papers mentioned above have implicitly – and a few quite explicitly – allowed for car substitution within the household, their primary purpose was to develop comprehensive models of car ownership, choice of car type and car use. Our purpose in this paper is at the same time more modest but also more specific. We do not model car ownership decisions but explicitly focus on car use, conditional on households owning different cars of given fuel efficiency.2 We are interested in finding out how such households adapt their use of the different cars in response to changes in fuel prices. This paper is the first to estimate car substitution effects within the household based on a first-difference econometric model to control for household-specific time-invariant factors such as, for example, the car owner’s age, and his or her gender.

The paper is structured as follows. In Section 2, we describe the setup of a basic economic model that serves as background for the empirical analysis. Section 3 presents the specification of the empirical model, and it describes the data and the main characteristics of the sample selection process. Empirical results are presented and discussed in Section 4, emphasising the implications of the estimates for substitution within the household. Conclusions are summarised in Section 5.

Section snippets

Substitution between cars within the household: a simple theoretical framework

In this section, we present a simple economic framework for the choice of car use by households, conditional on owning two cars. Assume that the household cares for a general numeraire consumption good x and for kilometres travelled by the two cars owned. Denote the demand for kilometres by q1, q2 for the first and second cars, respectively. Car i’s fuel efficiency is Ei; it gives the distance a car can travel per litre of fuel consumed. It will be instructive to also define inverse fuel

The empirical model: specification and data

In this section, we first describe the specification of the empirical model and the identification strategy, next we present the data and discuss the sample selection.

Empirical results

In this section we report the empirical results. We first analyse the results of estimating the basic model as given by (6a), (6b) and briefly discuss the robustness of the substitution effects with respect to some underlying assumptions. We then turn to the estimation results of an extended model that tries to capture driver heterogeneity and the role of car characteristics for substitution between cars.

Conclusions

The purpose of this paper was to study how two-car households react to changes in fuel prices that affect the relative per-kilometre cost of using the different cars, which are of different fuel efficiency. Based on a simple theoretical framework, we developed an econometric model to investigate whether and to what extent there is substitution between cars within the household. Using detailed Danish register data we estimated, for each car owned by the two-cars-households that do not change

Acknowledgements

The authors thank Statistics Denmark and the Danish car dealer association (Danmarks Automobilforhandler Forening) for providing the data. Seminar participants at the 6th Kuhmo-Nectar Conference, the Swedish National Road and Transport Research Institute, and the Department of Economics at the University of Copenhagen provided helpful comments. The remarks of anonymous referees substantially improved previous versions of the paper. Research support from the Danish Council for Strategic Research

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