1 Introduction

The European perspective is optimistic and pushes policy to facilitate the research, testing and introduction of autonomous vehicles (AVs) [24]. But what role are AVs to play? Are they mostly set out to be present in long-haul trips, to improve freight or can they have a role in urban areas as well? And, if so, what role are they supposed to play?

No matter if people live in urban, suburban or rural areas, the means of transportation available to them and the commute time to their workplace, local schools or hospitals can be essential for a person’s socio-economic wellbeing. The latter is a multi-dimensional concept as defined by the European Commission and the Human Development Index covering indicators on amongst others education, employment, income and health ([29], pp. 8, 42 [54];). In general, urban areas show a higher density of locations of interest or opportunities including workplaces, shops, schools as well as health centres and hospitals [46]. This paper focuses on four functional urban areas (FUA), as defined by the EU and the OECD and their political cores [11, 21]. While it is generally recognised that FUAs are associated with greater economic growth and development than rural areas, it is not clear whether all inhabitants share the same opportunities offered by the denser infrastructure of FUAs.

Nowadays most countries “transport policies generally aim to improve accessibility and reduce the negative impacts of motorised transport” ([27], p. 474). Thus, accessibility has become a central concept in spatial and transportation planning ([15], p. 3). Geurs & van Wee, [16] «define accessibility as the extent to which land-use and transport systems enable (groups of) individuals to reach activities or destinations by means of a (combination of) transport mode(s)» (p. 128). The authors also identify four components of accessibility in the literature: (1) land-use, (2) transportation, (3) temporal and (4) individual [16]. Every component of accessibility can be distributed inequitably, and in turn, transportation and spatial planning policy affect equity in accessibility and cause socio-economic developments.

Here, it is noteworthy to say that there are various understandings of the concept of equity, different types of equity, various indicators and criteria to measure it and to categorize people into classes [25, 49, 57]. For example Ramjerdi [43] evaluated an equity objective for road pricing schemes in Norway. His research highlights the difficulty to assess equity on single measures yielding contradictory results and shows the sensitivity of these measures to the geographical level of analysis.

Further, there are multiple analysis on accessibility measures in European transport appraisals: Geurs, Boon, & Wee [14] developed a theoretical framework to describe the relationship between determinants of social impacts of transport, compare UK and Dutch UK transport appraisal guidelines and come to the conclusion that social impacts of transport appraisals are still far from being as complete as economic and ecological assessments. Lucas [26] and Halden [18] argue that due to the great flexibility in UK policy to assess accessibility, most local authorities struggle to find the right range and choice of calculation and that their mapping tools downplay the complexity and barriers causing social exclusion (cit. in [15]). Consequently, Pitarch-Garrido [37] for example, suggests the concept of spatial equity as indicator for social sustainability in transportation policy and uses time-distance to measure socio-spatial equity in Valencia.

More globally, Portnov et al. [38] were able to showcase that accessibility plays an important role in development when comparing accessibility in Swiss municipalities over the second half of the twenty-first century. Along those lines the ITF [21], was able to show “a correlation between income and accessibility by public transport” in the Paris FUA on a 500 m2 grid-level analysis (p. 64), highlighting inequity in accessibility along social and spatial lines.

Of recent, research has begun to analyse the effects of shared mobility as well as autonomous vehicles in regards to their effects on accessibility and equity: Clark & Curl [5], as well as Boldrini et al. [3] analysed travel data of car- and bike sharing-data in Glasgow and in other 10 European cities, respectively. While they outline the potential of shared transportation in overcoming barriers of access such as upfront cost or maintenance, they showcase that only a small percentage of the population is making use of these services. These are mostly highly educated, middle to high income individuals who use shared mobility as a substitute for other means of transport. Pritchard, et al. [39] came to similar results in their assessments of bike-sharing in Sao Paolo, Brazil and its potential to alleviate spatiotemporal inequality in job accessibility, as measured by Gini coefficients. These findings highlight that car-hailing users increasingly substitute public transportation trips, wherein the current most well-off users put “convenience over cost” ([6, 12], p. 5) and therefore, bear the question on whether the introduction of Shared Autonomous Vehicles (SAVs) will reinforce similar trends.

Level 4 and 5 AVs are already being tested on public roads in several countries including the US, Singapore and many European countries and bring many benefits to accessibility [47]: AVs promise to improve road safety, by reducing crashes and by optimising traffic at large, improving reliability, which in turn reduces congestion and travel time [55, 56]. Their deployment has the potential to reduce pollution rates in urban areas as they are primarily electric vehicles and if the infrastructure is well connected, AVs offer an opportunity to decrease energy consumption [8]. Lastly, AVs are expected to strongly lower the cost of travel. On the one hand the cost per kilometre is reduced as the cost of a driver and most of the operating cost of vehicles are eliminated, especially if implemented in shared schemes [4]. On the other hand, AVs offer the opportunity to use the time of travel productively and have a 24-h service. Therefore, Pendleton et al. [35] argue that AVs, as part of shared mobility, make access to mobility more affordable and could strongly benefit neighbourhoods with lower accessibility.

However, there is a range of risks concerning shared mobility and AVs: Due to the lower cost of travel, they bear the risk of accelerating the urban sprawl [12]. In addition, the spatial extension of SAVs will be limited, given the market imperative that lies at the core of these on-demand systems [5]. Also, SAVs bear the risk of technical unemployment in the mobility and transportation industry, industries that mostly offer low-skill jobs and are mainly held by marginalised communities, will be displaced by high-skilled tech jobs [36, 53, 59]. Lastly, SAVs also bring barriers of access best described by the STEPSFootnote 1 model created by Shaheen et al. [45] and adapted to include the usage of AVs by Fleming [12]. Overall, these findings raise the question:

1.1 Can shared autonomous vehicles improve equity in accessibility of European urban populations?

This paper proposes a three-step model for the introduction of SAVs which helps to address equity in accessibility and showcases concrete case-studies on accessibility in the European cities of Berlin, Paris, London and Vienna. Through the analysis of accessibility to shops within 30 min by car and public transportation and relating it to district-level socio-economic well-being indicators, it builds and tests the findings by the ITF [21], as well as Portnov et al. [38] and Pitarch-Garrido [37] and spatial mismatches are identified. Furthermore, it offers a tool to visualize city districts in which SAVs can aid to overcome identified spatial mismatches and contributes to the discussion of possible socio-economic developments caused by the introduction of SAVs and how these should be addressed.

2 Methodology and data

This analysis builds on four main underlying assumptions: Firstly, accessibility for low-income populations is improved through more affordable car travel [23]. Secondly, SAVs are expected to make car-travel more affordable [4]. Thirdly, SAVs offer an opportunity to improve equity in accessibility. And lastly, SAV travel needs to be regulated in order to improve equity in accessibility and bear socio-economic benefits [7, 12]. According to this logic, SAVs have the greatest opportunity to improve city populations’ socio-economic well-being if deployed in underserved, low-income areas. In order to identify such areas, the authors propose a three-step model (see Fig. 1).

Fig. 1
figure 1

Three-step process to identify SAV districts

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Step 1. entails showing that a relationship between accessibility and socio-economic well-being exists, by applying the four OLS regression models explained in Section 2.1. These relationships lay the ground for data-driven policy decisions. Step 2 ensures that accessibility is improved in city districts that will benefit the most from the deployment of SAVs: If the number of shops accessible within 30 min is greater in a district by car travel than by public transportation, AVs and SAVs offer room for improving the inhabitants’ accessibility. Lastly, Step 3. adds the significant socio-economic well-being indicator(s) to the equation, in order for SAVs to yield economic, societal and environmental benefit to the cities’ populations. Steps 2 and 3 are summarized by the ‘SAV identification matrix’ explained in Section 2.2, whilst the third section provides an overview of the data used.

2.1 OLS regression models for accessibility and socio-economic well-being

Based on the literature above, the authors of this paper test whether better accessibility by private car and public transport is present where yearly income is higher (H1), unemployment rates are lower (H2) and where educational attainment levels are higher (H3) in European cities.

Therefore, the linear relationship between accessibility rates and the defined socio-economic well-being variables are established as follows:

$$ {\mathrm{Y}}_d^{C, PT}={\upbeta}_0+{\beta}_1^{C, PT}\ {\mathrm{INC}}_d+{\upmu}_d $$
(1)
$$ {\mathrm{Y}}_d^{C, PT}={\upbeta}_0+{\beta}_2^{C, PT}\ {\mathrm{UEM}}_d+{\upmu}_d $$
(2)
$$ {\mathrm{Y}}_d^{C, PT}={\upbeta}_0+{\beta}_3^{C, PT}\ {\mathrm{EDU}}_{\mathrm{d}}+{\upmu}_d $$
(3)

The regression is formulated for \( {\mathrm{Y}}_d^{C, PT} \), the accessibility in a specific city district (d) by the two modes of transportation: car (C) and public transportation (PT). More precisely, \( {\mathrm{Y}}_d^{C, PT} \) is the average number of shops accessible in any given d within 30 min by the two selected means of transportation. This point of interest and time are selected as they are very representative of overall accessibility (see Section 2.3 and Appendix 3). The district-level independent variables are the following: in Model (I), INCd is the indicator for mean or median yearly incomeFootnote 2 in Euros (€) or British Pounds (£) in any given d; in Model (II) UEMd is the unemployment rate in any given d, as a percentage of the labour forceFootnote 3; and in Model (III) EDUd is the calculated weighted average educational attainment index on a scale from one to three in every d. The educational attainment index EDUd is based on the percentage of the population with low (ISCED 2011 levelsFootnote 4 01–2), medium (ISCED 2011 levels 3–4) and high (ISCED 2011 levels 5–8) educational attainment. The authors attributed the values 1 to low; 2 to medium and 3 to high educational attainment. The weighted average was calculated based on the percentages of the population attributed to these three categories for every d. Finally, μd represents the error of the OLS regression models for any d.

Building on the literature above, the authors expect a positive linear effect of yearly income (INCd), and a negative linear effect of increasing unemployment rates (UEMd) on accessibility by public transportation (\( {\mathrm{Y}}_d^{PT} \)). Since highly educated adults make use of shared mobility in Europe and because these services are mostly provided in core city areas, the authors expect a positive linear correlation between average educational attainment (EDUd) and accessibility. The comparison to accessibility by car (\( {\mathrm{Y}}_d^C \)) gives insights on the success of the European focus on PT in spatial and transportation planning. Furthermore, it offers the opportunity to learn about d where C and potential transportation by SAVs could bring greater benefits (see Section 2.2 for more details). Therefore, bivariate Models (I), (II) and (III) are tested for accessibility by car (\( {\mathrm{Y}}_d^C \)), as well as public transportation (\( {\mathrm{Y}}_d^{PT} \)).

However, all three independent variables are also known to be interrelated: Firstly, yearly income and unemployment are connected by definition, as the latter is a description of a state in which a person in working age is without work [20]. Naturally, an increasing unemployment rate, will negatively affect yearly income in a specific area. Secondly, income and income inequality are connected to educational attainment and inequality thereof, since a certain wealth and income is necessary to complete higher educational levels and higher educational attainment is associated with better paid jobs ([44, 50], pp. 389–390).

Given these interrelations between the independent variables, it is likely that there are cumulative effects on accessibility. To test this relationship and discuss potential multicollinearity, multiple linear regression Model (IV) is added to the analysis:

$$ {\mathrm{Y}}_d^{C, PT}={\upbeta}_0+{\beta}_1^{C, PT}\ {\mathrm{INC}}_d+{\beta}_2^{C, PT}\ {\mathrm{UEM}}_d+{\beta}_3^{C, PT}\ {\mathrm{EDU}}_d+{\upmu}_d $$
(4)

Together these four Models, enable the authors (1) to test whether there are spatial mismatches in terms of accessibility and socio-economic well-being in European cities and (2) how accessibility by car (\( {\mathrm{Y}}_d^C \)) and public transportation (\( {\mathrm{Y}}_d^{PT} \)) compare. The four Models are applied to district-level datasets of Paris, Berlin, London and Vienna.

2.2 SAV district identification matrix

Figure 2 exemplifies how SAV districts can be identified graphically. The y-axis showcases the difference (∆) between the number of shops accessible within 30 min by public transportation (PT) and the number accessible within the same timeframe by car travel (C). The green arrow indicates that ∆ between \( {\mathrm{Y}}_d^C \) and \( {\mathrm{Y}}_d^{PT} \) equals zero. If the number is positive, for a particular district (d), PT performs better, and d finds itself in the upper half of the matrix. If C performs better in a d it finds itself in the bottom half of the matrix. This is the case for example district dx (see red dot). In this paper ∆ is normalised (only positive numbers) if one means of transport performs better than the other in every d of a city.

Fig. 2
figure 2

SAV district identification matrix

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The x-axis showcases the previously identified significant mean or median socio-economic well-being indicator for each d, as well as the city mean or median (blue arrow). The mean is applied to the UEMd, as well as the index for EDUd, while the median is used for INCd. In the case of district dx in Fig. 2, its socio-economic well-being indicator value lies below the city average or mean. In result, example district dx is identified as a SAV district.

2.3 Accessibility and socio-economic well-being data

The accessibility dataFootnote 5 for the two dependent variables \( {\mathrm{Y}}_d^C \) and \( {\mathrm{Y}}_d^{PT} \) is obtained from the ITF and is based on TomTom navigation calculations ([21], p. 22). The socio-economic well-being data, for the three independent variables yearly income (INCd), unemployment rate (UEMd) and educational attainment (EDUd) is publicly accessible and stems from corresponding city statistics offices. See Appendix 1 for a description table of the data and Appendix 3 for overview plots for each city.

2.3.1 Accessibility data

The FUA grid map data is obtained in a combined Shapefile for all cities. It is first imported, separated and combined with the corresponding FUA accessibility datasets in QGIS.Footnote 6The estimated number of points of interest accessible within a specific timeframe were previously established by the ITF [21] on the basis of TomTom calculations for road travel and schedule data for public transportation. For road travel the estimations also include two city-specific coefficients to include congestion, depending on the capacity of the roads and commuting zones for every grid field.

Given the focus of this paper on SAVs, the datasets are limited to car travel (C) and public transportation (PT), and the number of shops accessible within 30 min. The number of accessible shops per districts within 30 min shows some of the greatest differences between districts in the four cities and is representative also of accessibility by PT to hospitals and schools (see Appendix 3).

To compare the selected accessibility data to district-level indicators, publicly accessible district maps of the four cities in Shapefile-format are added in QGIS and the union vector geoprocessing tool is applied. Data preparation and selection are performed in R.Footnote 7 The data cleaning procedure reduces the number of observations (500m2 grid fields) from n = 50′159 to n = 20′424 for the Paris FUA dataset; from n = 73′428 to n = 20′723 for the Berlin FUA dataset; from n = 28′579 to n = 17′570 for the London dataset and; from n = 38′381 to n = 2′012 for the Vienna dataset.Footnote 8

On the basis of these cleaned FUA accessibility datasets, the mean number of stores accessible by C or PT from every city-district are calculated, apt to be merged with the socio-economic well-being data set explained below.

2.3.2 Socio-economic well-being data

The socio-economic well-being indicators are compiled in a search effort at the various statistics offices, their publicly available databases and publications (see Appendix 2 for city-district socio-economic well-being data).

For the city of Paris, the Institut national de la statistique et des études économiques (Insee) provides the following district-level indicators for the year 2016: median yearly disposable household income, the unemployment rate for 15–64-year olds, and percentages of the population 15 and above who have completed five different schooling levelsFootnote 9 [19].

The Berlin socio-economic well-being data is available at the Amt für Statistik Berlin-Brandenburg. Yearly mean income data stems from the 2014 handbook, while the unemployment rate and the percentage of the population who has attained a high, medium or low level of education according to ISCED 2014, are based micro-census database established in 2017 [1, 2].

For London the data is provided by the Office for National Statistics (ONS). The yearly median income in 2016–7 by borough is presented before taxes and deductions [33]. The unemployment rate is calculated for the population of 16 years of age and above for the year 2017 and qualifications of the working population ages 16–64 in 2018 are subdivided into six categoriesFootnote 10 [28, 34].

Lastly, the datapoints for the socio-economic well-being variables for Vienna are: median yearly income after taxes and deductions for the year 2014, the unemployed population per district in 2013, as well as percentages of district populations’ highest attained degreesFootnote 11 [48].

3 Results

In the first subsection, the OLS regressions are performed and the correlations in each city explained. The second subsection displays the districts (d) for every city, which are most promising for the deployment of SAVs.

3.1 Relating accessibility and socio-economic well-being in European cities

Tables 1 and 2 showcase the regression results and coefficient estimates of the four linear OLS regression models explained in Section 2.1. Table 2 displays the obtained results on the dependent variable accessibility by public transportation (PT), \( {\mathrm{Y}}_d^{PT} \), while Table 2 shows the relationship of the omitted variables on accessibility by car travel (C), \( {\mathrm{Y}}_d^C \). See Appendix 4 for detailed regression tables for each city.

Table 1 Summary of city regression tables for four models on PT.
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Table 2 Summary of city regression tables for four models on C
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The predictors vary in format amongst each other within and between the cities. However, in sight of the result Tables 1 and 2, it becomes obvious that the estimates \( {\beta}_1^{C, PT} \) for yearly income (INCd) are by far the smallest (between 100 and 101), while estimates \( {\beta}_2^{C, PT} \) for the unemployment rate (UEMd) range between 102 and 105 and estimates \( {\beta}_3^{C, PT} \) for educational attainment (EDUd) range between 104 and 105. In case of a significant correlation, a small change in EDUd (values between 1 and 3) will increase \( {\mathrm{Y}}_d^{C, PT} \) greatly, while a similar change in INCd will only have a limited effect. The two tables also describe minimum, maximum and median \( {\mathrm{Y}}_d^{C, PT} \), in order to gain a relative understanding between the cities. In the following the results of the bivariate and the multiple linear regression models are outlined separately.

3.1.1 Simple linear regression model

Model (I) only shows a significant effect between \( {\mathrm{Y}}_{\mathrm{d}}^{\mathrm{PT}} \) and INCd in London with estimate \( {\beta}_1^{PT} \) of 12.44 at p < .001 (see Table 2). This relationship is positive and strong (R2 of .62 for 33 boroughs d). Nevertheless, the simple linear regression Model (I) performed on \( {\mathrm{Y}}_d^C \), displays positive, significant relationships with INCd (see Table 2) both for London (\( {\beta}_1^C \) = 3.01, p < .001) and Paris (\( {\beta}_1^C \) = 3.89, p < .01). INCd predicts \( {\mathrm{Y}}_d^C \) better in London (R2 = .56) than in Paris (R2 = 0.32). In summary, H1 (see Section 2.1) is confirmed for London’s political centre and is shown for \( {\mathrm{Y}}_d^C \) for the city of Paris.

In comparison, Model (II) showed negative effect (p < .05) between UEMd and \( {\mathrm{Y}}_{\mathrm{d}}^{\mathrm{PT}} \) in Vienna (\( {\beta}_2^{PT} \) = − 3′241) and between UEMd and \( {\mathrm{Y}}_{\mathrm{d}}^C \) in Paris (\( {\beta}_2^C \) = − 11′488). In both cases, the negative relationship confirms H2, although the validity of Model (II) is lower than in Model (I) with R2 = .27 in Vienna and R2 = .25 in Paris. No relationship between UEMd and \( {Y}_{\mathrm{d}}^{C, PT} \) is identified for Berlin and London.

Across the cities, EDUd shows positive significant relationships with \( {\mathrm{Y}}_d^{C, PT} \) in all cities but Berlin, strongly supporting H3. In Paris, the values of \( {\beta}_3^{PT} \) are 210′897 (p < .05) and \( {\beta}_3^C \) is of 142′660 (p < .05) with R2 of .28 and .2 respectively. In London as well, EDUd is a better predictor for \( {\mathrm{Y}}_d^{PT} \) (R2 = .44) than \( {\mathrm{Y}}_d^C \) (R2 = .32) with corresponding estimates \( {\beta}_3^{PT} \) of 356′024 (p < .001) and \( {\beta}_3^C \) equalling 81′139 (p < .001). Lastly, in Vienna \( {\beta}_3^{PT} \) is of 45′523 (p < .05, R2 = .38) and \( {\beta}_3^C \) amounts to 34′469 (p < .05, R2 = .2).

When taking a within city perspective on these three univariate models it becomes clear that the only determinant showing a relationship with both accessibility by C and PT, \( {\mathrm{Y}}_d^{C, PT} \), in Paris, as well as London and Vienna, is EDUd. However, in Paris changes in INCd explain a greater change of \( {\mathrm{Y}}_d^C \), than EDUd. Similarly, in London, both INCd and EDUd show significant effects with \( {\mathrm{Y}}_d^{C, PT} \), but INCd explains a greater share of the change of \( {\mathrm{Y}}_d^{C, PT} \) than EDUd. Finally, none of the univariate models show any relationship between \( {\mathrm{Y}}_d^{C, PT} \) and the three determinants in Berlin.

3.1.2 Multiple linear regression models

For Paris, the additive Model (IV) does not identify any significant relationship neither for PT nor for C. Meanwhile, the Berlin dataset shows significant correlations between both dependent variables and EDUd, as well as UEMd in the additive Model (IV). While the positive relationship between \( {\mathrm{Y}}_d^{C, PT} \) and EDUd (\( {\beta}_3^{PT} \) = 170′604 and \( {\beta}_3^C \) = 175′007 at p < .01) exhibited by Model (IV) confirms H3, the relationship between \( {\mathrm{Y}}_d^{C, PT} \) and UEMd (\( {\beta}_2^{PT} \) = 7′299, p < .05 and \( {\beta}_2^C \) = 7′310, p < .01) is also positive, defeating H2. In London, the multiple linear regression model showcases that the effect of EDUd on \( {\mathrm{Y}}_d^{C, PT} \) is absorbed by INCd, confirming H1 with estimates \( {\beta}_1^{PT} \) = 13.98 (p < .01) and \( {\beta}_1^C \) = 4.60 (p < .001). Nonetheless, like in Paris, the single linear regression models perform better than Model (IV). Finally, in Vienna, the significant effects of EDUd and UEMd on \( {\mathrm{Y}}_d^{PT} \) is not found in Model (IV), but the significant coefficient measured in the single linear regression model between \( {\mathrm{Y}}_d^C \) and EDUd becomes stronger (\( {\beta}_3^C \) = 67,652, p < .01).

3.2 Identifying SAV city-districts in European cities

As explained in Section 2, the selection of the relevant socio-economic well-being indicator is first explained for every city, before the performance of car travel (C) and public transportation (PT) are compared and the ‘SAV identification matrix’ is applied (see Fig. 3).

Fig. 3
figure 3

SAV district identification matrixes per city

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3.2.1 Paris

In Paris, EDUd has an effect on both \( {\mathrm{Y}}_d^{C,} \) and \( {\mathrm{Y}}_d^{PT} \). However, INCd explains a greater share of the change in \( {\mathrm{Y}}_d^C \), and as SAVs offer a great opportunity for low-income households to gain improved \( {\mathrm{Y}}_d^C \), both INCd and EDUd are included in the identification process. Furthermore, Paris offers greater accessibility by car in every district (d), thus creating a vast opportunity for the deployment of SAVs.

Figure 3 shows the two identification matrixes for Paris’ political core. Applying INCd in the identification matrix highlights how strongly accessibility \( {\mathrm{Y}}_d^{C, PT} \) could be improved in districts d12, d13, d14, d17, d18, d19 and d20, increasing \( {\mathrm{Y}}_d^{C, PT} \) by more than 100′000 shops within 30 min. Also, d10 and d11 would potentially improve their \( {\mathrm{Y}}_d^{C, PT} \) by 50′000 to 100′000 shops. Similarly, EDUd spotlights the same d, except of d14 which performs better in terms of socio-economic well-being and d17 which performs clearly below average here.

3.2.2 Berlin

In Berlin, the selection of a significant socio-economic well-being variable is more difficult, as the three single linear regression models do not show any relationship between \( {\mathrm{Y}}_d^{C, PT} \) and the socio-economic well-being indicators. However, since EDUd is positive and significant in the multiple linear regression models, confirming H3 for both dependent variables, it is selected. d5, d9, d10 and d12 have the lowest accessibility rates both by PT and C. The latter promises larger improvements in Berlin with possible improvements within 30 min between 10′000 and 20′000. However, in order to improve Berlins urban populations’ socio-economic well-being, policymakers should focus on districts d1, d5, d8, d10 and d12, where the educational index scores below average (see Fig. 3).

3.2.3 London

As displayed in Section 3.1 there is a significant effect of both INCd and EDUd on \( {\mathrm{Y}}_d^{C, PT} \) in London, confirming H1 and H3. Therefore, both these socio-economic well-being indicators are included in the second part of analysis.

Since London is the only city where \( {\mathrm{Y}}_d^C \) does not outperform \( {\mathrm{Y}}_d^{PT} \) in every district, the identification matrixes in Fig. 3 show four fields, as described in Section 2.2. The benefits of improving \( {\mathrm{Y}}_d^{C, PT} \) by C are limited to a maximum of 20′000 more shops within 30 min. On the contrary, the difference ∆ between \( {\mathrm{Y}}_d^{PT} \) and \( {\mathrm{Y}}_d^C \) can reach up to more than 330′000 shops (see d1). When applying either socio-economic well-being variable (INCd or EDUd), the identified SAV districts in the bottom left corner are: d4, d8, d11, d16, d17, d26 and d29. The Sutton borough (d29) performs slightly below average in terms of INCd, while its EDUd equals the city average. The borough of Havering (d16) has the highest potential of improvement.

3.2.4 Vienna

H2 and therefore, an effect of EDUd on \( {\mathrm{Y}}_d^{C, PT} \) is confirmed in Section 3.1. Therefore, this predictor is selected for the identification of SAV districts in Vienna.

In terms of accessibility \( {\mathrm{Y}}_d^{C, PT} \), C performs better than PT in all 15 districts where data for both means of transportation is available. The city mean educational attainment index score is of 1.97. In result, d2, d5, d11, d12, d15, d16 and d20 all find themselves below the mean and could potentially benefit from the deployment of SAVs (see Fig. 3). Especially, d11 offers a great potential, as it has by far the lowest EDUd of all districts d and it could increase its \( {\mathrm{Y}}_d^{C, PT} \) by over 30′000 shops within 30 min, almost quadrupling its current \( {\mathrm{Y}}_d^{PT} \).

4 Discussion and policy recommendations

AVs and especially shared AVs (SAVs) are expected to bring many benefits to its users, including, amongst others, improved security as well as the time and comfort gained for its users during travel. However, the expected reduced costs of car travel (C) through SAVs are likely to expand the urban sprawl, increase congestion within urban centres and cause a loss of employment opportunities in the transportation industry [4, 30, 31]. These negative externalities can be mitigated by policies aimed at ensuring the complementarity of SAVs to public transportation (PT) and their focused introduction so to improve social equity. As showcased by the ITF and confirmed in this paper, C offers better accessibility, in terms of the number of accessible shops within 30 min, in most European cities [21]. Nevertheless, this is only possible, since PT systems carry the majority of passenger traffic, relieving much of the potential C. Therefore, the three-step model developed in this paper, aims to purposefully deploy and support SAVs in city districts in which accessibility should be improved in order to increase accessibility and socio-economic well-being.

The first step of analysis showcases that there is a relationship between accessibility and socio-economic well-being in the investigated European urban areas, as this relationship is evidenced in the cities of Paris, London as well as Vienna and partially shown in the city of Berlin. Overall, educational attainment (EDUd) is the best-performing socio-economic well-being indicator for accessibility across the cities. It showcases significant positive effects on district-level accessibility to shops within 30 min by C and PT (\( {\mathrm{Y}}_d^{C, PT} \)) in the simple linear regression models for Paris, London and Vienna, as well as in the multiple linear regression models for Berlin and partially in Vienna, thereby providing strong evidence for H3 (see Section 3.1). This tendency can likely be explained by (1) the greater share of high-skill employment in urban centres ([9], pp. 27–32, 2) the greater number of higher education institutions in urban centres and (3) the stability of educational attainment over generations ([32], pp. 76–77).

However, given the reasoning above and the significant correlations between yearly income (INCd) and EDUd identified within all four cities analysed, the authors also expect a significant effect between INCd and \( {\mathrm{Y}}_d^{C, PT} \) confirming H1. The latter is only supported in Paris and London. On the one hand, this can be explained by the focus of the analysis on the political core and its districts, which creates a “small n” problem in all cities analysed, and especially in Berlin.Footnote 12 Hence, in future analysis, a neighbourhood-level analysis would be beneficial to resolve the “small n” problem and improve comparability between the observations.

On the other hand, urban planning policies (including centrally located social housing) in Berlin and Vienna, likely decelerated the urban sprawl and gentrification, rendering the effect of INCd less significant in these two cities. Meanwhile, if INCd has a significant effect on \( {\mathrm{Y}}_d^{C, PT} \), it has greater predictive ability than EDUd in relative city terms. Therefore, INCd is included in the identification process of SAV districts in Paris and London (see Section 3.2).

H2 is only confirmed for the effect of the unemployment rate (UEMd) on accessibility by C (\( {\mathrm{Y}}_d^C \)) in Paris and on accessibility by PT (\( {\mathrm{Y}}_d^{PT} \)) in Vienna. While UEMd is one of the most often measured and used economic socio-economic well-being indicators, it is less stable over time than INCd and EDUd, due to its responsiveness to cyclical downturns. In result, this predictor is not applied in any cities’ ‘SAV district identification matrix’.

In general, the simple linear regression models perform better than the multiple linear regression models in Paris, London and Vienna for \( {\mathrm{Y}}_d^{C, PT} \). While this hints at multicollinearity the Variance Inflation Factor does not show any alarming rates. In future research, it would be interesting to include data on employment and unfilled positions to gain more direct needs-based insight and see whether the models behave similarly, as described by Silva and Larsson (cit. in [22]) and to include more complex accessibility measures as proposed by Geurs & van Wee [16], Geurs et al. [14] as well as by [40]). However, we tried to the best of our knowledge to fill this gap with literature on the potential benefits and risks of SAVs. By doing so, we follow the logic typically found in equity assessment of transportation policy as described in the recent literature review by Guo et al. [17] and their three identified main components: population measurement, cost-benefit measurement as well as equity measurement.

Throughout this paper we have highlighted the importance of regulation to include equity in accessibility assessment alongside the introduction of SAVs. The ‘SAV district identification matrix’ is the very result of this. In literature, there are mainly three policy areas which can help to yield the benefits of SAVs and help improve overcome social and spatial inequity of urban inhabitants’ [12, 51]: (1) incentivise the usage of shared mobility including SAVs by overcoming technical and economic barriers in underserved low-income areas and (2) incentivise the usage of public transport, shared vehicles and other means of transport in well-served areas and (3) offer a platform to share data between service providers both public and private to coordinate and optimise service provision and accessibility.

In the realm of policies (1) and (2), this paper offers a data-driven three-step model identifying districts where the deployment and focused support of SAVs may prove helpful in overcoming the spatial barrier described in the STEPS model by Fleming [12] and Shaheen et al. [45]. In order to be successful, the policies must be adapted to the various business models for the introduction of SAVs in European cities: The desired focused and complementary deployment of SAVs to PT is achieved easiest if all means of transportation are organised by the same entity, allowing for a simplified data-generation and analysis. If SAVs are privately owned, regulation is necessary to oblige companies and the corresponding sharing systems to focus their services on the identified districts and overcome part of the market incentive at the core of their services. The latter is strongly connected to the policies necessary to defeat the economic barriers discussed in the STEPS model as subsidies should be included for low-income urban populations. This can be offered through a monthly or yearly budget to use the services in the SAV districts or through adapted pricings schemes according to a user’s registered address or depending on a users’ address of departure or destination. Overall, these policies must be adapted to spatial planning measures, as well as existing and potentially growing transportation needs in every city. Policy (3) is therefore detrimental to help monitor and evaluate policies and their impact. Economic policy measures to facilitate access to required technologies (smartphones, mobile data subscriptions and alternative payment systems) are relevant to either business models. These measures are also closely connected to policies directed at overcoming the social barriers, as the sharing economy mainly is used by younger, more affluent and well-educated adults. With EDUd being the best indicator for accessibility in European cities, it becomes evident that the urban populations with the greatest opportunity to improve their accessibility and socio-economic well-being need to be integrated in the sharing economy. Facilitating eased access to the required technologies and organising events to raise awareness is prerequisite to a successful deployment of SAVs.

5 Conclusion

In summary, this paper provides new evidence for spatial mismatches in European urban areas and offers insights on how SAVs can improve equity in accessibility and socio-economic well-being in the four European capitals analysed. Nevertheless, how SAVs will be deployed, which business models will prevail, how car-ownership will be affected and ultimately, who the largest beneficiaries of SAVs will be, remains to be seen. Certainly, policies must be introduced alongside and in preparation to the deployment of SAVs, in order to ensure their complementarity to PT, asses their effect on equity in accessibility and forego possible negative externalities. Therefore, policies must be implemented that are (1) data-driven, requiring the deployment and support of SAVs in areas with lower accessibility and socio-economic well-being, and (2) raise awareness among low-education as well as low-income populations and provide technologies and support to facilitate their access to SAVs. These policies will need to be continuously adapted, as to respond to user needs and market developments. Further research on a neighbourhood level and the application of broader accessibility measures, especially to include job-market data, are important as to secure the data-driven and well-directed approach described. The three-step model proposed in this paper can aid policymakers to maintain overview and aim at improving accessibility for European urban populations.