Do car drivers respond differently to fuel price changes? Evidence from German household data

Khanna, Arpita Asha; Dubernet, Ilka; Jochem, Patrick Article — Published Version Do car drivers respond differently to fuel price changes? Evidence from German household data Transportation Provided in Cooperation with: Springer Nature Suggested Citation: Khanna, Arpita Asha; Dubernet, Ilka; Jochem, Patrick (2023) : Do car drivers respond differently to fuel price changes? Evidence from German household data, Transportation, ISSN 1572-9435, Springer US, New York, NY, pp. 1-35, https://doi.org/10.1007/s11116-023-10431-y This Version is available at: https://hdl.handle.net/10419/308460 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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Evidence fromGerman household data ArpitaAshaKhanna1· IlkaDubernet2· PatrickJochem1 Accepted: 14 September 2023 © The Author(s) 2023 Abstract For cutting down greenhouse gas emissions in road transport, core economic measures are relying on the response to increasing fuel prices—i.e., the fuel price elasticity. A focal point of the effectiveness of these measures is the heterogeneity in fuel price elasticities of different vehicle users. These effects were often neglected in the transport-related literature and were only incorporated recently. The results show, however, sometimes contradicting conclusions on influencing parameters such as income, region-type or household size. In this paper, we used a pooled OLS model estimated on a German refuelling diary data set and analysed the impact of various household level characteristics on fuel price elasticities through an analysis of interaction terms and their marginal effects. This analysis provides a cornerstone in this discussion on fuel price elasticities. We found out that the overall results contrast the existing literature by identifying heterogeneity in fuel price elasticities among German households for different socio-economic and regional characteristics. The results are highly relevant for policy modellers and for introducing effective policy measures for mitigating greenhouse gas emissions in road transport. Keywords Fuel price· Elasticity· Heterogeneity· Germany· Price elasticity Introduction Despite the long-lasting political negotiations on the global level for reducing greenhouse gas emissions and achievements in some sectors such as electricity generation in developed countries, the transportation sector is still not showing a downward trend in most countries—not to mention the global level (Lamb etal. 2021; Intergovernmental Panel on Climate Change (IPCC) 2022). This is especially true for aviation and road transport. Road transport, in particular, is still highly dependent on fossil oil and contributes the lions’ share of the total emissions stemming from the sector. Hence, it seems that cutting * Ilka Dubernet [email protected] 1 Institute ofNetworked Energy Systems, German Aerospace Center (DLR), Curiestraße 4, 70563Stuttgart, Germany 2 Institute ofTransport Research, German Aerospace Center (DLR), Rudower Chaussee 7, 12489Berlin, Germany Transportation 1 3 down greenhouse gas emissions in transportation is still a challenging task [Creutzig etal. (2015)] even though there is a comprehensive stream of literature on potential policy instruments [e.g., Kok etal. (2011); Stepp etal. (2009); Haasz etal. (2018); Whitehead etal. (2021)]. Many of these policy instruments, such as energy or carbon taxes, target at increasing fuel prices, which should decrease miles travelled (VMT) – depending on the fuel price elasticity. This is well documented in the literature [e.g., Dahl and Sterner (1991)]. We use the term "fuel price elasticity” to refer to a change in vehicle miles travelled due to fuel price changes. Thus, the term "price elasticity of passenger car usage” would be more specific. However, in the literature, the term "fuel price elasticity” is used more often, so we use this terminology in our paper. However, most of the econometric estimation of fuel price elasticities either consider only linear effects or if non-linear effects are considered, they are based on an approach which has been found questionable in the literature [see Brambor etal. (2006)]. Hence, the objective of this paper is to findstatistical evidence of heterogeneous effects, i.e., differences in fuel price elasticity among vehicle users across different socio-economic, demographic and spatial variables. Some studies [e.g., Alberini etal. (2022)] have investigated the issue of heterogeneity in elasticities regarding variables like income, rural vs. urban regions, employment of members in the household etc. They followed the split-sample approach to investigate the issue and found evidence that there is heterogeneity in elasticities among German residents. This methodological approach, however, is fraught with challenges: First, dividing the sample across the moderating variable and running separate regression equations do indeed provide us with elasticities for those different subsamples; however, it doesn’t provide any evidence if the elasticity estimates significantly differ from each other. To gain such knowledge, one needs to conduct separate statistical tests (for instance, that suggested by Cohen (1983) and Clogg etal. (1995), which have not been conducted and reported by any study so far). Second, splitting the sample across a moderating variable forces one to dichotomize a continuous variable (e.g., income). This leads to the loss of variance and valuable information, which may otherwise be interesting to study. We, therefore, follow the approach suggested by Brambor etal. (2006) and apply it to the representative mobility data set for German passenger car travel [Karlsruhe Institute of Technology (KIT) (2022)]. We analyse changes in mileage among private households as a reaction to changes in fuel prices. Herein, we also consider if these reactions differ across different carand household-specific characteristics. The research questions that we investigate are the following: • What are the factors influencing the price elasticity of passenger car usage in Germany? • Whether and how do these elasticities vary according to the car-specific and householdspecific characteristics? The results obtained are highly relevant for policymakers to design greenhouse gas mitigation policies more effectively and provide suitable compensation methods for socially disadvantaged private households which are sometimes highly dependent on cars. These households might be existence-threateningly affected if heterogeneity is not considered by policymakers. Furthermore, other modellers can also benefit from our results, as they may integrate our insights into their economic models such as general equilibrium models [cf. Mayer etal. (2021)]. Herewith, these models can improve their consideration of equity issues, which supports policymakers for designing suitable and effective policy instruments. Transportation 1 3 In the following sections, we start by providing an overview of the current literature (“Literature review” section) before we introduce our econometric model in “Methodology” section. This is followed by a results (“Empirical results” section) and discussion (“Conclusion” section). Finally, our conclusions provide corresponding policy recommendations. Literature review There is large literature on price elasticities in road passenger transport [e.g. Dahl and Sterner (1991); Goodwin etal. (2004); DeJong and Gunn (2001); Graham and Glaister (2004); Basso and Oum (2007); Sterner and Dahl (1992); Dahl (1995); Graham and Glaister (2002b, 2002a)]. Many of these studies differ regarding the time horizon of the effect. While short-term effects focus on the reduction of mileage by car (i.e. mainly avoidance of trips or short-term modal shifts), the long-term effects might even include the substitution of cars by more efficient cars or long-term modal shifts [cf. Blum etal. (1988); Drollas (1984); Oum etal. (1992)]. Therefore, the long-term elasticities have been found to be somewhat higher (e.g. −0.8) compared to the short-term elasticities [e.g. −0.3) Graham and Glaister (2004)]. The literature has also analysed if fuel price elasticities vary over time [e.g. Espey (1998)] and with the level of fuel prices [cf. Rouwendal and deVries (1999)]. Core insights into this issue were mainly gained during the sharp increases in fuel prices [cf. Rouwendal and deVries (1999)]. Rouwendal and deVries (1999) estimated a random effects panel model for the Netherlands, which distinguished the effects across trip purposes and other variables. They conducted their analysis across the two years, 1986 and 1991, during which the national petroleum tax was increased. They focussed on private road transport and found price elasticities to be between −0.44 and −0.65. The German specific literature, which focuses on private road transport, has also found the elasticities to be lying in the same range [e.g. Frondel etal. (2008); Frondel and Vance (2010); Frondel etal. (2012); Matiaske etal. (2012); Frondel and Vance (2014)]. Another research stream which is aligned to fuel price elasticities is the literature on rebound effects [cf. Goodwin etal. (2004); Sorrell (2007); Matiaske etal. (2012); Linn (2016)]. Most studies in the literature have identified the rebound effect almost exclusively via fuel price elasticities. These studies have relied on the assumption that both rebound and price effects are simply two sides of the same coin: decreasing unit costs of energy services such as car travelling leads to its more extensive usage. Some studies in the literature argue that fuel price elasticities are not constant across all groups of the population. Instead, they vary across the different socio-economic and geographical dynamics [e.g. Wadud etal. (2010a); Wadud etal. (2010b); Tilov and Weber (2020); Frondel etal. (2017); Archibald and Gillingham (1980, 1981); Greening et al. (1995); Kayser (2000); Nicol (2003); West and WilliamsIII (2004)]. These studies suggest that, for instance, car users in rural areas respond less to a price change as compared to those located in the urban areas. The argument is that in the rural areas, the availability of alternate modes of transportation is relatively lower [e.g. Wadud etal. (2009); Santos and Catchesides (2005)]. However, there is also contradictory evidence which suggests that car users in rural areas could, in fact, be more price elastic than those in urban areas (Spiller etal. 2017) One core focus in the literature is to understand the heterogeneity in fuel price elasticity across income. It is argued that lower income households would have higher fuel price Transportation 1 3 elasticities as compared to higher income households (e.g. West and WilliamsIII 2004). However, as pointed out by Kayser (2000), it is also possible for lower income households to be rather price inelastic. The rationale provided for this is that lower income households may already be driving as little as possible because of their budget constraints and, hence, may find it difficult to further reduce their level of driving (Kayser 2000). Moreover, it could be possible for higher income households to have higher price elasticities – as they may have more options to reduce their driving given that much of their travel could be discretionary (e.g. for leisure trips) (Kayser 2000). In addition, they may find it easier to switch to other modes of transport (e.g. air travel for holidays). All these factors suggest that one can expect considerable heterogeneity in elasticities across location and income. Moreover, in addition to these variables, one can expect the household’s response to a price change to vary regarding the household’s size, number of children, number of car users, vehicle type, vehicle usage, quality of public transportation etc. In context to Germany, some studies empirically investigated the possibility of heterogeneity in fuel price elasticities among German households [e.g. Frondel and Vance (2018, 2014)]. However, they, in contrast to the wider understanding, found out that the fuel price elasticities for Germany are rather homogeneous and don’t vary with regard to income and other household characteristics. These studies, to identify and analyse heterogeneity, employed interaction models, wherein they interacted fuel prices with income and other variables of interest. In employing and analysing interaction models, however, they failed to consider the econometric insights brought about by the seminal work of Brambor etal. (2006). Brambor etal. point out the common mistakes that are being made while using and interpreting the results of the interaction model. They also provide the guidelines and methodological steps that one must follow while using these models. Given this, the question arises whether the contradictory results obtained for Germany reflect the true empirical phenomenon, or are they just the artefact of the methodological approaches used, and the limitations associated with it. The objective of this paper is to throw light on this issue. The results suggest that when we use interaction models and follow all methodological steps as recommended by Brambor etal., we do uncover significant heterogeneity in fuel price responses among German households. These results have an important bearing on the policy; they could help policymakers in coming out with targeted instruments to accelerate modal shifts in the sustainable direction for the different groups in the society. Methodology Data anddata manipulation For the modelling, we used the German Mobility Panel (MOP), a longitudinal survey that collects detailed data about German mobility behaviour (Ecke etal. 2021). The data is available from 1994 onward and has been used extensively for estimating fuel price elasticities for Germany in the past. MOP has a rotating sample, that is, households stay in the panel for three consecutive years, and then are replaced by a new set of households. It consists of different survey modules. For this analysis, we draw on the module ’refuelling diary’ (‘Tankbuch’) which provides detailed data on car mileage, fuel consumption, fuel prices and car-specific Transportation 1 3 characteristics. The data is generated by a survey that happens every year for eight weeks during April and June. As part of the survey, the households are required to maintain a travel diary and record all their refuelling activities, odometer reading, fuel consumption, fuel prices, mileage etc. We merge the ‘Tankbuch’ module with the general survey that provides information about demographic, socio-economic and spatial characteristics of the households. Following the literature [e.g. Frondel etal. (2007); Frondel and Vance (2014, 2018)], we restrict our analysis to single car-owning households. This is done to abstract from complexities associated with the substitution between cars in multiple vehicle households. Past studies suggest that such substitution can substantially bias the results (see DeBorger etal. 2016).1 In Germany, the share of single-car (car-less) households equals about 53% (22%) (Nobis and Kuhnimhof 2018). The average number of cars per household in Germany is 1.1 (or 1.4 neglecting the car-less households). Our final sample consists of 4166 households which were analysed during the period 2002–2020. 19% of the households participated in only one period, 63% in two consecutive years and 18% of the households participated for three years. Although the MOP dataset provides data from 1994 onward, 2002 is the starting year of our analysis as some variables (e.g. income classes) are available only from 2002 onward. Modelling approach andbaseline model For the modelling, we explored the use of different panel data estimation techniques: pooled OLS method, fixed effects (FE) method, and random effects (RE) method. The latter two methods yield consistent and efficient estimates only when certain conditions are satisfied. For instance, RE model requires that the household-specific effects are randomly distributed and are uncorrelated with explanatory variables. We test for the fulfilment of these conditions by conducting the Hausman test. The test rejected the use of the RE models in favour of FE models. The use of FE models is, however, not appropriate for our analysis, as in our dataset the households stay in the panel for a short period of maximum 3 years, leading to a rather small t.The use of FE in this case can lead to misleading inferences (Wadud etal. 2009). We therefore use a pooled OLS model, as it is the most suitable given our data and variables. To estimate fuel price elasticities, we use the following baseline model: where: • VMT i ,t is the log of vehicle miles travelled (in kilometres) by household i at the time t, • 𝛼1 is the intercept, • 𝛼2 gives the fuel price elasticity, • FP i, t is the log of real fuel price per litre of household i at the time t, • Z is the vector of control variables, and • e i, t the error term. (1) VMT i,t=𝛼1+𝛼2⋅FPi,t+𝛼3⋅Z � i , t+ei, t 1 Although we primarily focus on single-car owning households, we also conduct estimations with multiple car-owning households. The results are presented in “Do fuel price elasticities vary according to the households’ characteristics?” section, Table3 Column 4 (p. 18) and Table4 (p. 19). Transportation 1 3 The dependent variable, VMT, is obtained by summing the total kilometres driven over the period of eight weeks and converting this sum into a monthly figure (total kilometres/number of days ⋅ 30). The real fuel price variable is derived by first taking an average of the fuel price per litre as reported on every visit to the gas station. The nominal fuel prices are then converted to real fuel prices by dividing them by the consumer price index (CPI), obtained from Germany’s Federal Statistical Office (2022). Across various price elasticity studies, the major issue of concern is the endogeneity of prices in the regression. We believe that at the macro level, fuel prices could be endogenous to the demand for travel. However, at the micro level, from the perspective of individual households, they are generally treated as exogenous [see, for instance, Frondel etal. (2012); Frondel and Vance (2018); Alberini etal. (2022)]. In other words, there is a lower possibility of endogeneity due to reserve causality between VMT and fuel prices. Following the literature, we control for the diesel dummy, horsepower (as a proxy for the power of the engine), age of car, size of household, and income. Descriptive statistics for these and other variables used in the model can be found in Table8 in the Appendix.2 We also control for year dummies to account for all changes that happen over time and that affect the households in the sample. To address the problem of heteroscedasticity and autocorrelation, we use cluster-robust standard errors (cf. White (1984), pp. 134–142) which allow for correlation of errors within households. Heterogeneity To test for heterogeneity in fuel price elasticities, we modify the model given in Eq.(1). The model used for analysing heterogeneity is given as follows: Where X is the moderating variable, the variable across which we are interested in testing for heterogeneity. This could be a continuous variable or a dummy variable. Z’ now represents the vector of other control variables included in the model. Fuel price elasticity is now given by Eq. (3). While testing for heterogeneity in fuel price elasticities, many of the existing studies in the literature have used interaction models, similar to the one given in Eq. (2). The existing approach looks at the significance of the interaction term – that is, the 𝛼4 coefficient – to form conclusions whether there is heterogeneity or not. When the interaction term is insignificant, it is concluded that there is no heterogeneity regarding the moderating variable, X [e.g. Frondel etal. (2012)]. However, this approach has been criticized by the seminal work of Brambor et al. (2006). According to Brambor etal., just looking at the significance of the interaction term and forming conclusions about heterogeneity could lead us to draw erroneous conclusions. They emphasize that while interpreting the results of an interaction model, one must first (2) VMT i,t=𝛼1+𝛼2⋅FPi,t+𝛼3⋅Xi,t+𝛼4⋅(FPi,t⋅Xi,t)+𝛼5⋅Z � i , t+ei, t (3) 𝜕VMT 𝜕FP =𝛼2+𝛼4⋅Xi t 2 For some variables, we use the log specification to correct for the skewness. Transportation 1 3 estimate the standard errors, given in Eq.(4). These standard errors do not get automatically reported by the standard software packages, but need to be estimated separately. To the best of our knowledge, there has not been a single study in the fuel price elasticity literature that has reported these standard errors, or drawn inferences based on that. Owing to this, it is difficult to trust the conclusions formed in the literature. Moreover, according to Brambor etal., just estimating the standard errors as given in Eq.(4), perhaps at some average or representative value of the moderating variable, is not enough. It is important to calculate and report the marginal effects and standard errors across all values of the moderating variable. Brambor etal. show, using examples, that the results and statistical significance could differ across the different values of the moderating variable. From the policy perspective, it is important to move beyond the aggregated/average picture, and calculate and analyse the effects across all possible values that the moderating variable can take. We therefore follow the rules and guidelines prescribed by Brambor etal. to test for heterogeneity in fuel price elasticities. Empirical results Baseline model elasticities We start with a parsimonious model, where we include only fuel prices and year dummies as independent variables. The results, as shown in Column 1 of Table1, suggest that a 1% increase in fuel prices leads to a 1.5% decrease in VMT. We now sequentially add other variables in the model. The results are presented in Column 2 to 7. On adding theother variables, the absolute value of the fuel price coefficient reduces in magnitude, but it remains significant at the 1% level of significance. The full model (cf. Column 7) suggests that 1% increase in fuel prices leads to 0.5% decrease in VMT. Regarding the control variables, the results are as expected and in line with the literature on short-term fuel price elasticities3. The coefficient of diesel dummy is significantly positive. The results suggest that driving a diesel car leads to around 33% more travel as compared to a non-diesel car (see Column 7). The coefficient of horsepower is also significantly positive, suggesting that 1% increase in horsepower leads to 0.2% increase in VMT. The age of a car, on the other hand, has a significantly negative effect on VMT. As the age of a car increases by one year, VMT decreases by 2%. Regarding socio-economic variables, the size of household as well as income have significantly positive effects on VMT; as the household size and income increase by one unit (i.e. adding a household member or switching to a higher income class), VMT increases by 8% and 3% respectively. Regarding regional variables, the full model suggests that living in a medium-sized city leads to 5% more travel as compared to living in a large city. Living in the countrysideleads to 16% more travel. (4) SE = √ Var(𝛼2)+X2 i,t ⋅Var(𝛼4)+2⋅Xi,t⋅Cov(𝛼2,𝛼4 ) 3 As there are no significant price shocks in the considered time horizon, we assume that the long-term price elasticity, which is based on measures such as buying a more efficient car or reducing commuting distance because of higher fuel prices, is marginal. Transportation 1 3 Table 1 Baseline model: fuel price elasticities and control variables Dependent variable is the log of monthly VMT (in kilometres). Pooled OLS estimation method is used Year dummies are used. Standard errors, clustered at household level, are reported in parentheses Please note that R2 values are not consistently comparable with each other ***, **, * Indicate that the estimates are statistically significant at 1%, 5%, and 10% levels respectively (1) (2) (3) (4) (5) (6) (7) Log(fuel price) − 1.464*** − 0.636*** − 0.604*** − 0.606*** − 0.550*** − 0.537*** − 0.529*** (0.107) (0.0863) (0.0841) (0.0821) (0.0786) (0.0784) (0.0768) Diesel dummy 0.406*** 0.347*** 0.314*** 0.302*** 0.297*** 0.288*** (0.0257) (0.0259) (0.0250) (0.0247) (0.0252) (0.0251) Log(horsepower) 0.324*** 0.244*** 0.214*** 0.174*** 0.158*** (0.0307) (0.0302) (0.0300) (0.0324) (0.0324) Age of car − 0.0261*** − 0.0255*** − 0.0242*** − 0.0240*** (0.00194) (0.00190) (0.00198) (0.00197) Size of household 0.0929*** 0.0802*** 0.0784*** (0.00952) (0.0105) (0.0104) Income 0.0239*** 0.0312*** (0.00613) (0.00619) In and around medium city 0.0466* (0.0257) Small town/countryside 0.151*** (0.0232) Constant 7.074*** 6.861*** 5.404*** 5.937*** 5.870*** 6.023*** 5.991*** (0.0500) (0.0486) (0.146) (0.146) (0.144) (0.164) (0.164) Observations 8228 8224 8217 8217 8217 7400 7388 Adjusted R2 0.074 0.115 0.138 0.172 0.187 0.193 0.201 Transportation 1 3 Table 5 Heterogeneity across the regional and locational characteristics: Results of interaction models (1) (2) (3) (4) (5) Region Parking situation Type of road Distance to travel for daily needs Distance to travel for leisure Log(fuel price) − 0.525*** − 0.597*** − 0.546*** − 0.662*** − 0.659*** (0.107) (0.132) (0.158) (0.131) (0.136) Diesel dummy 0.288*** 0.288*** 0.259*** 0.269*** 0.265*** (0.0252) (0.0253) (0.0425) (0.0365) (0.0354) Log(horsepower) 0.158*** 0.156*** 0.0663 0.151*** 0.149*** (0.0324) (0.0327) (0.0525) (0.0462) (0.0456) Age of car − 0.0240*** − 0.0238*** − 0.0261*** − 0.0239*** − 0.0223*** (0.00197) (0.00197) (0.00371) (0.00261) (0.00259) Size of household 0.0784*** (0.0104) 0.0772*** (0.0104) 0.0880*** (0.0150) 0.0625*** (0.0160) 0.0748*** (0.0159) Income 0.0312*** 0.0316*** 0.0389*** 0.0321*** 0.0340*** (0.00619) (0.00622) (0.0103) (0.00892) (0.00863) In and around medium city 0.0374 (0.0479) 0.0463* (0.0258) 0.0795* (0.0453) 0.0626* (0.0374) 0.0338 (0.0356) Small town/countryside 0.159*** (0.0420) 0.156*** (0.0238) 0.154*** (0.0424) 0.168*** (0.0339) 0.165*** (0.0327) Log(fuel price) ⋅ medium city 0.0310 (0.141) Log(fuel price) ⋅ small town/countryside − 0.0288(0.126) Easy curbside parking − 0.0460 (0.0417) Log(fuel price) ⋅ easy parking 0.0647 (0.125) Highways 0.396** (0.186) Country roads − 0.0498 (0.109) Log(fuel price) ⋅ Highways 0.161 (0.477) Log(fuel price) ⋅ Country roads 0.0903 (0.264) Distance (in km) for daily needs − 0.00346 (0.00590) Log(fuel price) ⋅ daily needs distance 0.0459* (0.0235) Distance (in km) for leisure 0.00695 (0.00602) Transportation 1 3 Dependent variable is the log of monthly vehicle miles travelled (in kilometres) Pooled OLS estimation method is used Standard errors, clustered at household level, are reported in parentheses ***, **, * Indicate that the estimates are statistically significant at 1%, 5% and 10% levels respectively Table 5 (continued) (1) (2) (3) (4) (5) Region Parking situation Type of road Distance to travel for daily needs Distance to travel for leisure Log(fuel price) ⋅ leisure distance 0.0147 (0.0198) Constant 5.629*** 6.036*** 6.351*** 6.328*** 6.164*** (0.146) (0.148) (0.251) (0.262) (0.247) Observations 8221 7219 2448 3271 3409 Adjusted R2 0.167 0.202 0.205 0.226 0.222 Year dummies Yes Yes Yes Yes Yes Transportation 1 3 to single car-owning households. This could be because households with multiple cars can choose among the most efficient cars, thereby maintaining their travel. Furthermore, possession of multiple cars can be seen as an indicator of wealth, suggesting that multiple-car households have lower elasticities as they can more easily transfer their non-travel budget for travel purposes. It is quite possible that the elasticities vary according to the local and regional characteristics of where households reside. To test for this, we start by investigating whether the elasticities differ according to where the households are located – that is, whether in and around a large city, in and around a medium city or in rural areas and the countryside. Table5 (Column 1) presents the results of the interaction model. The interaction terms are insignificant. We calculate the marginal effects and significance levels based on the corrected standard errors. These results are presented in Table6. The results suggest that the elasticities differ across the three regions, with rural dwellers might even be more price elastic. As our dependent variable is the VMT and people in rural areas need to drive longer distances, every trip is more costly and consequently the optimization of trips is very meaningful and leads to a mileage reduction. To further check our results, we calculated the marginal effects for the other spatial variables in the MOP data set (Table13). For further plausibility, we bootstrapped our model to investigate the distribution of our estimated parameters and validated the differences between the parameters with a T-test. The results highlight the robustness and significance of our findings (Fig.3). We also look at whether the ease or difficulty of parking, and the roads that the households typically travel on, affect the elasticities. The results of the interaction model are presented in Table5 (Column 2 and 3). Although the interaction terms are insignificant, we see from the Table6 that the elasticities are lower when the parking is relatively difficult. Furthermore, households travelling mostly on the inner-city roads react the most to fuel price changes (with the elasticity coefficient being − 0.55) followed by the households travelling on country roads ( − 0.45). The elasticity coefficient for the households mostly driving on highways is insignificant. Next, the distance that people need to travel for meeting their daily needs or for leisure and whether that affects households’ responsiveness to fuel price changes is considered. Column 4 and 5 of Table5 present the results from the interaction. The marginal Table 6 Marginal effects: fuel price elasticities across the regional and locational characteristics ***, **, * Indicate that the elasticities are significantly different from zero at 1%, 5% and 10% levels of significance respectively Variables Fuel price elasticities In and around large city − 0.52*** In and around medium city − 0.49*** Countryside/small town − 0.55*** Relative ease of road side parking − 0.53*** Relative difficulty in road side parking − 0.60*** Inner-city roads − 0.55*** Highways 0.38 Country roads − 0.45* Transportation 1 3 Fig. 2 Fuel price elasticities across distance to travel for daily needs and leisure activities Transportation 1 3 Table 7 Heterogeneity across the quality of public transportation (Walking time to different transportation modes): results of interaction models Dependent variable is the log of monthly vehicle miles travelled (in kilometres) Pooled OLS estimation method is used Standard errors, clustered at household level, are reported in parentheses ***, **, * Indicate that the estimates are statistically significant at 1%, 5% and 10% levels respectively (1) (2) (3) (4) (5) Bus stop Suburban train Underground train Tram Railway station Log(fuel price) − 0.563*** − 0.573** − 0.715*** − 0.859*** − 0.676*** (0.0929) (0.231) (0.266) (0.257) (0.148) Diesel dummy 0.288*** 0.294*** 0.343*** 0.274*** 0.291*** (0.0253) (0.0492) (0.0835) (0.0645) (0.0372) Log(horsepower) 0.165*** 0.196*** 0.167 0.229*** 0.185*** (0.0329) (0.0707) (0.106) (0.0749) (0.0528) Age of car − 0.0236*** − 0.0214*** − 0.0255*** − 0.0212*** − 0.0201*** (0.00199) (0.00457) (0.00620) (0.00498) (0.00293) Size of household 0.0734*** (0.0106) 0.0580** (0.0228) 0.0379 (0.0355) 0.0517** (0.0262) 0.0599*** (0.0147) Income 0.0295*** 0.0459*** 0.0302 0.0275* 0.0363*** (0.00630) (0.0137) (0.0225) (0.0148) (0.00941) In and around medium city 0.0380 (0.0260) − 0.00172 (0.0514) − 0.0168 (0.131) 0.0419 (0.0613) -7.38e − 06 (0.0376) Small town/countryside 0.159*** (0.0238) 0.0194 (0.0567) − 0.0406 (0.218) 0.194** (0.0975) 0.0791** (0.0362) Walking time − 0.00943** 0.000134 − 0.0157* − 0.0118*** − 0.00216 (0.00392) (0.00407) (0.00807) (0.00411) (0.00167) Log(fuel price) ⋅ walking time 0.00890 (0.0113) 0.00709 (0.0109) 0.0331 (0.0215) 0.0186* (0.0112) 0.000592 (0.00459) Constant 6.003*** 5.715*** 6.279*** 5.853*** 6.016*** (0.169) (0.376) (0.496) (0.376) (0.281) Observations 6983 1575 639 1353 3076 Adjusted R2 0.201 0.187 0.189 0.191 0.192 Year dummies Yes Yes Yes Yes Yes Transportation 1 3 effects and the corrected significance levels are presented in Fig.2. The results suggest that the elasticities reduce as the travelling distance increases; however, the effect is not significant across the entire range. For daily needs, the effects are significant until around 8kms, and for leisure, the effects are significant until around 18kms. These results support the argument that the distance to amenities is an important indicator of the household’s ability to refrain from car usage Kingham etal. (2001); Graham and Glaister (2002b). We also tested for whether the elasticities vary according to the quality of public transportation. To do so, we use walking time (in minutes) to different transportation modes as a proxy measure for the quality of public transportation. Lower walking time indicates the presence of a better quality of transportation. The results are presented in Table7 and Fig.5. Although the interactions terms in most specifications are insignificant (see Table7), the results presented in Fig.5 show that the elasticities vary according to the quality of public transportation (which is measured by walking distance to the next access point). The elasticities are higher when the walking time to different transportation modes is not as high. But as the walking time increases, the elasticities reduce and become insignificant. This supports the argument that the households are influenced by the infrastructure improvements that make public transit more convenient Kingham etal. (2001); Bamberg and Rölle (2003). Only in the case of railway station, we see elasticities to be mostly the same irrespective of the walking time (cf. Fig.5e). This is intuitive as railway stations are mostly used for infrequent longer duration travels rather than day to day travel and are approached by different means of transport. This insight supports our hypothesis that heterogeneity effects are decisive when considering fuel price elasticities. In sum, the overall results contrast the existing literature that there is not much heterogeneity in the fuel price elasticities among German households. The results in this study suggest that the elasticities, in fact, vary according to the different socio-economic and spatial characteristics. More explicitly, the results of the study lead to the following insights: • Heterogeneity in the number of household members The results support the hypothesis that the more the number of members in a household, the lower are the price elasticities. • Heterogeneity in income The insignificant effect of income, as found in the German literature, has been disproved. The results show a significantly negative effect of income – that is, the higher the income, the lower is the fuel price elasticity. • Heterogeneity in the quality of service by public transportation The effect of the quality of public transportation, which is associated with mixed evidence in the literature, is significantly positive – that is, the closer the access to public transportation, the higher is the fuel price elasticity). • Heterogeneity in regional characteristics The results confirm the recent evidence by Spiller etal. (2017) that car users in rural areas have higher price elasticities than those in the urban areas. Transportation 1 3 These insights can be used for improving the consideration of fuel-price changes and their impact on car mileage of traffic participants in transport models. Correspondingly, policymakers can develop more effective and fair policy measures of increased fuel prices for reducing car mileage. Nevertheless, while during the period of investigation no disproportionate price change occurred, our results should be handled with care for price changes above 20%. Conclusion Fuel price elasticities have been widely analysed during the last decades. They are a decisive factor in determining the socio-economic effects of policy instruments in the transportation sector, particularly the instruments that cause an increase in fuel prices. This paper contributes to the literature by analysing heterogeneity in fuel price elasticities for Germany. The paper uses an interaction model and follows all methodological steps as recommended by Brambor etal. (2006). The results contrast the existing literature and show that fuel price elasticities are not constant for the entire German population. Instead, they vary depending upon the socio-economic and spatial characteristics of German households. While most results such as the influence of the number of household members, income, and quality of public transportation are consistent with our expectation, the results on regional variables are rather surprising. They show that passenger car use is more price elastic in rural than in urban areas. This might illustrate that the economic burdens on rural dwellers are already high and that higher fuel prices cannot be compensated for but lead directly to a significant reduction in mileage. Our results help transport modellers and policymakers identify the differentiated effects on households as a result of higher fuel prices. This in turn could help in the formulation of targeted policies and prevent the households from undergoing unacceptable and unfair burdens (e.g. by implementing a compensation via the annual income tax for highly cardependent but low-income households). Our statistical results say little about causal mechanisms, which could be an interesting domain for researchers to explore in the future research. Moreover, our data set does not allow identifying avoidance strategies of high prices by individuals (i.e. refueling at lower-price gas stations or refueling at other day times). Finally, while this study focuses on household-level characteristics, it will be interesting to study the differences across individual-level variables such as age, gender, nature, and form of employment etc. This is an important area for future research. A. Appendix A.1. Variable description See Table8. Transportation 1 3 Table 8 Description of variables used in our models Variable Level (& unit) N % Mean Std. deviation Min Max VMT (km/month) 8221 100 1046 697.8 12 8310 μ fuel price CPI (€ 2002 /liter) 8221 100 1.36 0.20 0.44 4.05 Drivetrain shares from 2016 (numbers) Diesel 714 26 Petrol 1930 70.2 Gas 41 1.5 Hybrid 65 2.4 Missing 5471 Drivetrain shares 2001–2015 (numbers) Petrol 3362 61.5 Diesel 1218 22.3 Petrol super 120 2.2 Petrol normal 211 3.9 Other 18 0.3 Super E10 464 8.5 Hydrogen 3 0.1 Gas 35 0.6 CNG/LNG and petrol 5 0.1 CNG/LNG and diesel 1 0.0 LPG and petrol 26 0.5 LPG and diesel 1 0.0 Hybrid (petrol) 3 0.1 Missing 2754 Age of car (years) 8221 100 7.9 5.2 0 39 Horsepower (PS) 8221 100 112 42 12 730 Transportation 1 3 Table 8 (continued) Variable Level (& unit) N % Mean Std. deviation Min Max Number of car users 1 2878 35 1.46 0.57 1 5 2 2021 24.6 3 100 1.2 4 18 0.2 5 4 0.0 Missing 3200 38.9 No. of main car user 1 4062 49.4 1.2 0.4 1 2 2 862 10.5 Car use Missing 3297 40.1 Only private 6992 85.1 Private and business related 1143 13.9 Only business-related 36 0.4 Missing 50 0.6 No. HH members (number) 8215 99.9 1.89 0.93 1 7 Number of children <10y n HH 0 7478 91.0 0.13 0.45 0 4 1 453 5.5 2 242 2.9 3 40 0.5 4 2 0.0 Missing 6 0.1 Income class (unit) 7402 90.0 5.37 1.82 1 8 Transportation 1 3 Table 8 (continued) Variable Level (& unit) N % Mean Std. deviation Min Max Place of residence Inner area large city 967 11.8 Suburb large city 1678 20.4 Inner area medium city 679 8.3 Suburb medium city 1332 16.2 Small town, large municipality 1887 23.0 Countryside/rural 1553 18.9 Missing 125 1.5 Distance Shopping daily needs (1994–2016) (km) 688 8.4 4.90 2.79 0.30 22 Distance Shopping daily needs (since 2016) (km) 2710 33 2.05 2.57 0.00 50 Distance Shopping further needs (1994–2016) (km) 2245 27.3 7.70 5.83 0.30 70 Distance Shopping further needs (since 2016) (km) 2698 32.8 6.67 7.23 0.00 70 Distance Cinema (1994–2016) (km) 3291 39.8 11.38 8.56 0.10 66 Distance Cinema (since 2016) (km) 2681 32.6 10.38 10.04 0.00 90 Distance Dinner/Pub (1994–2016) (km) 868 10.5 5.84 3.93 0.30 30 Distance Dinner/Pub (since 2016) (km) 2698 32.8 2.88 3.67 0.00 40 Walking time bus stop (minutes) 7659 93.2 5.74 4.71 0.00 100 Walking time tram (minutes) 1505 18.3 8.81 7.95 0.00 90 Walking time S-Bahn (minutes) 1734 21.1 15.32 9.50 1.00 90 Walking time Metro (minutes) 713 8.7 11.44 8.76 1.00 90 Walking time Train Station (minutes) 3343 40.7 19.59 12.70 1.00 150 Parking Curbside/street parking 1476 18.0 Garage/own parking spot 6616 80.5 Missing 129 1.6 Transportation 1 3 A.7. Fuel price elasticities acrossdifferent walking timestothetransportation mode See Fig.5. Fig. 5 Fuel price elasticities across different walking times to the transportation modes Transportation 1 3 Acknowledgements Most of this research has been financed by the Ökonver II and the VMo4Orte projects, which is an internal research project of the German Aerospace Center (DLR). We thank Christian Winkler, Marlene O’Sullivan, Thomas Baldauf, Jonas Eschmann, Peter Kasten, Lukas Minnich, Moritz Mottschall, Jonathan Schreiber and Manuela Weber for their useful comments and suggestions. Funding Open Access funding enabled and organized by Projekt DEAL. 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Ilka Dubernet is head of the department of Transport Markets and Mobility Services at the German Aerospace Center (DLR). Holding a PhD in transportation planning from ETH Zurich, her expertise lies in mobility behavior modeling and the analysis and evaluation of the economic effects of transport changes. Another focus of her work is the design, implementation, and analysis of mobility behavior surveys across diverse transportation topics. Patrick Jochem is head of the department Energy System Analysis at the German Aerospace Center (DLR) and a lecturer at the Karlsruhe Institute of Technology (KIT). He made strong research contributions to electric vehicles and holds an PhD in transport economics. He studied economics at the universities in Heidelberg, Mannheim and Bayreuth.