Low-emission zones, modes of transport and house prices: evidence from Berlin’s commuter belt

We study the impact of a tightening of a private driving restriction in Germany’s capital, the city of Berlin, on house prices in its affluent suburbs. Using geo-referenced data on train stations, motorway access points and offers of single-family houses for sale from Germany’s leading online property broker ImmobilienScout24 in a spatially staggered DiD framework, we find evidence for sizeable price growth premia for houses located in walking distance of train stations that lie within 30 min commuting duration to Berlin main station. Property located in immediate vicinity (5 min walking distance) of train stations within 30–40 min commuting duration, however, face penalties. Our findings are of relevance for the design of public infrastructure planning policies that seek to accommodate and facilitate changes in local demands for alternative and more environmentally sustainable modes of transport induced by private driving restrictions.


Introduction
Internationally, environmental policy to reduce pollution levels caused by vehicle traffic is implemented most forcefully by means of private driving restrictions. This holds true also for member states of the European Union (EU). However, EU member states are free to pursue policies of their own choice to cope with pollution limits upheld by the EU. This freedom of choice makes evaluations of the policies chosen by EU member states highly relevant for decision-makers and also potentially informative for the design of future policies.
The most common form of driving restrictions introduced in Europe to meet pollution limits are so-called low-emission zones (LEZs). Given their objective, most evaluations of LEZs are concerned with the ability of LEZs to reduce pollution levels. For Germany, several studies confirm that LEZs improve air quality (Wolff 2014;Malina and Scheffler 2015;Gehrsitz 2017). Nevertheless, some (26) German cities (including early LEZ adopters, such as the capital city of Berlin) currently face potential penalties invoked by the Court of Justice of the European Union, resulting from the inability of meeting air pollution limits, in accordance with the Air Quality Directive 2008/50/EC of the European Parliament and Council, throughout the years 2010-2016, making the discussion of past and potential future policies, aimed at improving air quality, an ongoing exigent topic of interest (European Parliament, Council of the European Union 2008; European Commission 2021; Court of Justice of the European Union 2021). By reducing air pollution, however, LEZs are likely to exert an impact also in other areas, as suggested by the literature which connects clean air to health, labor productivity, or the housing market. Notwithstanding, policy evaluations and empirical evidence on such broader effects are still comparatively scarce. We aim to fill part of this gap in the literature by studying whether LEZs cause higher (perceived) demand for public transport, as evidenced by differential offer price growth of houses within four different walking distance bands of train stations, following a significant tightening (in 2010) of the LEZ in the city of Berlin, Germany. Constructing treatment and comparison groups of houses based on their proximity to train stations, we use hedonic pricing models and a spatial difference-in-differences design in our analysis to explore potential spillover effects in the cities' affluent suburbs and commuting belt.
Analysis of the 2010 tightening of the LEZ in Berlin has three main advantages for identification. First, Berlin's LEZ is geographically isolated from similar driving restrictions in other cities, which precludes confounding effects from other LEZs in the city's surroundings. Second, the LEZ in Berlin comprises a large area that covers the majority of Berlin's city center. This makes it difficult, if not impossible, to avoid treatment by driving around the restricted zone. Third, the regions we study lie in Berlin's commuter belt in the surrounding federal state of Brandenburg. In these regions, people rely more heavily on a single mode of transport for commuting (cars or trains), a dichotomous setting which simplifies the analysis considerably and aids identification. 1 Moreover, for these areas in Brandenburg, the policy we study (the tightening of the LEZ in Berlin) constitutes arguably an exogenous shock, as the LEZ in Berlin was decided upon and implemented outside the administrative borders and jurisdiction of their own state. The population of commuters into Berlin we study in our setup is nevertheless sizeable and proliferating yearly since at least 2007. In 2019, 222,766 people commuted regularly from Brandenburg to Berlin, accounting for roughly 68% of the total commuter inflow (328,028 persons) into the city (Statistik der Bundesagentur für Arbeit 2020). The commuter inflow was and still is most pronounced in adjacent regions to Berlin. In 2008, roughly 40% of all commuters from adjacent counties commuted to Berlin. Corresponding figures for non-adjacent counties amount to an average of only 8.5% outbound commuters to Berlin. 2 In our analysis, we consider walking distance bands to train stations for housing to approximate the (perceived) demand for public transport. Our baseline estimation, which includes time and municipality fixed effects as well as property and neighborhood characteristics, suggests for the third half-year after the tightening of the LEZ in Berlin a price premium of 5%-points for property located in 5-10 min walking distance to a train station relative to the average asking price for property that lies in more than 20 min walking distance from such access points for public transport. We further investigate this finding by considering more homogeneous comparison groups which we obtain by (i) studying exclusively houses within 40 min walking distance to/from a train station and (ii) constructing commuting duration bands from sampled train stations to Berlin main station. The first restriction provides for more comparable observations around respective train stations. The second adjustment ensures that observations studied are similar also in their relative distance to Berlin. Former estimates for rail accessibility become quantitatively smaller and are estimated with less precision, resulting in statistically insignificant coefficients when we restrict the estimation sample to properties located in 40 min walking distance from train stations, and when we additionally impose a commuting duration band of between 40-60 min drive to Berlin, i.e. in our farthest commuting band. For the closest commuting band of 30 min maximum drive to Berlin, however, we observe a sizeable increase in asking price growth premia (of 9.15%-points). We probe the robustness of these findings in several ways. First, we extend the length of our observation period and consider an additional 18 months post treatment. Second, we add pre-treatment-trends in neighborhood-specific characteristics to account for potentially diverging patterns in region-specific house price growth before the LEZ tightening. Third, we include a full set of region-specific linear time trends throughout the observation period, in order to address potential concerns regarding diverging price growth patterns between treatment and control regions that may have prevailed absent treatment. Fourth, we include time-varying controls at municipality level to alleviate potential concerns about contemporaneous shocks that may confound the relationship of interest. In all sensitivity tests, observed price premia patterns prove robust for housing within 5-10 min walking distance to train stations. Furthermore, we consider various stratified estimation samples based on direct connectivity to Berlin and the type of train stations by kind of service provided. These and further explorations support the notion that proximity to train stations is valued differently in different distance bands around Berlin.
Our results also indicate price penalties for houses in immediate walking distance (up to 5 min) to train stations in our second closest commuting band (30-40 min driving duration to Berlin main station). This finding is in line with the literature which identifies close proximity to train stations as a disamenity, resulting from noise pollution, congestion, or anticipated crime nearby such stations (Bowes and Ihlanfeldt 2001). The same applies to our results that indicate price premia for houses at marginally farther walking proximity (5-10 min walking distance), complementing previous findings by Xu et al. (2015) that indicate similar price premia for housing in vicinity of train stations after the implementation of a private driving restriction in Beijing.
Our findings contribute to the literature in several ways. First and foremost, we provide first empirical evidence for a growth premium in asking prices for housing in vicinity of train stations caused by a non-local driving restriction in the form of a LEZ. Second, our analysis connects two strands of literature, research that uses housing market data and from data by the State Office for Statistics Berlin-Brandenburg (Amt für Statistik Berlin-Brandenburg), and the Federal Employment Agency (Bundesagentur für Arbeit-BA).
Footnote 2 (continued) hedonic pricing models to identify demands for clean air, respectively access to public transport stations, and studies that evaluate the effectiveness of private driving restrictions to reduce air pollution. We connect these strands of literature and contribute to the same by using hedonic pricing models to identify the (perceived) demand for alternative transportation modes following the tightening of a private driving restriction in the form of a LEZ. Third, we extend existing analyses of effect heterogeneity by considering different walking distance and driving duration bands, which we construct from actual walking or driving durations and not just Euclidean (or linear) distances in miles or kilometers commonly used in the literature. Last but not least, our analysis shows that housing data based on asking prices, which is more easily accessible to researchers, produces similar findings to those obtained from transaction data, as evidenced by the study of Xu et al. (2015) who use a similar empirical research design.
The remainder of this paper is structured as follows. Section Background describes in detail the Berlin LEZ policy and discusses the relevant literature. Section Empirical strategy and data describes the data and empirical framework. Section Results presents our baseline results and discusses various additional explorations we carried out. Finally, section Conclusion provides a brief summary of our main findings.

Low-emission zones in Germany
Driving restrictions are used internationally as policy means to improve ambient air quality. However, great differences exist in the type and nature of private driving restrictions enforced in different countries. For example, private driving restrictions based on vehicle license plate numbers have been introduced in Mexico City or Beijing. In Europe, including Germany, in contrast, the most prominent form of private driving restrictions are lowemission zones (LEZs). EU directives, which put binding thresholds for measured air quality into legislation, caused governments to enact policies to meet such limits. Wolff and Perry (2010), who also describe the European Union's directives in more detail, show that between 2005 and 2007, 79 cities in Germany violated the daily limits. As the regulated pollutant was a prime product of vehicle traffic, German cities responded to these violations most aggressively by imposing private driving restrictions in the form of LEZs.
A LEZ targets vehicles by restricting them from entering a predetermined area of a city if they are of a certain emission category. Driving restrictions were typically enforced in areas that recorded excess pollution levels, such as city centers that suffered from high volumes of vehicle traffic. In contrast to vehicle restrictions that target only parts of specific streets (as currently considered in different cities), LEZs hence comprised bigger areas that made it difficult to circumvent the restricted regions. For entry rights into LEZs, motor vehicles were assigned emission classifications based on their emission level and other attributes, such as motor type. Emission classifications ranged from Euro 1 to Euro 4. 3 Euro 1 vehicles are the most and Euro 4 vehicles the least emitting type. LEZs were generally introduced in three stages based on these emission classifications. First, so-called stage 1 LEZs were introduced, which only restricted Euro-1-type motor vehicles, a stage 2 LEZ also restricted Euro 2 vehicles, and a stage 3 LEZ in addition also vehicles classified as Euro 3 vehicles. Early adopters of LEZ policies generally followed this stepwise implementation. Late adopters, in contrast, sometimes skipped stages, implementing, for instance, a stage 2 or stage 3 LEZ immediately. Decisions on LEZs, their type and timing, are taken by the respective cities/municipalities. The German Environment Agency (Umweltbundesamt-UBA) provides a summary and history of LEZs in Germany (Umweltbundesamt 2020a). The first LEZs were implemented in 2008. Since then, a cumulative total of 58 LEZs have been installed in Germany. 4 Disregarding cities that jumped stages, it took on average 2.4 years to update a stage 1 LEZ to a stage 2 LEZ, and 1.6 years to transit from stage 2 LEZ to stage 3 LEZ. In total, 28 LEZs skipped the first stage, of which 17 also skipped the stage 2 tightening and introduced a stage 3 LEZ directly. Implementing a stage 3 directly can be viewed as a means for 'catching-up' with early adopters. Direct jumps to a stage 2 or stage 3 LEZ occurred occasionally from 2010 onwards. However, each of the 19 LEZs that were implemented since 2013 skipped at least one stage.
Although Berlin was one of the first cities to introduce a LEZ in Germany, 5 it was and still is the only city that has moved directly from a stage 1 LEZ to a stage 3 LEZ. The LEZ in Berlin is one of the biggest in Germany, covering roughly 88 km 2 or 10% of the city's entire area, hosting about one million inhabitants, i.e., well above a quarter of the city's population. The LEZ in Berlin was first announced on 16th August 2005 (Berlin Senate 2005). The announcement envisaged a stage 1 LEZ (restricting vehicles up to Euro 1) taking effect on 1st January 2008 that was to be replaced by a stage 2 LEZ (restricting vehicles up to Euro 2) on 1st January 2010. However, on 20th March 2007, the initial LEZ policy was changed (Berlin Senate 2007). While the scheduled introduction of the stage 1 LEZ remained unchanged, the planned update to a stage 2 LEZ was replaced by a direct stage 3 LEZ update that restricts vehicles up to Euro 3 classification instead of only Euro 2. Although in 2021 only roughly 13.8% of all registered vehicles in Berlin are restricted by the LEZ (Kraftfahrt-Bundesamt 2021), descriptive statistics suggest a relatively slow updating mechanism in the overall car fleet. The unexpected change in the initially announced policy might have introduced some degree of uncertainty regarding future restrictions. This makes a purchasing decision of a nonrestricted EURO-4 vehicle right before the policy tightening in 2010 a risky long-term venture since there is no guarantee that this vehicle will remain unrestricted. Hence, purchasing a EURO-4 vehicle to evade the restriction may be considered a relatively expensive option to avoid the treatment, when commuters do not know with certainty if the vehicle can be utilized in the near future or not. In fact, changes in nonrestricted vehicle numbers appeared rather reserved. On the day of the stage 1 LEZ implementation in 2008, a total of 168,787 Euro-1-type vehicles were registered in Berlin (Kraftfahrt-Bundesamt 2008). These vehicles, which accounted for 15.5% of all registered M 1 -category vehicles 6 in Berlin at the time, were no longer allowed to enter the city's center. On the day of the tightening of the policy to a stage 3 LEZ in 1 3 2010, in contrast, a total of 600,686 registered vehicles, or 54.3% of all registered M 1 -category vehicles in Berlin, still had an emission classification of Euro 3 or worse (Kraftfahrt-Bundesamt 2010). This great increase in the number of vehicles that were denied entry to the Berlin LEZ area illustrates how severe, in terms of bite and coverage, the immediate jump from a stage 1 LEZ to a stage 3 LEZ was in Berlin. This abrupt and severe tightening of the LEZ in Berlin in January 2010 constitutes our treatment of interest. The LEZ in Berlin and its tightening is of great interest for methodological reasons, as it constitutes a regionally isolated private driving restriction that is not affected and confounded by other LEZs in the city's hinterlands, unlike the LEZs in other large cities in Germany, such as those in Stuttgart, Cologne or Frankfurt, which precludes potential external spillovers to Berlin and the regions surrounding it. The three closest LEZs to Berlin are located in Magdeburg (150 km distance), Halle (170 km), and Leipzig (190 km). Furthermore, Magdeburg and Halle implemented their LEZs only in September 2011, which lies outside our baseline sampling period. The LEZ in Leipzig should also be of minor concern at best, as it is located even farther from Berlin and was implemented also only towards the end of our sample period in March 2011.

Previous research
Our analysis builds on and connects two bodies of literature, studies on the effects of private driving restrictions on air quality and studies on the effects of air quality and public transport stations on house prices. Private driving restrictions based on digits of license plates, which are referred to as an odd-even-rule, were implemented as early as 1989 in Mexico City and later introduced across Latin America (Buenos Aires, Bogota, Lima, Sao Paulo, or Santiago de Chile) and also Asia (Beijing, Tianjin or New Delhi) (Davis 2008;Guerra and Millard-Ball 2017). These policies restrict the use of vehicles according to the (last) digit(s) on license plates for certain days of the week. The policy did not yield any improvements in ambient air quality in Mexico City (Davis 2008). Several reasons may account for this lack of effectiveness. Davis argues that the population simply registered a second car to circumvent the restriction and Guerra and Millard-Ball (2017) suggest that the population avoided the restriction by deviating to less costly behavioral responses, such as shuffling travel days. Sun et al. (2014) come to a similar conclusion for the private driving restriction implemented in Beijing. Overall, in fact, no consistent pattern emerged in empirical analyses of the odd-even-rule and its effectiveness in reducing air pollution. Individual results are also difficult to generalize because of geographic and socio-economic differences of countries and differences also in research methodologies employed that tend to fuel diverging results, as argued by Sun et al. (2014).
In contrast to the odd-even-rule, the LEZ is a form of driving restriction that, once implemented, upholds the restriction continuously, i.e., an 'on/off-switch' altering according to the day of the week is not present. Early evaluations of LEZs mostly took the form of case studies due to the small number of cities that had yet implemented such a policy and used but simple analyses of changes over time in ambient air quality measured by particulate matter and nitrogen dioxide. Cyrys et al. (2014) compile findings which suggest an improvement in particulate matter (PM 10 ) 7 measures in Munich, Cologne, and Berlin. The study by Wolff (2014) is the first sophisticated empirical analysis of LEZs and their impact on air quality in Germany. Exploiting the staggered introduction of LEZs in Germany, the study uses a difference-in-differences design with fixed effects to control for time-invariant characteristics of individual cities. Findings from the most homogeneous sample studied suggest an average decline in fine particulate matter of roughly 9% in cities that host a LEZ compared to cities that do not. These findings are supported by similar work by Malina and Scheffler (2015) who control also for local traffic volume, and Gehrsitz (2017) who uses the longest panel and provides the most recent analysis. Gehrsitz (2017) finds a decrease in average particulate matter emissions of roughly 4-8% in LEZ cities. The study also considers the effect of LEZs on infant health but does not find evidence for an impact. Margaryan (2021) studies direct health effects of LEZs, using data on outpatients diagnosed with cardiovascular diseases for its health measure. The study also finds improvements in the levels of fine particulate matter and nitrogen dioxide and furthermore a reduction of 2-3% in the number of patients with cardiovascular diagnoses. Similarly, while also providing evidence for improvements in ambient air quality, Pestel and Wozny (2021) find a reduction in the share of hospitalizations of inpatients diagnosed with diseases of the circulatory system and chronic lower respiratory diseases. In summary, this branch of literature hence suggests that LEZs do improve air quality, a finding that is backed by supporting evidence from the analysis of other outcomes, such as health measures.
The second and larger body of literature on which we build, and which we connect to the afore-discussed literature on LEZs and their effects, is concerned with the consequences of air pollution in different areas, including the housing market. Health studies are most numerous, providing vast evidence for a causal link between high levels of air pollution and negative health effects (Deryugina et al. 2019;Chay and Greenstone 2003;Currie and Neidell 2005;Pope and Dockery 2006). Connected to this literature on health impacts are analyses which tie these impacts of pollution to labor outcomes. Hanna and Oliva (2015), for example, discuss effects on labor supply at the extensive margin. Analyzing labor productivity and variation in ozone levels, Zivin and Neidell (2012) were the first to explore potential effects on labor at the intensive margin. They find a 5.5% decline in the productivity of agricultural workers. Declines in labor productivity were also found for PM 2.5 and an indoor pollution setting (Chang et al. 2016(Chang et al. , 2019. Concerning impacts on housing markets, first studies date back more than 40 years (Ridker and Henning 1967;Harrison and Rubinfeld 1978) and discuss the demand for clean air based on the hedonic pricing method (Lancaster 1966;Rosen 1974). More recent work in this area by Chay and Greenstone (2005) studies regulations for U.S. counties imposed by the Clean Air Act Amendments, providing evidence for a 0.2-0.4% increase in housing values caused by a one μg/m 3 reduction in total suspended particles. Recent studies have also focused on the ability to approximate the demand for clean air by, for instance, analyzing the effects of industrial plant openings and shutdowns on housing prices. Currie et al. (2015) suggest a negative link between housing values and the opening of an industrial plant in five large U.S. states (Texas, New Jersey, Pennsylvania, Michigan, and Florida) analyzed in the study. They find a decrease in housing values of 11% within a 0.5-mile radius of a plant opening. Plant closures, in contrast, do not show any impact on housing values. A potential explanation for this finding is that negative effects caused by a closure, e.g. a decrease in labor demand, might cover up potential improvements in local amenities such as better air quality. This view receives support by the study of Bauer et al. (2017) which considers closures of nuclear power plants in Germany. The study finds negative effects of plant closures. Unlike industrial plants, nuclear power plants are not emitters of local pollution. Hence, closures of such sites do not cause an immediate improvement in local air quality. Bauer et al. (2017) find that housing values decreased by 4.9% near nuclear power plants that shut down, which suggests that local negative economic effects of plant closures affected house prices more than potential safety gains (positive changes in local amenities) associated with closures of nuclear power plant sites.
As the above review shows, air pollution can affect different areas of the economy. However, private driving restrictions, like a LEZ, are likely to exert also direct (and possibly unintended) effects in certain areas, not just indirect effects by reducing air pollution. To study such direct effects, the scope of outcomes considered in empirical analyses needs to be broadened beyond mere measures of ambient air quality and areas affected by pollution levels. Concerning the former, health outcomes have been analyzed for different driving restrictions (Zhong et al. 2017), including LEZs (Gehrsitz 2017;Margaryan 2021;Pestel and Wozny 2021). Productivity effects too have been discussed in the context of LEZs (Lichter et al. 2017) based on worker productivity data of professional football players in Germany (measured by the number of passes played in games of the German Bundesliga) and city data on LEZs. To the best of our knowledge, however, no studies have yet inquired into the effects of LEZs on housing markets. This is surprising, and also a clear gap in the literature (one we aim to fill), as housing constitutes an immobile durable consumption good and major wealth asset whose valuation depends critically on neighborhood amenities and whose price responds (shows measurable changes) very quickly if local amenities change or are merely expected to change. The closest and most relevant empirical work in this context is the study by Xu et al. (2015) which analyzes the implementation of the oddeven-rule in Beijing and its potential effect on the demand for public transport, as measured by housing market data. Unlike the general housing literature which connects the (dis) amenity provided by a railway/public transport station to housing values (see Debrezion et al. (2007) for a meta-analysis), Xu et al. (2015) study the additional willingness to pay for housing in the vicinity of subway stations that results from a private driving restriction, using a spatial difference-in-differences model in which they compare housing prices close to subway stations with housing prices further away before and after the implementation of the private driving restriction. Xu et al. (2015) find a 1.8-2.7%-points increase in house prices within a 2 or 3 km radius of subway stations. Although confirming previous findings in the literature that link proximity to railway stations to price premia, the study also finds that no such gains materialized within the closest distance band of 1 km around subway stations. Xu et al. (2015) attribute this finding to the possibility that inhabitants in this 1 km distance band valued the proximity to a subway station (used subways as a prime mode of transport) already before the driving restriction so that this restriction did not exert any additional price effect when it was implemented. A study by Bowes and Ihlanfeldt (2001), in turn, finds negative effects of railway stations on housing values in immediate proximity of such sites. Stations hence appear to constitute a disamenity if close, because of increased noise levels or criminal activity, but an amenity if located a little further away. The study by Bowes and Ihlanfeldt (2001) illustrates that analyses of the effects of railway station proximity should take great care to account for such qualitative changes in the valuation of access points for public infrastructure.
Similar to the study by Xu et al. (2015), we aim to identify and quantify potential asking price premia for property in proximity to railway stations following the introduction of a private driving restriction. However, instead of considering the very urbanized region in which the driving restriction is imposed, as done in Xu et al. (2015), we will focus on the suburban and more rural regions surrounding Berlin, i.e., adjacent counties in the federal state of Brandenburg, to identify potential spatial spillover effects of the LEZ in Berlin.

Data and setting
We use three main types of data in our empirical analysis: property data from ImmobilienScout24 8 , Germany's leading online property broker, 9 geo-referenced locations of train stations from the public transport authority for the federal states of Berlin and Brandenburg (Verkehrsverbund Berlin-Brandenburg (VBB)), and geo-referenced locations of motorway access points from the road construction administration in the federal state of Brandenburg (Landesbetrieb Straßenwesen Brandenburg).
The property data we use covers the universe of monthly geo-referenced individual offers of single-owner-occupier houses for sale, which were posted on ImmobilienScout24 between January 2007 and September 2016. Covering a large part of the German housing market, the data are suitable for the analysis of property prices at fine spatial levels (Bauer et al. 2013;Georgi and Barkow 2010). ImmobilienScout24 data have been utilized in recent empirical research on location-specific exogenous shocks and their effects on regional property prices of residential housing in Germany, such as nuclear power plant closures following the Fukushima Daiichi incident in 2011 (Bauer et al. 2017), the establishment of wind turbines (Frondel et al. 2019), and refugee immigration in the heyday of the 2015 European refugee crisis (Kürschner Rauck and Kvasnicka 2018). The Immobil-ienScout24 data contain an average of 85 thousand observations on detached (77.4%) and semi-detached (22.6%) houses per calendar month. Information on house prices and their characteristics stem from offer listings that are posted by private owners and real estate agents on the online broker's platform. 10 We pool observations of house listings in the federal state of Brandenburg into a pre and post period of equal length, which we use in spatially staggered difference-in-differences (DiD) regressions with regional fixed effects at a small administrative unit (municipality). Figure 1 summarizes in a timeline the framework of our analysis, which we describe more formally in section Empirical framework. To study the effect of the tightening of the private driving restriction in Berlin on house prices in its broader commuter belt in the federal state of Brandenburg, we exploit for identification the exogenous shock provided by Berlin's, to this date unprecedented, 'jump' (direct transit) from a stage 1 to a stage 3 low-emission zone (LEZ) on 1st January 2010. The pre-LEZ (stage 3) period we consider covers the months January 2008 to June 2009, and the post-LEZ (stage 3) period the months January 2010-June 2011. 11 In the simplest variant of 8 See https://www.immobilienscout24.de/ and Bauer et al. (2013) for a detailed description of the data. 9 In an average month in 2008, approximately 1.2 million objects were listed on ImmobilienScout24, and around four million registered users (potential buyers and renters) participated on the platform (Enderle 2009). Furthermore, according to the Unique Visitors ranking of a market research institution (comScore Media Metrix), ImmobilienScout24 had a market share of approximately 63% of the German online property market in March 2016 (ImmobilienScout24 2017). This figure, however, understates ImmobilienS-cout24's true market coverage, as the overlap between ads posted on ImmobilienScout24 and competing online real estate brokers as well as alternative means to property marketing is large, since landlords and letting agents typically market available property via several available channels. 10 The data facilitate the analysis of instantaneous pricing responses to region-specific shocks since property-specific information, e.g., its price, may be modified at any time during the purchased posting duration. Fees payable depend on the listing term (two weeks, respectively one or three months) and offer type (houses, respectively apartments on offer for sale or rent). 11 Besides avoiding a contamination of the control group related to anticipatory pricing behavior closer to the implementation date, excluding data covering the months July to December 2009 additionally minimizes potential confounding influences provided by unexpected temporary restrictions to a part of Berlin's settings considered, the treatment group comprises observations on houses located within four walking distance bands of train stations (STNs), houses within 5 min walking distance, houses in 5-10 min walking distance, houses in 10-15 min walking distance and houses in 15-20 min walking distance of STNs. Houses listed for sale in regions more than 20 min walking distance from STNs are assigned to the control group. As dependent variable, we consider the log price of a house offered for sale.
We exclude from our estimation sample observations on houses for which information on property-specific characteristics is missing or for which there is no other listing in its municipality in the total 36 month period under investigation. We also exclude special property, such as villas, farmsteads, and bungalows as well as offers with extreme characteristics. 12 Our baseline estimation sample consists of approximately 130 thousand monthly observations on about 39 thousand detached and semi-detached houses. The detailed information on individual houses contained in these data and the size of our estimation sample allow us to control for standard hedonic items in our house price regressions, such as the base area and living space [ m 2 ] of a house (amongst others). Table 1 provides a full list of summary statistics on these house-specific attributes for the estimation sample by pre-and post-LEZ (stage 3) period. In addition, Appendix Table 3 summarizes the corresponding mean and standard deviation of each variable by distance to train stations for both the preand post-LEZ (stage 3) period. Offer prices for houses increased from the pre-to post-LEZ (stage 3) period by, on average, 6,582 Euro. In addition, houses on offer in the post-LEZ (stage 3) period are on average three years older, feature a larger average base area and living space (of 43.3, respectively 2 square meters), and spread over 4.74 rooms, compared to 4.67 rooms in the pre-LEZ (stage 3) period. The proportion of houses listed that are currently under construction also declined pre-to post-LEZ (stage 3) implementation by, on average, 1.1%-points, whereas the share of detached houses on offer for sale increased from 83.3% to 86.3%.
The second type of data we use is open access data from the VBB which provides georeferenced access points to public transport stations (Verkehrsverbund Berlin-Brandenburg Fig. 1 Timeline of setting, framework of analysis and data sampling strategy 12 We exclude houses offered for a price less than 1,000 or more than 10 million Euro, houses with less than one or more than 11 rooms, houses with a living space less than 25 or more than 500 square meters, houses with a base area of less than 50 or more than 500 square meters, and houses that are dilapidated. We also exclude houses under construction with an expected duration until completion exceeding two years and houses that are aged 200 years or more. Footnote 11 (continued) public transportation network, which occurred during these months. Section Empirical Framework provides a detailed discussion of these disruptions. 2017). The data cover, and identify, stations that serve regional traffic via trains and stations that serve local public transportation. We disregard information on bus and tram stations and manually checked the operation status of stations identified in the data as being closed. Our final data set covers only counties in Brandenburg that share a direct border with Berlin, and identifies 227 train stations, which function as reference points from which we calculate the walking distance bands (described above) for individual property in our data with the STATA module osrmtime (Huber and Rust 2016) using the shortest walking distance routes between each pairwise combination of sampled properties and train stations.
For our spatial difference-in-differences analysis, we define treatment and control group based on these walking distances (i.e., a purely local attribute) of observed property to train stations. The policy studied, however, was implemented in Berlin. As our analysis focuses on potential effects in the commuter belt of Berlin, the LEZ in Berlin can be considered a non-local/distant policy treatment. In order to emphasize the importance of Berlin as a commuter destination to its surrounding regions we utilize special data on the total number of commuters to Berlin and other municipality-level characteristics, provided by the State Office for Construction and Transport (Landesamt für Bauen und Verkehr-LBV) as time series data refined from data by the State Office for Statistics Berlin-Brandenburg (Amt für Statistik Berlin-Brandenburg), and the Federal Employment Agency (Bundesagentur für Arbeit -BA). Panel (a) of Fig. 2 illustrates the relevance of Berlin for surrounding regions by displaying the share of the population in the respective municipalities in Brandenburg commuting into Berlin in 2008. Counties in Brandenburg, that are adjacent to Berlin have an average share of 10.2% of the population (or close to 40% of commuters) commuting to Berlin. In contrast on average only 1.2% of the population (or roughly only 8.5% of commuters) from the other counties in Brandenburg commute to Berlin. A systematic pattern between commuter inflow into Berlin from its suburbs becomes evident: regions/municipalities located closer to Berlin show higher numbers of workers commuting to Berlin. This holds true for previous and later years, as well. We therefore, restrict Berlin's commuter belt in our estimations to counties in Brandenburg sharing a direct border with Berlin. Nevertheless,  (1)) and post-LEZ (stage 3) period January 2010-June 2011 (column (2)). Standard deviations are reported in square brackets

Pre-LEZ (stage 3)
Post-LEZ (stage 3) (1) House price [EUR] 198, 860 [117,977] 205, 442 [127,999] log we also construct three commuting duration bands to analyze outcomes for different commuting distances, measured in driving duration, to Berlin main train station. The calculation of shortest driving durations is again done with the STATA module osrmtime (Huber and Rust 2016). Constructed commuting duration bands are divided into (i) 30 min or less, (ii) beyond 30-40 min, and (iii) beyond 40-60 min. 13 Panel (b) of Fig. 2 displays the spatial distribution of train stations in Brandenburg and provides a visual reference for the constructed commuting bands. Out of the sampled 227 train stations, 33 are located in the closest commuting belt, 54 stations are located in 30-40 min driving duration from Berlin main station, 59 train stations lie in the 40-60 min driving duration band, and the remaining 81 stations are located in 60 or more minutes driving duration to/from Berlin main station. The third type of data we use contains information on the road network of Brandenburg, which we obtained from the Infrastructure for Spatial Information in the European Community (INSPIRE) and its corresponding web feature service (WFS) provided by the federal state of Brandenburg (Landesbetrieb Straßenwesen Brandenburg 2018). Metadata, such as geo-referenced motorway access points, are accessible via this interface. We used geographic Fig. 2 Population share of outbound commuters to Berlin (at municipality-level) and train stations in Brandenburg by commuting duration to Berlin main station. Notes Panel (a) displays the share of the population in a respective municipality that is commuting to Berlin (darker shades of grey indicate higher shares of commuters). Panel (b) depicts exact (geo-referenced) locations of train stations for counties in Brandenburg that share an administrative border with Berlin by commuting duration (marked by different symbols (see legend) and different shades of gray (darker shades indicate more distant locations)) to Berlin main station (marked by a cross). The LEZ inside the administrative borders of Berlin is also marked and highlighted by hatching information system software to extract these metadata. 14 We identified a total of 79 geo-referenced motorway access points in Brandenburg's adjacent counties to Berlin. Analogous to train stations in our research design, we use information on the location of motorway access points in our empirical analysis to identify the proximity of a house to the closest motorway.

Empirical framework
To identify the effect of the tightening (from stage 1 to stage 3) of Berlin's low-emission zone (LEZ) on prices of residential houses in the federal state of Brandenburg that lie in Berlin's commuter belt, we apply a spatially staggered difference-in-differences approach by estimating variants of the following hedonic price function: where the dependent variable, log House Price igmt , is the log offer price (in Euro) of house i in municipality m, respectively in 1 km grid g, in month t. To capture the piecewise common time-trend in asking prices between regions as well as region-specific characteristics that are time-invariant, all regressions include a full set of time fixed effects (quarterly dummies), denoted by t , and region fixed effects at a small administrative unit (municipality), denoted by m . In addition, a set of hedonic characteristics of houses and their location, denoted by vector X igt , is included in the regressions to address potential changes in local (within-municipality) property compositions over time 15 as well as region-specific trends in house price growth related to pre-treatment neighborhood characteristics at 1 km grid level. These grid-level characteristics introduce two types of additional controls to our set of explanatory variables, two for socio-economic and one for property-compositional characteristics of neighborhoods at fine spatial level, which we obtained from the RWI-GEO-GRID (Breidenbach and Eilers 2018;microm Consumer Marketing 2016). These controls include the unemployment rate (RWI and microm 2017f), the share of the foreignborn population (RWI and microm 2017e), and the share of buildings that are predominantly in commercial use in 2009 (RWI and microm 2017b). POST t is a set of biannual indicators for the three consecutive half-years in the post-LEZ (stage 3) period. Notably, the grid-level controls enter both in levels and as interactions with these post-LEZ (stage 3) period indicators and intend to control for spatial differences in housing prices related to differences in socio-economic compositions of neighborhoods before the treatment as well as differential trends in neighborhood-level house price growth in the post-LEZ (stage 3) period that are related to pre-treatment local economic conditions, housing market structure, and neighborhoods' ethnic composition. Since it is a priori unclear at which distance threshold train stations (STNs) may exert an effect on house price growth and what sign and functional relationship (linear or non-linear) any such effects may have to distance to Berlin, we use piece-wise constant specifications that consider multiple indicator variables at staggered walking distance bands from STNs. Specifically, the vector DIST i,STN min comprises a set of binary variables that equal one for houses located within 14 We used the open source software QGIS to export information on motorway access points. 15 Appendix Table 3 provides a complete list of these house-specific attributes by distance to train stations, i.e., for treatment and control regions.
( ∈ 5, 5 − 10, 10 − 15, 15 − 20 ) min walking distance of a STN. The treatment effect of interest is given by the interaction between these regional indicators and the post-LEZ (stage 3) period indicators. We also aim to take into account a potentially confounding influence of the relationship of interest by conditioning on the variable DIST i,MOT 10 min , which is an indicator that captures access to motorways (MOT) within 10 min driving distance by car from property i, and its interaction with the indicators for the post-LEZ (stage 3) period. The error term is denoted by igmt . Note that the model does not identify the coefficients on the biannual indicators for the post-LEZ period, POST t , i.e. the counterfactual time trend, since a full set of time indicators for individual quarters is included. Similarly, due to the inclusion of a full set of region fixed effects at municipality level, the vector of coefficients , which captures the time-invariant mean level-difference in offer prices between houses located within the four walking distance bands of up to 5 min, 5-10 min, 10-15 min, and 15-20 min, and houses located beyond the 20-minute walking distance threshold is identified only from municipalities that contain observations both in the staggered treatment and in the control region. Figure 3 illustrates our empirical strategy graphically. Listings of houses within 20 min walking distance of train stations (those within the dotted line) are assigned to the four subregions (within 5, 5-10, 10-15, and 15-20 min walking distance of STNs) that comprise the treatment group, listings located in regions beyond that threshold are assigned to the Fig. 3 Identification strategy. Notes The figure illustrates the assignment of individual observations on houses for sale in the estimation sample to the treatment group (within 20 min walking distance to a train station-threshold marked by the dotted line) and to the control group (beyond 20 min, alternatively within 20-40 min walking distance to a train station-threshold marked by the solid line) according to their exact (geo-referenced) locations control group. 16 In adapted versions of this model, we employ a regionally restricted estimation sample which disregards observations on property listed for sale in regions more than 40 min walking distance from STNs (solid line). This restriction effectively assigns a more homogenous subset of houses (those that are located in 20-40 min walking distance of STNs) to the control group. Maintaining this regional sample restriction, to obtain a plausible commuter-belt we consider in further explorations stratified estimation samples based on commuting duration bands of up to (and including) 30 min, 30-40 min, and 40-60 min driving duration to Berlin main station. We disregard distance bands in which train stations are located in more than a 60-minute drive to Berlin main station due to the small number of observations and their mismatch in terms of commuters to Berlin (see Fig. 2). Figure 4 illustrates the identification strategy for the two closest commuting bands from Berlin main station using actual data on the location of properties and train stations in our estimation sample. Houses are assigned to the treatment and control group according to the shortest walking distance to train stations, which in turn are assigned to commuting duration bands according to the shortest driving duration (by car) to Berlin main station.
In all specifications and estimation samples used, the vector of main coefficients of interest, , captures the percentage point difference in the pre-to post-LEZ (stage 3) change in average asking prices for houses that are located within each of the four walking distance Fig. 4 Example of the identification strategy for train stations in 30 min and 30-40 min commuting duration. Notes The figure shows Potsdam, a city located in the south-west of Berlin, and pinpoints exact locations of houses and train stations in our estimation sample according to different walking distance and driving duration intervals. Houses at farther distances from train stations are depicted by darker shades of gray bands of up to 5 min, 5-10 min, 10-15 min, and 15-20 min, relative to houses located in more than 20 min walking distance from STNs. Causal interpretation of this vector of coefficients relies on (i) the LEZ being the main treatment, i.e., no alternative treatment biasing estimates and (ii) the main identifying assumption that conditional on the above-mentioned controls, price trends would have evolved similarly in treatment and control regions absent treatment, i.e., absent the tightening of the LEZ in Berlin from first to third stage on 1st January 2010.
Concerning the former, the fact that Berlin's LEZ (tightening) is geographically isolated from other LEZs aids identification, however, does not account for the possibility that other potential alternative treatments might tamper with the analysis. One such phenomenon in need of discussion is a disturbance to a part of the public transportation infrastructure in Berlin, witnessed predominantly in the second half of 2009. Berlin's public transportation network connects the city via four main modes of transport: trams, buses, subways, and suburban trains (S-Bahn), which can be viewed as substitutes, i.e., they frequently connect same/conjoint stations in Berlin. More precisely, this distress affected the suburban train network from July 2009 until early 2010 and was referred to as the so-called 'S-Bahn crisis' (S-Bahn Berlin GmbH 2010).The cause of the disturbance was a derailed suburban train, whereafter additional checkups and train maintenance were scheduled in order to prioritize passenger safety. This resulted in temporary reductions in the available operational train fleet, which were frequently communicated by the S-Bahn Berlin through press releases (PRs) and repeated updates to train schedules (PR 08.05.09 and 05.06.2009). 17 On the one hand, a negative shock to S-Bahn services might affect house prices negatively, leading to a downward bias in estimated treatment effects, whereas, on the other hand, expectations of large scale investments into public transportation infrastructures may analogously induce an upward bias in the coefficient estimates of interest. However, just as in the case of traffic disruptions due to unforeseen bad weather conditions, any short-lived restrictions that affect trains or train lines randomly, should not interfere with our empirical analysis. Nevertheless, the presence of this contemporaneous phenomenon, begs the question of whether the LEZ tightening is the relevant/stronger treatment and also whether the two events can be distinguished from another.
We argue that the LEZ tightening constitutes the relevant treatment in focus since compared to the LEZ restriction, the reduction of the S-Bahn train fleet is: (i) not persistent, i.e., gradually fading in its intensity due to inspected trains rejoining the available operational fleet, and (ii) not covering a comprehensive area of Berlin. Moreover, fleet reductions were actively superseded by alternative transportation links, in form of regional trains and buses, in addition to the already existing substitutes (subways, trams, and original bus connections). We studied relevant PRs from the S-Bahn authorities covering the years 2009 and 2010 and checked corresponding S-Bahn timetables, in order to provide some insight into the extent and duration of the shock. A total number of 136 press releases (74 in 2009 and 62 in 2010) were issued in these two years. In 2009, a total of 23 press releases cover updates on the train network and provide information on alternative modes of transport. 21 of these 23 updates fell between July and December. In 2010, a total of nine press releases relevant to this context can be identified, where the first six releases communicated improvements of the status quo. The remaining three network updates occurred in December and were accompanied by issues resulting from unexpected weather conditions. In both years, two press releases were issued due to restrictions caused by bad weather conditions. It needs to be noted that restrictions in form of the unavailability of a train does not necessarily result in canceled connections. Such restrictions are gradually affecting the suburban train network by, for instance, operation of shorter trains (fewer wagons) or less frequent trips (every 20 instead of 10 min), before heavily impacting the network with major cancellations (PR 26.06.09). A first emergency timetable for S-Bahn traffic was implemented on 20th July 2009, when only a third of the S-Bahn train fleet was available for operation (PR: 16.07.2009). The lowest number of available trains was reached during September 2009, with only 163 available trains for about 20 days (PR 07.09.09, 11.09.09, and 28.09.09). At the time, responsible authorities strived to minimize any disruptive effect on the transportation network by actively installing buses and also trains provided by the S-Bahn Munich and S-Bahn Stuttgart to maintain train connections and frequencies, in particular, during peak travel times. Only four lines were temporarily not serviced by suburban trains, the remaining ten lines were affected by lower train frequencies (PR 07.09.09, 11.09.09, and 28.09.09). Availability of the train fleet rose gradually thereafter, with 429 trains back on track in November, allowing for 95% of the usual network to be serviced again (PR 18.11.09). Fleet availability fluctuated further into 2010, albeit never plummeting to figures as low as those witnessed in September 2009 again. Compared with a persistent restriction, such as the LEZ tightening we study, short-term disruptions of this kind should arguably not affect long-term investment decisions, such as housing (or vehicle) purchases. Moreover, any announced investments in light of the S-Bahn crisis mainly concerned improvements in station-based services, in particular, information transmission to passengers, rather than new expansions or updates of the train fleet (PR 1.10.09). 18 Nevertheless, in our empirical strategy outlaid above (see section Data and setting), observations on housing listed for sale in the second half of 2009 (the core period of the S-Bahn crisis) are excluded from the estimation sample by design. Thereby, any remaining concerns about potential confounding influences, stemming from the short-term reductions in the operational S-Bahn fleet, are further mitigated.
Nonetheless, we have constructed hedonic indices for house prices by walking distance to suburban, respectively, intercity and regional train stations, which account for the full set of property-specific characteristics (including location-specific factors, i.e., motorway accessibility and socio-economic characteristics at the level of 1 km grids) in order to visually inspect regional differences in the evolution of the quality-adjusted property data across the relevant pre-and post-LEZ (stage 3) observation periods (see Appendix Fig. 7). Concerning the two closest commuting bands 19 pronounced structural breaks (deviations of selected walking distance bands from the trend of the control regions) are visible for both types of train stations after the LEZ tightening. This structural break not being exclusive to suburban train services suggests, furthermore, that the LEZ tightening rather than the temporary S-Bahn crisis is the relevant treatment.
Furthermore, comparably little deviations in trends across walking distance bands are observable prior to the relevant treatment in 2010, providing some first (descriptive) intuition regarding common pre-treatment trends. This notwithstanding, to corroborate the validity of the common trend assumption in our empirical analysis, we conduct two types of robustness tests: First, to capture potentially diverging pre-trends in neighborhood-specific house price growth that are related to regional differences in socio-economic conditions (pre-treatment changes therein), we add as additional regressors also pre-trends (between 2005 and 2009) in the neighborhood-specific measures described above as well as their interactions with the post-LEZ (stage 3) period indicators. We extend these tests to further integrate pre-trends in the neighborhood-level credit default risk composition of households (RWI and microm 2017d), respectively, the share of families with children (RWI and microm 2017c) to account for intra-municipality variation (and pre-treatment changes) in local household compositions that may correlate with distance to train stations, resulting, for instance, from the financial crisis or migration into Berlin and (associated spillovers) to its surrounding commuter belt. Second, we explore the addition of linear time trends by staggered treatment and control regions throughout the sampled time periods.

Baseline results
We start our analysis by estimating simplified variants of the DiD model specified in Eq.
(1) in which we disregard neighborhood-specific characteristics and access to motorways (MOT). We do control, however, for time (quarter) and region (municipality) fixed effects. Notably, house prices and their rate of growth between two points in time may not be directly comparable between treatment and control regions, as characteristics of houses on offer may systematically differ between those regions over time. Therefore, we include a set of house-specific controls to our regressions to address such potential changes in regional property compositions (see Appendix Table 3 for a full list of these characteristics of houses). The coefficient estimates for the treatment effect at the 5, 5-10, 10-15, and 10-20 min walking distance bands to train stations (STNs) are reported in column (1) of Table 2. 20 Splitting the 18-month post-LEZ (stage 3) period into three subperiods of six months each, we obtain a positively signed and statistically significant (at the 5% level) estimate of 0.0507 for the treatment effect within 5-10 min walking distance of train stations in the third half-year of the 18-month post-LEZ period, which suggests that house price growth between the pre-LEZ (stage 3) period (January 2008-June 2009) and January-June 2011 exceeded that of houses on offer located beyond the 20-minute walking distance threshold by an average 5.07%-points. Results hardly change when we control for motorway accessibility in 10 min driving distance and in addition add the set of socioeconomic and property compositional characteristics of neighborhoods at 1 km grid level and their interactions with the binaries for the post-LEZ (stage 3) period (see column (2)). Moreover, the within R 2 increases only marginally, from 0.4541 to 0.4558. 21 Coefficient estimates for proximity to motorways are positively signed throughout, albeit statistically significant only in the first half-year of the 18-month period since the implementation of the third stage LEZ. This suggests that, immediately after the intervention, houses in vicinity  The dependent variable is the log of the nominal house price posted. Neighborhood characteristics at 1 km grid level (from 2009) include the unemployment rate, the share of buildings that are predominantly in commercial use, and the share of the foreign-born population. Standard errors are clustered at the municipality level. ***, **, * denote statistical significance at the 1%, 5% and 10% level of motorway access points were characterized by offer price growth premia compared to dwellings beyond 10 min driving distance to motorways. Anticipation of a reduction in negative externalities provided by (or associated with) such sites, and likewise adjacent roads, such as (noise) pollution, elevated traffic, and road congestion, may sign responsible for this finding. However, it should already be noted that coefficient estimates for proximity to motorways do not prove robust in the proceeding of this paper, which is why we refrain from putting much weight on the interpretation of the respective coefficients. The specifications we considered so far employed the full estimation sample of detached and semi-detached houses listed for sale in the federal state of Brandenburg's counties that share a border with Berlin in the periods January 2008-June 2009 (pre-LEZ (stage 3) period) and January 2010-June 2011 (post-LEZ (stage 3) period). We will consider next four regionally restricted sub-samples. The first sample restriction aims to obtain a more homogenous sub-sample of houses in the treatment and control regions by increasing their relative proximity. Specifically, we restrict the estimation sample to houses located within 40 min walking distance to train stations, which eliminates from the control group property in very remote locations (-38,776 observations). The corresponding estimation results are shown in column (3) of Table 2. Associated price growth premia for houses located in 5-10 min walking distance of train stations turn out no longer statistically significant in the first half of 2011 (the coefficient estimate is decreased in size, by about 1.5%-points, whereas the standard error is almost unchanged).
We next subject the sub-sample of house listings within 40 min walking distance of STNs to further regional restrictions so as to obtain more plausible long-and short-distance dailycommuter belts around the city of Berlin. We use stratified estimation samples for this purpose that are based on three commuting duration bands: For the long-distance daily-commuter belt, we consider only houses located within 40 min walking distance of train stations, from which the commuting duration (by car) to Berlin main station ranges between 60-40 min (see column (4)), respectively, between 40-30 min in the next closest belt (see column (5)), and up to 30 min for the short-distance daily-commuter belt (see column (6)). 22 House listings in the 60-40 min commuting duration band show no statistically significant price growth premia or penalties attached to train station proximity. Moreover, houses that are located within 40 min walking distance of stations and within 10 min driving distance to motorway access points receive statistically significant price growth premia (at the 10% level) of on average 8.1%-points only in the third half-year of the post-LEZ (stage 3) period. The latter finding, may again be attributable to (the anticipation of) lower congestion and (noise) pollution near motorways after the LEZ tightening on 1st January 2010. Likewise, nearby access to an alternative mode of transport (car) to accessible rail-road travel (in 40 min walking distance) may have been valued particularly strongly in regions at farther distance from Berlin, in which residents tend to rely more on a single mode of transport (car) for conventional activities, such as shopping and recreation. Houses in the adjacent commuting duration band of 40-30 min driving duration that are listed for sale in immediate vicinity of train stations (in 5 min walking distance) exhibit sizeable price growth penalties (of on average 7.97-13.12%-points) after the implementation of the third stage LEZ. Similarly, a tendency for smaller, yet still sizeable (and in the second half of 2010 also statistically significant) price growth penalties is observable for property in the 5-10 min walking distance range. This tendency is also observable for listings in the adjacent 10-15 min walking distance band, for which estimated coefficients change sign from positive (albeit close to zero at 0.82%-points) to negative in the second half of 2010 and increase absolutely thereafter from −2.09 to −5.49%-points (statistically significant at the 10% level) in the first half of 2011. Such penalties vanish, however, for house listings at farther distance (15-20 min walk) from train stations. Concerns about negative externalities, such as elevated noise pollution, increased crime rates in the immediate surroundings of train stations, or congestion of public modes of transport, may sign responsible for these findings. When we restrict the estimation sample to the short-distance commuting region, however, we obtain treatment effects for proximity to STNs (in 5-10 min walking distance) that change sign from negative to positive (but remain statistically insignificant) in the first two half-years after the tightening of the LEZ and indicate a much more sizeable (statistically significant at the 5% level) price growth premium of 9.15%-points in the first six months of 2011. Similarly, in the second half of 2010, listings in 10-15 min walking distance from train stations receive a premium of on average 5.28%-points compared to property located in a 20-40 min walk. Houses in vicinity of motorway access points, in turn, witness price growth penalties of around 5.1%-points in the first half-year of 2011. The former finding speaks for an (anticipated) increase in the demand for rail-based public transit as a means to commute to Berlin after the policy, whereas the latter finding may be indicative of (anticipated) substitution between car-and public-transitbased modes of commuting in Berlin's affluent suburbs.
Considering the four distance bands to train stations, level differences in average house prices prior to the LEZ (stage 3) implementation are mostly negatively signed, albeit statistically insignificant throughout specifications (1) to (6). Houses within 10 min driving distance to motorway access points, in contrast, are characterized by statistically significant lower average house prices (of approximately 5.5% to 6.6%) in the pre-LEZ (stage 3) period than houses listed for sale beyond that threshold (see columns (2) and (3)). Such price-level differences may again be attributable to the presence of negative externalities in vicinity of those access points of the kind we discussed above. Considering stratified samples by commuting duration to Berlin, in columns (4), (5), and (6), corresponding coefficients of -0.0586, -0.0561, and -0.0527 are, however, estimated with less precision.
Notably, the baseline results in Table 2 report standard errors clustered at municipality level throughout to account for heteroscedasticity and serial correlation. However, the stratified estimation samples employed to produce the corresponding results in columns (4), (5), and (6) are comparably small, reducing the number of municipality clusters to 46, 44, and 22, respectively, which may be insufficient. Therefore, Appendix Table 5 reports the analogous results with bootstrapped standard errors, as suggested in Cameron et al. (2008), with 500 replications. Strikingly, price growth premia or penalties attached to motorway proximity are estimated with much less precision, considering in particular, the stratified samples in columns (4) through (6), which suggests that the results for motorway accessibility, described above, may be interpreted only with caution. Estimated treatment effects concerning train station proximity remain, however, highly consistent throughout, increasing or decreasing the appendant standard errors only by little.
Summarizing the above, our results show systematic regional differences in treatment effect tendencies by commuter-belt type and elapsed time post treatment. In section Additional explorations and robustness tests, we further explore the importance of commuting duration between train stations and Berlin main station for the magnitude and direction of the effects of proximity to train stations on house price growth following the tightening of the LEZ in the city of Berlin. Doing so, we maintain the control regions restricted to the 40-minute walking distance band from train stations introduced above and focus on the two closest commuting bands surrounding Berlin to explore the evolution of treatment effects beyond the 18-month post-LEZ (stage 3) period considered so far, subject our samples to further restrictions, and test yet further the robustness of our findings, reporting estimation results with bootstrapped standard errors based on 500 replications throughout.

Additional explorations and robustness tests
In the following, we first explore how the treatment effects in the two closest commuting duration bands in immediate vicinity of Berlin, which we discussed in section Baseline results, evolved beyond the 18-month period since the implementation of the third stage LEZ on 1st January 2010 that we considered so far. In these explorations, and in others that follow, we maintain the restriction of control regions to the 40-minute walking distance band from train stations and extend the observation period by an additional 18 months post treatment (i.e., until December 2012). Figure 5 depicts the associated coefficient estimates (including 90% confidence intervals) by walking distance to train stations 23 for the two suburban commuting distance bands of up to 30 min, and 30-40 min commuting duration from train stations to Berlin main station. 24 Considering the first-row set of coefficient plots in the top-panel of Fig. 5, price growth premia for property in 5-10 min walking distance of train stations appear indeed to have prevailed in Berlin's affluent suburbs (i.e., property located within 40 min of train stations that are within 30 min commuting duration to Berlin main station). Although sizeable in magnitude, these price growth premia are rather short-lived (they are statistically significant only throughout the year 2011), which may be attributable to different changes in car fleet compositions of regions across time. While an in-depth analysis of changes in the fleet composition across regions lies beyond the scope of this paper, mainly due to lack of available data at such a fine spatial resolution, data on changes in the number of registered private vehicles (irrespective of car type or emission classification) per household at neighborhood level (RWI and microm 2017a), reveals differences across commuting and also walking distance bands (see Appendix Table7). Interestingly, these changes do not only vary across the distance intervals we consider but also between the pre-and post-LEZ tightening time frames. Turning to data concerning emission classifications of vehicles at the county-level (the finest dimension for this type of data available to us) reveals that at the beginning of 2010, well above 50% of the private vehicle fleet in Brandenburg's counties was restricted (57.3% for counties adjacent to Berlin and 58.8% in counties that do not share an administrative border with Berlin) (Kraftfahrt-Bundesamt 2010). At the county-level adaptations in the vehicle fleet grew steadily, with the share of restricted vehicles dropping consistently by roughly 5%-points per year. 25 This slow but consistent adjustment of the vehicle fleet, i.e., a reduction in vehicles that are restricted by the LEZ tightening, gives credence to the notion that short-lived effects may be attributable to car fleet adjustments. In addition, tendencies for similarly short-lived patterns of price growth premia, albeit smaller in magnitude than in the 5-10 min walking distance band, are visible in 10-15 and 15-20 min walking distance from train stations relative to property located at farther distances, i.e., in 20-40 min walking distance from train stations. Notably, the validity of our findings, thus far, hinges on the common trend assumption, i.e., conditional on controls, trends in house price growth in the four walking distance bands (the staggered treatment regions) evolved similarly to that of property located in 20-40 min walking distance of train stations (the control region) absent treatment. Notably, our preferred specifications include time and regional fixed effects (at the level of quarters and municipalities) and control, moreover, for region-specific heterogeneity at the level of walking distance bands to train stations as well as neighborhoods, i.e., a set of socio-economic characteristics at 1 km-grid level. Differential trends in neighborhood-specific house price growth, related to these characteristics, are captured by the interaction of the latter with the semi-annual post-LEZ (stage 3) period indicators. This notwithstanding, underlying (and potentially not fully captured by the above mentioned controls) diverging trends in house price growth between treatment and control regions that prevailed (absent treatment) throughout the observation period may still confound the relationship of interest. To address such potential concerns, we add a full set of region-specific linear (quarterly) time trends to our regressions. 26 The results from this robustness test are illustrated by the second-row set of coefficient plots in the top-panel of Fig. 5. Tabulated results are attainable from Appendix Table 6 column (2). The linear trend coefficient estimate for the control region (20-40 min walking distance from train stations) is positively signed, corresponding to an average house price growth rate of 1.18%, albeit statistically insignificant. The trend differential in the treatment regions is negatively signed throughout the four walking distance bands from train stations and statistically significant at the 1% level in the 5-10 min walking distance band. Namely, quarterly house price growth in this region was lower by an average 2.14%-points compared to that of housing located in 20-40 min walking distance from train stations. Taking into account this trend divergence, estimated treatment effects in the 5-10 min walking distance band are positively signed throughout, increase vastly in magnitude and precision from 0.0693 to 0.2850 (significant at the 10% and 1% level, respectively) over the four half-years immediately after the LEZ (stage 3) implementation and remain persistent at 0.2484 and 0.2672 (statistically significant at the 5% level) thereafter. Similarly, estimated treatment effects for housing located closer to train stations (in 5 min walking distance) are positively signed throughout and exhibit an increasing pattern, albeit imprecisely estimated, when regionspecific trend differentials are taken into account. The same is true for property located at farther distances from train stations: a more concise price growth pattern, yet statistically significant only throughout the year 2010, emerges in 10-15 min walking distance. Furthermore, houses located in 15-20 min walking distance receive sizeable and statistically significant price growth premia ranging between 12.43 and 20.31%-points compared to houses located beyond 20-40 min walking distance from stations. Notably, growth premia are smaller in magnitude (compared to housing in 5-10 min walking distance) when regions at farther walking distances are considered (see both the 10-15 min and 15-20 min walking distance band) and take more time to unfold (see the 15-20 min walking distance band).
Moreover, and confirming our shorter-term findings for house listings in the 30-40 min commuting region discussed in section Baseline results, pronounced price penalties appear to have persisted for houses in the immediate surroundings (5 min walking distance) of train stations (see first-row set of coefficient plots in the bottom-panel of Fig. 5). There are also indications for a dip in listing prices in the adjacent 5-10 min (10-15 min) walking distance band for the four (five) consecutive half-years starting in January (July) 2010. Only the dip in the second half of that year, however, is statistically significant at the 10% level in the 5-10 min walking distance band (the point estimate is −0.0418 with a standard error of 0.0244). Furthermore, in 2012 price growth in this region takes a turn, as evidenced by positively signed (and in the second half of 2012 also statistically significant) coefficient estimates. In the 10-15 min walking distance band, only the dip in the first half of 2011 is statistically significant at the 10% level (the point estimate is −0.0577 with a standard error of 0.0306). Turning to the second-row set of coefficient plots in the bottom-panel of Fig. 5, the systematic pattern of price growth penalties pertains in immediate vicinity of train stations, albeit imprecisely estimated. Notably, a negative trend differential prevails in the three closest walking distance bands from stations, which are furthermore sizeable and statistically significant in 5-10 min and 10-15 min walking distance from stations (the point estimates are −0.0136 (standard error 0.0076) and −0.0233 (standard error 0.0061), respectively). Houses located in the control regions (beyond 20-40 min walking distance) are characterized by a positive and statistically significant quarterly price growth trend (the point estimate is 0.0262 with a standard error of 0.0091). Controlling for the negative trend differentials between treatment and control regions estimated treatment effects in the 5-10 min walking distance region turn consistently positively signed throughout the post LEZ (stage 3) period, albeit statistically significant only throughout the year 2012. Point estimates in the adjacent 10-15 min walking distance band are statistically significant throughout and proliferating, corresponding to price growth differentials ranging from an average 8.82%-points in the first half of 2010 to 29.21%-points in the second half of 2012. Finally, and in line with our results for the shorter-term horizon, we do not find any evidence for a systematic pattern of differential house price growth for property on offer in 15-20 min from stations both when we neglect and take into account regionspecific trends.
We next consider the possibility that the scope of the policy may have differed among certain sub-regions within the commuting duration bands considered. For this purpose, we employ, for each commuting duration band, three versions of additionally restricted estimation samples. 27 The first of these considers exclusively train stations that offer direct rail services to Berlin, which provide a comparably attractive alternative to car-based commuting. Note that the share of train stations offering direct services to Berlin gets larger, when train stations are closer to Berlin. Estimation samples are hence almost identical for the 30 and 30-40 min commuting regions and the corresponding regressions, for houses near train stations with direct rail routes to Berlin, produce virtually identical results to those we obtained for the unrestricted estimation samples. 28 Nevertheless, in these particular regions, other rail-service-related factors may have been of relevance for the facilitation of the private driving restriction (its scope) considered. We therefore consider two further restrictions which partition these estimation samples according to train type, distinguishing between suburban trains (S-Bahn) and regional or intercity trains. The former run typically more frequently and at comparably low fares, whereas the latter are typically faster and call at less stations en route. As shown in the toppanel coefficient plots of Fig. 6 for suburban train stations as well as intercity and regional trains in Appendix Fig. 8, estimated treatment effects in Berlin's affluent suburbs (in 30 min commuting duration to Berlin main station) differ in pattern and direction when we consider these stratified estimation samples by type of rail-service. In this short-distance commuting region, 28,885 (19,565) observations on houses listed for sale are situated 27 Tabulated results for these analyses and all explorations in the remainder of this section are available from the authors upon request. 28 Eliminating house listings in vicinity of train stations that do not offer direct rail routes to Berlin reduces the estimation sample for the 30 min commuting distance region by just slightly more than one thousand observations (from 48,450 to 47,441), and the estimation sample for the 30-40 min commuting distance region by 1,644 observations (from 47,949 to 46,305). within 40 min walking distance of stations for suburban (regional and intercity) trains. 29 Considering train stations offering (direct) suburban train services to Berlin (see first-row set of coefficient plots in the top-panel of Fig. 6), treatment effects for the 5-10, 10-15, and 15-20 min walking distance bands follow a similar, yet much more concise, pattern to the one observed for the entire set of train stations within the 30 min commuting duration region, whereas treatment effects in immediate vicinity of suburban train stations show a declining, albeit statistically insignificant, trend. What is more, positive and statistically significant coefficient estimates in 5-10 min walking distance of such train stations extend into the first half of 2012 and are larger in magnitude (by about 0.8 in the first half of 2011 and up to 9.5%-points in the first half of 2012). The same is true for the appendant specifications that control for differential trends between treatment and control regions (see second-row set of coefficient plots in the top-panel of Fig. 6). Estimated treatment effects, their tendencies, are more distinct and pronounced in terms of magnitude and statistical significance, in particular within 5, 5-10, and 10-15 min walking distance from suburban train stations. Notably, in these areas, which were presumably characterized by a comparably large proportion of public-transit commuters already prior to the implementation of the policy, even train station proximity within 10-15 min walking distance has been valued considerably. This may be due to suburban trains providing a relatively convenient, highly frequented, and affordable means to travel into the city.
Turning to train stations from which comparably faster, albeit less frequented and more expensive trains run, positive and statistically significant coefficient estimates appear to be shifted away from the 5-10 min walking distance band onto its surrounding regions in less than 5, 10-15 and particularly 15-20 min walking distance from train stations (see toppanel of Appendix Fig. 8). Although less clearly visible in pattern and estimated with less precision, it seems that asking price premia are partially crowded out onto areas that are more distant and arguably less likely to suffer from noise pollution and elevated traffic or congestion by public-transit commuters. This finding may be related to the type of trains that depart from those stations, i.e., trains that run less frequently and service typically fewer (larger) train stations within the city, which may not constitute a sufficiently convenient and practicable alternative mode of transport to car-based commuting. Corresponding results for the 30-40 min commuting distance band are depicted in the bottom-panel of Fig. 6 and Appendix Fig. 8, respectively. Notably, in this region, differences by type of train station are less prevalent. Sizeable penalties in asking prices prevail in immediate vicinity of both types of train stations. Anyhow, taking into account differential trends in house price growth between treatment and control regions, patterns of point estimates that indicate sizeable positive price growth differentials are more prevalent, both in 5-10 and 10-15 min walking distance of stations, for suburban trains than for regional and intercity trains. Notably, in this comparably farther commuting belt surrounding Berlin, the number of observations near train stations for regional and intercity trains (26,244) exceeds that near stations for suburban trains (21,705) by roughly 4,500. A summary of our main findings by commuting duration to Berlin main station, walking distance to train station and type of train is provided in Appendix Table 8.
Finally, the neighborhood controls (i.e., an indicator for motorway accessibility, respectively, the pre-treatment (from 2009) unemployment rate, the share of the foreign-born population, and the share of buildings that are predominantly in commercial use) we employed in all regressions, thus far, capture spatial differences in house prices related to differences in property-specific access to motorway links and socioeconomic compositions of neighborhoods before the treatment. Furthermore, interactions of these controls with the post-period indicators capture differential trends in house price growth related to these location-specific factors after the treatment. To further corroborate the validity of the common trend assumption, we have probed the robustness of the above findings in a battery of sensitivity tests, in which we replace said level controls (from 2009) by pre-trends in these (between 2005 and 2009). The pre-trends enter, analogously, both in levels and interactions with the indicators for the post-LEZ Fig. 6 Evolution of treatment effects-stratified estimation samples by commuting duration and type of train: suburban train (S-Bahn) (semi-annually). Notes Point estimates (marked by a square) illustrate treatment effects for the treatment variables DIST i,STN 5 min (left), DIST i,STN 5−10 min (center left), DIST i,STN 10−15 min (center right), and DIST i,STN 15−20 min (right) for stratified estimation samples that consider exclusively property located within 40 min walking distance of train stations that are located within 30 min (top panel), and 30-40 min (bottom panel) commuting duration to Berlin main station. Treatment effects correspond to percentage point house price growth differentials (depicted in decimal units) between treatment and control regions. Second row top-and bottom-panel graphs depict point estimates, controlling for region-specific time trends. Vertical bands indicate the 90% confidence interval for each estimate (stage 3) period to capture diverging trends in neighborhood-specific house price growth related to differences in pre-trends in socio-economic characteristics between those regions. We also extend these specifications, to include pre-trends in additional neighborhood compositional factors that may correlate with both train station proximity and house prices, namely pre-treatment changes in the neighborhood-level share of households at above/below average credit default risk (RWI and microm 2017d) as well as the share of families with children (RWI and microm 2017c). Altogether, these three sets of tests intend to capture a broad variety of within-municipality heterogeneity in socio-economic factors at fine spatial grid level, such as local exposures of households to the financial crisis or changes in spatial differences in relative valuations of train station proximity due to (selective) migration by parts of the population, for which train station proximity may be of particular importance. If unobserved and uncontrolled for, these factors may induce bias in the estimated treatment effects. Appendix Figs. 9, 10, 11 and 12 illustrate the results from these tests for stratified estimation samples by type of train and commuting duration. Further robustness checks include linear time trends at the administrative region (county) level as well as time-varying controls at municipality level (in addition to both municipality fixed effects and neighborhood-level socio-economic characteristics (from 2009) at the level of 1 km grids and their interactions with the post period indicators) to capture potential regional differences in relative exposures to the implementation of the driving restriction as well as (potentially endogenous) region-specific contemporaneous shocks in house price growth related to these. These time-variant controls include an additional indicator of the local housing market structure (the number of residential apartments normalized by the local population) and the population share of outbound commuters to the city of Berlin. The afore-discussed results (their pattern) are qualitatively, and in most instances also quantitatively, robust to these tests, albeit at times less (or more) precisely estimated.

Conclusion
This study investigated the impact of the tightening of a private driving restriction, Berlin's abrupt change of its low-emission zone (LEZ) from a stage 1 to a stage 3 LEZ on 1st January 2010, on prices of single-family houses for sale in the city's commuter belt. Using data on exact locations of train stations provided by the public transport authority for the federal states of Berlin and Brandenburg Verkehrsverbund Berlin-Brandenburg (VBB), motorway access points provided by Landesbetrieb Straßenwesen, which oversees the road construction administration in Brandenburg, and geo-referenced data on monthly offer listings of detached and semi-detached houses from Germany's leading online property broker Immo-bilienScout24, we find compelling evidence in spatially staggered difference-in-differences regressions for price premia witnessed by property in 5-10 min walking distance of train stations in Berlin's affluent suburbs that lie within 30 min commuting duration from Berlin main station. Furthermore, house listings in 5 min walking distance to train stations in the next closest commuting duration band to Berlin (30-40 min driving duration to Berlin main station) exhibit sizeable price growth penalties after the policy implementation.
Substitution effects between car-and rail-based transit may sign responsible for the former finding, and elevated congestion levels of public modes of transport, noise pollution, and (perceived) increases in crime rates near train stations for the latter result. Furthermore, our findings on heterogenous treatment effects by type of train station suggest 1 3 that the kind of transportation services on offer plays an important role. Particularly in the short-distance commuting regions, price growth premia are visible in 5-10 min walking distance from suburban train stations, whereas such price premia appear to be crowded out, in particular onto outer walking distance bands in 15-20 min from train stations that offer regional or intercity rail services. In addition to the factors listed above, the type of train service offered may itself be an important driver of these findings (regional and intercity trains run typically less frequently, service fewer stations en route, and are relatively more expensive than suburban trains).
Notwithstanding these findings, associated treatment effects (their tendencies) materialize in most instances with a time lag and are often not very persistent in specifications that do not explicitly account for region-specific trend divergences. Several factors may contribute to this finding. First, anticipatory pricing behavior may have occurred, in particular since the introduction of the first stage LEZ in 2008 and the announcement (already in 2007) that Berlin would change directly to a stage 3 LEZ (instead of a stage 2 LEZ as originally envisaged) in January 2010. Due to data limitations, we cannot verify empirically to which extent identification is complicated by early pricing responses to the announcement made in early 2007. However, Berlin was not just among the first cities in Germany to implement a LEZ, it was also the first (and still is the only city) to jump directly from a stage 1 to a stage 3 LEZ. The scope of the policy change at the time was hence rather unexpected, if not indeed unforeseeable. It may also have taken time for any pricing effects in the housing market to materialize, when changes, for instance, in the congestion of motorways and train stations, became visible only with delay. Second, treatment effects may have been lagging behind because the degree of enforcement in the dawn of these policy implementations may not have been tight enough, impeding their credibility and limiting their scope. Overall, these factors suggest that our baseline results should be seen rather as a lower bound. Similarly, the transience of the estimated treatment effects may stem from different changes in car-fleet compositions of regions across time.
In summary, our finding of a positive effect on house prices of a private driving restriction in proximity to public train stations aligns well with corresponding findings in Xu et al. (2015) for Beijing's housing market. Our findings also suggest that infrastructure planning, in particular the provision of sufficient and suitable alternative modes of transport, is of high relevance for the design of public policies to facilitate and accommodate private driving restrictions in the future that aid the transition towards more environmentally sustainable modes of transport and improved ambient-air quality. In fact, the necessity to accelerate the implementation or tightening of private driving restrictions in various locations across Germany has been emphasized recently by the German Federal Environmental Agency (Umweltbundesamt 2020b). In light of the even more recent judgement against Germany by the Court of Justice of the European Union, due to the country's misconduct with respect to the Air Quality Directive 2008/50/ EC (European Parliament, Council of the European Union 2008; European Commission 2021; Court of Justice of the European Union 2021), (adequate) policy responses are to be expected in the near future. The formulation of such policies, however, ought to involve careful consideration of potential unanticipated and unwanted side-effects, such as distortions in the housing market, which may result in an unequal distribution of costs among the resident population.  -trends (2005-2009) in neighborhood characteristics (at 1 km grid level)-stratified estimation sample: suburban train (S-Bahn) in 30 min commuting duration (semi-annually). Notes Point estimates (marked by a square) illustrate treatment effects for the treatment variables DIST i,STN 5 min (left), DIST i,STN 5−10 min (center left), DIST i,STN 10−15 min (center right), and DIST i,STN 15−20 min (right) for stratified estimation samples that consider exclusively property located within 40 min walking distance of suburban train (S-Bahn) stations that are located within 30 min commuting duration to Berlin main station. Treatment effects correspond to percentage point house price growth differentials (depicted in decimal units) between treatment and control regions. To ease comparison, first row graphs replicate the baseline results from regressions that include municipality and time fixed effects as well as property-and neighborhood-specific characteristics at 1 km grid level (from 2009), i.e., the unemployment rate, the share of buildings that are predominantly in commercial use, and the share of the foreign-born population, which enter both in levels and interactions with the semi-annual indicators for the post-LEZ (stage 3) period (see also first row top-panel graphs in Fig. 7). Second row graphs depict point estimates, replacing controls for baseline neighbourhood characteristics by pre-trends (between 2005 and 2009) in these. Point estimates from regressions that additionally control for pre-trends (between 2005 and 2009) in the neighborhood-level share of: households with above average (high) and below average (low) default risk (third row graphs), respectively, families with children (fourth row graphs). Vertical bands indicate the 90% confidence interval for each estimate  DIST i, for stratified estimation samples that consider exclusively property located within 40 min walking distance of suburban train (S-Bahn) stations that are located within 30-40 min commuting duration to Berlin main station. Treatment effects correspond to percentage point house price growth differentials (depicted in decimal units) between treatment and control regions. To ease comparison, first row graphs replicate the baseline results from regressions that include municipality and time fixed effects as well as property-and neighborhood-specific characteristics at 1 km grid level (from 2009), i.e., the unemployment rate, the share of buildings that are predominantly in commercial use, and the share of the foreign-born population, which enter both in levels and interactions with the semi-annual indicators for the post-LEZ (stage 3) period (see also first row bottom-panel graphs in Fig. 6). Second row graphs depict point estimates, replacing controls for baseline neighbourhood characteristics by pre-trends (between 2005 and 2009) in these. Point estimates from regressions that additionally control for pre-trends (between 2005 and 2009) in the neighborhood-level share of: households with above average (high) and below average (low) default risk (third row graphs), respectively, families with children (fourth row graphs). Vertical bands indicate the 90% confidence interval for each estimate Fig. 11 Robustness tests: additional controls for pre-trends (2005)(2006)(2007)(2008)(2009) in neighborhood characteristics (at 1 km grid level)-stratified estimation sample: intercity and regional train in 30 min commuting duration (semi-annually). Notes Point estimates (marked by a square) illustrate treatment effects for the treatment variables DIST i,STN 5 min (left), DIST i,STN 5−10 min (center left), DIST i,STN 10−15 min (center right), and DIST i,STN 15−20 min (right) for stratified estimation samples that consider exclusively property located within 40 min walking distance of intercity and regional train stations that are located within 30 min commuting duration to Berlin main station. Treatment effects correspond to percentage point house price growth differentials (depicted in decimal units) between treatment and control regions. To ease comparison, first row graphs replicate the baseline results from regressions that include municipality and time fixed effects as well as property-and neighborhood-specific characteristics at 1 km grid level (from 2009), i.e., the unemployment rate, the share of buildings that are predominantly in commercial use, and the share of the foreign-born population, which enter both in levels and interactions with the semi-annual indicators for the post-LEZ (stage 3) period (see also first row top-panel graphs in Fig. 8). Second row graphs depict point estimates, replacing controls for baseline neighbourhood characteristics by pre-trends (between 2005 and 2009) in these. Point estimates from regressions that additionally control for pre-trends (between 2005 and 2009) in the neighborhood-level share of: households with above average (high) and below average (low) default risk (third row graphs), respectively, families with children (fourth row graphs). Vertical bands indicate the 90% confidence interval for each estimate Fig. 12 Robustness tests: additional controls for pre-trends (2005)(2006)(2007)(2008)(2009) in neighborhood characteristics (at 1 km grid level)-stratified estimation Ssample: intercity and regional train in 30-40 min commuting duration (semi-annually). Notes Point estimates (marked by a square) illustrate treatment effects for the treatment variables DIST i,STN 5 min (left), DIST i,STN 5−10 min (center left), DIST i,STN 10−15 min (center right), and DIST i,STN 15−20 min (right) for stratified estimation samples that consider exclusively property located within 40 min walking distance of intercity and regional train stations that are located within 30-40 min commuting duration to Berlin main station. Treatment effects correspond to percentage point house price growth differentials (depicted in decimal units) between treatment and control regions. To ease comparison, first row graphs replicate the baseline results from regressions that include municipality and time fixed effects as well as property-and neighborhood-specific characteristics at 1 km grid level (from 2009), i.e., the unemployment rate, the share of buildings that are predominantly in commercial use, and the share of the foreign-born population, which enter both in levels and interactions with the semi-annual indicators for the post-LEZ (stage 3) period (see also first row bottom-panel graphs in Fig. 8). Second row graphs depict point estimates, replacing controls for baseline neighbourhood characteristics by pre-trends (between 2005 and 2009) in these. Point estimates from regressions that additionally control for pre-trends (between 2005 and 2009) in the neighborhood-level share of: households with above average (high) and below average (low) default risk (third row graphs), respectively, families with children (fourth row graphs). Vertical bands indicate the 90% confidence interval for each estimate Table 3 Summary statistics by distance to train station, pre-and post-LEZ period (full estimation sample) Columns (1) to (12) show the mean of each variable for property located within 5 min (columns (1) and (7)), beyond 5-10 min (columns (2) and (8)), beyond 10-15 min (columns (3) and (9)), beyond 15-20 min (columns (4) and (10)) and beyond 20-40 min (columns (5) and (11)) walking distance of train stations, respectively, for property located beyond the 40 min walking distance threshold (columns (6) and (12)). Averages are calculated for the pre-LEZ (stage 3) period January 2008-June 2009 (columns (1) to (6)) and the post-LEZ (stage 3) period January 2010-June 2011 (columns (7) to (12) (3) (8) (10) House price [EUR] 192, 872 [101,419] 182, 517 [103,361] 187, 596 [81,304] 195, 924 [98,635] 210, 866 [126,365] 195, 664 [135,248] 185, 732 [86,800] 198, 525 [121,562] 198, 850 [101,863] 206, 116 [127,857] 213, 350 [125,083] 203, 527  234, 127 [114,192] 229, 283 [107,136] 207, 569 [81,732] 216, 468 [110,260] 258, 908 [162,539] 224, 596 [87,717] 221, 599 [106,789] 225, 662 [120,987] 222, 497 [136,071] 249, 759 Commuting duration from train station to Berlin main station:

>30-40 min
House price [EUR] 191, 820 [91,768] 183, 144 [90,779] 180, 426 [80,933] 191, 182 [84,292] 190, 310 [87,883] 177, 632 [64,170] 197, 842 [135,129] 189, 195 [78,196] 213, 231 [88,101] 208, 632  The dependent variable is the log of the nominal house price posted. Neighborhood characteristics at 1 km grid level (from 2009) include the unemployment rate, the share of buildings that are predominantly in commercial use, and the share of the foreign-born population. Standard errors are bootstrapped with 500 replications. ***, **, * denote statistical significance at the 1%, 5% and 10% level   The dependent variable is the log of the nominal house price posted. Specifications (1) through (4) include municipality and time fixed effects as well as property-and neighborhood-specific characteristics at 1 km grid level (from 2009), which include the unemployment rate, the share of buildings that are predominantly in commercial use, and the share of the foreign-born population. Standard errors are bootstrapped with 500 replications. ***, **, * denote statistical significance at the 1%, 5% and 10% level  (1), (2) and (3) Table 8 Summary of main findings by commuting duration to Berlin main station, walking distance to train station and type of train The table summarizes directions and magnitude ranges of statistically significant coefficient estimates (p-value < 0.1) for treatment effects, i.e., price growth differentials (in %-pts) between treatment and control regions, by walking distance to train station, type of train service and driving duration from train stations to Berlin main station. Treatment effect ranges within 30 min as well as beyond 30-40 min driving duration to Berlin main station are reported for suburban train (S-Bahn) stations in columns (1) and (3), respectively, for intercity and regional train stations in columns (2) and (4)  Her research focuses on topics at the intersection of the economics of migration, transportation, and housing economics.